mlsanityData to 14 Oct 2026

Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization

arXiv 2309.00508 ↗First posted 1 Sep 2023cs.LG math.DScited by 4

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Abstract (arXiv)

Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate: (i) how global minima with zero generalization error become geometrically separated from other global minima as the sample size grows; and (ii) the local convergence properties and rate of gradient flow dynamics. Our results indicate that two-layer neural networks can be locally recovered in the regime of overparameterization.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 4 of its 33 references that are in the map. First posted on arXiv 1 Sep 2023.

Builds on

4 of 33 references.

References · 4

  1. 2016Understanding deep learning requires rethinking generalizationcited by 1,674
  2. 2021Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariancescited by 127
  3. 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 95
  4. 2020The Global Landscape of Neural Networks: An Overviewcited by 57

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 0; 2026: 1.

4 papers.

  1. 2026Towards Understanding Adam Convergence on Highly Degenerate Polynomialscited by 4
  2. 2024Geometry of Critical Sets and Existence of Saddle Branches for Two-layer Neural Networkscited by 2
  3. 2024Disentangle Sample Size and Initialization Effect on Perfect Generalization for Single-Neuron Targetcited by 0
  4. 2024Linear Independence of Generalized Neurons and Related Functionscited by 0