mlsanityData to 14 Oct 2026

When does gradient descent with logistic loss find interpolating two-layer networks?

arXiv 2012.02409 ↗First posted 4 Dec 2020stat.ML cs.LG math.OCcited by 12

Not on the map. Why?

Abstract (arXiv)

We study the training of finite-width two-layer smoothed ReLU networks for binary classification using the logistic loss. We show that gradient descent drives the training loss to zero if the initial loss is small enough. When the data satisfies certain cluster and separation conditions and the network is wide enough, we show that one step of gradient descent reduces the loss sufficiently that the first result applies.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Dec 2020.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 3; 2023: 1; 2024: 2; 2025: 1; 2026: 2.

12 papers.

  1. 2021A Field Guide to Federated Optimizationcited by 315
  2. 2022High-dimensional Asymptotics of Feature Learning: How One Gradient Step Improves the Representationcited by 150
  3. 2021Learning in High Dimension Always Amounts to Extrapolationcited by 66
  4. 2021Overparameterization of deep ResNet: zero loss and mean-field analysiscited by 24
  5. 2023Generalization and Stability of Interpolating Neural Networks with Minimal Widthcited by 21
  6. 2024Implicit Optimization Bias of Next-Token Prediction in Linear Modelscited by 14
  7. 2022Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networkscited by 5
  8. 2024Towards certification: A complete statistical validation pipeline for supervised learning in industrycited by 4
  9. 2025On the Role of Label Noise in the Feature Learning Processcited by 4
  10. 2022High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Modelscited by 2
  11. 2026Demystifying Variance in Circuit Discovery of LLMscited by 2
  12. 2026PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theorycited by 0