Hebbian Learning through the lens of SAE traning.

Likely, modern competitive Hebbian learning rules train Sparse Autoencoders implicitly - and their approximations make them worse at it. These algorithms specify weight updates directly, without computing a loss and the consequent gradients. But their updates contain terms closely related to both. This raises a question: how much of their feature-learning behavior can we understand as approximate SAE optimization ?This post develops that connection for tied-weight SAEs, identifies where the upda...