Phase Retrieval in High Dimensions: Statistical and Computational Phase Transitions

on YouTube ↗39m

" summary

Random Gaussian measurements require weak threshold m/d = β/2 (real 1/2, complex 1) and strong threshold m/d = β (real 1, complex 2); orthogonal ensembles push the weak threshold to m/d ≈ 1+β/2. Results come from replica formulas proved by interpolation for rotationally invariant matrices of the form W B, and algorithms use VAMP/state evolution which empirically stalls above the information limit. Two spectral constructions emerge — one from linearizing AMP and one from the free‑energy Hessian — and deep generative priors (random nets) substantially shrink the hard phase.

AI-written summary · about

" chapters (8)

1. 0:00Introduction and welcome
2. 0:59Phase retrieval basics
3. 4:52Strong recovery analysis
4. 7:56Algorithmic implementation
5. 10:48Spectral methods research
6. 19:00Advanced priors and deep learning
7. 26:28Concluding remarks
8. 27:22Q&A session

" related talks

• 35mPhase Retrieval In High Dimensions: Statistical And Computational Phase TransitionsAntoine Maillard · Rigorous Evidence for Information-Computation Trade-offs
• 01h 04mStatistical Physics and Computation in High DimensionFlorent Krzakala, Lenka Zdeborova · Probability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)
• 01h 14mRecent Progress in High-Dimensional LearningAnkur Moitra · Probability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)
• 45mPhase Transitions in Low-Rank Matrix EstimationFlorent Krzakala · Random Instances and Phase Transitions (Simons Institute, 2016)
• 38mAll-or-Nothing Statistical and Computational Phase Transitions in Sparse Spiked Matrix EstimationCynthia Rush · Rigorous Evidence for Information-Computation Trade-offs
• 01h 11mStatistical Physics and Computation in High DimensionFlorent Krzakala, Lenka Zdeborova · Probability, Geometry, and Computation in High Dimensions Boot Camp (Simons Institute, Fall 2020)
• 01h 06mTutorial: Methods from Statistical Physics IIAhmed El Alaoui · Deep Learning Theory Workshop and Summer School 2022
• 43mInformation-Theoretic Bounds and Phase Transitions in Community Detection and High-Dimensional ClustCris Moore · Random Instances and Phase Transitions (Simons Institute, 2016)