发表机构
Central China Normal University（华中师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出生成式热力学计算的在线局部训练方法，利用局部残差相关性梯度即时更新，在MNIST模拟中达到与批量训练相当的验证损失且释放更少热量，并揭示了噪声结构与精度的影响。
AI 中文摘要
生成式热力学计算机通过朗之万动力学将热噪声转化为结构化数据。我们在每个积分步骤中采用局部更新来训练这些系统。反向路径的Onsager-Machlup目标产生一个耦合梯度，该梯度是局部残差状态相关性的对称和。我们立即应用该梯度，而不是在整个轨迹上累积它。在使用MNIST原型的数字模拟中，在线训练和轨迹批量训练在固定噪声路径上达到相似的验证损失。在所有五个独立种子的配对中，在线训练的模型在采样时平均释放更少的热量，且两个模型的参数在采样期间保持固定。辅助分类器和最近原型度量变化适中，而成对多样性下降。对噪声的响应强烈依赖于误差进入的位置：在形成的更新中，独立的零均值误差在有限的噪声幅度范围内产生很小的热量变化，而残差偏移和时间相关性则产生大得多的影响。存储训练后的耦合所需的精度远低于训练期间解析确定性更新所需的精度。总之，这些结果建立了一种局部在线训练方法，并展示了更新时机、噪声结构和精度如何影响生成式热力学计算。
英文摘要
Generative thermodynamic computers turn thermal noise into structured data through Langevin dynamics. We train these systems with a local update at each integration step. The reverse-path Onsager-Machlup objective yields a coupling gradient that is a symmetric sum of local residual-state correlations. We apply this gradient immediately rather than accumulating it over a full trajectory. In digital simulations using MNIST prototypes, online and trajectory-batch training reach similar validation losses on fixed noising paths. Models trained online release less heat on average in all five independently seeded pairs, with both models' parameters held fixed during sampling. Auxiliary classifier and nearest-prototype measures change modestly, while pairwise diversity decreases. The response to noise depends strongly on where the errors enter: independent zero-mean errors in the formed updates produce little heat change over a finite range of noise amplitudes, whereas residual offset and temporal correlation have much larger effects. Storing trained couplings requires substantially less precision than resolving deterministic updates during training. Together, these results establish a local online training method and show how update timing, noise structure, and precision affect generative thermodynamic computing.
