mlsanityData to 7 Oct 2026

Gradient Descent Converges to Minimizers

arXiv 1602.04915 ↗First posted 16 Feb 2016stat.ML cs.LG math.OCcited by 25

Not on the map. Why?

Abstract (arXiv)

We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Feb 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 6; 2023: 4; 2024: 3; 2025: 2; 2026: 2.

25 papers.

Sort:

By area:

  1. 2021Provable Model-based Nonlinear Bandit and Reinforcement Learning: Shelve Optimism, Embrace Virtual Curvaturecited by 32
  2. 2023Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grokcited by 31
  3. 2023Beyond NTK with Vanilla Gradient Descent: A Mean-Field Analysis of Neural Networks with Polynomial Width, Samples, and Timecited by 20
  4. 2022Visualizing high-dimensional loss landscapes with Hessian directionscited by 16
  5. 2022Stochastic noise can be helpful for variational quantum algorithmscited by 16
  6. 2021Optimal Rate Adaption in Federated Learning with Compressed Communicationscited by 15
  7. 2022Offline Policy Evaluation and Optimization under Confoundingcited by 12
  8. 2022Special Properties of Gradient Descent with Large Learning Ratescited by 10
  9. 2021Why Do Local Methods Solve Nonconvex Problems?cited by 8
  10. 2024Loss Landscape of Shallow ReLU-like Neural Networks: Stationary Points, Saddle Escape, and Network Embeddingcited by 6
  11. 2021Escaping Saddle Points in Distributed Newton's Method with Communication Efficiency and Byzantine Resiliencecited by 3
  12. 2021Distributed stochastic optimization with large delayscited by 3
13 more
  1. 2026Lower Bounds and Proximally Anchored SGD for Non-Convex Minimization Under Unbounded Variancecited by 2
  2. 2021The Landscape of Multi-Layer Linear Neural Network From the Perspective of Algebraic Geometrycited by 1
  3. 2022CoShNet: A Hybrid Complex Valued Neural Network using Shearletscited by 1
  4. 2024Lecture Notes on Linear Neural Networks: A Tale of Optimization and Generalization in Deep Learningcited by 1
  5. 2021Boundary Conditions for Linear Exit Time Gradient Trajectories Around Saddle Points: Analysis and Algorithmcited by 0
  6. 2021Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifoldcited by 0
  7. 2022Accelerated Gradient Flow: Risk, Stability, and Implicit Regularizationcited by 0
  8. 2023Towards guarantees for parameter isolation in continual learningcited by 0
  9. 2023Harmonic Control Lyapunov Barrier Functions for Constrained Optimal Control with Reach-Avoid Specificationscited by 0
  10. 2024Local vs Global continual learningcited by 0
  11. 2025Implicit Bias in Matrix Factorization and its Explicit Realization in a New Architecturecited by 0
  12. 2025k-SVD with Gradient Descentcited by 0
  13. 2026Riemannian Optimization for Multi-Player Quantum Games on Product Unitary Manifoldscited by 0