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

arXiv: https://arxiv.org/abs/2605.19152 · HTML: https://mlsanity.com/paper/2605.19152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 61 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 13 of 13)

- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Benchmarking Keyword Spotting Efficiency on Neuromorphic Hardware](https://mlsanity.com/paper/1812.01739/) (2018)
- [A Unifying Framework for Information Processing in Stochastically Driven Dynamical Systems](https://mlsanity.com/paper/1906.04608/) (2019)
- [Memory and forecasting capacities of nonlinear recurrent networks](https://mlsanity.com/paper/2004.11234/) (2020)
- [Deep Time-Delay Reservoir Computing: Dynamics and Memory Capacity](https://mlsanity.com/paper/2006.06322/) (2020)
- [Memory of recurrent networks: Do we compute it right?](https://mlsanity.com/paper/2305.01457/) (2023)
- [Short-term Memory of Deep RNN](https://mlsanity.com/paper/1802.00748/) (2018)
- [Master memory function for delay-based reservoir computers with single-variable dynamics](https://mlsanity.com/paper/2108.12643/) (2021)
- [Limitations of the recall capabilities in delay based reservoir computing systems](https://mlsanity.com/paper/2010.15562/) (2020)
- [Memory Capacity of Nonlinear Recurrent Networks: Is it Informative?](https://mlsanity.com/paper/2502.04832/) (2025)
- [Asymptotic evaluation of the information processing capacity in reservoir computing](https://mlsanity.com/paper/2502.15769/) (2025)
- [Deep photonic reservoir computing recurrent network](https://mlsanity.com/paper/2309.05246/) (2023)
- [Weak Kerr Nonlinearity Boosts the Performance of Frequency-Multiplexed Photonic Extreme Learning Machines: A Multifaceted Approach](https://mlsanity.com/paper/2312.12296/) (2023)

## Abstract (arXiv)

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.