Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Low-rank Solutions of Linear Matrix Equations via Procrustes Flow
Authors: Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, Ben Recht
ICML 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper we study the problem of recovering a low-rank matrix from linear measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate obtained by a thresholding scheme followed by gradient descent on a non-convex objective. We show that as long as the measurements obey a standard restricted isometry property, our algorithm converges to the unknown matrix at a geometric rate. In the case of Gaussian measurements, such convergence occurs for a n1 n2 matrix of rank r when the number of measurements exceeds a constant times (n1 + n2)r. |
| Researcher Affiliation | Academia | Stephen Tu, Ross Boczar, Max Simchowitz EMAIL EECS Department, UC Berkeley, Berkeley, CA. Mahdi Soltanolkotabi EMAIL Ming Hsieh Department of Electrical Engineering, USC, Los Angeles, CA. Benjamin Recht EMAIL EECS Department, UC Berkeley, Berkeley, CA. |
| Pseudocode | Yes | Algorithm 1 Procrustes Flow (PF) Require: {Ak}m k=1, {bk}m k=1, {ατ} τ=1, {µτ} τ=1, T0 N. // Initialization phase. f M0 := 0n n. for τ = 0, 1, ..., T0 1 do // Projection onto rank r PSD matrices. f Mτ+1 Pr( f Mτ ατ+1 Pm k=1( Ak, f Mτ bk)Ak). end for // SVD of f MT0, with Q Rn r, Σ Rr r. QΣQT := f MT0. U0 := QΣ1/2. // Gradient descent phase. repeat Uτ+1 Uτ µτ+1 U0 2 f(Uτ). until convergence |
| Open Source Code | No | The paper does not contain any explicit statement about open-source code release or a link to a code repository. |
| Open Datasets | No | The paper discusses theoretical models like "Gaussian measurements" but does not refer to any specific publicly available dataset for training. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments with data, therefore no dataset split information is provided. |
| Hardware Specification | No | The paper does not describe any specific hardware used for running experiments, as it is primarily theoretical. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers, as it is a theoretical work without reported experimental implementations. |
| Experiment Setup | No | The paper is theoretical and does not detail any experimental setup, hyperparameters, or training configurations. |