Moment-Resolved Readout and Reservoir Diversity in Nonequilibrium Langevin Computing

Abstract

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.