A wild speculation about a possible application of this to network interpretability:
Given a dog-cat classifying network with the following layer format Input→V→S→U→ReLU→Output,[1] this can be viewed as a sequence of compressions and information-throwing-away-operations (the zeros in the S, and the taking of all negative values to 0 in ReLU discard information), where for any given input, the information relevant to the classification task is placed into the entries which get preserved (the non-zero entries in S, and the positive entries in the ReLU).
In other words, the network is playing a very similar version of the generalized heat engine game, but where the energy being extracted is relevant information, and the transformations are subject to the constraint that they must all be orthogonal and linear.
If this framing is useful, we should expect that if you hold each S constant, randomize the Vs and Us, then find the optimal Vs and Us, we should get back similar Vs and Us to what we started with.
A wild speculation about a possible application of this to network interpretability:
Given a dog-cat classifying network with the following layer format Input→V→S→U→ReLU→Output,[1] this can be viewed as a sequence of compressions and information-throwing-away-operations (the zeros in the S, and the taking of all negative values to 0 in ReLU discard information), where for any given input, the information relevant to the classification task is placed into the entries which get preserved (the non-zero entries in S, and the positive entries in the ReLU).
In other words, the network is playing a very similar version of the generalized heat engine game, but where the energy being extracted is relevant information, and the transformations are subject to the constraint that they must all be orthogonal and linear.
If this framing is useful, we should expect that if you hold each S constant, randomize the Vs and Us, then find the optimal Vs and Us, we should get back similar Vs and Us to what we started with.
Where USV is an SVD of our learned weight matrix.