Robust posterior sampling under adversarial noise

Establish robust posterior sampling recovery bounds for noisy one-bit compressed sensing when the pre-quantization measurement noise is adversarial rather than additive Gaussian.

Background

The paper analyzes one-bit compressed sensing with additive Gaussian noise before quantization and proves recovery guarantees for ideal posterior sampling, including robustness to mismatch between the true and learned signal priors. Its separation and stability arguments rely on the probabilistic structure of Gaussian noise.

The authors explicitly identify adversarial noise as an unaddressed extension. Such a result would determine whether comparable posterior-sampling guarantees remain valid when the noise is chosen adversarially, potentially requiring new binary separation and robustness techniques.