mlsanityData to 14 Oct 2026

Neon2: Finding Local Minima via First-Order Oracles

arXiv 1711.06673 ↗First posted 17 Nov 2017cs.LG cs.DS cs.NEcited by 36

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Abstract (arXiv)

We propose a reduction for non-convex optimization that can (1) turn an stationary-point finding algorithm into an local-minimum finding one, and (2) replace the Hessian-vector product computations with only gradient computations. It works both in the stochastic and the deterministic settings, without hurting the algorithm's performance. As applications, our reduction turns Natasha2 into a first-order method without hurting its performance. It also converts SGD, GD, SCSG, and SVRG into algorithms finding approximate local minima, outperforming some best known results.

Key facts. Cited by 36 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 Nov 2017.

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Citing papers per year: 2021: 8; 2022: 11; 2023: 6; 2024: 3; 2025: 3; 2026: 5.

36 papers.

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  1. 2023Gradient Norm Aware Minimization Seeks First-Order Flatness and Improves Generalizationcited by 57
  2. 2023Flatness-Aware Minimization for Domain Generalizationcited by 27
  3. 2022Efficiently Escaping Saddle Points in Bilevel Optimizationcited by 19
  4. 2022Restarted Nonconvex Accelerated Gradient Descent: No More Polylogarithmic Factor in the O(ε-7/4) Complexitycited by 17
  5. 2023Near-Optimal Nonconvex-Strongly-Convex Bilevel Optimization with Fully First-Order Oraclescited by 17
  6. 2021Escape saddle points by a simple gradient-descent based algorithmcited by 11
  7. 2022On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walkscited by 9
  8. 2021Escaping Saddle Points Faster with Stochastic Momentumcited by 8
  9. 2024Improved Complexity for Smooth Nonconvex Optimization: A Two-Level Online Learning Approach with Quasi-Newton Methodscited by 7
  10. 2022Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradientscited by 6
  11. 2022Simple and Optimal Stochastic Gradient Methods for Nonsmooth Nonconvex Optimizationcited by 5
  12. 2026Lower Bounds and Proximally Anchored SGD for Non-Convex Minimization Under Unbounded Variancecited by 5
24 more
  1. 2024Quantum Algorithms and Lower Bounds for Finite-Sum Optimizationcited by 4
  2. 2021Escaping Saddle Points in Distributed Newton's Method with Communication Efficiency and Byzantine Resiliencecited by 3
  3. 2025Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimismcited by 3
  4. 2022Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD for Communication Efficient Nonconvex Distributed Learningcited by 2
  5. 2022Tackling benign nonconvexity with smoothing and stochastic gradientscited by 2
  6. 2022A Newton-CG based barrier method for finding a second-order stationary point of nonconvex conic optimization with complexity guaranteescited by 2
  7. 2022Variance-Reduced Conservative Policy Iterationcited by 2
  8. 2023A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimizationcited by 2
  9. 2023Achieving O(ε-1.5) Complexity in Hessian/Jacobian-free Stochastic Bilevel Optimizationcited by 2
  10. 2021Escaping Saddle Points with Compressed SGDcited by 1
  11. 2021Faster Perturbed Stochastic Gradient Methods for Finding Local Minimacited by 1
  12. 2024Noise is All You Need: Private Second-Order Convergence of Noisy SGDcited by 1
  13. 2025Faster Gradient Methods for Highly-Smooth Stochastic Bilevel Optimizationcited by 1
  14. 2026AdaCubic: An Adaptive Cubic Regularization Optimizer for Deep Learningcited by 1
  15. 2026Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimizationcited by 1
  16. 2021Boundary Conditions for Linear Exit Time Gradient Trajectories Around Saddle Points: Analysis and Algorithmcited by 0
  17. 2021Exclusive Topic Modelingcited by 0
  18. 2021Escaping Saddle Points with Stochastically Controlled Stochastic Gradient Methodscited by 0
  19. 2022HOUDINI: Escaping from Moderately Constrained Saddlescited by 0
  20. 2022Versatile Single-Loop Method for Gradient Estimator: First and Second Order Optimality, and its Application to Federated Learningcited by 0
  21. 2023Newton-CG methods for nonconvex unconstrained optimization with H"older continuous Hessiancited by 0
  22. 2025Stable Coresets via Posterior Sampling: Aligning Induced and Full Loss Landscapescited by 0
  23. 2026A Parameter-Free First-Order Algorithm for Non-Convex Optimization with tildemkern1mu O(ε-5/3) Global Ratecited by 0
  24. 2026To Solve Bilevel Optimization with Nonconvex Lower Levels, We Need Second-Order Stationaritycited by 0