Differentiating inputs with Siamese networks

Let's see how the similarity function is implemented through Siamese networks. The idea was first implemented at paper published by Taigman in 2014, DeepFace: Closing the Gap to Human-Level Performance in Face Verification. Then we will see how Siamese networks learn by giving a slightly more formal definition.

First, we will continue to use convolution architectures with many convolution layers:

The fully connected layers within neurons, and the softmax for the prediction.

Let's fit the first image we want to compare, X¹:

And what we will do is, through a forward pass, grab the activation values of the last fully connected layer, and we will refer to those values as F(x¹), or sometimes also the encoded values of the image, because we transform this image through the forward paths to another set of values of the activation...