Energy-Conserved Neural Pipelines: Attenuating Error Propagation in Modular Neural Networks via Physical Conservation Constraints

2026-06-09

AI Summary

This work addresses the issue of error accumulation in modular neural networks caused by inter-module noise propagation. It introduces, for the first time, the physical principle of energy conservation as a hard constraint on information transfer between modules, enforcing strict conservation of the squared L2 norm of feature activations—interpreted as activation energy—to theoretically suppress noise propagation. The proposed method integrates this energy-conserving activation constraint with a deep modular architecture and a ResNet-18 variant. Evaluated on CIFAR-10 with input noise of standard deviation 0.2, it achieves a substantial accuracy improvement from the baseline 35.1% to 77.4%, with 93.3% depth invariance. Further experiments on MuJoCo robotic simulation and real-world pipeline tasks demonstrate an average performance gain of 18.9 percentage points.

Abstract

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.

Problem

• error propagation
• modular neural networks
• noise amplification
• energy conservation
• module boundaries

Innovation

• energy conservation
• modular neural networks
• error propagation
• physical constraints
• noise robustness