KO: Kinetics-inspired Neural Optimizer with PDE Simulation Approaches

2025-05-20

AI Summary

Addressing parameter collapse—a critical challenge in neural network optimization where parameters concentrate into low-dimensional subspaces—this paper proposes KO (Kinetics-inspired Optimizer), the first optimizer to integrate kinetic theory and numerical solutions of the Boltzmann Transport Equation (BTE). KO models parameter updates as the evolution of a stochastic particle system governed by physical laws: particle collisions enhance parameter diversity, while an explicit thermal diffusion analogy suppresses collapse. The method ensures mathematical rigor and physical interpretability, providing both theoretical guarantees and intuitive dynamical insights. Evaluated on benchmark datasets—including CIFAR, ImageNet, IMDB, and Snips—KO consistently outperforms Adam and SGD in accuracy, with comparable computational overhead.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Designing optimization algorithms for neural networks beyond heuristic gradient-based methods
• Addressing parameter condensation by modeling training dynamics with kinetic theory
• Improving accuracy in image and text classification tasks with physics-inspired optimizer

Innovation

• Kinetics-inspired optimizer using particle system dynamics
• PDE simulation with Boltzmann transport equation
• Thermal diffusion analogy prevents parameter condensation