AI 中文总结
研究基于朗之万动力学的非线性热力学计算机，将读出范式从均值扩展到矩分辨，引入异构多储层架构，通过特征级融合在MNIST数据再现中取得高准确率，为有限时间朗之万计算提供候选设计原则。
AI 中文摘要
基于朗之万动力学的非线性热力学计算机利用热涨落作为计算的物理基础。近期工作表明，四次方受限的涨落自由度可作为能在有限观测时间进行非线性函数逼近的热力学神经元。本文将该范式从仅均值读出扩展到矩分辨读出，构建了由元素级原始多项式矩构成的响应向量。还引入了异构多储层架构，在固定的MNIST数据再现协议下，特征级融合取得了96.95%的最佳观测准确率。结果表明高阶多项式矩读出和储层异构性可作为有限时间朗之万计算的候选设计原则。
英文摘要
Nonlinear thermodynamic computers based on Langevin dynamics exploit thermal fluctuations as a physical substrate for computation. Recent work has shown that quartic-confined fluctuating degrees of freedom can act as thermodynamic neurons capable of nonlinear function approximation at finite observation times. Here we extend this paradigm from mean-only readout to moment-resolved readout. Instead of representing each driven reservoir solely by its first moment, we construct a response vector from the elementwise raw polynomial moments \(\mathbb{E}[\bm{x}]\), \(\mathbb{E}[\bm{x}^{\odot 2}]\), and \(\mathbb{E}[\bm{x}^{\odot 4}]\). These observables combine displacement and central-shape contributions and are naturally aligned with the linear, quadratic, and quartic terms of the local driven dynamics. We further introduce a heterogeneous multi-reservoir architecture in which three reservoirs with distinct initialization and training histories form a joint \(2304\)-dimensional response representation. Under the fixed MNIST \(60000/10000\) reproduction protocol, feature-level fusion achieves the best observed accuracy of \(9695/10000=96.95\%\), compared with \(9682/10000=96.82\%\) for the strongest single-reservoir model and \(9684/10000=96.84\%\) for equal-weight logit averaging. An exact paired McNemar test does not establish a statistically significant improvement over the strongest single reservoir, but the ablation and wrong-set overlap results provide suggestive evidence of complementary classification errors. These results motivate higher-order polynomial-moment readout and reservoir heterogeneity as candidate design principles for finite-time Langevin computing.
