Landscape analysis of an improved power method for tensor decomposition
Authors: Joe Kileel, Timo Klock, João M Pereira
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conclude with numerics that show a practical preferability for using the SPM functional over a more established counterpart. Here we present numerical experiments that corroborate the theoretical findings of Section 4. |
| Researcher Affiliation | Academia | Joe Kileel UT Austin Timo Klock Simula Research Laboratory João M. Pereira UT Austin |
| Pseudocode | Yes | Due to space constraints, we leave precise descriptions of Algorithm 1 and our deflation bounds to the supplementary material. |
| Open Source Code | Yes | We use the implementation of SPM of the first and third authors, available at https://github.com/joaompereira/SPM, which is licensed under the MIT license. We will upload the Matlab code for conducting our experiments. |
| Open Datasets | No | With m = 2n as the tensor order, we create noiseless tensors with ai Unif(SD 1)) as the tensor components and λi = p Dm/K λi as the tensor weights, where λi Unif([1/2, 2]). ... We construct noisy tensors ˆT T by adding independent copies of ϵ N(0, m!σ2) to each entry of the tensor and then project onto Sym(T m D ). |
| Dataset Splits | No | The paper describes conducting experiments over 1000 trials (10 distances per tensor, 100 tensors) and 100 repetitions for different scenarios. However, it does not explicitly provide details about training, validation, or test dataset splits, as it generates synthetic data for its experiments rather than using a pre-existing dataset with fixed splits. |
| Hardware Specification | Yes | All experiments in the main submission can be conducted on a personal laptop with a Intel Core i7-7700HQ CPU and 16.0GB of RAM in less than an hour. |
| Software Dependencies | No | The paper mentions using 'Matlab code' for their experiments and references 'Tensorlab'. While it states the SPM implementation is licensed under MIT, it does not provide specific version numbers for Matlab, Tensorlab, or any other software dependencies. |
| Experiment Setup | Yes | We set D = 20, K = 100 for the 4th order tensor (n = 2) and D = 10, K = 100 for the 6th order (n = 3). ...while in Figure 4b σ ranges from 10 5 to 1. |