I am reading this paper on image retrieval where the goal is to train a network that produces highly discriminative descriptors (aka embeddings) for input images. If you are familiar with facial recognition architectures, it is similar in that the network is trained with matching / non-matching pairs and triplet loss.

The paper discusses the use of PCA and whitening on the training set of descriptors as a means of further improving the discriminability (second to last block in image below, fig 1a of paper). This all make sense to me.

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Where I'm confused is where they replace PCA/whitening with a trainable fully connected layer with bias. I do understand that PCA+whitening is just the composition of of two linear transformations (ie rotation + (un)squishing in each dimension) and that these are the same as having one linear transformation but:

  • How is PCA+whitening equivalent to a learnable fully connected layer? Is there some theorem or paper explaining that training a fully connected layer with triplet loss is somehow statistically equivalent to PCA and whitening?
  • Why is there a bias?

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