Daily Papers

While recent works (e.g. o1, DeepSeek R1) have demonstrated great promise of using long Chain-of-Thought (CoT) to improve reasoning capabilities of language models, scaling it up during test-time is challenging due to inefficient memory usage -- intermediate computations accumulate indefinitely in context even no longer needed for future thoughts. We propose PENCIL, which incorporates a reduction mechanism into the autoregressive generation process, allowing the model to recursively clean up intermediate thoughts based on patterns learned from training. With this reduction mechanism, PENCIL significantly reduces the maximal context length required during generation, and thus can generate longer thoughts with limited memory, solving larger-scale problems given more thinking time. For example, we demonstrate PENCIL achieves 97\% accuracy on the challenging Einstein's puzzle -- a task even large models like GPT-4 struggle with -- using only a small 25M-parameter transformer with 2048 context length. Theoretically, we prove PENCIL can perform universal space-efficient computation by simulating Turing machines with optimal time and space complexity, and thus can solve arbitrary computational tasks that would otherwise be intractable given context window constraints.

Large language models (LLMs) have shown remarkable performance in complex reasoning tasks, but their efficiency is hindered by the substantial memory and computational costs associated with generating lengthy tokens. In this paper, we propose LightThinker, a novel method that enables LLMs to dynamically compress intermediate thoughts during reasoning. Inspired by human cognitive processes, LightThinker compresses verbose thought steps into compact representations and discards the original reasoning chains, thereby significantly reducing the number of tokens stored in the context window. This is achieved by training the model on when and how to perform compression through data construction, mapping hidden states to condensed gist tokens, and creating specialized attention masks. Additionally, we introduce the Dependency (Dep) metric to quantify the degree of compression by measuring the reliance on historical tokens during generation. Extensive experiments on four datasets and two models show that LightThinker reduces peak memory usage and inference time, while maintaining competitive accuracy. Our work provides a new direction for improving the efficiency of LLMs in complex reasoning tasks without sacrificing performance. Code will be released at https://github.com/zjunlp/LightThinker.

Large language models (LLMs) can spend extra compute during inference to generate intermediate thoughts, which helps to produce better final responses. Since Chain-of-Thought (Wei et al., 2022), many such System 2 techniques have been proposed such as Rephrase and Respond (Deng et al., 2023a), System 2 Attention (Weston and Sukhbaatar, 2023) and Branch-Solve-Merge (Saha et al., 2023). In this work we investigate self-supervised methods to ``compile'' (distill) higher quality outputs from System 2 techniques back into LLM generations without intermediate reasoning token sequences, as this reasoning has been distilled into System 1. We show that several such techniques can be successfully distilled, resulting in improved results compared to the original System 1 performance, and with less inference cost than System 2. We posit that such System 2 distillation will be an important feature of future continually learning AI systems, enabling them to focus System 2 capabilities on the reasoning tasks that they cannot yet do well.

Large Language Models (LLMs) have demonstrated remarkable performance in solving complex reasoning tasks through mechanisms like Chain-of-Thought (CoT) prompting, which emphasizes verbose, step-by-step reasoning. However, humans typically employ a more efficient strategy: drafting concise intermediate thoughts that capture only essential information. In this work, we propose Chain of Draft (CoD), a novel paradigm inspired by human cognitive processes, where LLMs generate minimalistic yet informative intermediate reasoning outputs while solving tasks. By reducing verbosity and focusing on critical insights, CoD matches or surpasses CoT in accuracy while using as little as only 7.6% of the tokens, significantly reducing cost and latency across various reasoning tasks.

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

Agents, as user-centric tools, are increasingly deployed for human task delegation, assisting with a broad spectrum of requests by generating thoughts, engaging with user proxies, and producing action plans. However, agents based on large language models (LLMs) often face substantial planning latency due to two primary factors: the efficiency limitations of the underlying LLMs due to their large size and high demand, and the structural complexity of the agents due to the extensive generation of intermediate thoughts to produce the final output. Given that inefficiency in service provision can undermine the value of automation for users, this paper presents a human-centered efficient agent planning method -- Interactive Speculative Planning -- aiming at enhancing the efficiency of agent planning through both system design and human-AI interaction. Our approach advocates for the co-design of the agent system and user interface, underscoring the importance of an agent system that can fluidly manage user interactions and interruptions. By integrating human interruptions as a fundamental component of the system, we not only make it more user-centric but also expedite the entire process by leveraging human-in-the-loop interactions to provide accurate intermediate steps. Code and data will be released.

Table-based reasoning with large language models (LLMs) is a promising direction to tackle many table understanding tasks, such as table-based question answering and fact verification. Compared with generic reasoning, table-based reasoning requires the extraction of underlying semantics from both free-form questions and semi-structured tabular data. Chain-of-Thought and its similar approaches incorporate the reasoning chain in the form of textual context, but it is still an open question how to effectively leverage tabular data in the reasoning chain. We propose the Chain-of-Table framework, where tabular data is explicitly used in the reasoning chain as a proxy for intermediate thoughts. Specifically, we guide LLMs using in-context learning to iteratively generate operations and update the table to represent a tabular reasoning chain. LLMs can therefore dynamically plan the next operation based on the results of the previous ones. This continuous evolution of the table forms a chain, showing the reasoning process for a given tabular problem. The chain carries structured information of the intermediate results, enabling more accurate and reliable predictions. Chain-of-Table achieves new state-of-the-art performance on WikiTQ, FeTaQA, and TabFact benchmarks across multiple LLM choices.

We present Thinking with Generated Images, a novel paradigm that fundamentally transforms how large multimodal models (LMMs) engage with visual reasoning by enabling them to natively think across text and vision modalities through spontaneous generation of intermediate visual thinking steps. Current visual reasoning with LMMs is constrained to either processing fixed user-provided images or reasoning solely through text-based chain-of-thought (CoT). Thinking with Generated Images unlocks a new dimension of cognitive capability where models can actively construct intermediate visual thoughts, critique their own visual hypotheses, and refine them as integral components of their reasoning process. We demonstrate the effectiveness of our approach through two complementary mechanisms: (1) vision generation with intermediate visual subgoals, where models decompose complex visual tasks into manageable components that are generated and integrated progressively, and (2) vision generation with self-critique, where models generate an initial visual hypothesis, analyze its shortcomings through textual reasoning, and produce refined outputs based on their own critiques. Our experiments on vision generation benchmarks show substantial improvements over baseline approaches, with our models achieving up to 50% (from 38% to 57%) relative improvement in handling complex multi-object scenarios. From biochemists exploring novel protein structures, and architects iterating on spatial designs, to forensic analysts reconstructing crime scenes, and basketball players envisioning strategic plays, our approach enables AI models to engage in the kind of visual imagination and iterative refinement that characterizes human creative, analytical, and strategic thinking. We release our open-source suite at https://github.com/GAIR-NLP/thinking-with-generated-images.

We present THOUGHTSCULPT, a general reasoning and search method for tasks with outputs that can be decomposed into components. THOUGHTSCULPT explores a search tree of potential solutions using Monte Carlo Tree Search (MCTS), building solutions one action at a time and evaluating according to any domain-specific heuristic, which in practice is often simply an LLM evaluator. Critically, our action space includes revision actions: THOUGHTSCULPT may choose to revise part of its previous output rather than continuing to build the rest of its output. Empirically, THOUGHTSCULPT outperforms state-of-the-art reasoning methods across three challenging tasks: Story Outline Improvement (up to +30% interestingness), Mini-Crosswords Solving (up to +16% word success rate), and Constrained Generation (up to +10% concept coverage).

The remarkable success of Chain-of-Thought (CoT), which enhances performance by scaling generation steps at test-time, inspires us to ask: can we leverage a similar scaling of computational steps during pretraining to improve the generation of each individual token? To address this, we propose a novel pre-training methodology: Pretraining Language Models with Latent Thoughts (PonderLM-2). Our approach pretrains a language model (LM) to first generate an intermediate latent thought-the last hidden state of the current position-which is then used as input to predict the actual subsequent token. This additional computational step enables the LM to refine its prediction within unconstrained continuous space. Our experiments demonstrate that, at an identical inference cost, a LM that generates one additional latent thought per token outperforms a standard model with double the parameters. For instance, our PonderLM-2-Pythia-1.4B, pretrained on 300B tokens from the Pile, significantly surpasses the vanilla Pythia-2.8B trained on the same data on both language modeling and a range of general downstream tasks. Furthermore, increasing the number of latent thoughts generated before each actual token-forming a chain analogous to CoT-consistently improves the model's performance.

Recently, with the development of tool-calling capabilities in large language models (LLMs), these models have demonstrated significant potential for automating electronic design automation (EDA) flows by interacting with EDA tool APIs via EDA scripts. However, considering the limited understanding of EDA tools, LLMs face challenges in practical scenarios where diverse interfaces of EDA tools exist across different platforms. Additionally, EDA flow automation often involves intricate, long-chain tool-calling processes, increasing the likelihood of errors in intermediate steps. Any errors will lead to the instability and failure of EDA flow automation. To address these challenges, we introduce EDAid, a multi-agent collaboration system where multiple agents harboring divergent thoughts converge towards a common goal, ensuring reliable and successful EDA flow automation. Specifically, each agent is controlled by ChipLlama models, which are expert LLMs fine-tuned for EDA flow automation. Our experiments demonstrate the state-of-the-art (SOTA) performance of our ChipLlama models and validate the effectiveness of our EDAid in the automation of complex EDA flows, showcasing superior performance compared to single-agent systems.

3D visual grounding is the ability to localize objects in 3D scenes conditioned by utterances. Most existing methods devote the referring head to localize the referred object directly, causing failure in complex scenarios. In addition, it does not illustrate how and why the network reaches the final decision. In this paper, we address this question Can we design an interpretable 3D visual grounding framework that has the potential to mimic the human perception system?. To this end, we formulate the 3D visual grounding problem as a sequence-to-sequence task by first predicting a chain of anchors and then the final target. Interpretability not only improves the overall performance but also helps us identify failure cases. Following the chain of thoughts approach enables us to decompose the referring task into interpretable intermediate steps, boosting the performance and making our framework extremely data-efficient. Moreover, our proposed framework can be easily integrated into any existing architecture. We validate our approach through comprehensive experiments on the Nr3D, Sr3D, and Scanrefer benchmarks and show consistent performance gains compared to existing methods without requiring manually annotated data. Furthermore, our proposed framework, dubbed CoT3DRef, is significantly data-efficient, whereas on the Sr3D dataset, when trained only on 10% of the data, we match the SOTA performance that trained on the entire data.

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the popular Chain of Thought approach to prompting language models, and enables exploration over coherent units of text (thoughts) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models' problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: https://github.com/ysymyth/tree-of-thought-llm.

Spoken dialogue systems increasingly employ large language models (LLMs) to leverage their advanced reasoning capabilities. However, direct application of LLMs in spoken communication often yield suboptimal results due to mismatches between optimal textual and verbal delivery. While existing approaches adapt LLMs to produce speech-friendly outputs, their impact on reasoning performance remains underexplored. In this work, we propose Think-Verbalize-Speak, a framework that decouples reasoning from spoken delivery to preserve the full reasoning capacity of LLMs. Central to our method is verbalizing, an intermediate step that translates thoughts into natural, speech-ready text. We also introduce ReVerT, a latency-efficient verbalizer based on incremental and asynchronous summarization. Experiments across multiple benchmarks show that our method enhances speech naturalness and conciseness with minimal impact on reasoning. The project page with the dataset and the source code is available at https://yhytoto12.github.io/TVS-ReVerT

Chain-of-thoughts (CoT) requires large language models (LLMs) to generate intermediate steps before reaching the final answer, and has been proven effective to help LLMs solve complex reasoning tasks. However, the inner mechanism of CoT still remains largely unclear. In this paper, we empirically study the role of CoT tokens in LLMs on two compositional tasks: multi-digit multiplication and dynamic programming. While CoT is essential for solving these problems, we find that preserving only tokens that store intermediate results would achieve comparable performance. Furthermore, we observe that storing intermediate results in an alternative latent form will not affect model performance. We also randomly intervene some values in CoT, and notice that subsequent CoT tokens and the final answer would change correspondingly. These findings suggest that CoT tokens may function like variables in computer programs but with potential drawbacks like unintended shortcuts and computational complexity limits between tokens. The code and data are available at https://github.com/solitaryzero/CoTs_are_Variables.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Program errors can occur in any type of programming, and can manifest in a variety of ways, such as unexpected output, crashes, or performance issues. And program error diagnosis can often be too abstract or technical for developers to understand, especially for beginners. The goal of this paper is to present a novel machine-learning approach for Multi-task Program Error Repair and Explanatory Diagnosis (mPRED). A pre-trained language model is used to encode the source code, and a downstream model is specifically designed to identify and repair errors. Programs and test cases will be augmented and optimized from several perspectives. Additionally, our approach incorporates a "chain of thoughts" method, which enables the models to produce intermediate reasoning explanations before providing the final correction. To aid in visualizing and analyzing the program structure, we use a graph neural network for program structure visualization. Overall, our approach offers a promising approach for repairing program errors across different programming languages and providing helpful explanations to programmers.

While open-source multi-modal language models perform well on simple question answering tasks, they often fail on complex questions that require multiple capabilities, such as fine-grained recognition, visual grounding, and reasoning, and that demand multi-step solutions. We present TACO, a family of multi-modal large action models designed to improve performance on such complex, multi-step, and multi-modal tasks. During inference, TACO produces chains-of-thought-and-action (CoTA), executes intermediate steps by invoking external tools such as OCR, depth estimation and calculator, then integrates both the thoughts and action outputs to produce coherent responses. To train TACO, we create a large dataset of over 1M synthetic CoTA traces generated with GPT-4o and Python programs. We then experiment with various data filtering and mixing techniques and obtain a final subset of 293K high-quality CoTA examples. This dataset enables TACO to learn complex reasoning and action paths, surpassing existing models trained on instruction tuning data with only direct answers. Our model TACO outperforms the instruction-tuned baseline across 8 benchmarks, achieving a 3.6% improvement on average, with gains of up to 15% in MMVet tasks involving OCR, mathematical reasoning, and spatial reasoning. Training on high-quality CoTA traces sets a new standard for complex multi-modal reasoning, highlighting the need for structured, multi-step instruction tuning in advancing open-source mutli-modal models' capabilities.

LLM developers are increasingly reliant on synthetic data, but generating high-quality data for complex long-context reasoning tasks remains challenging. We introduce CLIPPER, a compression-based approach for generating synthetic data tailored to narrative claim verification - a task that requires reasoning over a book to verify a given claim. Instead of generating claims directly from the raw text of the book, which results in artifact-riddled claims, CLIPPER first compresses the book into chapter outlines and book summaries and then uses these intermediate representations to generate complex claims and corresponding chain-of-thoughts. Compared to naive approaches, CLIPPER produces claims that are more valid, grounded, and complex. Using CLIPPER, we construct a dataset of 19K synthetic book claims paired with their source texts and chain-of-thought reasoning, and use it to fine-tune three open-weight models. Our best model achieves breakthrough results on narrative claim verification (from 28% to 76% accuracy on our test set) and sets a new state-of-the-art for sub-10B models on the NoCha leaderboard. Further analysis shows that our models generate more detailed and grounded chain-of-thought reasoning while also improving performance on other narrative understanding tasks (e.g., NarrativeQA).

Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater computation that additional tokens allow. We show that transformers can use meaningless filler tokens (e.g., '......') in place of a chain of thought to solve two hard algorithmic tasks they could not solve when responding without intermediate tokens. However, we find empirically that learning to use filler tokens is difficult and requires specific, dense supervision to converge. We also provide a theoretical characterization of the class of problems where filler tokens are useful in terms of the quantifier depth of a first-order formula. For problems satisfying this characterization, chain-of-thought tokens need not provide information about the intermediate computational steps involved in multi-token computations. In summary, our results show that additional tokens can provide computational benefits independent of token choice. The fact that intermediate tokens can act as filler tokens raises concerns about large language models engaging in unauditable, hidden computations that are increasingly detached from the observed chain-of-thought tokens.

Large language models (LLMs) have achieved impressive performance across various mathematical reasoning benchmarks. However, there are increasing debates regarding whether these models truly understand and apply mathematical knowledge or merely rely on shortcuts for mathematical reasoning. One essential and frequently occurring evidence is that when the math questions are slightly changed, LLMs can behave incorrectly. This motivates us to evaluate the robustness of LLMs' math reasoning capability by testing a wide range of question variations. We introduce the adversarial grade school math (\datasetname) dataset, an extension of GSM8K augmented with various mathematical perturbations. Our experiments on 25 LLMs and 4 prompting techniques show that while LLMs exhibit different levels of math reasoning abilities, their performances are far from robust. In particular, even for problems that have been solved in GSM8K, LLMs can make mistakes when new statements are added or the question targets are altered. We also explore whether more robust performance can be achieved by composing existing prompting methods, in which we try an iterative method that generates and verifies each intermediate thought based on its reasoning goal and calculation result. Code and data are available at https://github.com/qtli/GSM-Plus.

To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

Images usually convey richer detail than text, but often include redundant information which potentially downgrades multimodal reasoning performance. When faced with lengthy or complex messages, humans tend to employ abstract thinking to convert them into simple and concise abstracts. Inspired by this cognitive strategy, we introduce Visual Abstract Thinking (VAT), a novel thinking paradigm that prompts Multimodal Large Language Models (MLLMs) with visual abstract instead of explicit verbal thoughts or elaborate guidance, permitting a more concentrated visual reasoning mechanism. Explicit thinking, such as Chain-of-thought (CoT) or tool-augmented approaches, increases the complexity of reasoning process via inserting verbose intermediate steps, external knowledge or visual information. In contrast, VAT reduces redundant visual information and encourages models to focus their reasoning on more essential visual elements. Experimental results show that VAT consistently empowers different models, and achieves an average gain of 17% over GPT-4o baseline by employing diverse types of visual abstracts, demonstrating that VAT can enhance visual reasoning abilities for MLLMs regarding conceptual, structural and relational reasoning tasks. VAT is also compatible with CoT in knowledge-intensive multimodal reasoning tasks. These findings highlight the effectiveness of visual reasoning via abstract thinking and encourage further exploration of more diverse reasoning paradigms from the perspective of human cognition.

Compressing long chain-of-thought (CoT) from large language models (LLMs) is an emerging strategy to improve the reasoning efficiency of LLMs. Despite its promising benefits, existing studies equally compress all thoughts within a long CoT, hindering more concise and effective reasoning. To this end, we first investigate the importance of different thoughts by examining their effectiveness and efficiency in contributing to reasoning through automatic long CoT chunking and Monte Carlo rollouts. Building upon the insights, we propose a theoretically bounded metric to jointly measure the effectiveness and efficiency of different thoughts. We then propose LongotimesShort, an efficient reasoning framework that enables two LLMs to collaboratively solve the problem: a long-thought LLM for more effectively generating important thoughts, while a short-thought LLM for efficiently generating remaining thoughts. Specifically, we begin by synthesizing a small amount of cold-start data to fine-tune LLMs for long-thought and short-thought reasoning styles, respectively. Furthermore, we propose a synergizing-oriented multi-turn reinforcement learning, focusing on the model self-evolution and collaboration between long-thought and short-thought LLMs. Experimental results show that our method enables Qwen2.5-7B and Llama3.1-8B to achieve comparable performance compared to DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-Llama-8B, while reducing token length by over 80% across the MATH500, AIME24/25, AMC23, and GPQA Diamond benchmarks. Our data and code are available at https://github.com/yasNing/Long-otimes-Short/.

In this study, we investigate whether non-English-centric LLMs, despite their strong performance, `think' in their respective dominant language: more precisely, `think' refers to how the representations of intermediate layers, when un-embedded into the vocabulary space, exhibit higher probabilities for certain dominant languages during generation. We term such languages as internal latent languages. We examine the latent language of three typical categories of models for Japanese processing: Llama2, an English-centric model; Swallow, an English-centric model with continued pre-training in Japanese; and LLM-jp, a model pre-trained on balanced English and Japanese corpora. Our empirical findings reveal that, unlike Llama2 which relies exclusively on English as the internal latent language, Japanese-specific Swallow and LLM-jp employ both Japanese and English, exhibiting dual internal latent languages. For any given target language, the model preferentially activates the latent language most closely related to it. In addition, we explore how intermediate layers respond to questions involving cultural conflicts between latent internal and target output languages. We further explore how the language identity shifts across layers while keeping consistent semantic meaning reflected in the intermediate layer representations. This study deepens the understanding of non-English-centric large language models, highlighting the intricate dynamics of language representation within their intermediate layers.

Large Language Models (LLMs), such as OpenAI's o1-series have demonstrated compelling capabilities for complex reasoning tasks via the extended chain-of-thought (CoT) reasoning mechanism. However, recent studies reveal substantial redundancy in the CoT reasoning traces, which not only increases inference latency but also negatively impacts model performance by diverting attention to unnecessary reasoning paths. To address this issue, we investigate the internal reasoning structures of LLMs and categorize them into three primary thought types: execution, reflection, and transition thoughts. Moreover, our analysis reveals that excessive reflection and transition thoughts are strongly correlated with failure cases and these thought categories exhibit clear separation in the latent space. Based on these, we introduce SEAL (Steerable reasoning calibration), a training-free approach that seamlessly calibrates the CoT process, improving accuracy while demonstrating significant efficiency gains. SEAL consists of an offline stage for extracting the reasoning steering vector in the latent space, followed by an on-the-fly calibration of the reasoning trace through representation intervention using the steering vector. Notably, the steering vector exhibits strong transferability across various tasks. Extensive experiments across multiple models (DeepSeek-R1-Distill and QwQ-32B-Preview) and benchmarks (Math500, GSM8K, LiveCodeBench) validate the effectiveness of SEAL, up to a 11% improvement in accuracy while reducing reasoning tokens by 11.8% to 50.4%. Our code is publicly available at https://github.com/VITA-Group/SEAL.

It has been well-known that Chain-of-Thought can remarkably enhance LLMs' performance on complex tasks. However, because it also introduces slower inference speeds and higher computational costs, many researches have attempted to use implicit CoT, which does not need LLMs to explicitly generate the intermediate steps. But there is still gap between their efficacy and typical explicit CoT methods. This leaves us a doubt that, does implicit CoT really equal to explicit CoT? Therefore, in this study, we address this question through experiments. We probe the information of intermediate steps from the model's hidden states when it is performing implicit CoT. The results surprisingly indicate that LLMs hardly think about intermediate steps, suggesting they may just rely on experience rather than strict step-by-step reasoning. Moreover, we find LLMs' implicit reasoning capabilities are susceptible and unstable, reaffirming the necessity of explicit CoT to effectively support complex tasks.

Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the initial decisions, causing errors in early steps to accumulate and impact the final answers. In contrast, humans adopt recursive thinking when tackling complex reasoning problems, i.e., iteratively breaking the original problem into approachable sub-problems and aggregating their answers to resolve the original one. Inspired by the human cognitive process, we propose SOCRATIC QUESTIONING, a divide-and-conquer style algorithm that mimics the recursive thinking process. Specifically, SOCRATIC QUESTIONING leverages large language models to raise and answer sub-questions until collecting enough information to tackle the original question. Unlike CoT, SOCRATIC QUESTIONING explicitly navigates the thinking space, stimulates effective recursive thinking, and is more robust towards errors in the thinking process. Extensive experiments on several complex reasoning tasks, including MMLU, MATH, LogiQA, and visual question-answering demonstrate significant performance improvements over the state-of-the-art prompting methods, such as CoT, and Tree-of-Thought. The qualitative analysis clearly shows that the intermediate reasoning steps elicited by SOCRATIC QUESTIONING are similar to humans' recursively thinking process of complex reasoning problems.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

When leveraging language models for reasoning tasks, generating explicit chain-of-thought (CoT) steps often proves essential for achieving high accuracy in final outputs. In this paper, we investigate if models can be taught to internalize these CoT steps. To this end, we propose a simple yet effective method for internalizing CoT steps: starting with a model trained for explicit CoT reasoning, we gradually remove the intermediate steps and finetune the model. This process allows the model to internalize the intermediate reasoning steps, thus simplifying the reasoning process while maintaining high performance. Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication. Furthermore, our method proves effective on larger language models, such as Mistral 7B, achieving over 50% accuracy on GSM8K without producing any intermediate steps.

Spoken Language Models (SLMs) are designed to take speech inputs and produce spoken responses. However, current SLMs lack the ability to perform an internal, unspoken thinking process before responding. In contrast, humans typically engage in complex mental reasoning internally, enabling them to communicate ideas clearly and concisely. Thus, integrating an unspoken thought process into SLMs is highly desirable. While naively generating a complete chain-of-thought (CoT) reasoning before starting to talk can enable thinking for SLMs, this induces additional latency for the speech response, as the CoT reasoning can be arbitrarily long. To solve this issue, we propose Stitch, a novel generation method that alternates between the generation of unspoken reasoning chunks and spoken response chunks. Since the audio duration of a chunk of spoken response is much longer than the time to generate the tokens in a chunk of spoken response, we use the remaining free time to generate the unspoken reasoning tokens. When a chunk of audio is played to the user, the model continues to generate the next unspoken reasoning chunk, achieving simultaneous thinking and talking. Remarkably, Stitch matches the latency of baselines that cannot generate unspoken CoT by design while outperforming those baselines by 15% on math reasoning datasets; Stitch also performs equally well on non-reasoning datasets as those baseline models. Some animations and demonstrations are on the project page: https://d223302.github.io/STITCH.

We explore how generating a chain of thought -- a series of intermediate reasoning steps -- significantly improves the ability of large language models to perform complex reasoning. In particular, we show how such reasoning abilities emerge naturally in sufficiently large language models via a simple method called chain of thought prompting, where a few chain of thought demonstrations are provided as exemplars in prompting. Experiments on three large language models show that chain of thought prompting improves performance on a range of arithmetic, commonsense, and symbolic reasoning tasks. The empirical gains can be striking. For instance, prompting a 540B-parameter language model with just eight chain of thought exemplars achieves state of the art accuracy on the GSM8K benchmark of math word problems, surpassing even finetuned GPT-3 with a verifier.

Chain-of-thought prompting (e.g., "Let's think step-by-step") primes large language models to verbalize rationalization for their predictions. While chain-of-thought can lead to dramatic performance gains, benefits appear to emerge only for sufficiently large models (beyond 50B parameters). We show that orders-of-magnitude smaller models (125M -- 1.3B parameters) can still benefit from chain-of-thought prompting. To achieve this, we introduce Symbolic Chain-of-Thought Distillation (SCoTD), a method to train a smaller student model on rationalizations sampled from a significantly larger teacher model. Experiments across several commonsense benchmarks show that: 1) SCoTD enhances the performance of the student model in both supervised and few-shot settings, and especially for challenge sets; 2) sampling many reasoning chains per instance from the teacher is paramount; and 3) after distillation, student chain-of-thoughts are judged by humans as comparable to the teacher, despite orders of magnitude fewer parameters. We test several hypotheses regarding what properties of chain-of-thought samples are important, e.g., diversity vs. teacher likelihood vs. open-endedness. We release our corpus of chain-of-thought samples and code.

Large reasoning models (LRMs) have led to new possibilities in terms of problem-solving, through the devising of a natural language thought process prior to answering a query. While their capabilities are well known across mathematics and coding tasks, their impact on the task of machine translation (MT) remains underexplored. In this work, we explore the benefits of the generation of intermediate tokens when performing MT across multiple language pairs of different levels of resourcedness and multiple setups. We find that "thinking tokens" do not help LRMs better perform MT. This result generalizes to models fine-tuned to reason before translating using distilled chain of thought (CoT) inspired by human translators' practices. Specifically, fine-tuning a model with synthetic CoT explanations detailing how to translate step-by-step does not outperform standard input-output fine-tuning. However, constructing the intermediate tokens by combining the outputs of modular translation-specific prompting strategies results in improvements. Our findings underscore that the contribution of intermediate tokens during fine-tuning highly depends on the presence of translation attempts within them. More broadly, our results suggest that using a teacher to refine target translations or to expand parallel corpora is more impactful than distilling their CoT explanations into "thinking" MT models.

A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is inspired by cognitive neuroscience theories of consciousness, seen as a bottleneck through which just a few elements, after having been selected by attention from a broader pool, are then broadcast and condition further processing, both in perception and decision-making. The set of recently selected elements one becomes aware of is seen as forming a low-dimensional conscious state. This conscious state is combining the few concepts constituting a conscious thought, i.e., what one is immediately conscious of at a particular moment. We claim that this architectural and information-processing constraint corresponds to assumptions about the joint distribution between high-level concepts. To the extent that these assumptions are generally true (and the form of natural language seems consistent with them), they can form a useful prior for representation learning. A low-dimensional thought or conscious state is analogous to a sentence: it involves only a few variables and yet can make a statement with very high probability of being true. This is consistent with a joint distribution (over high-level concepts) which has the form of a sparse factor graph, i.e., where the dependencies captured by each factor of the factor graph involve only very few variables while creating a strong dip in the overall energy function. The consciousness prior also makes it natural to map conscious states to natural language utterances or to express classical AI knowledge in a form similar to facts and rules, albeit capturing uncertainty as well as efficient search mechanisms implemented by attention mechanisms.

Recent reasoning models through test-time scaling have demonstrated that long chain-of-thoughts can unlock substantial performance boosts in hard reasoning tasks such as math and code. However, the benefit of such long thoughts for system-2 reasoning is relatively less explored in other domains such as perceptual tasks where shallower, system-1 reasoning seems sufficient. In this paper, we introduce LongPerceptualThoughts, a new synthetic dataset with 30K long-thought traces for perceptual tasks. The key challenges in synthesizing elaborate reasoning thoughts for perceptual tasks are that off-the-shelf models are not yet equipped with such thinking behavior and that it is not straightforward to build a reliable process verifier for perceptual tasks. Thus, we propose a novel three-stage data synthesis framework that first synthesizes verifiable multiple-choice questions from dense image descriptions, then extracts simple CoTs from VLMs for those verifiable problems, and finally expands those simple thoughts to elaborate long thoughts via frontier reasoning models. In controlled experiments with a strong instruction-tuned 7B model, we demonstrate notable improvements over existing visual reasoning data-generation methods. Our model, trained on the generated dataset, achieves an average +3.4 points improvement over 5 vision-centric benchmarks, including +11.8 points on V^* Bench. Notably, despite being tuned for vision tasks, it also improves performance on the text reasoning benchmark, MMLU-Pro, by +2 points.

Visual-Interleaved Chain-of-Thought (VI-CoT) enables MLLMs to continually update their understanding and decisions based on step-wise intermediate visual states (IVS), much like a human would, which demonstrates impressive success in various tasks, thereby leading to emerged advancements in related benchmarks. Despite promising progress, current benchmarks provide models with relatively fixed IVS, rather than free-style IVS, whch might forcibly distort the original thinking trajectories, failing to evaluate their intrinsic reasoning capabilities. More importantly, existing benchmarks neglect to systematically explore the impact factors that IVS would impart to untamed reasoning performance. To tackle above gaps, we introduce a specialized benchmark termed ViC-Bench, consisting of four representive tasks: maze navigation, jigsaw puzzle, embodied long-horizon planning, and complex counting, where each task has dedicated free-style IVS generation pipeline supporting function calls. To systematically examine VI-CoT capability, we propose a thorough evaluation suite incorporating a progressive three-stage strategy with targeted new metrics. Besides, we establish Incremental Prompting Information Injection (IPII) strategy to ablatively explore the prompting factors for VI-CoT. We extensively conduct evaluations for 18 advanced MLLMs, revealing key insights into their VI-CoT capability. Our proposed benchmark is publicly open at Huggingface.

Humans acquire knowledge by observing the external world, but also by introspection. Introspection gives a person privileged access to their current state of mind (e.g., thoughts and feelings) that is not accessible to external observers. Can LLMs introspect? We define introspection as acquiring knowledge that is not contained in or derived from training data but instead originates from internal states. Such a capability could enhance model interpretability. Instead of painstakingly analyzing a model's internal workings, we could simply ask the model about its beliefs, world models, and goals. More speculatively, an introspective model might self-report on whether it possesses certain internal states such as subjective feelings or desires and this could inform us about the moral status of these states. Such self-reports would not be entirely dictated by the model's training data. We study introspection by finetuning LLMs to predict properties of their own behavior in hypothetical scenarios. For example, "Given the input P, would your output favor the short- or long-term option?" If a model M1 can introspect, it should outperform a different model M2 in predicting M1's behavior even if M2 is trained on M1's ground-truth behavior. The idea is that M1 has privileged access to its own behavioral tendencies, and this enables it to predict itself better than M2 (even if M2 is generally stronger). In experiments with GPT-4, GPT-4o, and Llama-3 models (each finetuned to predict itself), we find that the model M1 outperforms M2 in predicting itself, providing evidence for introspection. Notably, M1 continues to predict its behavior accurately even after we intentionally modify its ground-truth behavior. However, while we successfully elicit introspection on simple tasks, we are unsuccessful on more complex tasks or those requiring out-of-distribution generalization.

Chain-of-Thought (CoT) reasoning enables Large Language Models (LLMs) to solve complex reasoning tasks by generating intermediate reasoning steps. However, most existing approaches focus on hard token decoding, which constrains reasoning within the discrete vocabulary space and may not always be optimal. While recent efforts explore continuous-space reasoning, they often suffer from catastrophic forgetting, limiting their applicability to state-of-the-art LLMs that already perform well in zero-shot settings with a proper instruction. To address this challenge, we propose a novel approach for continuous-space reasoning that does not require modifying the underlying LLM. Specifically, we employ a lightweight assistant model to generate instance-specific soft thought tokens speculatively as the initial chain of thoughts, which are then mapped into the LLM's representation space via a projection module. Experimental results on five reasoning benchmarks demonstrate that our method enhances LLM reasoning performance through supervised, parameter-efficient fine-tuning.

We introduce thoughts of words (ToW), a novel training-time data-augmentation method for next-word prediction. ToW views next-word prediction as a core reasoning task and injects fine-grained thoughts explaining what the next word should be and how it is related to the previous contexts in pre-training texts. Our formulation addresses two fundamental drawbacks of existing next-word prediction learning schemes: they induce factual hallucination and are inefficient for models to learn the implicit reasoning processes in raw texts. While there are many ways to acquire such thoughts of words, we explore the first step of acquiring ToW annotations through distilling from larger models. After continual pre-training with only 70K ToW annotations, we effectively improve models' reasoning performances by 7% to 9% on average and reduce model hallucination by up to 10%. At the same time, ToW is entirely agnostic to tasks and applications, introducing no additional biases on labels or semantics.

Recent advancements in Large Language Models (LLMs) have revolutionized decision-making by breaking down complex problems into more manageable language sequences referred to as ``thoughts''. An effective thought design should consider three key perspectives: performance, efficiency, and flexibility. However, existing thought can at most exhibit two of these attributes. To address these limitations, we introduce a novel thought prompting approach called ``Everything of Thoughts'' (XoT) to defy the law of ``Penrose triangle of existing thought paradigms. XoT leverages pretrained reinforcement learning and Monte Carlo Tree Search (MCTS) to incorporate external domain knowledge into thoughts, thereby enhancing LLMs' capabilities and enabling them to generalize to unseen problems efficiently. Through the utilization of the MCTS-LLM collaborative thought revision framework, this approach autonomously produces high-quality comprehensive cognitive mappings with minimal LLM interactions. Additionally, XoT empowers LLMs to engage in unconstrained thinking, allowing for flexible cognitive mappings for problems with multiple solutions.

Humans have a powerful and mysterious capacity to reason. By working through a series of purely mental steps, we can make inferences we would not be capable of making directly -- despite the fact that we get no additional data from the world. Similarly, when large language models generate a series of intermediate steps (a chain of thought) before answering a question, they often produce better answers than they otherwise would. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences in order to estimate relationships between variables that were not seen together in training. We prove that there will exist a "reasoning gap", where reasoning through intermediate variables improves inference, for the simple case of an autoregressive density estimator trained on local samples from a chain-structured probabilistic model. We then test our hypothesis empirically in more complex models, training an autoregressive language model on samples from Bayes nets but only including a subset of variables in each sample. We test language models' ability to match conditional probabilities with and without intermediate reasoning steps, finding that intermediate steps are only helpful when the training data is locally structured with respect to dependencies between variables and that the combination of locally-structured observations and reasoning is much more data-efficient than training on all variables. Our results illustrate how the effectiveness of reasoning step by step is rooted in the local statistical structure of the training data.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

Modern large language models (LLMs) like ChatGPT have shown remarkable performance on general language tasks but still struggle on complex reasoning tasks, which drives the research on cognitive behaviors of LLMs to explore human-like problem-solving strategies. Along this direction, one representative strategy is self-reflection, which asks an LLM to refine the solution with the feedback generated by itself iteratively. However, our study shows that such reflection-style methods suffer from the Degeneration-of-Thought (DoT) problem: once the LLM has established confidence in its solutions, it is unable to generate novel thoughts later through reflection even if its initial stance is incorrect. To address the DoT problem, we propose a Multi-Agent Debate (MAD) framework, in which multiple agents express their arguments in the state of "tit for tat" and a judge manages the debate process to obtain a final solution. Clearly, our MAD framework encourages divergent thinking in LLMs which would be helpful for tasks that require deep levels of contemplation. Experiment results on two challenging datasets, commonsense machine translation and counter-intuitive arithmetic reasoning, demonstrate the effectiveness of our MAD framework. Extensive analyses suggest that the adaptive break of debate and the modest level of "tit for tat" state are required for MAD to obtain good performance. Moreover, we find that LLMs might not be a fair judge if different LLMs are used for agents. Codes: https://github.com/Skytliang/Multi-Agents-Debate

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by generating more intermediate steps, recent studies in Coconut and SoftCoT have demonstrated that thinking in the continuous latent space can further enhance the reasoning performance. Such latent thoughts encode informative thinking without the information loss associated with autoregressive token generation, sparking increased interest in continuous-space reasoning. Unlike discrete decoding, where repeated sampling enables exploring diverse reasoning paths, latent representations in continuous space are fixed for a given input, which limits diverse exploration, as all decoded paths originate from the same latent thought. To overcome this limitation, we introduce SoftCoT++ to extend SoftCoT to the Test-Time Scaling paradigm by enabling diverse exploration of thinking paths. Specifically, we perturb latent thoughts via multiple specialized initial tokens and apply contrastive learning to promote diversity among soft thought representations. Experiments across five reasoning benchmarks and two distinct LLM architectures demonstrate that SoftCoT++ significantly boosts SoftCoT and also outperforms SoftCoT with self-consistency scaling. Moreover, it shows strong compatibility with conventional scaling techniques such as self-consistency. Source code is available at https://github.com/xuyige/SoftCoT.

Recently, techniques such as explicit structured reasoning have demonstrated strong test-time scaling behavior by enforcing a separation between the model's internal "thinking" process and the final response. A key factor influencing answer quality in this setting is the length of the thinking stage. When the reasoning is too short, the model may fail to capture the complexity of the task. Conversely, when it is too long, the model may overthink, leading to unnecessary computation and degraded performance. This paper explores and exploits the underlying mechanisms by which LLMs understand and regulate the length of their reasoning during explicit thought processes. First, we show that LLMs encode their progress through the reasoning process and introduce an interactive progress bar visualization, which is then used to reveal insights on the model's planning dynamics. Second, we manipulate the internal progress encoding during inference to reduce unnecessary steps and generate a more concise and decisive chain of thoughts. Our empirical results demonstrate that this "overclocking" method mitigates overthinking, improves answer accuracy, and reduces inference latency. Our code is publicly available.

Large language models (LLMs) are restricted to reason in the "language space", where they typically express the reasoning process with a chain-of-thought (CoT) to solve a complex reasoning problem. However, we argue that language space may not always be optimal for reasoning. For example, most word tokens are primarily for textual coherence and not essential for reasoning, while some critical tokens require complex planning and pose huge challenges to LLMs. To explore the potential of LLM reasoning in an unrestricted latent space instead of using natural language, we introduce a new paradigm Coconut (Chain of Continuous Thought). We utilize the last hidden state of the LLM as a representation of the reasoning state (termed "continuous thought"). Rather than decoding this into a word token, we feed it back to the LLM as the subsequent input embedding directly in the continuous space. Experiments show that Coconut can effectively augment the LLM on several reasoning tasks. This novel latent reasoning paradigm leads to emergent advanced reasoning patterns: the continuous thought can encode multiple alternative next reasoning steps, allowing the model to perform a breadth-first search (BFS) to solve the problem, rather than prematurely committing to a single deterministic path like CoT. Coconut outperforms CoT in certain logical reasoning tasks that require substantial backtracking during planning, with fewer thinking tokens during inference. These findings demonstrate the promise of latent reasoning and offer valuable insights for future research.

We explore how iterative revising a chain of thoughts with the help of information retrieval significantly improves large language models' reasoning and generation ability in long-horizon generation tasks, while hugely mitigating hallucination. In particular, the proposed method -- *retrieval-augmented thoughts* (RAT) -- revises each thought step one by one with retrieved information relevant to the task query, the current and the past thought steps, after the initial zero-shot CoT is generated. Applying RAT to GPT-3.5, GPT-4, and CodeLLaMA-7b substantially improves their performances on various long-horizon generation tasks; on average of relatively increasing rating scores by 13.63% on code generation, 16.96% on mathematical reasoning, 19.2% on creative writing, and 42.78% on embodied task planning. The demo page can be found at https://craftjarvis.github.io/RAT

Chain-of-Thought (CoT) prompting reveals that large language models are capable of performing complex reasoning via intermediate steps. CoT prompting is primarily categorized into three approaches. The first approach utilizes straightforward prompts like ``Let's think step by step'' to generate a sequential thought process before yielding an answer. The second approach makes use of human-crafted, step-by-step demonstrations to guide the model's reasoning process. The third automates the generation of reasoned demonstrations with the 'Let's think step by step'.This approach sometimes leads to reasoning errors, highlighting the need to diversify demonstrations to mitigate its misleading effects. However, diverse demonstrations pose challenges for effective representations. In this work, we propose ECHO, a self-harmonized chain-of-thought prompting method. It consolidates diverse solution paths into a uniform and effective solution pattern.ECHO demonstrates the best overall performance across three reasoning domains.

Recent advancements in large language models (LLMs) have demonstrated their impressive abilities in various reasoning and decision-making tasks. However, the quality and coherence of the reasoning process can still benefit from enhanced introspection and self-reflection. In this paper, we introduce Multiplex CoT (Chain of Thought), a method that enables LLMs to simulate a form of self-review while reasoning, by initiating double Chain of Thought (CoT) thinking. Multiplex CoT leverages the power of iterative reasoning, where the model generates an initial chain of thought and subsequently critiques and refines this reasoning with a second round of thought generation. This recursive approach allows for more coherent, logical, and robust answers, improving the overall decision-making process. We demonstrate how this method can be effectively implemented using simple prompt engineering in existing LLM architectures, achieving an effect similar to that of the Learning-Refinement Model (LRM) without the need for additional training. Additionally, we present a practical guide for implementing the method in Google Colab, enabling easy integration into real-world applications.

LLMs are typically trained to answer user questions or follow instructions similarly to how human experts respond. However, in the standard alignment framework they lack the basic ability of explicit thinking before answering. Thinking is important for complex questions that require reasoning and planning -- but can be applied to any task. We propose a training method for equipping existing LLMs with such thinking abilities for general instruction following without use of additional human data. We achieve this by an iterative search and optimization procedure that explores the space of possible thought generations, allowing the model to learn how to think without direct supervision. For each instruction, the thought candidates are scored using a judge model to evaluate their responses only, and then optimized via preference optimization. We show that this procedure leads to superior performance on AlpacaEval and Arena-Hard, and shows gains from thinking on non-reasoning categories such as marketing, health and general knowledge, in addition to more traditional reasoning & problem-solving tasks.

Generating a Chain of Thought (CoT) has been shown to consistently improve large language model (LLM) performance on a wide range of NLP tasks. However, prior work has mainly focused on logical reasoning tasks (e.g. arithmetic, commonsense QA); it remains unclear whether improvements hold for more diverse types of reasoning, especially in socially situated contexts. Concretely, we perform a controlled evaluation of zero-shot CoT across two socially sensitive domains: harmful questions and stereotype benchmarks. We find that zero-shot CoT reasoning in sensitive domains significantly increases a model's likelihood to produce harmful or undesirable output, with trends holding across different prompt formats and model variants. Furthermore, we show that harmful CoTs increase with model size, but decrease with improved instruction following. Our work suggests that zero-shot CoT should be used with caution on socially important tasks, especially when marginalized groups or sensitive topics are involved.

Large language models (LLMs) are becoming increasingly capable, but the mechanisms of their thinking and decision-making process remain unclear. Chain-of-thoughts (CoTs) have been commonly utilized to monitor LLMs, but this strategy fails to accurately reflect LLMs' thinking process. Techniques based on LLMs' hidden representations provide an inner perspective to monitor their latent thinking. However, previous methods only try to develop external monitors instead of making LLMs themselves easier to monitor. In this paper, we propose a novel method TELLME, improving the transparency of LLMs and helping monitors identify unsuitable and sensitive behaviors. Furthermore, we showcase the applications of TELLME on trustworthiness tasks (\eg, safety risks monitoring tasks and detoxification tasks), where LLMs achieve consistent improvement in transparency and task performance. More crucially, we theoretically analyze the improvement of TELLME on LLMs' generalization ability through optimal transport theory.

Recent advancements in Large Vision-Language Models have showcased remarkable capabilities. However, they often falter when confronted with complex reasoning tasks that humans typically address through visual aids and deliberate, step-by-step thinking. While existing methods have explored text-based slow thinking or rudimentary visual assistance, they fall short of capturing the intricate, interleaved nature of human visual-verbal reasoning processes. To overcome these limitations and inspired by the mechanisms of slow thinking in human cognition, we introduce VisuoThink, a novel framework that seamlessly integrates visuospatial and linguistic domains. VisuoThink facilitates multimodal slow thinking by enabling progressive visual-textual reasoning and incorporates test-time scaling through look-ahead tree search. Extensive experiments demonstrate that VisuoThink significantly enhances reasoning capabilities via inference-time scaling, even without fine-tuning, achieving state-of-the-art performance in tasks involving geometry and spatial reasoning.

Large language models (LLMs) have shown remarkable performances across a wide range of tasks. However, the mechanisms by which these models encode tasks of varying complexities remain poorly understood. In this paper, we explore the hypothesis that LLMs process concepts of varying complexities in different layers, introducing the idea of "Concept Depth" to suggest that more complex concepts are typically acquired in deeper layers. Specifically, we categorize concepts based on their level of abstraction, defining them in the order of increasing complexity within factual, emotional, and inferential tasks. We conduct extensive probing experiments using layer-wise representations across various LLM families (Gemma, LLaMA, QWen) on various datasets spanning the three domains of tasks. Our findings reveal that models could efficiently conduct probing for simpler tasks in shallow layers, and more complex tasks typically necessitate deeper layers for accurate understanding. Additionally, we examine how external factors, such as adding noise to the input and quantizing the model weights, might affect layer-wise representations. Our findings suggest that these factors can impede the development of a conceptual understanding of LLMs until deeper layers are explored. We hope that our proposed concept and experimental insights will enhance the understanding of the mechanisms underlying LLMs. Our codes are available at https://github.com/Luckfort/CD.

Large language models' reasoning abilities benefit from methods that organize their thought processes, such as chain-of-thought prompting, which employs a sequential structure to guide the reasoning process step-by-step. However, existing approaches focus primarily on organizing the sequence of thoughts, leaving structure in individual thought steps underexplored. To address this gap, we propose Table as Thought, a framework inspired by cognitive neuroscience theories on human thought. Table as Thought organizes reasoning within a tabular schema, where rows represent sequential thought steps and columns capture critical constraints and contextual information to enhance reasoning. The reasoning process iteratively populates the table until self-verification ensures completeness and correctness. Our experiments show that Table as Thought excels in planning tasks and demonstrates a strong potential for enhancing LLM performance in mathematical reasoning compared to unstructured thought baselines. This work provides a novel exploration of refining thought representation within LLMs, paving the way for advancements in reasoning and AI cognition.

Language has long been conceived as an essential tool for human reasoning. The breakthrough of Large Language Models (LLMs) has sparked significant research interest in leveraging these models to tackle complex reasoning tasks. Researchers have moved beyond simple autoregressive token generation by introducing the concept of "thought" -- a sequence of tokens representing intermediate steps in the reasoning process. This innovative paradigm enables LLMs' to mimic complex human reasoning processes, such as tree search and reflective thinking. Recently, an emerging trend of learning to reason has applied reinforcement learning (RL) to train LLMs to master reasoning processes. This approach enables the automatic generation of high-quality reasoning trajectories through trial-and-error search algorithms, significantly expanding LLMs' reasoning capacity by providing substantially more training data. Furthermore, recent studies demonstrate that encouraging LLMs to "think" with more tokens during test-time inference can further significantly boost reasoning accuracy. Therefore, the train-time and test-time scaling combined to show a new research frontier -- a path toward Large Reasoning Model. The introduction of OpenAI's o1 series marks a significant milestone in this research direction. In this survey, we present a comprehensive review of recent progress in LLM reasoning. We begin by introducing the foundational background of LLMs and then explore the key technical components driving the development of large reasoning models, with a focus on automated data construction, learning-to-reason techniques, and test-time scaling. We also analyze popular open-source projects at building large reasoning models, and conclude with open challenges and future research directions.

Large Language Models (LLMs) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive results, especially when combined with self-consistency. Nonetheless, some tasks remain particularly difficult for LLMs to solve. Tree of Thoughts (ToT) and Graph of Thoughts (GoT) emerged as alternatives, dividing the complex problem into paths of subproblems. In this paper, we propose Tree of Problems (ToP), a simpler version of ToT, which we hypothesise can work better for complex tasks that can be divided into identical subtasks. Our empirical results show that our approach outperforms ToT and GoT, and in addition performs better than CoT on complex reasoning tasks. All code for this paper is publicly available here: https://github.com/ArmelRandy/tree-of-problems.

Memory-augmented Large Language Models (LLMs) have demonstrated remarkable performance in long-term human-machine interactions, which basically relies on iterative recalling and reasoning of history to generate high-quality responses. However, such repeated recall-reason steps easily produce biased thoughts, i.e., inconsistent reasoning results when recalling the same history for different questions. On the contrary, humans can keep thoughts in the memory and recall them without repeated reasoning. Motivated by this human capability, we propose a novel memory mechanism called TiM (Think-in-Memory) that enables LLMs to maintain an evolved memory for storing historical thoughts along the conversation stream. The TiM framework consists of two crucial stages: (1) before generating a response, a LLM agent recalls relevant thoughts from memory, and (2) after generating a response, the LLM agent post-thinks and incorporates both historical and new thoughts to update the memory. Thus, TiM can eliminate the issue of repeated reasoning by saving the post-thinking thoughts as the history. Besides, we formulate the basic principles to organize the thoughts in memory based on the well-established operations, (i.e., insert, forget, and merge operations), allowing for dynamic updates and evolution of the thoughts. Furthermore, we introduce Locality-Sensitive Hashing into TiM to achieve efficient retrieval for the long-term conversations. We conduct qualitative and quantitative experiments on real-world and simulated dialogues covering a wide range of topics, demonstrating that equipping existing LLMs with TiM significantly enhances their performance in generating responses for long-term interactions.

Recent large language models have shown promising capabilities in long-form reasoning, following structured chains of thought before arriving at a final answer. However, we observe that these reasoning paths tend to include substantial redundancy; analyzing attention patterns reveals that attention scores are widely scattered, particularly incorrect answers exhibit greater attention sparsity. In this paper, we demonstrate that deliberately removing this redundancy in the reasoning process significantly improves performance through clear thinking, i.e., removing distraction. Specifically, we systematically identify reasoning redundancy by measuring token-level attention scores to a special end-of-thinking token, which is appended to an explicit instruction inserted to conclude each intermediate reasoning step. Furthermore, we propose structure-aware pruning that prioritizes removing tokens in low-contributing reasoning chunks over individual tokens. After evicting redundant tokens, we remove the injected end-of-thinking instruction, then resume the reasoning generation. We demonstrate that our method significantly improves overall accuracy across reasoning-intensive benchmarks without any training involved. In particular, our method shows strong performance on challenging mathematical competition benchmarks such as AIME and AMC, where reasoning redundancy is more prevalent.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

We introduce Graph of Thoughts (GoT): a framework that advances prompting capabilities in large language models (LLMs) beyond those offered by paradigms such as Chain-of-Thought or Tree of Thoughts (ToT). The key idea and primary advantage of GoT is the ability to model the information generated by an LLM as an arbitrary graph, where units of information ("LLM thoughts") are vertices, and edges correspond to dependencies between these vertices. This approach enables combining arbitrary LLM thoughts into synergistic outcomes, distilling the essence of whole networks of thoughts, or enhancing thoughts using feedback loops. We illustrate that GoT offers advantages over state of the art on different tasks, for example increasing the quality of sorting by 62% over ToT, while simultaneously reducing costs by >31%. We ensure that GoT is extensible with new thought transformations and thus can be used to spearhead new prompting schemes. This work brings the LLM reasoning closer to human thinking or brain mechanisms such as recurrence, both of which form complex networks.

Chain-of-thought (CoT) decoding enables language models to improve reasoning performance at the cost of high generation latency in decoding. Recent proposals have explored variants of contemplation tokens, a term we introduce that refers to special tokens used during inference to allow for extra computation. Prior work has considered fixed-length sequences drawn from a discrete set of embeddings as contemplation tokens. Here we propose Compressed Chain-of-Thought (CCoT), a framework to generate contentful and continuous contemplation tokens of variable sequence length. The generated contemplation tokens are compressed representations of explicit reasoning chains, and our method can be applied to off-the-shelf decoder language models. Through experiments, we illustrate how CCoT enables additional reasoning over dense contentful representations to achieve corresponding improvements in accuracy. Moreover, the reasoning improvements can be adaptively modified on demand by controlling the number of contemplation tokens generated.

Large Language Model can reasonably understand and generate human expressions but may lack of thorough thinking and reasoning mechanisms. Recently there have been several studies which enhance the thinking ability of language models but most of them are not data-driven or training-based. In this paper, we are motivated by the cognitive mechanism in the natural world, and design a novel model architecture called TaS which allows it to first consider the thoughts and then express the response based upon the query. We design several pipelines to annotate or generate the thought contents from prompt-response samples, then add language heads in a middle layer which behaves as the thinking layer. We train the language model by the thoughts-augmented data and successfully let the thinking layer automatically generate reasonable thoughts and finally output more reasonable responses. Both qualitative examples and quantitative results validate the effectiveness and performance of TaS. Our code is available at https://anonymous.4open.science/r/TadE.

With the widespread use of large language models (LLMs) in NLP tasks, researchers have discovered the potential of Chain-of-thought (CoT) to assist LLMs in accomplishing complex reasoning tasks by generating intermediate steps. However, human thought processes are often non-linear, rather than simply sequential chains of thoughts. Therefore, we propose Graph-of-Thought (GoT) reasoning, which models human thought processes not only as a chain but also as a graph. By representing thought units as nodes and connections between them as edges, our approach captures the non-sequential nature of human thinking and allows for a more realistic modeling of thought processes. Similar to Multimodal-CoT, we modeled GoT reasoning as a two-stage framework, generating rationales first and then producing the final answer. Specifically, we employ an additional graph-of-thoughts encoder for GoT representation learning and fuse the GoT representation with the original input representation through a gated fusion mechanism. We implement a GoT reasoning model on the T5 pre-trained model and evaluate its performance on a text-only reasoning task (GSM8K) and a multimodal reasoning task (ScienceQA). Our model achieves significant improvement over the strong CoT baseline with 3.41% and 5.08% on the GSM8K test set with T5-base and T5-large architectures, respectively. Additionally, our model boosts accuracy from 84.91% to 91.54% using the T5-base model and from 91.68% to 92.77% using the T5-large model over the state-of-the-art Multimodal-CoT on the ScienceQA test set. Experiments have shown that GoT achieves comparable results to Multimodal-CoT(large) with over 700M parameters, despite having fewer than 250M backbone model parameters, demonstrating the effectiveness of GoT.

Recent Large Reasoning Models (LRMs) excel at complex reasoning tasks but often suffer from overthinking, generating overly long and redundant reasoning trajectories. To explore its essence, our empirical analysis reveals that LRMs are primarily limited to recognizing task properties (i.e., difficulty levels) like humans before solving the problem, leading to a one-size-fits-all reasoning process. Inspired by this, a pressing and natural question emerges: Can we explicitly bootstrap such ability to alleviate overthinking in LRMs? In this paper, we propose Think-How-to-Think (TH2T), a novel two-stage fine-tuning strategy that progressively inspires LRMs' difficulty cognition and redundancy cognition of LRMs. Specifically, we first inject difficulty hypnosis into output prefixes to guide the model toward adaptive reasoning depth, trained on a hybrid dataset mixing short and long reasoning paths. Then, we incorporate redundancy hypnosis, which supervises the intermediate reasoning steps to identify and eliminate unnecessary reasoning patterns. Experiments on 7B/14B/32B models demonstrate that TH2T significantly reduces inference costs by over 70% on easy tasks and 40% on hard tasks while maintaining performance stability. The resulting outputs exhibit clear signs of difficulty-aware capabilities and reduced redundancy (e.g., reflection and looping).

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

We introduce Buffer of Thoughts (BoT), a novel and versatile thought-augmented reasoning approach for enhancing accuracy, efficiency and robustness of large language models (LLMs). Specifically, we propose meta-buffer to store a series of informative high-level thoughts, namely thought-template, distilled from the problem-solving processes across various tasks. Then for each problem, we retrieve a relevant thought-template and adaptively instantiate it with specific reasoning structures to conduct efficient reasoning. To guarantee the scalability and stability, we further propose buffer-manager to dynamically update the meta-buffer, thus enhancing the capacity of meta-buffer as more tasks are solved. We conduct extensive experiments on 10 challenging reasoning-intensive tasks, and achieve significant performance improvements over previous SOTA methods: 11% on Game of 24, 20% on Geometric Shapes and 51% on Checkmate-in-One. Further analysis demonstrate the superior generalization ability and model robustness of our BoT, while requiring only 12% of the cost of multi-query prompting methods (e.g., tree/graph of thoughts) on average. Notably, we find that our Llama3-8B+BoT has the potential to surpass Llama3-70B model. Our project is available at: https://github.com/YangLing0818/buffer-of-thought-llm

Numerous applications of large language models (LLMs) rely on their ability to perform step-by-step reasoning. However, the reasoning behavior of LLMs remains poorly understood, posing challenges to research, development, and safety. To address this gap, we introduce landscape of thoughts-the first visualization tool for users to inspect the reasoning paths of chain-of-thought and its derivatives on any multi-choice dataset. Specifically, we represent the states in a reasoning path as feature vectors that quantify their distances to all answer choices. These features are then visualized in two-dimensional plots using t-SNE. Qualitative and quantitative analysis with the landscape of thoughts effectively distinguishes between strong and weak models, correct and incorrect answers, as well as different reasoning tasks. It also uncovers undesirable reasoning patterns, such as low consistency and high uncertainty. Additionally, users can adapt our tool to a model that predicts the property they observe. We showcase this advantage by adapting our tool to a lightweight verifier that evaluates the correctness of reasoning paths. The code is publicly available at: https://github.com/tmlr-group/landscape-of-thoughts.

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to an external modus operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. This mode escalates the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways, pioneering a new mode of in-context learning. By employing algorithmic examples, we exploit the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and stands on par with a recent multi-query strategy that employs an extensive tree search algorithm. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application.

Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation beyond the core LLM capabilities (e.g. search/running code). Prior work on CoT prompting and tool use typically requires hand-crafting task-specific demonstrations and carefully scripted interleaving of model generations with tool use. We introduce Automatic Reasoning and Tool-use (ART), a framework that uses frozen LLMs to automatically generate intermediate reasoning steps as a program. Given a new task to solve, ART selects demonstrations of multi-step reasoning and tool use from a task library. At test time, ART seamlessly pauses generation whenever external tools are called, and integrates their output before resuming generation. ART achieves a substantial improvement over few-shot prompting and automatic CoT on unseen tasks in the BigBench and MMLU benchmarks, and matches performance of hand-crafted CoT prompts on a majority of these tasks. ART is also extensible, and makes it easy for humans to improve performance by correcting errors in task-specific programs or incorporating new tools, which we demonstrate by drastically improving performance on select tasks with minimal human intervention.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

When presented with questions involving visual thinking, humans naturally switch reasoning modalities, often forming mental images or drawing visual aids. Large language models have shown promising results in arithmetic and symbolic reasoning by expressing intermediate reasoning in text as a chain of thought, yet struggle to extend this capability to answer text queries that are easily solved by visual reasoning, even with extensive multimodal pretraining. We introduce a simple method, whiteboard-of-thought prompting, to unlock the visual reasoning capabilities of multimodal large language models across modalities. Whiteboard-of-thought prompting provides multimodal large language models with a metaphorical `whiteboard' to draw out reasoning steps as images, then returns these images back to the model for further processing. We find this can be accomplished with no demonstrations or specialized modules, instead leveraging models' existing ability to write code with libraries such as Matplotlib and Turtle. This simple approach shows state-of-the-art results on four difficult natural language tasks that involve visual and spatial reasoning. We identify multiple settings where GPT-4o using chain-of-thought fails dramatically, including more than one where it achieves 0% accuracy, while whiteboard-of-thought enables up to 92% accuracy in these same settings. We present a detailed exploration of where the technique succeeds as well as its sources of error.

Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely on natural language, exchanging tokens or their embeddings. To go beyond language, we introduce a new paradigm, thought communication, which enables agents to interact directly mind-to-mind, akin to telepathy. To uncover these latent thoughts in a principled way, we formalize the process as a general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in a nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees. Guided by the established theory, we develop a framework that extracts latent thoughts from all agents prior to communication and assigns each agent the relevant thoughts, along with their sharing patterns. This paradigm naturally extends beyond LLMs to all modalities, as most observational data arise from hidden generative processes. Experiments on both synthetic and real-world benchmarks validate the theory and demonstrate the collaborative advantages of thought communication. We hope this work illuminates the potential of leveraging the hidden world, as many challenges remain unsolvable through surface-level observation alone, regardless of compute or data scale.

Large language models (LLMs) have demonstrated impressive capabilities in various reasoning tasks, aided by techniques like chain-of-thought (CoT) prompting that elicits verbalized reasoning. However, LLMs often generate text with obvious mistakes and contradictions, raising doubts about their ability to robustly process and utilize generated rationales. In this work, we investigate CoT reasoning in LLMs through the lens of internal representations, focusing on how these representations are influenced by generated rationales. Our preliminary analysis reveals that while generated rationales improve answer accuracy, inconsistencies emerge between the model's internal representations in middle layers and those in final layers, potentially undermining the reliability of their reasoning processes. To address this, we propose internal consistency as a measure of the model's confidence by examining the agreement of latent predictions decoded from intermediate layers. Extensive empirical studies across different models and datasets demonstrate that internal consistency effectively distinguishes between correct and incorrect reasoning paths. Motivated by this, we propose a new approach to calibrate CoT reasoning by up-weighting reasoning paths with high internal consistency, resulting in a significant boost in reasoning performance. Further analysis uncovers distinct patterns in attention and feed-forward modules across layers, providing insights into the emergence of internal inconsistency. In summary, our results demonstrate the potential of using internal representations for self-evaluation of LLMs.

Recent advancements in large reasoning models (LRMs) have demonstrated the effectiveness of scaling test-time computation to enhance reasoning capabilities in multiple tasks. However, LRMs typically suffer from "overthinking" problems, where models generate significantly redundant reasoning steps while bringing limited performance gains. Existing work relies on fine-tuning to mitigate overthinking, which requires additional data, unconventional training setups, risky safety misalignment, and poor generalization. Through empirical analysis, we reveal an important characteristic of LRM behaviors that placing external CoTs generated by smaller models between the thinking token (<think> and </think>) can effectively manipulate the model to generate fewer thoughts. Building on these insights, we propose a simple yet efficient pipeline, ThoughtMani, to enable LRMs to bypass unnecessary intermediate steps and reduce computational costs significantly. We conduct extensive experiments to validate the utility and efficiency of ThoughtMani. For instance, when applied to QwQ-32B on the LiveBench/Code dataset, ThoughtMani keeps the original performance and reduces output token counts by approximately 30%, with little overhead from the CoT generator. Furthermore, we find that ThoughtMani enhances safety alignment by an average of 10%. Since model vendors typically serve models of different sizes simultaneously, ThoughtMani provides an effective way to construct more efficient and accessible LRMs for real-world applications.

Chain of Thought (CoT) was introduced in recent research as a method for improving step-by-step reasoning in Large Language Models. However, CoT has limited applications such as its need for hand-crafted few-shot exemplar prompts and no capability to adjust itself to different queries. In this work, we propose a system to automatically generate rationales using CoT. Our method improves multi-step implicit reasoning capabilities by decomposing the implicit query into several explicit questions. This provides interpretability for the model, improving reasoning in weaker LLMs. We test our approach with two Q\&A datasets: StrategyQA and HotpotQA. We show an increase in accuracy with both, especially on StrategyQA. To facilitate further research in this field, the complete source code for this study has been made publicly available on GitHub: https://github.com/miralab-ai/autoreason.

Despite the advancements in in-context learning (ICL) for large language models (LLMs), current research centers on specific prompt engineering, such as demonstration selection, with the expectation that a single iteration of demonstrations processing can generalize effectively to a given test sample. However, this perspective overlooks the potential benefits derived from multiple iterations involving demonstrations, a practice aligning more closely with the iterative decision-making process exhibited by humans, who often learn through analogy. In this study, we introduce a novel two-stage framework to boost ICL in LLMs. Specifically, our framework delineates the ICL process into two distinct stages: Deep-Thinking and test stages. The Deep-Thinking stage incorporates a unique attention mechanism, i.e., iterative enhanced attention, which enables multiple rounds of information accumulation. This mechanism operates by manipulating the Key-Value matrices without training, fostering enhanced understanding capabilities in LLMs by thinking demonstrations multiple times. We evaluated Deep-Thinking across a range of benchmarks and LLMs, showing its superior performance over vanilla ICL methods and its effectiveness in challenging tasks where demonstration selection is infeasible.

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length n, previous works have shown that constant-depth transformers with finite precision poly(n) embedding size can only solve problems in TC^0 without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in AC^0, a proper subset of TC^0. However, with T steps of CoT, constant-depth transformers using constant-bit precision and O(log n) embedding size can solve any problem solvable by boolean circuits of size T. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers.

While pretrained models such as BERT have shown large gains across natural language understanding tasks, their performance can be improved by further training the model on a data-rich intermediate task, before fine-tuning it on a target task. However, it is still poorly understood when and why intermediate-task training is beneficial for a given target task. To investigate this, we perform a large-scale study on the pretrained RoBERTa model with 110 intermediate-target task combinations. We further evaluate all trained models with 25 probing tasks meant to reveal the specific skills that drive transfer. We observe that intermediate tasks requiring high-level inference and reasoning abilities tend to work best. We also observe that target task performance is strongly correlated with higher-level abilities such as coreference resolution. However, we fail to observe more granular correlations between probing and target task performance, highlighting the need for further work on broad-coverage probing benchmarks. We also observe evidence that the forgetting of knowledge learned during pretraining may limit our analysis, highlighting the need for further work on transfer learning methods in these settings.

Research on LLM technologies is rapidly emerging, with most of them employing a 'fast thinking' approach to inference. Most LLMs generate the final result based solely on a single query and LLM's reasoning capabilities. However, with the advent of OpenAI-o1, 'slow thinking' techniques have garnered increasing attention because its process is closer to the human thought process. Inspired by the human ability to constantly associate and replenish knowledge during thinking, we developed the novel Chain-of-Associated-Thoughts (CoAT) framework, which introduces an innovative synergy between the Monte Carlo Tree Search (MCTS) algorithm and a dynamic mechanism for integrating new key information, termed 'associative memory'. By combining the structured exploration capabilities of MCTS with the adaptive learning capacity of associative memory, CoAT significantly expands the LLM search space, enabling our framework to explore diverse reasoning pathways and dynamically update its knowledge base in real-time. This allows the framework to not only revisit and refine earlier inferences but also adaptively incorporate evolving information, ensuring that the final output is both accurate and comprehensive. To validate the effectiveness of our framework, we conducted extensive experiments across a range of generative and reasoning tasks. These experiments demonstrated that our framework outperforms conventional inference processes on accuracy, coherence, and diversity. The framework's ability to iteratively expand its search space while retaining contextually relevant information results.

Recent advancements in large reasoning models (LRMs) have introduced an intermediate "thinking" process prior to generating final answers, improving their reasoning capabilities on complex downstream tasks. However, the potential of LRMs as evaluators for machine translation (MT) quality remains underexplored. We provides the first systematic analysis of LRM-as-a-judge in MT evaluation. We identify key challenges, revealing LRMs require tailored evaluation materials, tend to "overthink" simpler instances and have issues with scoring mechanisms leading to overestimation. To address these, we propose to calibrate LRM thinking by training them on synthetic, human-like thinking trajectories. Our experiments on WMT24 Metrics benchmarks demonstrate that this approach largely reduces thinking budgets by ~35x while concurrently improving evaluation performance across different LRM scales from 7B to 32B (e.g., R1-Distill-Qwen-7B achieves a +8.7 correlation point improvement). These findings highlight the potential of efficiently calibrated LRMs to advance fine-grained automatic MT evaluation.

Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate reasoning steps can inadvertently introduce hallucinations and accumulated errors, thereby limiting models' ability to solve complex reasoning tasks. Inspired by how humans engage in careful and meticulous deductive logical reasoning processes to solve tasks, we seek to enable language models to perform explicit and rigorous deductive reasoning, and also ensure the trustworthiness of their reasoning process through self-verification. However, directly verifying the validity of an entire deductive reasoning process is challenging, even with advanced models like ChatGPT. In light of this, we propose to decompose a reasoning verification process into a series of step-by-step subprocesses, each only receiving their necessary context and premises. To facilitate this procedure, we propose Natural Program, a natural language-based deductive reasoning format. Our approach enables models to generate precise reasoning steps where subsequent steps are more rigorously grounded on prior steps. It also empowers language models to carry out reasoning self-verification in a step-by-step manner. By integrating this verification process into each deductive reasoning stage, we significantly enhance the rigor and trustfulness of generated reasoning steps. Along this process, we also improve the answer correctness on complex reasoning tasks. Code will be released at https://github.com/lz1oceani/verify_cot.

Human cognition naturally engages with abstract and fluid concepts, whereas existing reasoning models often rely on generating discrete tokens, potentially constraining their expressive capabilities. Recent advancements aim to address this limitation by enabling large language models (LLMs) to generate soft, abstract tokens, thus facilitating reasoning within a continuous concept space. This paper explores the `Soft Thinking' capabilities of various LLMs by examining the models' internal behavior using a suite of probing techniques. Contrary to the common belief that Soft Thinking enables the simultaneous exploration of diverse reasoning paths, our findings reveal that LLMs predominantly rely on the most influential component of the soft inputs during subsequent decoding steps. This reliance hinders the exploration of different reasoning paths and reduces vanilla Soft Thinking to a form of greedy decoding, obscuring the advantage of transmitting more information through Soft Tokens. To tackle this issue, we explore sampling strategies to introduce randomness, employing methods such as Dirichlet resampling and the Gumbel-Softmax trick. Our experiments demonstrate that incorporating randomness can alleviate the limitations of vanilla approaches and unleash the potential of Soft Thinking. Notably, the Gumbel-Softmax trick provides adequate randomness with controlled smoothness, resulting in superior performance across eight reasoning benchmarks.

Humans ponder before articulating complex sentence elements, enabling deeper cognitive processing through focused effort. In this work, we introduce this pondering process into language models by repeatedly invoking the forward process within a single token generation step. During pondering, instead of generating an actual token sampled from the prediction distribution, the model ponders by yielding a weighted sum of all token embeddings according to the predicted token distribution. The generated embedding is then fed back as input for another forward pass. We show that the model can learn to ponder in this way through self-supervised learning, without any human annotations. Our method is straightforward and can be seamlessly integrated with various existing language models. Experiments across three widely used open-source architectures-GPT-2, Pythia, and LLaMA-and extensive downstream task evaluations demonstrate the effectiveness and generality of our method. For language modeling tasks, pondering language models achieve performance comparable to vanilla models with twice the number of parameters. On 9 downstream benchmarks, our pondering-enhanced Pythia models significantly outperform the official Pythia models. Notably, pondering-enhanced Pythia-1B is comparable to TinyLlama-1.1B, which is trained on 10 times more data. The code is available at https://github.com/LUMIA-Group/PonderingLM.

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free framework that enables large reasoning models to guide smaller ones during inference at the reasoning level, distinct from speculative decoding, which operates at the token level. Our approach is based on two observations: (1) reasoning-supportive tokens such as "wait" frequently appear after structural delimiters like "\n\n", serving as signals for reflection or continuation; and (2) larger models exhibit stronger control over reflective behavior, reducing unnecessary backtracking while improving reasoning quality. By strategically delegating reflective steps to a more capable model, our method significantly boosts the reasoning accuracy of reasoning models while shortening their output. With the assistance of the 32B reasoning model, the 1.5B model's accuracy on MATH500 increases from 83.2% to 89.4%, marking a substantial improvement of 6.2%. Simultaneously, the average output length is reduced from 5439 tokens to 4583 tokens, representing a 15.7% decrease. Moreover, when applied to a non-reasoning model (Qwen-2.5-7B-Instruct), our framework boosts its accuracy from 74.0% to 81.8% on the same benchmark, achieving a relative improvement of 7.8%.

Large Language Models (LLMs) achieve superior performance through training-time scaling, and test-time scaling further enhances their capabilities by conducting effective reasoning during inference. However, as the scale of reasoning increases, existing test-time scaling methods suffer from accumulated historical information, which not only wastes computational resources but also interferes with effective reasoning. To address this issue, we observe that complex reasoning progress is often achieved by solving a sequence of independent subquestions, each being self-contained and verifiable. These subquestions are essentially atomic questions, relying primarily on their current state rather than accumulated history, similar to the memoryless transitions in a Markov process. Based on this observation, we propose Atom of Thoughts (AoT), where each state transition in the reasoning process consists of decomposing the current question into a dependency-based directed acyclic graph and contracting its subquestions, forming a new atomic question state. This iterative decomposition-contraction process continues until reaching directly solvable atomic questions, naturally realizing Markov transitions between question states. Furthermore, these atomic questions can be seamlessly integrated into existing test-time scaling methods, enabling AoT to serve as a plug-in enhancement for improving reasoning capabilities. Experiments across six benchmarks demonstrate the effectiveness of AoT both as a standalone framework and a plug-in enhancement. Notably, on HotpotQA, when applied to gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and DeepSeek-R1 by 10.6%. The code will be available at https://github.com/qixucen/atom.

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural language, improving interpretability at the cost of efficiency. To capture reasoning that is not easily represented in words, many works have explored recurrent architectures that aim to internalize reasoning in latent space, potentially supporting latent CoT. In this paper, we investigate whether such reasoning structures emerge in Huginn-3.5B, a depth-recurrent Transformer that reuses layers at inference time without increasing parameter count. We examine the model's internal behavior on arithmetic tasks using a suite of probing techniques including the Logit Lens and Coda Lens. Our findings reveal limited evidence of interpretable latent CoT by tracking rank trajectories of final and intermediate result tokens. Furthermore, we uncover significant probing inconsistencies across recurrent blocks, where the interpretability of hidden states depends heavily on both the layer index and the decoding method. Finally, we empirically show that increasing recurrence depth yields only marginal gains and falls well short of models that explicitly externalize reasoning steps. The code is available at https://github.com/wenquanlu/huginn-latent-cot.

Large language models (LLMs) demonstrate significant reasoning capabilities, particularly through long chain-of-thought (CoT) processes, which can be elicited by reinforcement learning (RL). However, prolonged CoT reasoning presents limitations, primarily verbose outputs due to excessive introspection. The reasoning process in these LLMs often appears to follow a trial-and-error methodology rather than a systematic, logical deduction. In contrast, tree-of-thoughts (ToT) offers a conceptually more advanced approach by modeling reasoning as an exploration within a tree structure. This reasoning structure facilitates the parallel generation and evaluation of multiple reasoning branches, allowing for the active identification, assessment, and pruning of unproductive paths. This process can potentially lead to improved performance and reduced token costs. Building upon the long CoT capability of LLMs, we introduce tree-of-thoughts RL (ToTRL), a novel on-policy RL framework with a rule-based reward. ToTRL is designed to guide LLMs in developing the parallel ToT strategy based on the sequential CoT strategy. Furthermore, we employ LLMs as players in a puzzle game during the ToTRL training process. Solving puzzle games inherently necessitates exploring interdependent choices and managing multiple constraints, which requires the construction and exploration of a thought tree, providing challenging tasks for cultivating the ToT reasoning capability. Our empirical evaluations demonstrate that our ToTQwen3-8B model, trained with our ToTRL, achieves significant improvement in performance and reasoning efficiency on complex reasoning tasks.

When writing and talking, people sometimes pause to think. Although reasoning-focused works have often framed reasoning as a method of answering questions or completing agentic tasks, reasoning is implicit in almost all written text. For example, this applies to the steps not stated between the lines of a proof or to the theory of mind underlying a conversation. In the Self-Taught Reasoner (STaR, Zelikman et al. 2022), useful thinking is learned by inferring rationales from few-shot examples in question-answering and learning from those that lead to a correct answer. This is a highly constrained setting -- ideally, a language model could instead learn to infer unstated rationales in arbitrary text. We present Quiet-STaR, a generalization of STaR in which LMs learn to generate rationales at each token to explain future text, improving their predictions. We address key challenges, including 1) the computational cost of generating continuations, 2) the fact that the LM does not initially know how to generate or use internal thoughts, and 3) the need to predict beyond individual next tokens. To resolve these, we propose a tokenwise parallel sampling algorithm, using learnable tokens indicating a thought's start and end, and an extended teacher-forcing technique. Encouragingly, generated rationales disproportionately help model difficult-to-predict tokens and improve the LM's ability to directly answer difficult questions. In particular, after continued pretraining of an LM on a corpus of internet text with Quiet-STaR, we find zero-shot improvements on GSM8K (5.9%rightarrow10.9%) and CommonsenseQA (36.3%rightarrow47.2%) and observe a perplexity improvement of difficult tokens in natural text. Crucially, these improvements require no fine-tuning on these tasks. Quiet-STaR marks a step towards LMs that can learn to reason in a more general and scalable way.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

One of the long-standing aspirations in conversational AI is to allow them to autonomously take initiatives in conversations, i.e., being proactive. This is especially challenging for multi-party conversations. Prior NLP research focused mainly on predicting the next speaker from contexts like preceding conversations. In this paper, we demonstrate the limitations of such methods and rethink what it means for AI to be proactive in multi-party, human-AI conversations. We propose that just like humans, rather than merely reacting to turn-taking cues, a proactive AI formulates its own inner thoughts during a conversation, and seeks the right moment to contribute. Through a formative study with 24 participants and inspiration from linguistics and cognitive psychology, we introduce the Inner Thoughts framework. Our framework equips AI with a continuous, covert train of thoughts in parallel to the overt communication process, which enables it to proactively engage by modeling its intrinsic motivation to express these thoughts. We instantiated this framework into two real-time systems: an AI playground web app and a chatbot. Through a technical evaluation and user studies with human participants, our framework significantly surpasses existing baselines on aspects like anthropomorphism, coherence, intelligence, and turn-taking appropriateness.

Recent advances in spoken dialogue language models (SDLMs) reflect growing interest in shifting from turn-based to full-duplex systems, where the models continuously perceive user speech streams while generating responses. This simultaneous listening and speaking design enables real-time interaction and the agent can handle dynamic conversational behaviors like user barge-in. However, during the listening phase, existing systems keep the agent idle by repeatedly predicting the silence token, which departs from human behavior: we usually engage in lightweight thinking during conversation rather than remaining absent-minded. Inspired by this, we propose Chronological Thinking, a on-the-fly conversational thinking mechanism that aims to improve response quality in full-duplex SDLMs. Specifically, chronological thinking presents a paradigm shift from conventional LLM thinking approaches, such as Chain-of-Thought, purpose-built for streaming acoustic input. (1) Strictly causal: the agent reasons incrementally while listening, updating internal hypotheses only from past audio with no lookahead. (2) No additional latency: reasoning is amortized during the listening window; once the user stops speaking, the agent halts thinking and begins speaking without further delay. Experiments demonstrate the effectiveness of chronological thinking through both objective metrics and human evaluations show consistent improvements in response quality. Furthermore, chronological thinking robustly handles conversational dynamics and attains competitive performance on full-duplex interaction metrics.

We introduce Seed1.5-Thinking, capable of reasoning through thinking before responding, resulting in improved performance on a wide range of benchmarks. Seed1.5-Thinking achieves 86.7 on AIME 2024, 55.0 on Codeforces and 77.3 on GPQA, demonstrating excellent reasoning abilities in STEM and coding. Beyond reasoning tasks, the method demonstrates notable generalization across diverse domains. For instance, it surpasses DeepSeek R1 by 8% in win rate on non-reasoning tasks, indicating its broader applicability. Compared to other state-of-the-art reasoning models, Seed1.5-Thinking is a Mixture-of-Experts (MoE) model with a relatively small size, featuring 20B activated and 200B total parameters. As part of our effort to assess generalized reasoning, we develop two internal benchmarks, BeyondAIME and Codeforces, both of which will be publicly released to support future research. Model trial link: https://www.volcengine.com/experience/ark.

Large language models (LLMs) have demonstrated enhanced performance through the Thinking then Responding paradigm, where models generate internal thoughts before final responses (aka, System 2 thinking). However, existing research lacks a systematic understanding of the mechanisms underlying how thinking patterns affect performance across model sizes. In this work, we conduct a comprehensive analysis of the impact of various thinking types on model performance and introduce ThinkPatterns-21k, a curated dataset comprising 21k instruction-response pairs (QA) collected from existing instruction-following datasets with five thinking types. For each pair, we augment it with five distinct internal thinking patterns: one unstructured thinking (monologue) and four structured variants (decomposition, self-ask, self-debate and self-critic), while maintaining the same instruction and response. Through extensive evaluation across different model sizes (3B-32B parameters), we have two key findings: (1) smaller models (<30B parameters) can benefit from most of structured thinking patterns, while larger models (32B) with structured thinking like decomposition would degrade performance and (2) unstructured monologue demonstrates broad effectiveness across different model sizes. Finally, we released all of our datasets, checkpoints, training logs of diverse thinking patterns to reproducibility, aiming to facilitate further research in this direction.

Recently, Chain-of-Thought (CoT) prompting has delivered success on complex reasoning tasks, which aims at designing a simple prompt like ``Let's think step by step'' or multiple in-context exemplars with well-designed rationales to elicit Large Language Models (LLMs) to generate intermediate reasoning steps. However, the generated rationales often come with mistakes, making unfactual and unfaithful reasoning chains. To mitigate this brittleness, we propose a novel Chain-of-Knowledge (CoK) prompting, where we aim at eliciting LLMs to generate explicit pieces of knowledge evidence in the form of structure triple. This is inspired by our human behaviors, i.e., we can draw a mind map or knowledge map as the reasoning evidence in the brain before answering a complex question. Benefiting from CoK, we additionally introduce a F^2-Verification method to estimate the reliability of the reasoning chains in terms of factuality and faithfulness. For the unreliable response, the wrong evidence can be indicated to prompt the LLM to rethink. Extensive experiments demonstrate that our method can further improve the performance of commonsense, factual, symbolic, and arithmetic reasoning tasks.

Recently, there has been significant progress in teaching language models to perform step-by-step reasoning to solve complex numerical reasoning tasks. Chain-of-thoughts prompting (CoT) is by far the state-of-art method for these tasks. CoT uses language models to perform both reasoning and computation in the multi-step `thought' process. To disentangle computation from reasoning, we propose `Program of Thoughts' (PoT), which uses language models (mainly Codex) to express the reasoning process as a program. The computation is relegated to an external computer, which executes the generated programs to derive the answer. We evaluate PoT on five math word problem datasets (GSM, AQuA, SVAMP, TabMWP, MultiArith) and three financial-QA datasets (FinQA, ConvFinQA, TATQA) for both few-shot and zero-shot setups. Under both few-shot and zero-shot settings, PoT can show an average performance gain over CoT by around 12\% across all the evaluated datasets. By combining PoT with self-consistency decoding, we can achieve SoTA performance on all math problem datasets and near-SoTA performance on financial datasets. All of our data and code are released in Github\url{https://github.com/wenhuchen/Program-of-Thoughts}.

Iterative human engagement is a common and effective means of leveraging the advanced language processing power of large language models (LLMs). Using well-structured prompts in a conversational manner, human users can effectively influence an LLM to develop more thoughtful and accurate responses. Motivated by this insight, we propose the Iteration of Thought (IoT) framework for enhancing LLM responses by generating "thought"-provoking prompts vis a vis an input query and the current iteration of an LLM's response. Unlike static or semi-static approaches, e.g. Chain of Thought (CoT) or Tree of Thoughts (ToT), IoT adapts its reasoning path dynamically, based on evolving context, and without generating alternate explorative thoughts which are ultimately discarded. The three components of the IoT framework are (1) an Inner Dialogue Agent (IDA) responsible for generating instructive, context-specific prompts; (2) an LLM Agent (LLMA) that processes these prompts to refine its responses; and (3) an iterative prompting loop that implements a conversation between the former two components. We introduce two variants of our framework: Autonomous Iteration of Thought (AIoT), where an LLM decides when to stop iterating, and Guided Iteration of Thought (GIoT), which always forces a fixed number iterations. We investigate the performance of IoT across various datasets, spanning complex reasoning tasks from the GPQA dataset, explorative problem-solving in Game of 24, puzzle solving in Mini Crosswords, and multi-hop question answering from the HotpotQA dataset. Our results show that IoT represents a viable paradigm for autonomous response refinement in LLMs, showcasing significant improvements over CoT and thereby enabling more adaptive and efficient reasoning systems that minimize human intervention.

Recent thinking models solve complex reasoning tasks by scaling test-time compute, but this scaling must be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient, generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under- and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention over a long reasoning trajectory to identify important steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate reasoning budget commensurate with example difficulty. Our approach improves accuracy, reduces reasoning steps, and enables adaptive thinking compared to base models and other RL baselines. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC also shows strong generalization: although our models are trained on math datasets, they show accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis further verifies that TRAAC provides fine-grained adjustments to thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks.

Large language models (LLMs) excel at zero-shot inference but continue to struggle with complex, multi-step reasoning. Recent methods that augment LLMs with intermediate reasoning steps such as Chain of Thought (CoT) and Program of Thought (PoT) improve performance but often produce undesirable solutions, especially in algorithmic domains. We introduce Per-Instance Program Synthesis (PIPS), a method that generates and refines programs at the instance-level using structural feedback without relying on task-specific guidance or explicit test cases. To further improve performance, PIPS incorporates a confidence metric that dynamically chooses between direct inference and program synthesis on a per-instance basis. Experiments across three frontier LLMs and 30 benchmarks including all tasks of Big Bench Extra Hard (BBEH), visual question answering tasks, relational reasoning tasks, and mathematical reasoning tasks show that PIPS improves the absolute harmonic mean accuracy by up to 8.6% and 9.4% compared to PoT and CoT respectively, and reduces undesirable program generations by 65.1% on the algorithmic tasks compared to PoT with Gemini-2.0-Flash.

Language is often considered a key aspect of human thinking, providing us with exceptional abilities to generalize, explore, plan, replan, and adapt to new situations. However, Reinforcement Learning (RL) agents are far from human-level performance in any of these abilities. We hypothesize one reason for such cognitive deficiencies is that they lack the benefits of thinking in language and that we can improve AI agents by training them to think like humans do. We introduce a novel Imitation Learning framework, Thought Cloning, where the idea is to not just clone the behaviors of human demonstrators, but also the thoughts humans have as they perform these behaviors. While we expect Thought Cloning to truly shine at scale on internet-sized datasets of humans thinking out loud while acting (e.g. online videos with transcripts), here we conduct experiments in a domain where the thinking and action data are synthetically generated. Results reveal that Thought Cloning learns much faster than Behavioral Cloning and its performance advantage grows the further out of distribution test tasks are, highlighting its ability to better handle novel situations. Thought Cloning also provides important benefits for AI Safety and Interpretability, and makes it easier to debug and improve AI. Because we can observe the agent's thoughts, we can (1) more easily diagnose why things are going wrong, making it easier to fix the problem, (2) steer the agent by correcting its thinking, or (3) prevent it from doing unsafe things it plans to do. Overall, by training agents how to think as well as behave, Thought Cloning creates safer, more powerful agents.

Large Language Models (LLMs) have demonstrated strong capabilities across various domains, with recent advancements in challenging reasoning tasks such as mathematics and programming. However, solving reasoning tasks often requires long decoding chains (of thoughts), which incur O(N) time and memory consumption, where N is the chain length. To mitigate O(N) time and memory consumption, existing sparsity-based algorithms propose retaining only the most critical token's intermediate data (i.e., key-value cache) and discarding the rest. However, these existing algorithms struggle with the ``impossible trinity'' of accuracy, time, and memory. For example, the state-of-the-art algorithm, Quest, achieves high accuracy with O(L) time but O(N) memory (L is the cache budget, L ll N). To address this issue, in this paper, we identify a new attention pattern during the decode stage of reasoning tasks, where milestone tokens (analogous to lemmas in mathematical proofs) emerge, are utilized, and then become unimportant afterward. Based on this pattern, we propose a new algorithm named RaaS that identifies and retains milestone tokens only until they are no longer needed, achieving high accuracy with O(L) time and O(L) memory complexity.

Recent studies show that the reasoning capabilities of Large Language Models (LLMs) can be improved by applying Reinforcement Learning (RL) to question-answering (QA) tasks in areas such as math and coding. With a long context length, LLMs may learn to perform search, as indicated by the self-correction behavior observed in DeepSeek R1. However, this search behavior is often imprecise and lacks confidence, resulting in long, redundant responses and highlighting deficiencies in intuition and verification. Inspired by the Dual Process Theory in psychology, we introduce a simple modification to the QA task that includes four stages: Fast Thinking, where the LLM must answer within a strict token budget; Verification, where the model evaluates its initial response; Slow Thinking, where it refines the initial response with more deliberation; and Summarization, where it distills the refinement from the previous stage into precise steps. Our proposed task improves average accuracy from 24.9% to 27.9% for Qwen2.5-1.5B, and from 45.9% to 49.8% for DeepSeek-R1-Qwen-1.5B. Notably, for Qwen2.5-1.5B, the Fast Thinking mode alone achieves 26.8% accuracy using fewer than 1000 tokens, demonstrating substantial inference efficiency gains. These findings suggest that intuition and deliberative reasoning are distinct, complementary systems benefiting from targeted training.

Recent work has demonstrated that Chain-of-Thought (CoT) often yields limited gains for soft-reasoning problems such as analytical and commonsense reasoning. CoT can also be unfaithful to a model's actual reasoning. We investigate the dynamics and faithfulness of CoT in soft-reasoning tasks across instruction-tuned, reasoning and reasoning-distilled models. Our findings reveal differences in how these models rely on CoT, and show that CoT influence and faithfulness are not always aligned.

Due to the proliferation of short-form content and the rapid adoption of AI, opportunities for deep, reflective thinking have significantly diminished, undermining users' critical thinking and reducing engagement with the reasoning behind AI-generated outputs. To address this issue, we propose an Interactive Chain-of-Thought (CoT) Framework that enhances human-centered explainability and responsible AI usage by making the model's inference process transparent, modular, and user-editable. The framework decomposes reasoning into clearly defined blocks that users can inspect, modify, and re-execute, encouraging active cognitive engagement rather than passive consumption. It further integrates a lightweight edit-adaptation mechanism inspired by preference learning, allowing the system to align with diverse cognitive styles and user intentions. Ethical transparency is ensured through explicit metadata disclosure, built-in bias checkpoint functionality, and privacy-preserving safeguards. This work outlines the design principles and architecture necessary to promote critical engagement, responsible interaction, and inclusive adaptation in AI systems aimed at addressing complex societal challenges.

Chain-of-thought reasoning, a cognitive process fundamental to human intelligence, has garnered significant attention in the realm of artificial intelligence and natural language processing. However, there still remains a lack of a comprehensive survey for this arena. To this end, we take the first step and present a thorough survey of this research field carefully and widely. We use X-of-Thought to refer to Chain-of-Thought in a broad sense. In detail, we systematically organize the current research according to the taxonomies of methods, including XoT construction, XoT structure variants, and enhanced XoT. Additionally, we describe XoT with frontier applications, covering planning, tool use, and distillation. Furthermore, we address challenges and discuss some future directions, including faithfulness, multi-modal, and theory. We hope this survey serves as a valuable resource for researchers seeking to innovate within the domain of chain-of-thought reasoning.

Using Large Language Models for complex mathematical reasoning is difficult, primarily due to the complexity of multi-step reasoning. The main challenges of this process include (1) selecting critical intermediate results to advance the procedure, and (2) limited exploration of potential solutions. To address these issues, we introduce a novel algorithm, namely Stepwise Self-Consistent Chain-of-Thought (SSC-CoT). SSC-CoT employs a strategy of selecting intermediate steps based on the intersection of various reasoning chains. Additionally, SSC-CoT enables the model to discover critical intermediate steps by querying a knowledge graph comprising relevant domain knowledge. To validate SSC-CoT, we present a new dataset, TriMaster100, tailored for complex trigonometry problems. This dataset contains 100 questions, with each solution broken down into scored intermediate steps, facilitating a comprehensive evaluation of the mathematical reasoning process. On TriMaster100, SSC-CoT triples the effectiveness of the state-of-the-art methods. Furthermore, we benchmark SSC-CoT on the widely recognized complex mathematical question dataset, MATH level 5, and it surpasses the second-best method by 7.2% in accuracy. Code and the TriMaster100 dataset can be found at: https://github.com/zhao-zilong/ssc-cot.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Since the advent of ChatGPT, Large Language Models (LLMs) have excelled in various tasks but remain largely as black-box systems. Consequently, their development relies heavily on data-driven approaches, limiting performance enhancement through changes in internal architecture and reasoning pathways. As a result, many researchers have begun exploring the potential internal mechanisms of LLMs, aiming to identify the essence of their reasoning bottlenecks, with most studies focusing on attention heads. Our survey aims to shed light on the internal reasoning processes of LLMs by concentrating on the interpretability and underlying mechanisms of attention heads. We first distill the human thought process into a four-stage framework: Knowledge Recalling, In-Context Identification, Latent Reasoning, and Expression Preparation. Using this framework, we systematically review existing research to identify and categorize the functions of specific attention heads. Furthermore, we summarize the experimental methodologies used to discover these special heads, dividing them into two categories: Modeling-Free methods and Modeling-Required methods. Also, we outline relevant evaluation methods and benchmarks. Finally, we discuss the limitations of current research and propose several potential future directions. Our reference list is open-sourced at https://github.com/IAAR-Shanghai/Awesome-Attention-Heads.

Chain-of-thought (CoT) prompting has become a widely used strategy for working with large language and multimodal models. While CoT has been shown to improve performance across many tasks, determining the settings in which it is effective remains an ongoing effort. In particular, it is still an open question in what settings CoT systematically reduces model performance. In this paper, we seek to identify the characteristics of tasks where CoT reduces performance by drawing inspiration from cognitive psychology, looking at cases where (i) verbal thinking or deliberation hurts performance in humans, and (ii) the constraints governing human performance generalize to language models. Three such cases are implicit statistical learning, visual recognition, and classifying with patterns containing exceptions. In extensive experiments across all three settings, we find that a diverse collection of state-of-the-art models exhibit significant drop-offs in performance (e.g., up to 36.3% absolute accuracy for OpenAI o1-preview compared to GPT-4o) when using inference-time reasoning compared to zero-shot counterparts. We also identify three tasks that satisfy condition (i) but not (ii), and find that while verbal thinking reduces human performance in these tasks, CoT retains or increases model performance. Overall, our results show that while there is not an exact parallel between the cognitive processes of models and those of humans, considering cases where thinking has negative consequences for human performance can help us identify settings where it negatively impacts models. By connecting the literature on human deliberation with evaluations of CoT, we offer a new tool that can be used in understanding the impact of prompt choices and inference-time reasoning.

Large reasoning models (LRMs) have demonstrated impressive capabilities in complex problem-solving, yet their internal reasoning mechanisms remain poorly understood. In this paper, we investigate the reasoning trajectories of LRMs from an information-theoretic perspective. By tracking how mutual information (MI) between intermediate representations and the correct answer evolves during LRM reasoning, we observe an interesting MI peaks phenomenon: the MI at specific generative steps exhibits a sudden and significant increase during LRM's reasoning process. We theoretically analyze such phenomenon and show that as MI increases, the probability of model's prediction error decreases. Furthermore, these MI peaks often correspond to tokens expressing reflection or transition, such as ``Hmm'', ``Wait'' and ``Therefore,'' which we term as the thinking tokens. We then demonstrate that these thinking tokens are crucial for LRM's reasoning performance, while other tokens has minimal impacts. Building on these analyses, we propose two simple yet effective methods to improve LRM's reasoning performance, by delicately leveraging these thinking tokens. Overall, our work provides novel insights into the reasoning mechanisms of LRMs and offers practical ways to improve their reasoning capabilities. The code is available at https://github.com/ChnQ/MI-Peaks.

Despite remarkable advances in the field, LLMs remain unreliable in distinguishing causation from correlation. Recent results from the Corr2Cause dataset benchmark reveal that state-of-the-art LLMs -- such as GPT-4 (F1 score: 29.08) -- only marginally outperform random baselines (Random Uniform, F1 score: 20.38), indicating limited capacity of generalization. To tackle this limitation, we propose a novel structured approach: rather than directly answering causal queries, we provide the model with the capability to structure its thinking by guiding the model to build a structured knowledge graph, systematically encoding the provided correlational premises, to answer the causal queries. This intermediate representation significantly enhances the model's causal capabilities. Experiments on the test subset of the Corr2Cause dataset benchmark with Qwen3-32B model (reasoning model) show substantial gains over standard direct prompting methods, improving F1 scores from 32.71 to 48.26 (over 47.5% relative increase), along with notable improvements in precision and recall. These results underscore the effectiveness of providing the model with the capability to structure its thinking and highlight its promising potential for broader generalization across diverse causal inference tasks.

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.

Large language models (LLMs) have achieved remarkable progress on mathematical tasks through Chain-of-Thought (CoT) reasoning. However, existing mathematical CoT datasets often suffer from Thought Leaps due to experts omitting intermediate steps, which negatively impacts model learning and generalization. We propose the CoT Thought Leap Bridge Task, which aims to automatically detect leaps and generate missing intermediate reasoning steps to restore the completeness and coherence of CoT. To facilitate this, we constructed a specialized training dataset called ScaleQM+, based on the structured ScaleQuestMath dataset, and trained CoT-Bridge to bridge thought leaps. Through comprehensive experiments on mathematical reasoning benchmarks, we demonstrate that models fine-tuned on bridged datasets consistently outperform those trained on original datasets, with improvements of up to +5.87% on NuminaMath. Our approach effectively enhances distilled data (+3.02%) and provides better starting points for reinforcement learning (+3.1%), functioning as a plug-and-play module compatible with existing optimization techniques. Furthermore, CoT-Bridge demonstrate improved generalization to out-of-domain logical reasoning tasks, confirming that enhancing reasoning completeness yields broadly applicable benefits.

What makes a difference in the post-training of LLMs? We investigate the training patterns of different layers in large language models (LLMs), through the lens of gradient, when training with different responses and initial models. We are specifically interested in how fast vs. slow thinking affects the layer-wise gradients, given the recent popularity of training LLMs on reasoning paths such as chain-of-thoughts (CoT) and process rewards. In our study, fast thinking without CoT leads to larger gradients and larger differences of gradients across layers than slow thinking (Detailed CoT), indicating the learning stability brought by the latter. Moreover, pre-trained LLMs are less affected by the instability of fast thinking than instruction-tuned LLMs. Additionally, we study whether the gradient patterns can reflect the correctness of responses when training different LLMs using slow vs. fast thinking paths. The results show that the gradients of slow thinking can distinguish correct and irrelevant reasoning paths. As a comparison, we conduct similar gradient analyses on non-reasoning knowledge learning tasks, on which, however, trivially increasing the response length does not lead to similar behaviors of slow thinking. Our study strengthens fundamental understandings of LLM training and sheds novel insights on its efficiency and stability, which pave the way towards building a generalizable System-2 agent. Our code, data, and gradient statistics can be found in: https://github.com/MingLiiii/Layer_Gradient.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague constraints often exceed the capacity of a single reasoning chain. Inspired by Minimal Free Resolution (MFR) in commutative algebra and algebraic geometry, we propose Syzygy of Thoughts (SoT)-a novel framework that extends CoT by introducing auxiliary, interrelated reasoning paths. SoT captures deeper logical dependencies, enabling more robust and structured problem-solving. MFR decomposes a module into a sequence of free modules with minimal rank, providing a structured analytical approach to complex systems. This method introduces the concepts of "Module", "Betti numbers","Freeness", "Mapping", "Exactness" and "Minimality", enabling the systematic decomposition of the original complex problem into logically complete minimal subproblems while preserving key problem features and reducing reasoning length. We tested SoT across diverse datasets (e.g., GSM8K, MATH) and models (e.g., GPT-4o-mini, Qwen2.5), achieving inference accuracy that matches or surpasses mainstream CoTs standards. Additionally, by aligning the sampling process with algebraic constraints, our approach enhances the scalability of inference time in LLMs, ensuring both transparent reasoning and high performance. Our code will be publicly available at https://github.com/dlMARiA/Syzygy-of-thoughts.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

In this paper, we address the challenging task of multimodal mathematical reasoning by incorporating the ability of ``slow thinking" into multimodal large language models (MLLMs). Contrary to existing methods that rely on direct or fast thinking, our key idea is to construct long chains of thought (CoT) consisting of atomic actions in a step-by-step manner, guiding MLLMs to perform complex reasoning. To this end, we design a novel AtomThink framework composed of three key modules: (i) a CoT annotation engine that automatically generates high-quality CoT annotations to address the lack of high-quality visual mathematical data; (ii) an atomic step fine-tuning strategy that jointly optimizes an MLLM and a policy reward model (PRM) for step-wise reasoning; and (iii) four different search strategies that can be applied with the PRM to complete reasoning. Additionally, we propose AtomMATH, a large-scale multimodal dataset of long CoTs, and an atomic capability evaluation metric for mathematical tasks. Extensive experimental results show that the proposed AtomThink significantly improves the performance of baseline MLLMs, achieving approximately 50\% relative accuracy gains on MathVista and 120\% on MathVerse. To support the advancement of multimodal slow-thinking models, we will make our code and dataset publicly available on https://github.com/Quinn777/AtomThink.

Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow for complex reasoning with LLMs that combines fast and slow thinking modes in an adaptive manner. Our approach consists of two key components: 1) a new approach for slow, deliberate reasoning called Dynamic Workflow, which automatically decomposes complex problems into more manageable sub-tasks and dynamically designs a workflow to assemble specialized LLM or symbolic reasoning tools to solve sub-tasks; 2) Hybrid Thinking, a general framework that dynamically combines fast and slow thinking based on problem complexity. Finally, we propose an easy-to-scale method for automatically synthesizing a large-scale dataset of 27K challenging reasoning problems for complex reasoning and a hybrid thinking tuning method that trains smaller LLMs on this dataset to internalize the fast/slow hybrid reasoning strategies. Experiments on four reasoning benchmark datasets demonstrate that our slow thinking with dynamic workflows significantly outperforms Chain-of-Thought, and hybrid thinking achieves the highest accuracy while providing an effective balance between computational efficiency and performance. Fine-tuning using our hybrid thinking approach also significantly boosts the complex reasoning capabilities of open-source language models. The results showcase the promise of slow thinking, dynamic workflows, and hybrid thinking in expanding the frontier of complex problem-solving with LLMsCode and data will be released at \url{https://github.com/wenlinyao/HDFlow.}.

Abstract reasoning, the ability to reason from the abstract essence of a problem, serves as a key to generalization in human reasoning. However, eliciting language models to perform reasoning with abstraction remains unexplored. This paper seeks to bridge this gap by introducing a novel structured reasoning format called Abstraction-of-Thought (AoT). The uniqueness of AoT lies in its explicit requirement for varying levels of abstraction within the reasoning process. This approach could elicit language models to first contemplate on the abstract level before incorporating concrete details, which is overlooked by the prevailing step-by-step Chain-of-Thought (CoT) method. To align models with the AoT format, we present AoT Collection, a generic finetuning dataset consisting of 348k high-quality samples with AoT reasoning processes, collected via an automated and scalable pipeline. We finetune a wide range of language models with AoT Collection and conduct extensive evaluations on 23 unseen tasks from the challenging benchmark Big-Bench Hard. Experimental results indicate that models aligned to AoT reasoning format substantially outperform those aligned to CoT in many reasoning tasks.

Reasoning models enhance performance by tackling problems in a step-by-step manner, decomposing them into sub-problems and exploring long chains of thought before producing an answer. However, applying extended reasoning to every step introduces substantial redundancy, as sub-problems vary widely in difficulty and complexity: a small number of pivotal steps are genuinely challenging and decisive for the final answer, while many others only involve straightforward revisions or simple computations. Therefore, a natural idea is to endow reasoning models with the ability to adaptively respond to this variation, rather than treating all steps with the same level of elaboration. To this end, we propose MixReasoning, a framework that dynamically adjusts the depth of reasoning within a single response. The resulting chain of thought then becomes a mixture of detailed reasoning on difficult steps and concise inference on simpler ones. Experiments on GSM8K, MATH-500, and AIME show that MixReasoning shortens reasoning length and substantially improves efficiency without compromising accuracy.

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long CoT, the number of reasoning steps exceeds manageable token limits and leads to higher computational demands. Inspired by the fundamental logic of human cognition, ``derive, then reduce'', we conceptualize the standard multi-step CoT as a novel Markov Chain of Thought (MCoT). In this study, we consider the mathematical reasoning task, defining each reasoning step as text accompanied by a Python code snippet. To facilitate a longer reasoning path, self-correction is enabled through interactions with the code interpreter. Our MCoT aims to compress previous reasoning steps into a simplified question, enabling efficient next-step inference without relying on a lengthy KV cache. In our experiments, we curate the MCoTInstruct dataset, and the empirical results indicate that MCoT not only significantly enhances efficiency but also maintains comparable accuracy. While much remains to be explored, this work paves the way for exploring the long CoT reasoning abilities of LLMs.

In this article, we introduce a neuro-symbolic approach that combines a low-level perception task performed by a neural network with a high-level reasoning task performed by a possibilistic rule-based system. The goal is to be able to derive for each input instance the degree of possibility that it belongs to a target (meta-)concept. This (meta-)concept is connected to intermediate concepts by a possibilistic rule-based system. The probability of each intermediate concept for the input instance is inferred using a neural network. The connection between the low-level perception task and the high-level reasoning task lies in the transformation of neural network outputs modeled by probability distributions (through softmax activation) into possibility distributions. The use of intermediate concepts is valuable for the explanation purpose: using the rule-based system, the classification of an input instance as an element of the (meta-)concept can be justified by the fact that intermediate concepts have been recognized. From the technical side, our contribution consists of the design of efficient methods for defining the matrix relation and the equation system associated with a possibilistic rule-based system. The corresponding matrix and equation are key data structures used to perform inferences from a possibilistic rule-based system and to learn the values of the rule parameters in such a system according to a training data sample. Furthermore, leveraging recent results on the handling of inconsistent systems of fuzzy relational equations, an approach for learning rule parameters according to multiple training data samples is presented. Experiments carried out on the MNIST addition problems and the MNIST Sudoku puzzles problems highlight the effectiveness of our approach compared with state-of-the-art neuro-symbolic ones.

Chain-of-Thought (CoT) prompting has proven highly effective for enhancing complex reasoning in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs). Yet, it struggles in complex spatial reasoning tasks. Nonetheless, human cognition extends beyond language alone, enabling the remarkable capability to think in both words and images. Inspired by this mechanism, we propose a new reasoning paradigm, Multimodal Visualization-of-Thought (MVoT). It enables visual thinking in MLLMs by generating image visualizations of their reasoning traces. To ensure high-quality visualization, we introduce token discrepancy loss into autoregressive MLLMs. This innovation significantly improves both visual coherence and fidelity. We validate this approach through several dynamic spatial reasoning tasks. Experimental results reveal that MVoT demonstrates competitive performance across tasks. Moreover, it exhibits robust and reliable improvements in the most challenging scenarios where CoT fails. Ultimately, MVoT establishes new possibilities for complex reasoning tasks where visual thinking can effectively complement verbal reasoning.

Real-time Spoken Language Models (SLMs) struggle to leverage Chain-of-Thought (CoT) reasoning due to the prohibitive latency of generating the entire thought process sequentially. Enabling SLMs to think while speaking, similar to humans, is attracting increasing attention. We present, for the first time, Mind-Paced Speaking (MPS), a brain-inspired framework that enables high-fidelity, real-time reasoning. Similar to how humans utilize distinct brain regions for thinking and responding, we propose a novel dual-brain approach, employing a "Formulation Brain" for high-level reasoning to pace and guide a separate "Articulation Brain" for fluent speech generation. This division of labor eliminates mode-switching, preserving the integrity of the reasoning process. Experiments show that MPS significantly outperforms existing think-while-speaking methods and achieves reasoning performance comparable to models that pre-compute the full CoT before speaking, while drastically reducing latency. Under a zero-latency configuration, the proposed method achieves an accuracy of 92.8% on the mathematical reasoning task Spoken-MQA and attains a score of 82.5 on the speech conversation task URO-Bench. Our work effectively bridges the gap between high-quality reasoning and real-time interaction.

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

Early research into data poisoning attacks against Large Language Models (LLMs) demonstrated the ease with which backdoors could be injected. More recent LLMs add step-by-step reasoning, expanding the attack surface to include the intermediate chain-of-thought (CoT) and its inherent trait of decomposing problems into subproblems. Using these vectors for more stealthy poisoning, we introduce ``decomposed reasoning poison'', in which the attacker modifies only the reasoning path, leaving prompts and final answers clean, and splits the trigger across multiple, individually harmless components. Fascinatingly, while it remains possible to inject these decomposed poisons, reliably activating them to change final answers (rather than just the CoT) is surprisingly difficult. This difficulty arises because the models can often recover from backdoors that are activated within their thought processes. Ultimately, it appears that an emergent form of backdoor robustness is originating from the reasoning capabilities of these advanced LLMs, as well as from the architectural separation between reasoning and final answer generation.

In this paper, we investigate whether Large Language Models (LLMs) actively recall or retrieve their internal repositories of factual knowledge when faced with reasoning tasks. Through an analysis of LLMs' internal factual recall at each reasoning step via Knowledge Neurons, we reveal that LLMs fail to harness the critical factual associations under certain circumstances. Instead, they tend to opt for alternative, shortcut-like pathways to answer reasoning questions. By manually manipulating the recall process of parametric knowledge in LLMs, we demonstrate that enhancing this recall process directly improves reasoning performance whereas suppressing it leads to notable degradation. Furthermore, we assess the effect of Chain-of-Thought (CoT) prompting, a powerful technique for addressing complex reasoning tasks. Our findings indicate that CoT can intensify the recall of factual knowledge by encouraging LLMs to engage in orderly and reliable reasoning. Furthermore, we explored how contextual conflicts affect the retrieval of facts during the reasoning process to gain a comprehensive understanding of the factual recall behaviors of LLMs. Code and data will be available soon.

We introduce the Diffusion Chain of Lateral Thought (DCoLT), a reasoning framework for diffusion language models. DCoLT treats each intermediate step in the reverse diffusion process as a latent "thinking" action and optimizes the entire reasoning trajectory to maximize the reward on the correctness of the final answer with outcome-based Reinforcement Learning (RL). Unlike traditional Chain-of-Thought (CoT) methods that follow a causal, linear thinking process, DCoLT allows bidirectional, non-linear reasoning with no strict rule on grammatical correctness amid its intermediate steps of thought. We implement DCoLT on two representative Diffusion Language Models (DLMs). First, we choose SEDD as a representative continuous-time discrete diffusion model, where its concrete score derives a probabilistic policy to maximize the RL reward over the entire sequence of intermediate diffusion steps. We further consider the discrete-time masked diffusion language model -- LLaDA, and find that the order to predict and unmask tokens plays an essential role to optimize its RL action resulting from the ranking-based Unmasking Policy Module (UPM) defined by the Plackett-Luce model. Experiments on both math and code generation tasks show that using only public data and 16 H800 GPUs, DCoLT-reinforced DLMs outperform other DLMs trained by SFT or RL or even both. Notably, DCoLT-reinforced LLaDA boosts its reasoning accuracy by +9.8%, +5.7%, +11.4%, +19.5% on GSM8K, MATH, MBPP, and HumanEval.

Structured image understanding, such as interpreting tables and charts, requires strategically refocusing across various structures and texts within an image, forming a reasoning sequence to arrive at the final answer. However, current multimodal large language models (LLMs) lack this multihop selective attention capability. In this work, we introduce ReFocus, a simple yet effective framework that equips multimodal LLMs with the ability to generate "visual thoughts" by performing visual editing on the input image through code, shifting and refining their visual focuses. Specifically, ReFocus enables multimodal LLMs to generate Python codes to call tools and modify the input image, sequentially drawing boxes, highlighting sections, and masking out areas, thereby enhancing the visual reasoning process. We experiment upon a wide range of structured image understanding tasks involving tables and charts. ReFocus largely improves performance on all tasks over GPT-4o without visual editing, yielding an average gain of 11.0% on table tasks and 6.8% on chart tasks. We present an in-depth analysis of the effects of different visual edits, and reasons why ReFocus can improve the performance without introducing additional information. Further, we collect a 14k training set using ReFocus, and prove that such visual chain-of-thought with intermediate information offers a better supervision than standard VQA data, reaching a 8.0% average gain over the same model trained with QA pairs and 2.6% over CoT.

Large reasoning models (LRMs) spend substantial test-time compute on long chain-of-thought (CoT) traces, but what *characterizes* an effective CoT remains unclear. While prior work reports gains from lengthening CoTs and increasing review (revisiting earlier steps) via appended *wait* tokens, recent studies suggest that shorter thinking can outperform longer traces. We therefore conduct a systematic evaluation across ten LRMs on math and scientific reasoning. Contrary to the "longer-is-better" narrative, we find that both naive CoT lengthening and increased review are associated with *lower* accuracy. As CoT unfolds step by step, token-level metrics can conflate verbosity with process quality. We introduce a graph view of CoT to extract structure and identify a single statistic-the *Failed-Step Fraction (FSF)*, the fraction of steps in abandoned branches-that consistently outpredicts length and review ratio for correctness across models. To probe causality, we design two interventions. First, we rank candidate CoTs by each metric at test time, where FSF yields the largest pass@1 gains; second, we edit CoTs to remove failed branches, which significantly improves accuracy, indicating that failed branches bias subsequent reasoning. Taken together, these results characterize effective CoTs as those that *fail less* and support *structure-aware* test-time scaling over indiscriminately generating long CoT.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Reasoning large language models have recently achieved state-of-the-art performance in many fields. However, their long-form chain-of-thought reasoning creates interpretability challenges as each generated token depends on all previous ones, making the computation harder to decompose. We argue that analyzing reasoning traces at the sentence level is a promising approach to understanding reasoning processes. We present three complementary attribution methods: (1) a black-box method measuring each sentence's counterfactual importance by comparing final answers across 100 rollouts conditioned on the model generating that sentence or one with a different meaning; (2) a white-box method of aggregating attention patterns between pairs of sentences, which identified ``broadcasting'' sentences that receive disproportionate attention from all future sentences via ``receiver'' attention heads; (3) a causal attribution method measuring logical connections between sentences by suppressing attention toward one sentence and measuring the effect on each future sentence's tokens. Each method provides evidence for the existence of thought anchors, reasoning steps that have outsized importance and that disproportionately influence the subsequent reasoning process. These thought anchors are typically planning or backtracking sentences. We provide an open-source tool (www.thought-anchors.com) for visualizing the outputs of our methods, and present a case study showing converging patterns across methods that map how a model performs multi-step reasoning. The consistency across methods demonstrates the potential of sentence-level analysis for a deeper understanding of reasoning models.

Complex Reasoning in Large Language Models can be dynamically optimized using Test-Time Scaling (TTS) to mitigate Overthinking. Methods such as Coconut, SoftCoT and its variant are effective in continuous latent space inference, the core bottleneck still lies in the efficient generation and utilization of high-quality Latent Thought. Drawing from the theory of SoftCoT++ that a larger variance in the generated Latent Thought distribution more closely approximates the golden truth distribution, we propose a Latent Thought-Augmented Training Framework--LTA-Thinker, which improves distributional variance and enhances reasoning performance from two perspectives. First, LTA-Thinker constructs a Latent Thought generation architecture based on a learnable prior. This architecture aims to increase the variance distribution of generated Latent Thought Vectors in order to simplify the overall structure and raise the performance ceiling. Second, LTA-Thinker introduces a distribution-based directional optimization paradigm that jointly constrains both distribution locality and distribution scale. This mechanism improves information efficiency and computational cost through a multi-objective co-training strategy, which combines standard Supervised Fine-Tuning (SFT) loss with two novel losses: Semantic Alignment Loss, which utilizes KL divergence to ensure that the Latent Thought is highly relevant to the semantics of the question; Reasoning Focus Loss, which utilizes a contrastive learning mechanism to guide the model to focus on the most critical reasoning steps. Experiments show that LTA-thinker achieves state-of-the-art (SOTA) performance among various baselines and demonstrates a higher performance ceiling and better scaling effects.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Depression poses significant challenges to patients and healthcare organizations, necessitating efficient assessment methods. Existing paradigms typically focus on a patient-doctor way that overlooks multi-role interactions, such as family involvement in the evaluation and caregiving process. Moreover, current automatic depression detection (ADD) methods usually model depression detection as a classification or regression task, lacking interpretability for the decision-making process. To address these issues, we developed InterMind, a doctor-patient-family interactive depression assessment system empowered by large language models (LLMs). Our system enables patients and families to contribute descriptions, generates assistive diagnostic reports for doctors, and provides actionable insights, improving diagnostic precision and efficiency. To enhance LLMs' performance in psychological counseling and diagnostic interpretability, we integrate retrieval-augmented generation (RAG) and chain-of-thoughts (CoT) techniques for data augmentation, which mitigates the hallucination issue of LLMs in specific scenarios after instruction fine-tuning. Quantitative experiments and professional assessments by clinicians validate the effectiveness of our system.

Equipped with Chain-of-Thought (CoT), Large language models (LLMs) have shown impressive reasoning ability in various downstream tasks. Even so, suffering from hallucinations and the inability to access external knowledge, LLMs often come with incorrect or unfaithful intermediate reasoning steps, especially in the context of answering knowledge-intensive tasks such as KBQA. To alleviate this issue, we propose a framework called Knowledge-Driven Chain-of-Thought (KD-CoT) to verify and modify reasoning traces in CoT via interaction with external knowledge, and thus overcome the hallucinations and error propagation. Concretely, we formulate the CoT rationale process of LLMs into a structured multi-round QA format. In each round, LLMs interact with a QA system that retrieves external knowledge and produce faithful reasoning traces based on retrieved precise answers. The structured CoT reasoning of LLMs is facilitated by our developed KBQA CoT collection, which serves as in-context learning demonstrations and can also be utilized as feedback augmentation to train a robust retriever. Extensive experiments on WebQSP and ComplexWebQuestion datasets demonstrate the effectiveness of proposed KD-CoT in task-solving reasoning generation, which outperforms the vanilla CoT ICL with an absolute success rate of 8.0% and 5.1%. Furthermore, our proposed feedback-augmented retriever outperforms the state-of-the-art baselines for retrieving knowledge, achieving significant improvement in Hit performance.

Vision-language models (VLMs) excel at multimodal understanding, yet their text-only decoding forces them to verbalize visual reasoning, limiting performance on tasks that demand visual imagination. Recent attempts train VLMs to render explicit images, but the heavy image-generation pre-training often hinders the reasoning ability. Inspired by the way humans reason with mental imagery-the internal construction and manipulation of visual cues-we investigate whether VLMs can reason through interleaved multimodal trajectories without producing explicit images. To this end, we present a Machine Mental Imagery framework, dubbed as Mirage, which augments VLM decoding with latent visual tokens alongside ordinary text. Concretely, whenever the model chooses to ``think visually'', it recasts its hidden states as next tokens, thereby continuing a multimodal trajectory without generating pixel-level images. Begin by supervising the latent tokens through distillation from ground-truth image embeddings, we then switch to text-only supervision to make the latent trajectory align tightly with the task objective. A subsequent reinforcement learning stage further enhances the multimodal reasoning capability. Experiments on diverse benchmarks demonstrate that Mirage unlocks stronger multimodal reasoning without explicit image generation.

Image editing with natural language has gained significant popularity, yet existing methods struggle with intricate object intersections and fine-grained spatial relationships due to the lack of an explicit reasoning process. While Chain-of-Thought (CoT) has been explored to enhance reasoning, purely textual CoT or CoT augmented with coordinate information is fundamentally limited in its ability to represent intricate visual layouts and lacks the necessary visual cues to guide the generation of fine-grained, pixel-level details. To address these challenges, we propose Multimodal Reasoning Edit (MURE), a novel framework that shifts the visual editing process from purely text-based reasoning to a series of interleaved textual and visual rationales. Our framework performs image editing using a natively multimodal, interleaved text-image CoT. This approach generates a step-by-step chain of reasoning where a textual description is followed by a corresponding visual cue, such as a positional mask that defined intended edited regions or a representation of new content. Furthermore, to mitigate the hallucination phenomenon of large language models, we introduce Multimodal Deep Confidence (MMDC) reasoning paradigm. This paradigm explores a tree of visual reasoning paths at each step. By pruning low-quality branches using a deep confidence score from a reward model, it ensures the model consistently follows a high-quality trajectory towards the final edited result. The proposed method decomposes complex editing tasks into interdependent sub-tasks, achieving greater precision at each stage and yielding high-fidelity edited results. We define the formulation for interleaved text-image chains and release the first CoT-Edit-14K dataset, comprising 14K high-quality editing examples. Extensive experiments show that our method yields significant improvements across three image editing benchmarks.

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

Large Reasoning Models (LRMs) demonstrate remarkable capabilities on complex tasks, exhibiting emergent, human-like thinking patterns. Despite their advances, we identify a fundamental limitation: current LRMs lack a dedicated meta-level cognitive system-an essential faculty in human cognition that enables "thinking about thinking". This absence leaves their emergent abilities uncontrollable (non-adaptive reasoning), unreliable (intermediate error), and inflexible (lack of a clear methodology). To address this gap, we introduce Meta-R1, a systematic and generic framework that endows LRMs with explicit metacognitive capabilities. Drawing on principles from cognitive science, Meta-R1 decomposes the reasoning process into distinct object-level and meta-level components, orchestrating proactive planning, online regulation, and adaptive early stopping within a cascaded framework. Experiments on three challenging benchmarks and against eight competitive baselines demonstrate that Meta-R1 is: (I) high-performing, surpassing state-of-the-art methods by up to 27.3%; (II) token-efficient, reducing token consumption to 15.7% ~ 32.7% and improving efficiency by up to 14.8% when compared to its vanilla counterparts; and (III) transferable, maintaining robust performance across datasets and model backbones.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

While chain-of-thought (CoT) prompting has revolutionized how LLMs perform reasoning tasks, its current methods and variations (e.g, Self-consistency, ReACT, Reflexion, Tree-of-Thoughts (ToT), Cumulative Reasoning (CR)) suffer from limitations like slowness, limited context grounding, hallucination and inconsistent outputs. To overcome these challenges, we introduce Evidence to Generate (E2G), a novel single-agent, two-step prompting framework. Instead of unverified reasoning claims, this innovative approach leverages the power of "evidence for decision making" by first focusing exclusively on the thought sequences (the series of intermediate steps) explicitly mentioned in the context which then serve as extracted evidence, guiding the LLM's output generation process with greater precision and efficiency. This simple yet powerful approach unlocks the true potential of chain-of-thought like prompting, paving the way for faster, more reliable, and more contextually aware reasoning in LLMs. \tool achieves remarkable results robustly across a wide range of knowledge-intensive reasoning and generation tasks, surpassing baseline approaches with state-of-the-art LLMs. For example, (i) on LogiQA benchmark using GPT-4 as backbone model, \tool achieves a new state-of-the Accuracy of 53.8% exceeding CoT by 18%, ToT by 11%, CR by 9% (ii) a variant of E2G with PaLM2 outperforms the variable-shot performance of Gemini Ultra by 0.9 F1 points, reaching an F1 score of 83.3 on a subset of DROP.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Reasoning-enhanced large language models (LLMs) explicitly generate intermediate reasoning steps prior to generating final answers, helping the model excel in complex problem-solving. In this paper, we demonstrate that this emerging generation framework offers a unique opportunity for more fine-grained control over model behavior. We propose Thinking Intervention, a novel paradigm designed to explicitly guide the internal reasoning processes of LLMs by strategically inserting or revising specific thinking tokens. We conduct comprehensive evaluations across multiple tasks, including instruction following on IFEval, instruction hierarchy on SEP, and safety alignment on XSTest and SORRY-Bench. Our results demonstrate that Thinking Intervention significantly outperforms baseline prompting approaches, achieving up to 6.7% accuracy gains in instruction-following scenarios, 15.4% improvements in reasoning about instruction hierarchies, and a 40.0% increase in refusal rates for unsafe prompts using open-source DeepSeek R1 models. Overall, our work opens a promising new research avenue for controlling reasoning LLMs.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to move beyond fast System-1 responses and engage in deliberative System-2 reasoning. However, this comes at the cost of significant inefficiency due to verbose intermediate output. Recent latent-space reasoning methods improve efficiency by operating on hidden states without decoding into language, yet they treat all steps uniformly, failing to distinguish critical deductions from auxiliary steps and resulting in suboptimal use of computational resources. In this paper, we propose System-1.5 Reasoning, an adaptive reasoning framework that dynamically allocates computation across reasoning steps through shortcut paths in latent space. Specifically, System-1.5 Reasoning introduces two types of dynamic shortcuts. The model depth shortcut (DS) adaptively reasons along the vertical depth by early exiting non-critical tokens through lightweight adapter branches, while allowing critical tokens to continue through deeper Transformer layers. The step shortcut (SS) reuses hidden states across the decoding steps to skip trivial steps and reason horizontally in latent space. Training System-1.5 Reasoning involves a two-stage self-distillation process: first distilling natural language CoT into latent-space continuous thought, and then distilling full-path System-2 latent reasoning into adaptive shortcut paths (System-1.5 Reasoning). Experiments on reasoning tasks demonstrate the superior performance of our method. For example, on GSM8K, System-1.5 Reasoning achieves reasoning performance comparable to traditional CoT fine-tuning methods while accelerating inference by over 20x and reducing token generation by 92.31% on average.

Reinforcement learning (RL) has emerged as an effective method for training reasoning models. However, existing RL approaches typically bias the model's output distribution toward reward-maximizing paths without introducing external knowledge. This limits their exploration capacity and results in a narrower reasoning capability boundary compared to base models. To address this limitation, we propose TAPO (Thought-Augmented Policy Optimization), a novel framework that augments RL by incorporating external high-level guidance ("thought patterns"). By adaptively integrating structured thoughts during training, TAPO effectively balances model-internal exploration and external guidance exploitation. Extensive experiments show that our approach significantly outperforms GRPO by 99% on AIME, 41% on AMC, and 17% on Minerva Math. Notably, these high-level thought patterns, abstracted from only 500 prior samples, generalize effectively across various tasks and models. This highlights TAPO's potential for broader applications across multiple tasks and domains. Our further analysis reveals that introducing external guidance produces powerful reasoning models with superior explainability of inference behavior and enhanced output readability.

Many cognitive approaches to well-being, such as recognizing and reframing unhelpful thoughts, have received considerable empirical support over the past decades, yet still lack truly widespread adoption in self-help format. A barrier to that adoption is a lack of adequately specific and diverse dedicated practice material. This work examines whether current language models can be leveraged to both produce a virtually unlimited quantity of practice material illustrating standard unhelpful thought patterns matching specific given contexts, and generate suitable positive reframing proposals. We propose PATTERNREFRAME, a novel dataset of about 10k examples of thoughts containing unhelpful thought patterns conditioned on a given persona, accompanied by about 27k positive reframes. By using this dataset to train and/or evaluate current models, we show that existing models can already be powerful tools to help generate an abundance of tailored practice material and hypotheses, with no or minimal additional model training required.

Extensive work has shown that the performance and interpretability of commonsense reasoning can be improved via knowledge-augmented reasoning methods, where the knowledge that underpins the reasoning process is explicitly verbalized and utilized. However, existing implementations, including "chain-of-thought" and its variants, fall short in capturing the introspective nature of knowledge required in commonsense reasoning, and in accounting for the mutual adaptation between the generation and utilization of knowledge. We propose a novel method to develop an introspective commonsense reasoner, Crystal. To tackle commonsense problems, it first introspects for knowledge statements related to the given question, and subsequently makes an informed prediction that is grounded in the previously introspected knowledge. The knowledge introspection and knowledge-grounded reasoning modes of the model are tuned via reinforcement learning to mutually adapt, where the reward derives from the feedback given by the model itself. Experiments show that Crystal significantly outperforms both the standard supervised finetuning and chain-of-thought distilled methods, and enhances the transparency of the commonsense reasoning process. Our work ultimately validates the feasibility and potential of reinforcing a neural model with self-feedback.

Reasoning quality in large language models depends not only on producing correct answers but also on generating valid intermediate steps. We study this through multiple-choice question answering (MCQA), which provides a controlled setting with fixed answer options. Our analysis shows that when questions are effectively unsolvable for a model, spurious chains of thought (CoTs) are more likely to appear, leading to false positives. By estimating the solvability of each question, we uncover an intermediate regime where learning is most effective. Building on this insight, we adapt outcome-supervised reward models and reinforcement learning with group-relative advantage to incorporate solvability into their objectives. Across experiments on math and multimodal datasets, these modifications consistently yield higher rates of process-correct reasoning and, in reinforcement learning, improved answer accuracy as well. Our results highlight solvability as a key factor for reducing hallucinations and increasing reliability in CoT reasoning.

This paper presents AlphaOne (alpha1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. alpha1 first introduces alpha moment, which represents the scaled thinking phase with a universal parameter alpha. Within this scaled pre-alpha moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the alpha moment, alpha1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate alpha1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

In this paper, we introduce the Tree-of-Thought (ToT) framework, a novel approach aimed at improving the problem-solving capabilities of auto-regressive large language models (LLMs). The ToT technique is inspired by the human mind's approach for solving complex reasoning tasks through trial and error. In this process, the human mind explores the solution space through a tree-like thought process, allowing for backtracking when necessary. To implement ToT as a software system, we augment an LLM with additional modules including a prompter agent, a checker module, a memory module, and a ToT controller. In order to solve a given problem, these modules engage in a multi-round conversation with the LLM. The memory module records the conversation and state history of the problem solving process, which allows the system to backtrack to the previous steps of the thought-process and explore other directions from there. To verify the effectiveness of the proposed technique, we implemented a ToT-based solver for the Sudoku Puzzle. Experimental results show that the ToT framework can significantly increase the success rate of Sudoku puzzle solving. Our implementation of the ToT-based Sudoku solver is available on GitHub: https://github.com/jieyilong/tree-of-thought-puzzle-solver.

As Test-Time Scaling emerges as an active research focus in the large language model community, advanced post-training methods increasingly emphasize extending chain-of-thought (CoT) generation length, thereby enhancing reasoning capabilities to approach Deepseek R1-like reasoning models. However, recent studies reveal that reasoning models (even Qwen3) consistently exhibit excessive thought redundancy in CoT generation. This overthinking issue arises from the inherent limitations of conventional outcome-reward reinforcement learning, which systematically overlooks the regulation of intermediate reasoning processes. This paper introduces Serial-Group Decaying-Reward Policy Optimization (S-GRPO), a novel reinforcement learning paradigm that enables models to implicitly evaluate the sufficiency of intermediate reasoning steps, thereby facilitating early exit in CoT generation. Unlike GRPO, which samples multiple possible reasoning paths in parallel (parallel group), S-GRPO only samples one reasoning path and serially selects multiple temporal positions from the path to exit thinking and directly generate answers (serial group). For correct answers within a serial group, rewards gradually decrease based on the exit positions along the reasoning path from front to back. This design encourages the model to produce more accurate and concise thoughts, while also incentivizing early thinking termination when appropriate. Empirical evaluations demonstrate that S-GRPO is compatible with state-of-the-art reasoning models, including Qwen3 and Deepseek-distill. Across diverse benchmarks such as GSM8K, AIME 2024, AMC 2023, MATH-500, and GPQA Diamond, S-GRPO achieves a substantial reduction in sequence length (35.4% - 61.1%) while simultaneously improving accuracy (absolute 0.72% - 6.08%).

Large Language Models (LLMs) have achieved impressive performance on complex reasoning tasks with Chain-of-Thought (CoT) prompting. However, conventional CoT relies on reasoning steps explicitly verbalized in natural language, introducing inefficiencies and limiting its applicability to abstract reasoning. To address this, there has been growing research interest in latent CoT reasoning, where inference occurs within latent spaces. By decoupling reasoning from language, latent reasoning promises richer cognitive representations and more flexible, faster inference. Researchers have explored various directions in this promising field, including training methodologies, structural innovations, and internal reasoning mechanisms. This paper presents a comprehensive overview and analysis of this reasoning paradigm. We begin by proposing a unified taxonomy from four perspectives: token-wise strategies, internal mechanisms, analysis, and applications. We then provide in-depth discussions and comparative analyses of representative methods, highlighting their design patterns, strengths, and open challenges. We aim to provide a structured foundation for advancing this emerging direction in LLM reasoning. The relevant papers will be regularly updated at https://github.com/EIT-NLP/Awesome-Latent-CoT.

Recent advances in inference time scaling with extended long chain-of thought have significantly improved the reasoning capabilities of both general and medical large language models (LLMs). However, these models tend to engage in lengthy reasoning processes regardless of the difficulty of the input question, leading to increased inference costs in real-world applications. Therefore, enabling adaptive thinking where models think less for simpler questions and think more for complex ones is critical for the effective use of medical LLMs in practice. Despite its importance, there is a lack of end-to-end approaches designed to enhance the adaptive thinking capabilities of medical LLMs while providing a comprehensive examination of the trade-off between performance and computational cost. To bridge this gap, we propose AdaThink-Med, the first end-to-end framework designed to enhance adaptive thinking ability in medical reasoning models with uncertainty-guided length calibration. AdaThink-Med first generates multiple candidate outputs for each question, evaluates the correctness and uncertainty of each candidate, and then estimates problem difficulty via an uncertainty-guided length calibration module. For outputs with low difficulty and correct answers, the framework penalizes longer reasoning paths; whereas for those with high difficulty and incorrect answers, it encourages extending the chain of thought to explore alternative solutions. On six public medical QA benchmarks, AdaThink-Med achieves up to 6.4x length reduction on average while retaining performance with only minimal degradation. Intriguingly, we observe that AdaThink-Med spontaneously develops two distinct reasoning modes, which we characterize as "non-thinking" and "thinking", demonstrating the model's ability to suppress redundant reasoning processes dynamically.

Large Reasoning Models (LRMs) have become a central focus in today's large language model (LLM) research, where models are designed to output a step-by-step thinking process before arriving at a final answer to handle complex reasoning tasks. Despite their promise, recent empirical studies (e.g., [Shojaee et al., 2025] from Apple) suggest that this thinking process may not actually enhance reasoning ability, where LLMs without explicit reasoning actually outperform LRMs on tasks with low or high complexity. In this work, we revisit these findings and investigate whether the limitations of LRMs persist when tool augmentations are introduced. We incorporate two types of tools, Python interpreters and scratchpads, and evaluate three representative LLMs and their LRM counterparts on Apple's benchmark reasoning puzzles. Our results show that, with proper tool use, LRMs consistently outperform their non-reasoning counterparts across all levels of task complexity. These findings challenge the recent narrative that reasoning is an illusion and highlight the potential of tool-augmented LRMs for solving complex problems.

Recent advances in large language models (LLMs) have demonstrated the power of reasoning through self-generated chains of thought. Multiple reasoning agents can collaborate to raise joint reasoning quality above individual outcomes. However, such agents typically interact in a turn-based manner, trading increased latency for improved quality. In this paper, we propose Group Think--a single LLM that acts as multiple concurrent reasoning agents, or thinkers. With shared visibility into each other's partial generation progress, Group Think introduces a new concurrent-reasoning paradigm in which multiple reasoning trajectories adapt dynamically to one another at the token level. For example, a reasoning thread may shift its generation mid-sentence upon detecting that another thread is better positioned to continue. This fine-grained, token-level collaboration enables Group Think to reduce redundant reasoning and improve quality while achieving significantly lower latency. Moreover, its concurrent nature allows for efficient utilization of idle computational resources, making it especially suitable for edge inference, where very small batch size often underutilizes local~GPUs. We give a simple and generalizable modification that enables any existing LLM to perform Group Think on a local GPU. We also present an evaluation strategy to benchmark reasoning latency and empirically demonstrate latency improvements using open-source LLMs that were not explicitly trained for Group Think. We hope this work paves the way for future LLMs to exhibit more sophisticated and more efficient collaborative behavior for higher quality generation.