Kirchhoff-Inspired Neural Networks for Evolving High-Order Perception
This addresses the problem of improving neural network interpretability and performance for researchers in computational physics and computer vision, though it appears incremental as it builds on existing neuroscience-inspired architectures.
The authors tackled the limitation of conventional deep networks lacking mechanisms to jointly characterize signal intensity, coupling structure, and state evolution by proposing Kirchhoff-Inspired Neural Networks (KINN), which outperformed state-of-the-art methods in PDE solving and ImageNet classification.
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.