Near-Isometric Properties of Kronecker-Structured Random Tensor Embeddings
Authors: Qijia Jiang
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we numerically investigate (1) embedding dimension scaling with d for the two types of random embeddings in Section 4 and 5; (2) signal recovery from random Gaussian measurements as elaborated in Section 6.1 where the signal is rank-1 belonging to a product of cones. |
| Researcher Affiliation | Academia | Qijia Jiang Lawrence Berkeley National Laboratory qjiang@lbl.gov |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found. |
| Open Source Code | No | The paper references a 'Matlab Tensor Toolbox' with a URL, but this is a third-party tool, not the authors' own source code for their methodology. No explicit statement or link to their own code was provided. |
| Open Datasets | No | For the first experiment, we let n = 10, d = 5 and pick each factor {uj} to be 20% sparse. The figure below reports the average distortion of the embedding |k Sxk2 1| over 25 runs for both the row-wise tensored and recursive sketch with Gaussian random factors. |
| Dataset Splits | No | No specific dataset split information (percentages, sample counts, or citations to predefined splits) for training, validation, or testing was found. |
| Hardware Specification | No | The paper's own checklist explicitly states 'N/A' for hardware specification, and no specific hardware details were found in the text. |
| Software Dependencies | No | We use the tucker-als function from the Matlab Tensor Toolbox1 for computing the best rank-(1, 1, 1) tensor approximation, after which gradient update is made on each factor followed by 1 projection. (1http://www.tensortoolbox.org) |
| Experiment Setup | Yes | For the first experiment, we let n = 10, d = 5 and pick each factor {uj} to be 20% sparse. The figure below reports the average distortion of the embedding |k Sxk2 1| over 25 runs for both the row-wise tensored and recursive sketch with Gaussian random factors. ... We set each factor {uj} to be 20% sparse and let d = 3, n = 10, m = 2 0.8 n d for 2 {1, , 3} and record the successful recovery out of 25 trials. Stepsize is picked to be 0.1 and success is defined as L(z1, , zd) 0.1 after 500 gradient steps. |