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

arXiv: https://arxiv.org/abs/2010.00525 · HTML: https://mlsanity.com/paper/2010.00525/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [Interneurons accelerate learning dynamics in recurrent neural networks for statistical adaptation](https://mlsanity.com/paper/2209.10634/) (2022)
- [Normative framework for deriving neural networks with multi-compartmental neurons and non-Hebbian plasticity](https://mlsanity.com/paper/2302.10051/) (2023)
- [Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetry](https://mlsanity.com/paper/2306.04810/) (2023)
- [Adaptive whitening with fast gain modulation and slow synaptic plasticity](https://mlsanity.com/paper/2308.13633/) (2023)
- [An online algorithm for contrastive Principal Component Analysis](https://mlsanity.com/paper/2211.07723/) (2022)
- [Duality Principle and Biologically Plausible Learning: Connecting the Representer Theorem and Hebbian Learning](https://mlsanity.com/paper/2309.16687/) (2023)
- [A Neural Network with Local Learning Rules for Minor Subspace Analysis](https://mlsanity.com/paper/2102.05501/) (2021)
- [Flexible Online Representation Learning Based on Similarity Matching](https://mlsanity.com/paper/2606.01546/) (2026)

## Abstract (arXiv)

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.