mlsanityData to 7 Oct 2026

Exact asymptotics for phase retrieval and compressed sensing with random generative priors

arXiv 1912.02008 ↗First posted 4 Dec 2019math.ST cond-mat.dis-nn cs.LGcited by 20

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Abstract (arXiv)

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural networks with random weight matrices and arbitrary activations. We compare the performance to sparse separable priors and conclude that generative priors might be advantageous in terms of algorithmic performance. In particular, while sparsity does not allow to perform compressive phase retrieval efficiently close to its information-theoretic limit, it is found that under the random generative prior compressed phase retrieval becomes tractable.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Dec 2019.

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Citing papers per year: 2021: 3; 2022: 5; 2023: 4; 2024: 4; 2025: 4.

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  1. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  2. 2023Deterministic equivalent and error universality of deep random features learningcited by 35
  3. 2024Bayes-optimal learning of an extensive-width neural network from quadratically many samplescited by 23
  4. 2022Theoretical characterization of uncertainty in high-dimensional linear classificationcited by 18
  5. 2024Fundamental computational limits of weak learnability in high-dimensional multi-index modelscited by 17
  6. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  7. 2023Escaping mediocrity: how two-layer networks learn hard generalized linear models with SGDcited by 14
  8. 2024Asymptotics of Learning with Deep Structured (Random) Featurescited by 13
  9. 2022Generative Principal Component Analysiscited by 12
  10. 2023Fundamental limits of overparametrized shallow neural networks for supervised learningcited by 12
  11. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  12. 2023Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priorscited by 4
8 more
  1. 2024Generalized Eigenvalue Problems with Generative Priorscited by 3
  2. 2025Learning Single Index Models with Diffusion Priorscited by 2
  3. 2022Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gapcited by 1
  4. 2021Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problemscited by 0
  5. 2022Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learningcited by 0
  6. 2025Phase transition of descending phase retrieval algorithmscited by 0
  7. 2025Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT viewcited by 0
  8. 2025Phase retrieval with rank d measurements -- descending algorithms phase transitionscited by 0