Stable Phase Retrieval for Spans of Independent Random Variables
arXiv:2607.06693
2026
Architecture
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper gives a sharp stability criterion for recovering a function from its pointwise magnitudes, up to one global sign, when the function lies in the span of independent centered random variables. The transferable asset is not phase retrieval itself, but the robustness principle: an absolute-value bottleneck is information-preserving only when nearly every independent coordinate has nondegenerate two-sided L1 mass after L2 normalization. This suggests a sign-invariant latent module for autoencoders, contrastive representations, or measurement-efficient encoders, with a reconstruction guarantee that can be directly stress-tested by injecting perturbations after the magnitude operation.
Ideas from this paper
Unverified
2026
Insert a magnitude-only bottleneck whose output is the absolute value of a random independent-feature expansion of the latent vector. Train a decoder to reconstruct the latent representation or input modulo one global sign, while explicitly rejecting feature distributions whose normalized L1 mass is too small. The module provides a controlled way to obtain sign-invariant representations without allowing arbitrary coordinate-wise sign loss.
Useful5/10
Difficulty4/10
Novelty7/10