Generative Models on Analog Hardware with Dynamics

2026-06-25

AI Summary

This work addresses the limited expressivity of modern analog hardware, which is constrained by fixed differential equations and lags far behind software-defined generative models. To bridge this gap, the authors propose the Analog Interaction Systems (AIS) framework, which substantially enhances the representational capacity of analog dynamical systems through time-segmented tunable parameters and latent physical states. By integrating a Wasserstein GAN training strategy, AIS enables end-to-end trainable generative modeling without requiring trajectory alignment. This study presents the first systematic quantification of the expressivity gap between analog systems and neural networks and introduces a hardware-compatible mechanism to close it. On MNIST and Fashion-MNIST, the model achieves FID scores of 27.6 and 80.8, respectively—outperforming prior analog generative models by 3–4×—while consuming only 23 microjoules per image, offering two orders of magnitude energy savings over digital counterparts.

Abstract

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.

Problem

• generative models
• analog hardware
• dynamical systems
• expressivity gap
• hardware-software mismatch

Innovation

• Analog Interaction Systems
• hardware-efficient generative modeling
• time-varying parameters
• hidden physical states
• Wasserstein GAN training