A biologically plausible neural network for multi-channel Canonical Correlation Analysis

TL;DR

This paper proposes a biologically plausible neural network model that implements multi-channel Canonical Correlation Analysis (CCA) using local synaptic rules, inspired by cortical pyramidal neuron circuitry.

Contribution

It introduces a novel online CCA algorithm compatible with biological neural networks, including multi-compartmental neurons and local learning rules.

Findings

The algorithm operates in an online setting with local synaptic updates.

The neural architecture resembles cortical pyramidal neuron circuitry.

Extension includes adaptive output rank and whitening, aligning with experimental observations.

Abstract

Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation Analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multi-channel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and its synaptic update rules are local. Starting from a novel CCA objective function, we derive an online optimization algorithm whose optimization steps can be implemented in a single-layer neural network with multi-compartmental neurons and local non-Hebbian learning rules. We also derive an extension of our online CCA algorithm with adaptive output rank and output whitening. Interestingly, the extension maps onto a neural network whose neural architecture and synaptic updates resemble neural circuitry and synaptic plasticity observed experimentally in cortical pyramidal neurons.