Log-Normal Multiplicative Dynamics for Stable Low-Precision Training of Large Networks

TL;DR

This paper introduces Log-Normal Multiplicative Dynamics (LMD), a biologically inspired training algorithm that enables stable, accurate low-precision training of large neural networks like Vision Transformer and GPT-2.

Contribution

It derives a Bayesian learning rule leading to a new multiplicative update algorithm inspired by biological synapses, improving low-precision training stability.

Findings

LMD achieves stable training with low-precision computations.

LMD performs well on Vision Transformer and GPT-2.

The method is simple to implement, comparable to Adam.

Abstract

Studies in neuroscience have shown that biological synapses follow a log-normal distribution whose transitioning can be explained by noisy multiplicative dynamics. Biological networks can function stably even under dynamically fluctuating conditions arising due to unreliable synaptic transmissions. Here we ask: Is it possible to design similar multiplicative training in artificial neural networks? To answer this question, we derive a Bayesian learning rule that assumes log-normal posterior distributions over weights which gives rise to a new Log-Normal Multiplicative Dynamics (LMD) algorithm. The algorithm uses multiplicative updates with both noise and regularization applied multiplicatively. The method is as easy to implement as Adam and only requires one additional vector to store. Our results show that LMD achieves stable and accurate training-from-scratch under low-precision forward operations for Vision Transformer and GPT-2. These results suggest that multiplicative dynamics, a biological feature, may enable stable low-precision inference and learning on future energy-efficient hardware.