Deep Regularized RNNs for Virtual Analog Modeling

Physical neural networks offer a transformative route to edge intelligence, providing superior inference speed and energy efficiency compared to conventional digital architectures. However, realizing scalable, end-to-end, fully analog recurrent neural networks for temporal information processing remains challenging due to the difficulty of faithfully mapping trained network models onto physical hardware. Here we present a fully analog resonant recurrent neural network (R$^2$NN) implemented via a metacircuit architecture composed of coupled electrical local resonators. A reformulated mechanical-electrical analogy establishes a direct mapping between the R$^2$NN model and metacircuit elements, enabling accurate physical implementation of trained neural network parameters. By integrating jointly trainable global resistive coupling and local resonances, which generate effective frequency-dependent negative resistances, the architecture shapes an impedance landscape that steers currents along frequency-selective pathways. This mechanism enables direct extraction of discriminative spectral features, facilitating real-time temporal classification of raw analog inputs while bypassing analog-to-digital conversion. We demonstrate the cross-domain versatility of this framework using integrated hardware for tactile perception, speech recognition, and condition monitoring. This work establishes a scalable, fully analog paradigm for intelligent temporal processing and paves the way for low-latency, resource-efficient physical neural hardware for edge intelligence.

Analog hardware platforms such as coupled oscillators and Analog Ising Machines naturally solve differential equations at a fraction of the energy cost of digital computation, making them attractive for low-power generative modeling, yet a fundamental mismatch exists: modern generative models assume flexible, software-defined dynamics, whereas analog hardware imposes fixed, physics-determined differential equations with limited approximation capacity. This paper introduces Analog Interaction Systems (AIS), a unified framework for hardware-implementable dynamical systems, and empirically characterizes their expressivity gap relative to neural network baselines. Two hardware-compatible mechanisms are proposed to narrow this gap - time-varying piecewise parameters and hidden physical states - and a Wasserstein GAN training procedure is developed to enable training of these models without requiring them to follow a specific trajectory. We characterize how area and power scale with connection density and precision, showing that sparse connectivity and low-bit-width quantized parameters are necessary for practical implementation, and estimate an energy cost of 23uJ per generated image for the chosen architecture, representing a 2-orders-of-magnitude improvement over digital baselines. On MNIST and Fashion-MNIST, our oscillator-based AIS achieves FID scores of 27.6 and 80.8, outperforming the best prior hardware-implementable analog generative models by 3-4x with a 4-bit sparse architecture.

The energy efficiency of analog computing makes it one of the most promising candidates for deploying resource-intensive machine learning workloads on constrained platforms such as mobile and embedded devices. However, analog accelerators are inherently susceptible to noise and non-idealities arising from physical component variations, whose behavior is further sensitive to environmental factors. These effects can significantly degrade inference accuracy. In this work, we conduct a comprehensive experimental study on a representative example of analog hardware to investigate the impact of temperature. We first characterize the behavior of stochastic and systematic non-idealities across a range of operating temperatures. Following this, we compare a set of simulation-based and hardware-based mitigation strategies aimed at improving robustness against temperature-induced performance degradation. Our results suggest that temperature-induced degradation is driven primarily by systematic non-idealities rather than stochastic noise alone. Noise-aware training improves robustness, while hardware-in-the-loop training and temperature-aware calibration provide the strongest accuracy retention across varying thermal conditions.