mlsanityData to 7 Oct 2026

Centre manifold theorem for maps along manifolds of fixed points

arXiv 2604.18202 ↗First posted 20 Apr 2026math.DS cs.LGcited by 0

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Abstract (arXiv)

We prove a centre manifold theorem for a map along a manifold-with-boundary of fixed points, and provide an application to the study of gradient descent with large step size on two-layer matrix factorisation problems.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 18 of its 37 references that are in the map. First posted on arXiv 20 Apr 2026.

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18 of 37 references.

References · 18

  1. 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
  2. 2021Gradient Descent on Neural Networks Typically Occurs at the Edge of Stabilitycited by 413
  3. 2022Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stabilitycited by 151
  4. 2022Understanding Gradient Descent on Edge of Stability in Deep Learningcited by 126
  5. 2022Understanding the unstable convergence of gradient descentcited by 84
  6. 2022Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stabilitycited by 61
  7. 2022Understanding Edge-of-Stability Training Dynamics with a Minimalist Examplecited by 54
  8. 2021Large Learning Rate Tames Homogeneity: Convergence and Balancing Effectcited by 48
  9. 2023Implicit Bias of Gradient Descent for Logistic Regression at the Edge of Stabilitycited by 42
  10. 2022Second-order regression models exhibit progressive sharpening to the edge of stabilitycited by 40
  11. 2022Beyond the Edge of Stability via Two-step Gradient Updatescited by 38
  12. 2024Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiencycited by 34
6 more
  1. 2023Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapultcited by 23
  2. 2023Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaoscited by 21
  3. 2023Gradient Descent Monotonically Decreases the Sharpness of Gradient Flow Solutions in Scalar Networks and Beyondcited by 20
  4. 2024Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimizationcited by 17
  5. 2025A Minimalist Example of Edge-of-Stability and Progressive Sharpeningcited by 4
  6. 2025Convergence Rates for Gradient Descent on the Edge of Stability in Overparametrised Least Squarescited by 3

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