将平衡传播拓展至波动系统，实现局部参数调控下的稳定训练。
Near-Equilibrium Propagation training in nonlinear wave systems
- 用可调局域势替代节点间连接，适配无明确节点的物理系统
- 在弱耗散条件下实现稳定收敛，支持逻辑运算与手写数字识别
- 适合硬件受限、仅能调节局部参数的物理神经网络
反向传播是现代人工智能的核心学习算法，但在物理神经网络中难以实现。平衡传播（EP）是一种效率相当且具备原位训练潜力的替代方案。本文将EP推广至离散与连续复值波系统，在弱耗散条件下有效，适用于广泛物理场景，即使缺乏明确节点结构，也可用可调局域势替代可训练的节点间连接。我们在受驱耗散的激子-极化子凝聚体（由广义格罗斯-皮塔耶夫斯基动力学支配）中测试该方法。数值实验在标准基准任务（包括简单逻辑任务和手写数字识别）上均实现稳定收敛，为受限于局部参数控制的物理系统提供了可行的原位学习路径。
原文摘要 · Abstract (English)
Backpropagation learning algorithm, the workhorse of modern artificial intelligence, is notoriously difficult to implement in physical neural networks. Equilibrium Propagation (EP) is an alternative with comparable efficiency and strong potential for in-situ training. We extend EP learning to both discrete and continuous complex-valued wave systems. In contrast to previous EP implementations, our scheme is valid in the weakly dissipative regime, and readily applicable to a wide range of physical settings, even without well defined nodes, where trainable inter-node connections can be replaced by trainable local potential. We test the method in driven-dissipative exciton-polariton condensates governed by generalized Gross-Pitaevskii dynamics. Numerical studies on standard benchmarks, including a simple logical task and handwritten-digit recognition, demonstrate stable convergence, establishing a practical route to in-situ learning in physical systems in which system control is restricted to local parameters.
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