Log-Normal Multiplicative Dynamics for Stable Low-Precision Training of Large Networks
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 35 of its 64 references that are in the map. First posted on arXiv 21 Jun 2025.
Builds on
35 of 64 references.
References · 35
- 2017Attention Is All You Needcited by 60,361
- 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 30,186
- 2017Mixed Precision Trainingcited by 1,156
- 2020Up or Down? Adaptive Rounding for Post-Training Quantizationcited by 621
- 2018signSGD: Compressed Optimisation for Non-Convex Problemscited by 571
- 2015Weight Uncertainty in Neural Networkscited by 554
- 2015Variational Dropout and the Local Reparameterization Trickcited by 490
- 2023Symbolic Discovery of Optimization Algorithmscited by 434
- 2015Deep Learning with Limited Numerical Precisioncited by 376
- 2019A Study of BFLOAT16 for Deep Learning Trainingcited by 232
- 2022FP8 Formats for Deep Learningcited by 196
- 2018Training Deep Neural Networks with 8-bit Floating Point Numberscited by 164
23 more
- 2023Microscaling Data Formats for Deep Learningcited by 152
- 2018Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batchescited by 133
- 2018Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adamcited by 131
- 2016Convolutional Neural Networks using Logarithmic Data Representationcited by 99
- 2021The Bayesian Learning Rulecited by 99
- 2023FP8-LM: Training FP8 Large Language Modelscited by 77
- 2024Variational Learning is Effective for Large Deep Networkscited by 65
- 2025Optimizing Large Language Model Training Using FP4 Quantizationcited by 56
- 2023With Shared Microexponents, A Little Shifting Goes a Long Waycited by 50
- 2022Anticorrelated Noise Injection for Improved Generalizationcited by 42
- 2022Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscapecited by 39
- 2025Training LLMs with MXFP4cited by 37
- 2019Exponentiated Gradient Meets Gradient Descentcited by 32
- 2020Learning compositional functions via multiplicative weight updatescited by 20
- 2015Network Plasticity as Bayesian Inferencecited by 13
- 2020Understanding Decoupled and Early Weight Decaycited by 12
- 2022Low-Precision Stochastic Gradient Langevin Dynamicscited by 12
- 2024Collage: Light-Weight Low-Precision Strategy for LLM Trainingcited by 10
- 2024Exploring Quantization for Efficient Pre-Training of Transformer Language Modelscited by 10
- 2021LNS-Madam: Low-Precision Training in Logarithmic Number System using Multiplicative Weight Updatecited by 7
- 2024Improving robustness to corruptions with multiplicative weight perturbationscited by 7
- 2023The Lie-Group Bayesian Learning Rulecited by 3
- 2024Ex Uno Pluria: Insights on Ensembling in Low Precision Number Systemscited by 1
Built on by
Citing papers per year: 2026: 2.
2 papers.