# Correlative Information Maximization Based Biologically Plausible Neural Networks for Correlated Source Separation

arXiv: https://arxiv.org/abs/2210.04222 · HTML: https://mlsanity.com/paper/2210.04222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 9 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [On Disentangled Representations Learned From Correlated Data](https://mlsanity.com/paper/2006.07886/) (2020)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [Self-Supervised Learning with an Information Maximization Criterion](https://mlsanity.com/paper/2209.07999/) (2022)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering](https://mlsanity.com/paper/1608.04290/) (2016)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithms](https://mlsanity.com/paper/2007.11446/) (2020)
- [Why do similarity matching objectives lead to Hebbian/anti-Hebbian networks?](https://mlsanity.com/paper/1703.07914/) (2017)
- [Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiability](https://mlsanity.com/paper/2202.09638/) (2022)
- [Blind nonnegative source separation using biological neural networks](https://mlsanity.com/paper/1706.00382/) (2017)
- [Biologically plausible single-layer networks for nonnegative independent component analysis](https://mlsanity.com/paper/2010.12632/) (2020)
- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [An Information Maximization Based Blind Source Separation Approach for Dependent and Independent Sources](https://mlsanity.com/paper/2205.00794/) (2022)
- [Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sources](https://mlsanity.com/paper/2209.12894/) (2022)
- [Blind Bounded Source Separation Using Neural Networks with Local Learning Rules](https://mlsanity.com/paper/2004.05479/) (2020)
- [On Identifiable Polytope Characterization for Polytopic Matrix Factorization](https://mlsanity.com/paper/2204.11534/) (2022)

## Built on by (most cited first, 3 of 3)

- [Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetry](https://mlsanity.com/paper/2306.04810/) (2023)
- [Normative Networks for Source Separation via Local Plasticity and Dendritic Computation](https://mlsanity.com/paper/2605.19965/) (2026)
- [Score Broadcast and Decorrelation: A General Framework for Broadcast-Based Credit Assignment](https://mlsanity.com/paper/2605.30638/) (2026)

## Abstract (arXiv)

The brain effortlessly extracts latent causes of stimuli, but how it does this at the network level remains unknown. Most prior attempts at this problem proposed neural networks that implement independent component analysis which works under the limitation that latent causes are mutually independent. Here, we relax this limitation and propose a biologically plausible neural network that extracts correlated latent sources by exploiting information about their domains. To derive this network, we choose maximum correlative information transfer from inputs to outputs as the separation objective under the constraint that the outputs are restricted to their presumed sets. The online formulation of this optimization problem naturally leads to neural networks with local learning rules. Our framework incorporates infinitely many source domain choices and flexibly models complex latent structures. Choices of simplex or polytopic source domains result in networks with piecewise-linear activation functions. We provide numerical examples to demonstrate the superior correlated source separation capability for both synthetic and natural sources.