Role of Synaptic Stochasticity in Training Low-Precision Neural Networks

Physical Review Letters
Carlo BaldassiRiccardo Zecchina

Abstract

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension that allows to train discrete deep neural networks is also investigated.

References

Jul 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S CoccoR Zecchina
Mar 11, 1996·Physical Review Letters·M Opper, O Winther
Jun 29, 2005·Proceedings of the National Academy of Sciences of the United States of America·Daniel H O'ConnorSamuel S-H Wang
Feb 21, 2006·Physical Review Letters·Alfredo Braunstein, Riccardo Zecchina
Sep 30, 2006·Proceedings of the National Academy of Sciences of the United States of America·Yonatan Loewenstein, H Sebastian Seung
Jun 22, 2007·Proceedings of the National Academy of Sciences of the United States of America·Carlo BaldassiRiccardo Zecchina
Dec 11, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Haiping Huang, Yoshiyuki Kabashima
May 29, 2015·Nature·Yann LeCunGeoffrey Hinton
Jun 15, 2016·Physical Review. E·Carlo BaldassiRiccardo Zecchina
Nov 20, 2016·Proceedings of the National Academy of Sciences of the United States of America·Carlo BaldassiRiccardo Zecchina
Feb 1, 2018·Proceedings of the National Academy of Sciences of the United States of America·Carlo Baldassi, Riccardo Zecchina

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Citations

Dec 25, 2019·Proceedings of the National Academy of Sciences of the United States of America·Carlo BaldassiRiccardo Zecchina
Jul 18, 2021·Physical Review. E·Marco BenedettiGleb Oshanin

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