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Extraction of latent sources of complex stimuli is critical for making senseof the world. While the brain solves this blind source separation (BSS) problemcontinuously, its algorithms remain unknown. Previous work onbiologically-plausible BSS algorithms assumed that observed signals are linearmixtures of statistically independent or uncorrelated sources, limiting thedomain of applicability of these algorithms. To overcome this limitation, wepropose novel biologically-plausible neural networks for the blind separationof potentially dependent/correlated sources. Differing from previous work, weassume some general geometric, not statistical, conditions on the sourcevectors allowing separation of potentially dependent/correlated sources.Concretely, we assume that the source vectors are sufficiently scattered intheir domains which can be described by certain polytopes. Then, we considerrecovery of these sources by the Det-Max criterion, which maximizes thedeterminant of the output correlation matrix to enforce a similar spread forthe source estimates. Starting from this normative principle, and using aweighted similarity matching approach that enables arbitrary lineartransformations adaptable by local learning rules, we derive two-layerbiologically-plausible neural network algorithms that can separate mixturesinto sources coming from a variety of source domains. We demonstrate that ouralgorithms outperform other biologically-plausible BSS algorithms on correlatedsource separation problems.

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