The Spatial Complexity of Optical Computing and How to Reduce It

2024-11-15

arXiv.org

AI Summary

Optical computing systems suffer from large device footprints and low spatial efficiency when tackling complex tasks such as classification. Method: This work proposes a spatially efficient, brain-inspired photonic computing paradigm. We introduce a novel theoretical framework—“spatial complexity”—to quantify the scaling law of physical footprint with problem size; incorporate wave-physics–driven structural sparsity constraints and neural pruning; and define and exploit “overlapping non-locality” to enhance resource reuse. Our approach integrates structural sparsity modeling, photonic system simulation, and scaling-law analysis. Contribution/Results: On both free-space and integrated photonic platforms, our design reduces device area to 1%–10% of conventional counterparts while maintaining negligible accuracy degradation. Crucially, we uncover, for the first time, the diminishing-return trade-off between accuracy and device size—a fundamental marginal-decay relationship governing photonic neural hardware.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Hardware-aware ML
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Optical computing systems
• Complex task execution
• Size-accuracy tradeoff

Innovation

• Space-efficient
• Neuromorphic Optical Computing
• Size-Accuracy Trade-off