mlsanityData to 7 Oct 2026

On implicit regularization: Morse functions and applications to matrix factorization

arXiv 2001.04264 ↗First posted 13 Jan 2020cs.LG stat.MLcited by 11

Not on the map. Why?

Abstract (arXiv)

In this paper, we revisit implicit regularization from the ground up using notions from dynamical systems and invariant subspaces of Morse functions. The key contributions are a new criterion for implicit regularization---a leading contender to explain the generalization power of deep models such as neural networks---and a general blueprint to study it. We apply these techniques to settle a conjecture on implicit regularization in matrix factorization.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Jan 2020.

Builds on

No reference list yet.

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 2; 2023: 4; 2024: 3; 2025: 1.

11 papers.

  1. 2023Trained Transformers Learn Linear Models In-Contextcited by 331
  2. 2022On the Implicit Bias in Deep-Learning Algorithmscited by 84
  3. 2022Implicit Regularization Towards Rank Minimization in ReLU Networkscited by 53
  4. 2023Understanding Incremental Learning of Gradient Descent: A Fine-grained Analysis of Matrix Sensingcited by 40
  5. 2021On Margin Maximization in Linear and ReLU Networkscited by 34
  6. 2023The Implicit Bias of Minima Stability in Multivariate Shallow ReLU Networkscited by 15
  7. 2023The Inductive Bias of Flatness Regularization for Deep Matrix Factorizationcited by 6
  8. 2024Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processescited by 4
  9. 2024Connectivity Shapes Implicit Regularization in Matrix Factorization Models for Matrix Completioncited by 3
  10. 2024Lecture Notes on Linear Neural Networks: A Tale of Optimization and Generalization in Deep Learningcited by 1
  11. 2025Implicit Bias in Matrix Factorization and its Explicit Realization in a New Architecturecited by 0