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Synaptic plasticity is widely accepted to be the mechanism behind learning inthe brain's neural networks. A central question is how synapses, with access toonly local information about the network, can still organize collectively andperform circuit-wide learning in an efficient manner. In single-layered andall-to-all connected neural networks, local plasticity has been shown toimplement gradient-based learning on a class of cost functions that contain aterm that aligns the similarity of outputs to the similarity of inputs. Whethersuch cost functions exist for networks with other architectures is not known.In this paper, we introduce structured and deep similarity matching costfunctions, and show how they can be optimized in a gradient-based manner byneural networks with local learning rules. These networks extend F\"oldiak'sHebbian/Anti-Hebbian network to deep architectures and structured feedforward,lateral and feedback connections. Credit assignment problem is solved elegantlyby a factorization of the dual learning objective to synapse specific localobjectives. Simulations show that our networks learn meaningful features.

Structured and Deep Similarity Matching via Structured and Deep Hebbian Networks