Singular Subspace Perturbation Bounds via Rectangular Random Matrix Diffusions
Authors: Peiyao Lai, Oren Mangoubi
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we present numerical simulations that illustrate the theoretical results in Theorem 2.2, and investigate the extent to which the bounds in Theorem 2.2 are tight. |
| Researcher Affiliation | Academia | Peiyao Lai Worcester Polytechnic Institute Worcester, MA, USA Oren Mangoubi Worcester Polytechnic Institute Worcester, MA, USA |
| Pseudocode | No | No explicit pseudocode or algorithm blocks are provided in the paper. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to code repositories. |
| Open Datasets | No | In this set of simulations, we compute the squared Frobenius error for the rank-k covariance approximation problem... In the following simulations we choose the input data matrix to be a synthetic data matrix with linearly decaying spectral profile spectral profile σi = m (d i + 1) for all i [d]. |
| Dataset Splits | No | The paper uses a synthetic data matrix for numerical simulations, but it does not specify any training, testing, or validation dataset splits. |
| Hardware Specification | No | The paper includes a 'Numerical Simulations' section, but it does not specify any hardware details (e.g., GPU/CPU models, memory) used for running these simulations. |
| Software Dependencies | No | The paper describes numerical simulations but does not provide any specific software dependencies or version numbers (e.g., programming languages, libraries, frameworks). |
| Experiment Setup | Yes | In this set of simulations, we compute the squared Frobenius error for the rank-k covariance approximation problem... We take an input data matrix A, perturb the matrix by iid Gaussian noise (that is, A = A + TG where G has iid N(0, 1) entries), and compute the error for different values of m, d, k. In the following simulations we choose the input data matrix to be a synthetic data matrix with linearly decaying spectral profile spectral profile σi = m (d i + 1) for all i [d]... Here, d = 15, k = 5, T = 1 and the input matrix has spectral profile σi = m (d i + 1) for all i [d]. |