Targeted search shows that random-device testing underestimates worst-case error in a simulated wave-based neural operator

2026-10-05

AI Summary

This study addresses the critical limitation that existing stochastic testing severely underestimates worst-case errors in wave-based neural operators, failing to evaluate maximum performance degradation induced by fabrication variations. We propose a worst-case device search methodology for analog coherent 4f optical processors that integrates hybrid Fourier neural operators, deterministic numerical simulation, Sobol' quasi-random sampling, and gradient-based fine-tuning to systematically explore the tolerance parameter space. Experimental results demonstrate that errors on the held-out set obtained via this approach reach 1.08 to 3.1 times the maximum values identified through Monte Carlo random sampling while surpassing the Wilks statistical bound. These findings confirm that stochastic testing significantly underestimates potential risks, thereby bridging a critical safety gap in the robustness verification framework for optical neural operators.

Abstract

Wave-based processors promise fast, energy-efficient Fourier layers for neural operators. They are usually validated on randomly sampled devices, but using them requires knowing how large their error can become under fabrication and alignment variation. In a stylised numerical case study, a hybrid Fourier neural operator runs its four spectral layers on simulated coherent 4f processors with 32 toleranced knobs, whose half-widths are representative rather than calibrated. For 120 models (four tasks, six training methods, five seeds), we compared the worst of N random in-spec devices with a searched one. On a deterministic simulator with one frozen draw of the random static errors, the searched device's held-out error was 1.08-3.10 times the maximum over 200 Monte Carlo devices and 1.06-2.71 times that over 1000. With 20 fresh static draws, it still exceeded the maximum over 200 random devices in 116 of 120 models. Under uniform sampling, the probability of drawing such a device is at most 0.37% per model (two-sided 95% Clopper-Pearson), which says nothing about how large its error is. The gap persisted with uniform or Sobol' sampling at the search's budget, shared knobs, a second crosstalk model, box scales of 0.25-2 and a pixel-level device model. Models trained only with random static errors reached 3.7-39.9 times their nominal error on searched devices, and fine-tuning on random and gradient-searched devices gave the lowest searched error of the six in all 20 task-seed pairs. For two heat-exchanger quantities, a search targeted at each exceeded the worst of 1000 random devices in all 39 models, and hence the Wilks 95/95 limit (worst of 59). For the mean pressure of 11 models, no random device exceeded a 1% error threshold, but the searched device did. Random testing estimates how often errors exceed a threshold; worst-device search gives a lower bound on how large they can be.

Problem

• wave-based neural operator
• worst-case error
• random-device testing
• fabrication variation
• Fourier layers

Innovation

• Wave-based neural operator
• Worst-case error search
• Fourier neural operator
• Hardware-in-the-loop fine-tuning
• Coherent 4f processor