A Hebbian/Anti-Hebbian Network for Online Sparse Dictionary Learning Derived from Symmetric Matrix Factorization

TL;DR

This paper introduces a biologically plausible neural network algorithm for online sparse dictionary learning based on symmetric matrix factorization, which learns Gabor-like receptive fields from natural images.

Contribution

It derives a new local learning rule for sparse dictionary learning from a symmetric matrix factorization cost function, improving biological plausibility.

Findings

Learns Gabor-filter receptive fields from natural images

Reproduces synaptic weight correlations of previous models

Uses only local, biologically plausible learning rules

Abstract

Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement with physiological experiments. Whereas the OF algorithm can be mapped onto the dynamics and synaptic plasticity in a single-layer neural network, the derived learning rule is nonlocal - the synaptic weight update depends on the activity of neurons other than just pre- and postsynaptic ones - and hence biologically implausible. Here, to overcome this problem, we derive sparse dictionary learning from a novel cost-function - a regularized error of the symmetric factorization of the input's similarity matrix. Our algorithm maps onto a neural network of the same architecture as OF but using only biologically plausible local learning rules. When trained on natural images our network learns Gabor-filter receptive fields and reproduces the correlation among synaptic weights hard-wired in the OF network. Therefore, online symmetric matrix factorization may serve as an algorithmic theory of neural computation.