mlsanityData to 14 Oct 2026

The nonsmooth landscape of phase retrieval

arXiv 1711.03247 ↗First posted 9 Nov 2017math.OCcited by 16

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Abstract (arXiv)

We consider a popular nonsmooth formulation of the real phase retrieval problem. We show that under standard statistical assumptions, a simple subgradient method converges linearly when initialized within a constant relative distance of an optimal solution. Seeking to understand the distribution of the stationary points of the problem, we complete the paper by proving that as the number of Gaussian measurements increases, the stationary points converge to a codimension two set, at a controlled rate. Experiments on image recovery problems illustrate the developed algorithm and theory.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Nov 2017.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 4; 2025: 1; 2026: 4.

16 papers.

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  1. 2023Escaping mediocrity: how two-layer networks learn hard generalized linear models with SGDcited by 15
  2. 2021Active manifolds, stratifications, and convergence to local minima in nonsmooth optimizationcited by 11
  3. 2023Catapult Dynamics and Phase Transitions in Quadratic Netscited by 8
  4. 2023Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterizationcited by 6
  5. 2026Spectral Gradient Descent Mitigates Anisotropy-Driven Misalignment: A Case Study in Phase Retrievalcited by 6
  6. 2022Gradient descent provably escapes saddle points in the training of shallow ReLU networkscited by 5
  7. 2021Escaping Saddle Points for Nonsmooth Weakly Convex Functions via Perturbed Proximal Algorithmscited by 4
  8. 2024On the Uniform Convergence of Subdifferentials in Stochastic Optimization and Learningcited by 3
  9. 2024Stable Phase Retrieval with Mirror Descentcited by 3
  10. 2025Fast Escape, Slow Convergence: Learning Dynamics of Phase Retrieval under Power-Law Datacited by 3
  11. 2022Provable Phase Retrieval with Mirror Descentcited by 2
  12. 2026Sharp description of local minima in the loss landscape of high-dimensional two-layer ReLU neural networkscited by 2
4 more
  1. 2026Convergence of Spectral Descent for Non-smooth Optimizationcited by 2
  2. 2024Smoothed Robust Phase Retrievalcited by 0
  3. 2024ℓ1-norm rank-one symmetric matrix factorization has no spurious second-order stationary pointscited by 0
  4. 2026Global Optimality for Constrained Exploration via Penalty Regularizationcited by 0