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The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add damped preconditioning (X^T X + λI)^{-1} to GD (ScaledGD(λ)) | overparameterized low-rank matrix sensing · Synthetic, n=150, r*=3, r=5, varying κ | convergence speed vs vanilla GD: >10x faster than GD at κ=7 | Helped |
| Use fixed damping ScaledGD(λ) instead of PrecGD's iteration-varying damping in overparameterized regime (ablation) | overparameterized rank sweep · Synthetic, r=3,5,10,20 | convergence rate | Helped |
| Exact parameterization (r=r*) PrecGD vs ScaledGD(λ) (ablation) | exact rank setting · Synthetic, r=3 | convergence rate | No clear effect |
| Decrease initialization scale α (ablation) | ScaledGD(λ) · Synthetic reconstruction error | relative reconstruction error | Helped |
| Use ScaledGD(λ) in noisy setting | ScaledGD(λ) · Noisy synthetic observations | final error vs information-theoretic bound E_stat | No clear effect |
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