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How much overparameterization does ALS need for tensor decomposition?
Prove that alternating least squares decomposes rank-r tensors with o(r^2) components, or that about r^2 are needed.
| 1 | { |
| 2 | "domain": "computer-science", |
| 3 | "topics": [ |
| 4 | "learning-theory", |
| 5 | "algorithms-complexity" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "also": [ |
| 9 | "algorithm" |
| 10 | ], |
| 11 | "source": { |
| 12 | "key": "colt", |
| 13 | "name": "COLT open problems", |
| 14 | "url": "https://proceedings.mlr.press/v336/arvanitakis26a.html", |
| 15 | "id": "v336/arvanitakis26a", |
| 16 | "curator": "Conference on Learning Theory (COLT)", |
| 17 | "poser": "Dionysis Arvanitakis, Vaidehi Srinivas and Aravindan Vijayaraghavan", |
| 18 | "status": "open", |
| 19 | "as_of": "2026-10-20", |
| 20 | "catalog": "0521c19bbd38" |
| 21 | }, |
| 22 | "review": true, |
| 23 | "approval": "first-time" |
| 24 | } |