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Implicit Regularization in Matrix Factorization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Optimize the matrix through a full-dimensional factorization with gradient descent instead of optimizing the matrix directly | Underdetermined matrix least squares · Simulated matrix reconstruction | nuclear norm | Helped |
| Initialize the factorization close to zero (ablation) | Factorized gradient flow · 3×3 PSD matrix completion grid search | deviation from minimum nuclear norm | Helped |
| Use initialization norm 1 instead of initialization close to zero (ablation) | Factorized gradient flow · 3×3 PSD matrix completion grid search | deviation from minimum nuclear norm | Hurt |
| Use small step sizes (ablation) | Gradient descent on the factorization · Underdetermined matrix regression | nuclear norm | Helped |
Closest papers by meaning
- Implicit Regularization in Deep Matrix Factorization (NeurIPS 2019 · similarity 0.93)
- Towards Resolving the Implicit Bias of Gradient Descent for Matrix Factorization: Greedy Low-Rank Learning (ICLR 2021 · similarity 0.92)
- Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent (ICML 2025 · similarity 0.90)
- Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion (NeurIPS 2024 · similarity 0.88)
- Provable Acceleration of Nesterov's Accelerated Gradient for Asymmetric Matrix Factorization and Linear Neural Networks (NeurIPS 2024 · similarity 0.88)
- Cauchy-Schwarz Regularizers (ICLR 2025 · similarity 0.86)
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