KO: Kinetics-inspired Neural Optimizer with PDE Simulation Approaches
This addresses the problem of parameter condensation in neural network optimization for researchers and practitioners, offering a novel physics-driven approach that is incremental in its application to existing tasks.
The paper tackled the challenge of designing optimization algorithms for neural networks by introducing KO, a kinetics-inspired optimizer that reimagines training dynamics as particle evolution governed by kinetic principles, achieving accuracy improvements on tasks like CIFAR-10/100 and ImageNet with comparable computation costs.
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.