# Neuronal Correlation: a Central Concept in Neural Network

arXiv: https://arxiv.org/abs/2201.09069 · HTML: https://mlsanity.com/paper/2201.09069/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 22 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Estimating Mixture Entropy with Pairwise Distances](https://mlsanity.com/paper/1706.02419/) (2017)
- [Caveats for information bottleneck in deterministic scenarios](https://mlsanity.com/paper/1808.07593/) (2018)
- [How does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks](https://mlsanity.com/paper/2010.05983/) (2020)
- [Scalable Kernel K-Means Clustering with Nystrom Approximation: Relative-Error Bounds](https://mlsanity.com/paper/1706.02803/) (2017)
- [Information Plane Analysis of Deep Neural Networks via Matrix-Based Renyi's Entropy and Tensor Kernels](https://mlsanity.com/paper/1909.11396/) (2019)
- [Nonparanormal Information Estimation](https://mlsanity.com/paper/1702.07803/) (2017)

## Built on by (most cited first, 2 of 2)

- [Exploring Cross-model Neuronal Correlations in the Context of Predicting Model Performance and Generalizability](https://mlsanity.com/paper/2408.08448/) (2024)
- [On the Adversarial Vulnerabilities of Transfer Learning in Remote Sensing](https://mlsanity.com/paper/2501.11462/) (2025)

## Abstract (arXiv)

This paper proposes to study neural networks through neuronal correlation, a statistical measure of correlated neuronal activity on the penultimate layer. We show that neuronal correlation can be efficiently estimated via weight matrix, can be effectively enforced through layer structure, and is a strong indicator of generalisation ability of the network. More importantly, we show that neuronal correlation significantly impacts on the accuracy of entropy estimation in high-dimensional hidden spaces. While previous estimation methods may be subject to significant inaccuracy due to implicit assumption on neuronal independence, we present a novel computational method to have an efficient and authentic computation of entropy, by taking into consideration the neuronal correlation. In doing so, we install neuronal correlation as a central concept of neural network.