Phase retrieval in high dimensions: Statistical and computational phase transitions
Authors: Antoine Maillard, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We rigorously prove the aforementioned formula in two particular cases. First, when the distribution P0 is Gaussian (real or complex) and Φ = WB is the product of a Gaussian matrix W with an arbitrary matrix B. Second, for a Gaussian matrix Φ (real or complex) with any separable distribution P0. These are non-trivial extensions of the the proofs of [13, 23 25]... The simulations are in very good agreement with the prediction, and our results on Hadamard matrices suggest that the curves of Fig. 1-right are valid for more general ensembles than uniformly sampled orthogonal matrices, and that one can allow some controlled structure in the matrix without harming the performance of the algorithm. |
| Researcher Affiliation | Academia | 1 Lab. de Physique de l École Normale Supérieure, PSL, CNRS & Sorbonne Universités, Paris. 2 Institut de Physique Théorique, CNRS, CEA, Université Paris-Saclay, France. 3 Ide PHICS laboratory, EPFL, Switzerland. 4 SPOC laboratory, EPFL, Switzerland. |
| Pseudocode | No | The paper discusses algorithms like G-VAMP and mentions state evolution equations, but it does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper states: 'To test the performance of the G-VAMP algorithm, we used the Tr AMP library [22] that provides an open-source implementation.' This refers to a third-party open-source library that the authors used, not open-source code for their own described methodology. |
| Open Datasets | No | The paper mentions 'Gaussian prior', 'Gaussian matrices', 'Hadamard matrices', 'natural image' and 'randomly subsampled DFT matrix' for experiments. However, it does not provide specific links, DOIs, repositories, or formal citations for these datasets to indicate their public availability for reproduction. |
| Dataset Splits | No | The paper mentions 'finite size simulations' with 'n = 8000', 'm = 8192', and 'n = 5000' but does not specify any training, validation, or test dataset splits in terms of percentages, absolute counts, or references to predefined splits for reproduction. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU models, CPU types, memory) used to run the experiments. |
| Software Dependencies | No | The paper mentions using the 'Tr AMP library [22]', but it does not specify any version numbers for this library or any other software dependencies, which is required for reproducibility. |
| Experiment Setup | No | The paper discusses state evolution equations and the G-VAMP algorithm, and mentions parameters like 'n' and 'm' for simulations. However, it does not provide concrete hyperparameter values (e.g., learning rate, batch size, number of epochs) or system-level training settings needed to reproduce the experimental setup. |