通过物理守恒约束，显著减少模块化神经网络中的误差传播。
Energy-Conserved Neural Pipelines: Attenuating Error Propagation in Modular Neural Networks via Physical Conservation Constraints
- 在模块边界强制激活能量守恒，杜绝能量增减
- 噪声下准确率保持77.4%，远超基线模型的30%~35%
- 适用于机器人控制等真实系统，且对正则化无负面影响
模块化神经网络易因误差累积导致性能下降。本文引入能量守恒作为硬性物理约束，要求每个模块边界的激活能量（特征向量的L2范数平方）严格保持不变。与软性惩罚不同，该约束不可违反：网络可重新分配能量，但不能创造或销毁。在CIFAR-10上的四组实验表明：（1）噪声标准差σ=0.2时，守恒模型保留77.4%干净准确率，远高于基线35.1%和能量惩罚模型30.9%（p<0.001，5次种子）；（2）网络深度不变性显著提升，在2~5层深度下仍保持93.3%准确率；（3）优势对系统性偏移、高斯噪声、对抗噪声均有效，对丢弃法影响极小（-0.3%）；（4）在无批归一化的ResNet-18上，σ=0.2时提升26.2个百分点，σ=0.5时达58.0个百分点。第五项实验在真实机器人系统（MuJoCo物理模拟，Franka Panda）中验证，三轮独立测试共90次试验，守恒策略平均提升18.9个百分点。理论证明：守恒后的噪声能量严格小于输入噪声能量。
原文摘要 · Abstract (English)
Modular neural network pipelines suffer from error compounding: noise at any module boundary propagates and potentially amplifies through subsequent modules. We introduce energy conservation as a hard physical constraint on inter-module information flow. Activation energy (the squared L2 norm of feature vectors) is enforced to be exactly preserved at every module boundary. Unlike soft energy penalties, conservation is an inviolable law: the network may redistribute energy across neurons but cannot create or destroy it. Four experiments on CIFAR-10 demonstrate: (1) conservation retains 77.4% of clean accuracy at noise sigma=0.2, versus 35.1% for baselines and 30.9% for energy-penalized models (p<0.001, 5 seeds); (2) pipelines become depth-invariant, retaining 93.3% at depths 2 through 5 with noise at every boundary; (3) the advantage generalizes to systematic bias (+45.1%), Gaussian (+40.4%), and adversarial noise (+4.8%), with a principled non-effect on dropout (-0.3%); (4) on ResNet-18, the conservation advantage scales inversely with intrinsic normalization: +0.3 pp with BatchNorm, +26.2 pp without at sigma=0.2, reaching +58.0 pp at sigma=0.5. Experiment 5 validates the operator on a real modular robotic pipeline (MuJoCo physics, Franka Panda). Across three independent runs on separate machines (90 trials per cell), conservation provides +18.9 pp average advantage on monocular-depth-style noise. A formal bound proves conserved noise energy is strictly less than input noise energy.
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