End-to-End Optimization of Incoherent Imaging for Classification Under Detector-Limited Readout

Optical readout in low-light imaging is fundamentally limited by measurement noise, including photon shot noise, detector noise, and quantization error. In this regime, downstream inference depends not only on the optical front end, but also on how noisy high-dimensional sensor measurements are represented before classification or decision-making. Here we show that eigentasks provide a measurement-adapted representation for optical sensor outputs by ordering readout features according to their resolvability under noise. Using experimental data from a lens-based optical imaging system and a reanalysis of published data from a single-photon-detection neural network, we find that eigentask representations frequently outperform standard baselines including principal component analysis and filtering-based compression. The advantage is most pronounced in photon-limited, few-shot, and higher-difficulty classification regimes. In few-shot MPEG-7 classification, for example, the advantage over other methods reaches about 10 percentage points as the number of classes increases. In these settings, eigentasks yield more informative low-dimensional features and improve sample-efficient downstream learning. These results identify measurement-adapted representation as a promising strategy for optical inference when photon budget, acquisition time, and task complexity are constrained.

Conventional machine-vision pipelines typically rely on high-quality optics that produce clean, human-interpretable images, and optical design has therefore been driven by image-level criteria such as resolution, aberration correction, and pixel fidelity. However, such optics are often impractical for size-, cost-, or form-factor-constrained applications, where compact meta-optics offer an attractive alternative but operate under strict physical efficiency limits. We propose CODA, a co-design framework that optimizes a continuous-density meta-optic front-end for frozen-model recognition using differentiable image formation and adjoint-gradient updates of Maxwell-based simulations. CODA directly optimizes the cross-entropy loss of a fixed zero-shot CLIP classifier without learned reconstruction, image signal processing, or image-fidelity auxiliary objectives. In a two-dimensional simulated imaging benchmark on ImageNet-100, CODA improves CLIP ViT-L/14 zero-shot accuracy from 53.75 $\pm$ 3.57$\%$ with a focal-concentration baseline to 65.41 $\pm$ 3.99$\%$. The optimized optics further transfer without re-optimization across CLIP, SigLIP, and DINOv2 on ImageNet-100, CIFAR-100, and Food-101. These results demonstrate that, under constrained meta-optic imaging, downstream recognition can be improved by aligning optical design with frozen vision-model objectives rather than conventional image-formation criteria.

A foundational assumption in CNN interpretability -- that deep encoders suppress background pixels while classifiers merely select from a cleaned feature pool (the Spatial Funnel Hypothesis) -- remains untested due to spatial hallucinations in existing visualization tools. We address this by introducing a hallucination-free inversion framework built on magnitude-phase decoupling and Local Adjoint Correctors. Our method mathematically guarantees that the spatial gradient support of every reconstruction stems strictly from genuinely active channels. Using this framework as a geometric probe, we uncover the first pixel-level evidence of strong superposition in vision encoders. We show that per-channel inversions are uniformly holographic: positive and negative weight reconstructions are visually and energetically indistinguishable. However, their algebraic sum sharply concentrates on the foreground. This proves classification operates via destructive interference -- classifier weights cancel a shared background direction in pixel space and constructively assemble class-discriminative residuals, directly falsifying the Spatial Funnel Hypothesis. This interference model identifies the volume of the admissible interference subspace as the geometric quantity governing channel requirements. We prove this volume is dual to the GAP covariance determinant, yielding a covariance-volume channel selection algorithm with a $(1-1/e)$ approximation guarantee. This algorithm mathematically reveals out-of-distribution (OOD) failure as a measurable collapse of the covariance volume essential for interference-based classification. Our framework extends seamlessly to attention-based heads without retraining.