通过电路启发的高阶结构，提升神经网络对动态过程的建模能力。
Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception
- 用基尔霍夫启发的级联单元构建高阶动态算子，实现可解释的表示演化。
- 在物理预测和图像识别任务中，比普通堆叠更稳定、精度更高。
- 适合需要精确建模动态系统或高阶导数敏感任务的研究者使用。
深度网络常依赖架构直觉来塑造表征演化，限制了其对内在动力学数据的建模能力。本文提出电路启发的高阶神经网络（CHONN），将表征演化视为潜在势能过程，并通过基尔霍夫启发的级联组合提升其有效阶数。单个基尔霍夫神经单元实现稳定的低阶更新，串行组合后可在单一模块内形成高阶动力学算子。该结构具有可解释性、数值稳定性，并兼容常见神经主干。理论分析表明，级联单元可诱导端到端高阶算子；控制实验显示，模块内高阶构造与通用深度堆叠存在差异，尤其在导数敏感指标上表现突出。在稳态算子学习、长时程物理预测和ImageNet-1K图像分类任务中，CHONN均提升了结构保真度、滚动稳定性与视觉表征学习性能。结果表明，高阶电路组合是神经动力学建模的一般原则。
原文摘要 · Abstract (English)
Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potential process and increases its effective order through Kirchhoff-inspired cascade composition. A single Kirchhoff Neural Cell implements a stable first-order update, while serially composed cells form higher-order dynamical operators within one block. This construction is interpretable, numerically stable and compatible with common neural backbones. Theoretical analysis shows that cascaded cells induce end-to-end high-order operators, and controlled experiments demonstrate that intra-block high-order construction differs from generic depth stacking, especially on derivative-sensitive measures. Across steady-state operator learning, long-horizon physical forecasting and ImageNet-1K recognition, CHONN improves structural fidelity, rollout stability and visual representation learning. These results identify high-order circuit composition as a general principle for neural dynamics modeling.
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