label="fig:failure_mode"}](figures/failure_mode.pdf){width="0.8\linewidth"}

Triplet Network Visualization {#triplet-network-visualization .unnumbered}
-----------------------------

Here we illustrate how a triplet network is trained. An anchor, positive example, and negative example are all passed through the same embedding network. The triplet loss is then computed which encourages the distance between the anchor and positive example to be some margin $\alpha$ closer together than the anchor and negative example.

![Illustration of how a triplet network works on the MNIST dataset.[]{data-label="triplet_net"}](figures/triplet_net.pdf){width="\textwidth"}

The triplet loss function is shown here for convenience:

$$L(x, x_{-}, x_{+}) = \mathrm{max}(0, \alpha + \mathrm{d}(x, x_{+}) - \mathrm{d}(x, x_{-}))$$

Agreement Between LeNet and Triplet Network {#agreement-between-lenet-and-triplet-network .unnumbered}
-------------------------------------------

We investigated the agreement between LeNet and triplet network we trained in order to confirm that a concordance based detector is a viable option, and does not result in false positives on normal images. Importantly, the models agree  90% (Table \[table:concordance\]) of the time on normal images, so false positives are not a major concern.

   Overall Concordance   Correct Concordance   Incorrect Concordance
  --------------------- --------------------- -----------------------
          0.911                 0.908                  0.003

  : Concordance between LeNet and triplet network on predictions on normal images.[]{data-label="table:concordance"}


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