Moment-Resolved Readout and Reservoir Diversity in Nonequilibrium Langevin Computing

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.