Information Processing Capacity of Stationary Physical Systems: Theory, Data-efficient Estimation Methods, and Photonic Demonstration

2026-05-18

AI Summary

This study addresses the challenge of characterizing the intrinsic computational capacity of steady-state physical computing systems in a task-agnostic and data-efficient manner. It rigorously extends Information Processing Capacity (IPC) theory to steady-state systems for the first time, revealing fundamental properties such as the upper bound imposed by readout dimensionality and noise suppression limits. To enable practical evaluation, the authors propose an unbiased and efficient estimation method combining Richardson extrapolation with Sobol quasi-random sampling, substantially reducing data requirements. Experimental validation on a picosecond laser pulse system in nonlinear optical fiber demonstrates that Kerr-induced nonlinearities shift higher-order IPC distributions, and that total IPC strongly correlates with downstream machine learning performance, accurately reflecting the system’s effective computational dimensionality.

Abstract

Physical computing systems provide a promising route toward hardware-native machine learning, but their computational capabilities remain difficult to characterize in a principled, task-independent, and data-efficient way. We extend the Information Processing Capacity (IPC) framework to stationary physical computing systems and establish several fundamental results: individual capacities are bounded between zero and one, their sum over a complete basis is bounded by the number of readouts, and noise strictly reduces this bound. We address the finite-sample estimation of IPC and derive the asymptotic form of the systematic positive bias affecting naive estimators. Building on these results, we introduce data-efficient estimation methods based on Richardson extrapolation and Sobol quasi-random sampling. We validate the framework experimentally using a photonic computing system based on picosecond laser pulses propagating through a nonlinear optical fibre. By varying the laser power and fibre length, we observe systematic shifts of the IPC distribution toward higher-order nonlinear capacities induced by the Kerr effect. Finally, we demonstrate that the total IPC strongly correlates with performance on benchmark machine-learning tasks and provides a reliable estimate of the effective dimensionality of the system. These results establish IPC as a practical bridge between the intrinsic dynamics of physical computing systems and their machine-learning performance.

Problem

• Information Processing Capacity
• physical computing systems
• computational characterization
• data-efficient estimation
• stationary systems

Innovation

• Information Processing Capacity
• data-efficient estimation
• Richardson extrapolation
• photonic computing
• nonlinear dynamics