arXiv:2605.19152stat.MLcs.ET2026-05

提出物理系统信息处理能力新度量,可高效评估硬件类脑计算性能。

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

论文配图:Information Processing Capacity of Stationary Physical Systems: Theory, Data-efficient Estimation Methods, and Photonic Demonstration
图 1 · 摘自论文原文
  • 扩展IPC框架至静态物理系统,理论证明容量有界且受噪声抑制
  • 用光子系统实验证明非线性效应提升高阶容量,总容量与模型性能强相关
  • 提出基于理查森外推和索博尔采样的高效估计算法,适合小样本场景

物理计算系统为硬件原生机器学习提供新路径,但其计算能力难以以普适、任务无关且数据高效的方式表征。本文将信息处理能力(IPC)框架扩展至静态物理系统,建立若干基本结论:单个容量介于0到1之间,完整基上容量之和受读出数量限制,噪声严格降低该上限。针对有限样本下的IPC估计问题,推导出朴素估计器的渐近正偏差形式。在此基础上,提出基于理查森外推和Sobol准随机采样的数据高效估计方法。通过基于皮秒激光脉冲在非线性光纤中传播的光子系统实验验证,改变激光功率与光纤长度可观察到由克尔效应引起的高阶非线性容量分布系统性偏移。最终证明,总IPC与基准机器学习任务性能高度相关,可可靠估计系统有效维度。这些结果确立了IPC作为连接物理系统内在动态与机器学习性能之间的实用桥梁。

原文摘要 · Abstract (English)

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.

物理计算信息容量光子计算机器学习

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