Conformalized Rate-Adaptive Sensing

Reliable probability estimates by classifiers are essential in high-risk applications. In practice, however, predicted probabilities are often miscalibrated, and many existing post-hoc calibration methods typically lack guarantees that a specific notion of calibration is achieved after the correction procedure is applied. We introduce a set-based perspective on calibration through the notion of cumulative mass calibration and the corresponding error measures. We propose a new calibration procedure based on conformal prediction that forms cumulative probabilities with guaranteed marginal coverage. We introduce an adaptive temperature scaling algorithm, with the temperature tuned for each input to satisfy the conformal coverage constraint. As we show, this procedure can be efficiently implemented. Across image classification tasks, particularly in settings with many classes, our method improves newly introduced calibration error measures (CMCE and $α$-CMCE) and standard metrics (such as ECE, cw-ECE, MCE) over the existing baselines.

Numerous modern applications in signal processing and medical imaging necessitate acquiring high-dimensional signals under tight resource constraints. Traditional sampling theory suggests that accurate signal reconstruction requires a number of measurements proportional to the signal's ambient dimension, a requirement often too expensive or impractical. Compressed sensing challenges this notion by demonstrating that sparse signals can be recovered with fewer measurements, provided the measurement operator meets certain conditions. This proof-of-concept study presents a task-aware flow-based generative framework -- a reformulation of the conventional Flow Matching training paradigm with a flow model trained to optimize subsampling in compressed sensing applications. We establish the fundamental feasibility of the proposed framework of learning subsampling masks that substantially enhance the performance of compressed sensing for image classification, image reconstruction, and MRI acceleration. For the image reconstruction task, our method demonstrated state-of-the-art performance, achieving Peak Signal-to-Noise Ratio of 25.17 dB at the subsampling rate of 5% on the CelebA dataset and 29.24 dB when reconstructing $8\times$ accelerated MRI measurements (fastMRI dataset) with the minimal computational overhead. These results highlight the effectiveness of task-conditioning within generative flow models and reveal a promising direction for representation learning strategies. Overall, the proposed framework offers a unified, flexible approach to designing data- and task-driven sensing schemes that can be potentially adapted to a broad range of inverse problems.

Single-pixel sensing encodes a scene as a short sequence of coded measurements, and image-free methods infer the task directly from that sequence. We show that removing image reconstruction relocates the central design problem to the lift: how 1D measurements become a 2D task representation. We organize this choice as a lift spectrum from a fixed-physics inverse, through a learned static projection, to content-adaptive retrieval. These are not interchangeable forms of reconstruction: the fixed-physics route reconstructs an image consumed at inference, whereas our spatiotemporal soft-fusion (STSF) network lifts measurements directly into task features, and task-prioritized loss scheduling (TPLS) uses a separate learned reconstruction branch only as scheduled training supervision. A probe-selected recurrent encoder and a parameter-matched lift ablation identify the STSF design. In simulation, STSF+TPLS exceeds the prior image-free baseline on three datasets at 3.13% sampling (+3.2 to +9.9 pp foreground mIoU) and remains competitive down to 0.39%. The strongest clean-trained reconstruct-then-segment baseline wins without measurement noise, but measurement noise reverses the ranking: the reconstructed task input carries a 20-70x larger normalized relative perturbation than the measurements themselves. Stressed to failure, the three lift regions exhibit distinct dominant signatures--collapse, imprinting, and coarsening. STSF+TPLS transfers without fine-tuning to a real single-pixel bench, where the reversal reappears as a proof of concept; inference takes about 14 ms per mask on an RTX 4090. Within the tested fixed-acquisition regime, measurement-to-space adaptivity therefore organizes both the clean-to-noisy operating envelope and the failure a system encounters. Code and pretrained weights: https://github.com/Hanyuyuan6/STSF-TPLS.