# Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sources

arXiv: https://arxiv.org/abs/2209.12894 · HTML: https://mlsanity.com/paper/2209.12894/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 68 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 19 of 19)

- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [Neuroscience-inspired online unsupervised learning algorithms](https://mlsanity.com/paper/1908.01867/) (2019)
- [Maximum Volume Inscribed Ellipsoid: A New Simplex-Structured Matrix Factorization Framework via Facet Enumeration and Convex Optimization](https://mlsanity.com/paper/1708.02883/) (2017)
- [Polytopic Matrix Factorization: Determinant Maximization Based Criterion and Identifiability](https://mlsanity.com/paper/2202.09638/) (2022)
- [A Normative Theory of Adaptive Dimensionality Reduction in Neural Networks](https://mlsanity.com/paper/1511.09426/) (2015)
- [Blind nonnegative source separation using biological neural networks](https://mlsanity.com/paper/1706.00382/) (2017)
- [A Hebbian/Anti-Hebbian Network Derived from Online Non-Negative Matrix Factorization Can Cluster and Discover Sparse Features](https://mlsanity.com/paper/1503.00680/) (2015)
- [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 Online Principal Component Analysis Without Recurrent Neural Dynamics](https://mlsanity.com/paper/1810.06966/) (2018)
- [A Spiking Neural Network with Local Learning Rules Derived From Nonnegative Similarity Matching](https://mlsanity.com/paper/1902.01429/) (2019)
- [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)
- [Bayesian anti-sparse coding](https://mlsanity.com/paper/1512.06086/) (2015)
- [Disorder and the neural representation of complex odors: smelling in the real world](https://mlsanity.com/paper/1707.01962/) (2017)
- [What the odor is not: Estimation by elimination](https://mlsanity.com/paper/1903.02580/) (2019)

## Built on by (most cited first, 6 of 6)

- [Disentanglement with Biological Constraints: A Theory of Functional Cell Types](https://mlsanity.com/paper/2210.01768/) (2022)
- [Range, not Independence, Drives Modularity in Biologically Inspired Representations](https://mlsanity.com/paper/2410.06232/) (2024)
- [Correlative Information Maximization Based Biologically Plausible Neural Networks for Correlated Source Separation](https://mlsanity.com/paper/2210.04222/) (2022)
- [Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetry](https://mlsanity.com/paper/2306.04810/) (2023)
- [Determinantal Point Process Attention Over Grid Cell Code Supports Out of Distribution Generalization](https://mlsanity.com/paper/2305.18417/) (2023)
- [Normative Networks for Source Separation via Local Plasticity and Dendritic Computation](https://mlsanity.com/paper/2605.19965/) (2026)

## Abstract (arXiv)

Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.