Research map / Optimization / Nonconvex and smooth optimization
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Lift the decision variable from l=1 to l=3 (ablation) | Matrix sensing · Matrix sensing, n=3 | success rate: 0.575 -> 0.62 | Helped |
| Lift the decision variable from l=1 to l=3 (ablation) | Matrix sensing · Matrix sensing, n=4 | success rate: 0.575 -> 0.68 | Helped |
| Lift the decision variable from l=1 to l=3 (ablation) | Matrix sensing · Matrix sensing, n=5 | success rate: 0.475 -> 0.75 | Helped |
| Increase tensor order from l=1 to l=4 (ablation) | Lifted matrix sensing · Matrix sensing, n=3 | smallest Hessian eigenvalue at spurious solution: 2.67 -> -0.17 | Mixed |
| Increase tensor order from l=1 to l=2 (ablation) | Lifted matrix sensing · Matrix sensing, n=5 | smallest Hessian eigenvalue at spurious solution: 1.87 -> -0.81 | Mixed |
| Increase tensor order from l=1 to l=2 (ablation) | Lifted matrix sensing · Matrix sensing, n=7 | smallest Hessian eigenvalue at spurious solution: 1.89 -> -1.64 | Mixed |
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