Kirchhoff-Inspired Neural Networks for Evolving High-Order Perception

TL;DR

This paper introduces Kirchhoff-Inspired Neural Networks (KINN), a novel architecture based on physical laws that enhances the encoding of dynamic, higher-order information in neural networks, improving PDE solving and image classification.

Contribution

The paper presents a new neural network design inspired by Kirchhoff's law, enabling explicit modeling of higher-order dynamics with improved stability and interpretability.

Findings

KINN outperforms existing methods in PDE solving.

KINN achieves superior accuracy in ImageNet classification.

The architecture maintains physical consistency and interpretability.

Abstract

Deep learning architectures are fundamentally inspired by neuroscience, particularly the structure of the brain's sensory pathways, and have achieved remarkable success in learning informative data representations. Although these architectures mimic the communication mechanisms of biological neurons, their strategies for information encoding and transmission are fundamentally distinct. Biological systems depend on dynamic fluctuations in membrane potential; by contrast, conventional deep networks optimize weights and biases by adjusting the strengths of inter-neural connections, lacking a systematic mechanism to jointly characterize the interplay among signal intensity, coupling structure, and state evolution. To tackle this limitation, we propose the Kirchhoff-Inspired Neural Network (KINN), a state-variable-based network architecture constructed based on Kirchhoff's current law. KINN derives numerically stable state updates from fundamental ordinary differential equations, enabling the explicit decoupling and encoding of higher-order evolutionary components within a single layer while preserving physical consistency, interpretability, and end-to-end trainability. Extensive experiments on partial differential equation (PDE) solving and ImageNet image classification validate that KINN outperforms state-of-the-art existing methods.