# Biologically plausible single-layer networks for nonnegative independent component analysis

arXiv: https://arxiv.org/abs/2010.12632 · HTML: https://mlsanity.com/paper/2010.12632/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Disentanglement with Biological Constraints: A Theory of Functional Cell Types](https://mlsanity.com/paper/2210.01768/) (2022)
- [Biologically-Plausible Determinant Maximization Neural Networks for Blind Separation of Correlated Sources](https://mlsanity.com/paper/2209.12894/) (2022)
- [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 Based Biologically Plausible Neural Networks for Correlated Source Separation](https://mlsanity.com/paper/2210.04222/) (2022)
- [Adaptive whitening with fast gain modulation and slow synaptic plasticity](https://mlsanity.com/paper/2308.13633/) (2023)
- [Duality Principle and Biologically Plausible Learning: Connecting the Representer Theorem and Hebbian Learning](https://mlsanity.com/paper/2309.16687/) (2023)
- [Similarity Matching Networks: Hebbian Learning and Convergence Over Multiple Time Scales](https://mlsanity.com/paper/2506.06134/) (2025)

## Abstract (arXiv)

An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; (iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al. [Neural Computation, 29, 2925--2954 (2017)], which considers Nonnegative Independent Component Analysis (NICA), a special case of blind source separation that assumes the mixture is a linear combination of uncorrelated, nonnegative sources. They derive an algorithm with a biologically plausible 2-layer network implementation. In this work, we improve upon their result by deriving 2 algorithms for NICA, each with a biologically plausible single-layer network implementation. The first algorithm maps onto a network with indirect lateral connections mediated by interneurons. The second algorithm maps onto a network with direct lateral connections and multi-compartmental output neurons.