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

TL;DR

This paper extends the Information Processing Capacity framework to stationary physical systems, introduces data-efficient estimation methods, and demonstrates their effectiveness through a photonic computing experiment, linking physical dynamics to machine learning performance.

Contribution

It provides a theoretical extension of IPC, develops practical estimation techniques, and experimentally validates the approach on a photonic system, connecting physical properties to computational capacity.

Findings

IPC bounds are established and noise effects are characterized.

New data-efficient estimation methods are introduced and validated.

Total IPC correlates with machine learning task performance.

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.