The Brain’s Learning Algorithm, Formally Solved: Convergence Across Three Timescales
A recent breakthrough in biologically plausible neural networks has provided the first complete convergence proof for the Similarity Matching Network, a system of three coupled dynamics—neural, lateral synaptic, and feedforward synaptic—evolving at fast, intermediate, and slow timescales. Drawing on Hebbian and anti-Hebbian learning rules, the researchers leveraged a multilevel optimization framework to demonstrate global exponential convergence at the first two levels and almost sure convergence to global minima at the third, despite its nonconvex and nonsmooth cost function. This formal analysis, long elusive in computational neuroscience, bridges the gap between biological plausibility and mathematical rigor, and suggests that the brain may implement dimensionality reduction through a principled, provably stable optimization process.
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