Kirchhoff-Inspired Neural Networks for Evolving High-Order Perception

2026-03-25

AI Summary

Existing deep networks struggle to systematically model the synergistic mechanisms among signal strength, coupling structure, and state evolution, limiting their capacity for higher-order dynamic perception. This work proposes a novel neural architecture grounded in Kirchhoff’s Current Law, introducing circuit-theoretic physical principles into deep learning for the first time. By leveraging ordinary differential equations, the framework enables numerically stable intra-layer state updates that explicitly disentangle and encode higher-order dynamic components. The resulting model maintains physical consistency, interpretability, and end-to-end differentiability, supporting higher-order dynamics modeling within a single layer. Empirical evaluations demonstrate its superiority over state-of-the-art methods in both partial differential equation solving and ImageNet image classification tasks.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• neural networks
• information encoding
• state evolution
• biological neurons
• deep learning

Innovation

• Kirchhoff-Inspired Neural Network
• state-variable-based architecture
• high-order perception
• ordinary differential equations
• physical consistency