Reconstructing the information processing capacity of physical systems from noisy observations
Abstract
Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. In this work, we clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, we show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. We explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. We then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. We find the same advantage in a quantum reservoir subject to unavoidable measurement noise. Our results provide a general route to recovering the computational structure of noisy physical systems from finite observations.
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BibTeX
@misc{kotoku2026reconstructing,
title = {{Reconstructing the information processing capacity of physical systems from noisy observations}},
author = {Shun Kotoku and Rodrigo Martínez-Peña and Takatomo Mihana and Felix Köster and Johannes Nokkala and Lina Jaurigue and Ryoichi Horisaki and André Röhm},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11268},
eprint = {2609.11268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11268},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reconstructing the information processing capacity of physical systems from noisy observations
AU - Shun Kotoku
AU - Rodrigo Martínez-Peña
AU - Takatomo Mihana
AU - Felix Köster
AU - Johannes Nokkala
AU - Lina Jaurigue
AU - Ryoichi Horisaki
AU - André Röhm
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11268
UR - https://arxiv.org/abs/2609.11268
AB - Driven dynamical systems can compute when their transient states encode complex transformations of past inputs. The information processing capacity (IPC) framework allows for a detailed accounting of these computational properties, however its interpretation in noisy systems has remained incomplete. In this work, we clarify how noise affects the IPC and how one can reconstruct the noiseless IPC. First, we show how to distinguish the dynamics of an unperturbed system from the noise-free component of the stochastic dynamics: The IPC measured for responses averaged over noise realizations is in general not the same as the IPC of the unperturbed system. We explicitly demonstrate that noise can redistribute computational capacity and sometimes even enhance performance on particular tasks, rather than merely degrading a fixed computation. We then introduce covariance reconstruction by orthogonal projection (CROP), which reconstructs the covariance and IPC of the noise-free component directly from noisy observations, without requiring a detailed model of either the system or the noise. At fixed total measurement budget, numerical tests on a classical nonlinear reservoir show that CROP estimates the noise-free IPC more accurately than the standard practice of ensemble averaging over repeated trials. We find the same advantage in a quantum reservoir subject to unavoidable measurement noise. Our results provide a general route to recovering the computational structure of noisy physical systems from finite observations.
ER -