发表机构
Hong Kong Shue Yan University; Beijing Normal-Hong Kong Baptist University; University of the Witwatersrand（香港树仁大学; 北京师范大学-香港浸会大学联合国际学院; 金山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探究物理学习系统的轨迹决定因素，构建有向分层传输网络模型，发现互惠性可分离梯度流与旋转，揭示守恒、互惠性及非互惠性在物理学习中的不同作用。
AI 中文摘要
物理学习允许可训练材料或网络利用自身物理响应传递误差信号，减少对单独编程的反向计算的需求。我们探究决定此类系统是遵循传统梯度下降还是沿完全不同的学习轨迹演化的因素。我们的典型模型是有向分层传输网络，其中每个节点重新分配固定数量的流，因此学习过程保持正性和总质量。在该模型中，守恒仅约束允许的学习方向。在本文研究的匹配响应类别中，伴随匹配使物理输出响应呈现对称形式。非负逐模式反馈随后产生互惠闭环响应和重新加权的梯度流。添加反对称边界分量使闭环响应具有旋转性：学习路径可以转向，而驱动该更新的误差在该时刻仍在减小。转向并非自动有益，其有限步效应由局部曲率决定，累积效应还取决于步长选择以及沿路径访问的新状态。数值一致性检查再现了精确的响应结构，预测了跨新网络家族的局部效应符号，并表明轨迹漂移如何抵消局部优势。这些结果分离了物理学习中守恒、互惠性和非互惠性的作用。
英文摘要
Physical learning lets a trainable material or network use its own physical response to carry error signals, reducing the need for a separately programmed backward computation. We ask what determines whether such a system follows conventional gradient descent or evolves along a genuinely different learning trajectory. Our canonical model is a directed layered transport network in which every node redistributes a fixed amount of flow, so learning preserves positivity and total mass. In this model, conservation constrains only the allowable learning directions. Within the matched response class studied here, adjoint matching gives the physical output response a symmetric form. Non-negative mode-wise feedback then produces a reciprocal closed-loop response and a reweighted gradient flow. Adding an antisymmetric boundary component makes the closed-loop response rotational: the learning path can turn while the error driving that update still decreases at that moment. Turning is not automatically beneficial. Its finite-step effect is set by local curvature, and its accumulated effect also depends on step selection and on the new states visited along the path. Numerical consistency checks reproduce the exact response structure, predict the sign of the local effect across new network families, and show how trajectory drift can negate a local advantage. These results separate the roles of conservation, reciprocity, and nonreciprocity in physical learning.
