Why do similarity matching objectives lead to Hebbian/anti-Hebbian networks?

Abstract

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet, derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules both in the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents. To illustrate the generality of our approach, we apply it to a novel formulation of dimensionality reduction combined with whitening. We confirm numerically that the networks with learning rules derived from principled objectives perform better than those with heuristic learning rules.

Accepted for publication in Neural Computation

References in corpus (5)

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Cited by in corpus (14)

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• Kernelized information bottleneck leads to biologically plausible 3-factor Hebbian learning in deep networks
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• Local Unsupervised Learning for Image Analysis
• Structured and Deep Similarity Matching via Structured and Deep Hebbian Networks
• Two "correlation games" for a nonlinear network with Hebbian excitatory neurons and anti-Hebbian inhibitory neurons
• Simulation of neural function in an artificial Hebbian network
• A Neural Network with Local Learning Rules for Minor Subspace Analysis
• Contrastive Similarity Matching for Supervised Learning
• Neuroscience-inspired online unsupervised learning algorithms
• Procrustean Orthogonal Sparse Hashing
• A Normative and Biologically Plausible Algorithm for Independent Component Analysis
• A Similarity-preserving Neural Network Trained on Transformed Images Recapitulates Salient Features of the Fly Motion Detection Circuit
• Modeling Winner-Take-All Competition in Sparse Binary Projections