Research map / Learning theory and algorithms / Matrix and tensor methods
Implicit Regularization in Deep Learning May Not Be Explainable by Norms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gradient flow on depth-2-or-greater matrix factorization for the specified 2-by-2 matrix completion problem, with positive determinant at initialization | Deep matrix factorization · 2-by-2 matrix completion | matrix norms and quasi-norms | Hurt |
| Use gradient flow on depth-2-or-greater matrix factorization for the specified 2-by-2 matrix completion problem, with positive determinant at initialization | Deep matrix factorization · 2-by-2 matrix completion | effective rank | Helped |
| Use gradient flow on depth-2-or-greater matrix factorization for the specified 2-by-2 matrix completion problem, with positive determinant at initialization | Deep matrix factorization · 2-by-2 matrix completion | distance to infimal rank | Helped |
| Apply gradient descent to tensor factorization with sufficiently large factorization rank | Tensor factorization · Tensor completion from low-rank ground truth | tensor rank of solutions | Helped |
| Decrease the initialization scale (ablation) | Tensor factorization · Tensor completion from low-rank ground truth | tensor rank of solutions | Helped |
| Increase factorization depth from 2 to 3 or more (ablation) | Deep matrix factorization · Analyzed matrix completion problem | growth of the absolute unobserved entry as loss decreases | Helped |
| Use smaller learning rate and initialization (ablation) | Deep matrix factorization · Analyzed matrix completion problem | growth of the absolute unobserved entry as loss decreases | Helped |
| Perturb the diagonal observed value away from zero (ablation) | Deep matrix factorization · Perturbed 2-by-2 matrix completion | guaranteed movement toward minimum rank | Hurt |
| Perturb the off-diagonal observed values while keeping the diagonal observation zero and both off-diagonal values nonzero (ablation) | Deep matrix factorization · Perturbed 2-by-2 matrix completion | growth of norms and quasi-norms as loss decreases | No clear effect |
| Use unbalanced rather than balanced random initialization (ablation) | Deep matrix factorization · Analyzed matrix completion problem | growth of the absolute unobserved entry as loss decreases | Mixed |
Closest papers by meaning
- Implicit Regularization in Deep Matrix Factorization (NeurIPS 2019 · similarity 0.95)
- Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent (ICML 2025 · similarity 0.89)
- Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completion (NeurIPS 2024 · similarity 0.89)
- Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetries (ICLR 2025 · similarity 0.89)
- Estimating Implicit Regularization in Deep Learning (NeurIPS 2026 · similarity 0.88)
- On the Implicit Bias of Adam (ICML 2024 · similarity 0.87)
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