KO: Kinetics-inspired Neural Optimizer with PDE Simulation Approaches

• URL: http://arxiv.org/abs/2505.14777v1
• Date: Tue, 20 May 2025 18:00:01 GMT
• Title: KO: Kinetics-inspired Neural Optimizer with PDE Simulation Approaches
• Authors: Mingquan Feng, Yixin Huang, Yifan Fu, Shaobo Wang, Junchi Yan,
• Abstract summary: This paper introduces KO, a novel neural gradient inspired by kinetic theory and partial differential equation (PDE) simulations.<n>We reimagine the dynamics of network parameters as the evolution of a particle system governed by kinetic principles.<n>This physics-driven approach inherently promotes parameter diversity during optimization, mitigating the phenomenon of parameter condensation.
• Score: 45.173398806932376
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The design of optimization algorithms for neural networks remains a critical challenge, with most existing methods relying on heuristic adaptations of gradient-based approaches. This paper introduces KO (Kinetics-inspired Optimizer), a novel neural optimizer inspired by kinetic theory and partial differential equation (PDE) simulations. We reimagine the training dynamics of network parameters as the evolution of a particle system governed by kinetic principles, where parameter updates are simulated via a numerical scheme for the Boltzmann transport equation (BTE) that models stochastic particle collisions. This physics-driven approach inherently promotes parameter diversity during optimization, mitigating the phenomenon of parameter condensation, i.e. collapse of network parameters into low-dimensional subspaces, through mechanisms analogous to thermal diffusion in physical systems. We analyze this property, establishing both a mathematical proof and a physical interpretation. Extensive experiments on image classification (CIFAR-10/100, ImageNet) and text classification (IMDB, Snips) tasks demonstrate that KO consistently outperforms baseline optimizers (e.g., Adam, SGD), achieving accuracy improvements while computation cost remains comparable.

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