Neural Langevin Machine: a local asymmetric learning rule can be creative

arXiv:2506.23546 · q-bio.NC, cond-mat.dis-nn, cs.LG, cs.NE · Submitted 2025-06-30 · Read on arXiv

q-bio.NC, cond-mat.dis-nn, cs.LG, cs.NE

Submitted: 2025-06-30

Updated: 2026-09-17

Comments: 23 pages, 15 figures, submitted to Phys Rev E

Code: https://github.com/yuzd610/Neural-Langevin-Machine

License: http://creativecommons.org/licenses/by/4.0/

The gist: Fixed points of recurrent neural networks can be leveraged to store and generate information.

Terminology

Abstract

Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points are captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that relax to those fixed points for generative learning of a real dataset. We call this type of generative model a neural Langevin machine, which derives an asymmetric and firing-rate-speed-adjusted learning rule requiring only local neural signals, thereby bearing biological relevance in terms of local predictive learning. An out-of-equilibrium regime of the generative process is revealed, together with a memorization-to-generalization transition with increasing training data size. The neuro-inspired machine can also realize a continuous exploration of the phase space for different kinds of generative images and can denoise a corrupted image as well.

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