arXiv:2411.10435physics.opticscs.ET2024-11被引 4

提出光计算空间复杂度新范式,显著缩小器件尺寸。

The Spatial Complexity of Optical Computing and How to Reduce It

  • 基于波物理启发的稀疏结构与神经剪枝设计光计算系统
  • 在自由空间与芯片光子平台实现1%-10%尺寸缩减
  • 揭示尺寸增大带来的精度收益递减规律

与算法消耗时间和内存类似,硬件运行也需资源。处理物理波的设备需足够“空间”,这由波物理定律决定。执行特定功能需要多少空间是光学中的基础问题,现有研究仅针对特定数学运算,未覆盖更通用的计算任务(如分类)。受计算复杂性理论启发,本文从尺度规律角度研究光计算系统的“空间复杂度”——即随数学运算维度增加,其物理尺寸应如何变化,并提出一种新型光计算系统设计范式:空间高效的类脑光子学,基于结构稀疏约束和受波物理启发(特别是“重叠非局域性”概念)的神经剪枝方法。在两大主流平台——自由空间光学和片上集成光子学上,该方法实现显著尺寸压缩(仅为传统设计的1%-10%),且性能损失极小。理论与计算结果揭示,随着结构尺寸增大,精度提升呈现边际递减趋势,为理解并逼近光计算的极限提供了新视角——器件尺寸与精度之间需权衡取舍。

原文摘要 · Abstract (English)

Similar to algorithms, which consume time and memory to run, hardware requires resources to function. For devices processing physical waves, implementing operations needs sufficient "space," as dictated by wave physics. How much space is needed to perform a certain function is a fundamental question in optics, with recent research addressing it for given mathematical operations, but not for more general computing tasks, e.g., classification. Inspired by computational complexity theory, we study the "spatial complexity" of optical computing systems in terms of scaling laws - specifically, how their physical dimensions must scale as the dimension of the mathematical operation increases - and propose a new paradigm for designing optical computing systems: space-efficient neuromorphic optics, based on structural sparsity constraints and neural pruning methods motivated by wave physics (notably, the concept of "overlapping nonlocality"). On two mainstream platforms, free-space optics and on-chip integrated photonics, our methods demonstrate substantial size reductions (to 1%-10% the size of conventional designs) with minimal compromise on performance. Our theoretical and computational results reveal a trend of diminishing returns on accuracy as structure dimensions increase, providing a new perspective for interpreting and approaching the ultimate limits of optical computing - a balanced trade-off between device size and accuracy.

光计算空间复杂度类脑光子学稀疏结构

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