Spike-timing-dependent Hebbian learning as noisy gradient descent

Fuente: arXiv
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Auteurs principaux: Dexheimer, Niklas, Gaudlitz, Sascha, Schmidt-Hieber, Johannes
Format: Preprint
Publié: 2025
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author Dexheimer, Niklas
Gaudlitz, Sascha
Schmidt-Hieber, Johannes
author_facet Dexheimer, Niklas
Gaudlitz, Sascha
Schmidt-Hieber, Johannes
contents Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability simplex. Despite the constant injection of noise and the non-convexity of the underlying optimization problem, one can rigorously prove that the considered Hebbian learning dynamic identifies the presynaptic neuron with the highest activity and that the convergence is exponentially fast in the number of iterations. This is non-standard and surprising as typically noisy gradient descent with fixed noise level only converges to a stationary regime where the noise causes the dynamic to fluctuate around a minimiser.
format Preprint
id arxiv_https___arxiv_org_abs_2505_10272
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Spike-timing-dependent Hebbian learning as noisy gradient descent
Dexheimer, Niklas
Gaudlitz, Sascha
Schmidt-Hieber, Johannes
Machine Learning
Statistics Theory
Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability simplex. Despite the constant injection of noise and the non-convexity of the underlying optimization problem, one can rigorously prove that the considered Hebbian learning dynamic identifies the presynaptic neuron with the highest activity and that the convergence is exponentially fast in the number of iterations. This is non-standard and surprising as typically noisy gradient descent with fixed noise level only converges to a stationary regime where the noise causes the dynamic to fluctuate around a minimiser.
title Spike-timing-dependent Hebbian learning as noisy gradient descent
topic Machine Learning
Statistics Theory
url https://arxiv.org/abs/2505.10272