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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements
Authors: Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan
IJCAI 2018 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we conducts experiments to first verify the exact recovery guarantee in Theorem 4 for (3) from Gaussian measurements, then to verify the exact recovery guarantee in Theorem 6 for tensor completion (8). Both (3) and (8) can be solved by the standard ADMM [Lu et al., 2018b]. First, we test on random tensors, provided sufficient number of measurements as suggested in Theorem 4. We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables. We generate A Rm (n2n3) with its entries being i.i.d., zero-mean, 1 m-variance Gaussian variables. Then, let y = Avec(X 0). We choose n = 10, 20, 30, n3 = 5, r = 0.2n and r = 0.3n. We set the number of measurements m = 3r(2n r)n3 +1 as in Theorem 4. The results are given in Table 1, in which ˆX is the solution to (11). It can be seen that the relative errors ˆX X 0 F / X 0 F are very small and the tubal ranks of ˆX are correct. |
| Researcher Affiliation | Collaboration | Canyi Lu1, Jiashi Feng2, Zhouchen Lin3,4 Shuicheng Yan5,2 1 Department of Electrical and Computer Engineering, Carnegie Mellon University 2 Department of Electrical and Computer Engineering, National University of Singapore 3 Key Laboratory of Machine Perception (MOE), School of EECS, Peking University 4 Cooperative Medianet Innovation Center, Shanghai Jiao Tong University 5 360 AI Institute |
| Pseudocode | Yes | Algorithm 1 T-SVD Input: A Rn1 n2 n3. Output: T-SVD components U, S and V of A. |
| Open Source Code | Yes | The codes of our methods can be found at https://sites.google.com/site/canyilu/ |
| Open Datasets | No | The paper generates synthetic data for its experiments, for example: 'We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables.' It does not use publicly available datasets. |
| Dataset Splits | No | The paper focuses on theoretical recovery guarantees and their empirical verification using generated data, rather than on standard training/validation/test splits of a dataset. |
| Hardware Specification | No | The paper does not specify any hardware details (e.g., GPU models, CPU types, or cloud platforms) used for conducting the experiments. |
| Software Dependencies | No | The paper mentions 'Matlab command fft' and that the problems can be solved by 'standard ADMM [Lu et al., 2018b]', but it does not provide specific version numbers for MATLAB or any other software libraries or dependencies. |
| Experiment Setup | Yes | We generate X 0 Rn n n3 of tubal rank r by X 0 = P Q, where P Rn r n3 and Q Rr n n3 are with i.i.d. standard Gaussian random variables. We generate A Rm (n2n3) with its entries being i.i.d., zero-mean, 1 m-variance Gaussian variables. Then, let y = Avec(X 0). We choose n = 10, 20, 30, n3 = 5, r = 0.2n and r = 0.3n. We set the number of measurements m = 3r(2n r)n3 +1 as in Theorem 4. |