# Weakly-correlated synapses promote dimension reduction in deep neural networks

arXiv: https://arxiv.org/abs/2006.11569 · HTML: https://mlsanity.com/paper/2006.11569/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Decomposing neural networks as mappings of correlation functions](https://mlsanity.com/paper/2202.04925/) (2022)
- [Eight challenges in developing theory of intelligence](https://mlsanity.com/paper/2306.11232/) (2023)
- [Fermi-Bose Machine achieves both generalization and adversarial robustness](https://mlsanity.com/paper/2404.13631/) (2024)
- [Autoencoders with Intrinsic Dimension Constraints for Learning Low Dimensional Image Representations](https://mlsanity.com/paper/2304.07686/) (2023)

## Abstract (arXiv)

By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations remains elusive. Here we propose a simplified model of dimension reduction, taking into account pairwise correlations among synapses, to reveal the mechanism underlying how the synaptic correlations affect dimension reduction. Our theory determines the synaptic-correlation scaling form requiring only mathematical self-consistency, for both binary and continuous synapses. The theory also predicts that weakly-correlated synapses encourage dimension reduction compared to their orthogonal counterparts. In addition, these synapses slow down the decorrelation process along the network depth. These two computational roles are explained by the proposed mean-field equation. The theoretical predictions are in excellent agreement with numerical simulations, and the key features are also captured by a deep learning with Hebbian rules.