{"total":86,"rows":[{"id":"2209.15594","title":"Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability","created":"2022-09-30","cited_by_count":155,"area":null},{"id":"2205.09745","title":"Understanding Gradient Descent on Edge of Stability in Deep Learning","created":"2022-05-19","cited_by_count":128,"area":null},{"id":"2207.14484","title":"Adaptive Gradient Methods at the Edge of Stability","created":"2022-07-29","cited_by_count":101,"area":null},{"id":"2206.04817","title":"The Slingshot Mechanism: An Empirical Study of Adaptive Optimizers and the Grokking Phenomenon","created":"2022-06-10","cited_by_count":94,"area":null},{"id":"2206.07085","title":"Understanding the Generalization Benefit of Normalization Layers: Sharpness Reduction","created":"2022-06-14","cited_by_count":86,"area":null},{"id":"2208.12591","title":"On the Implicit Bias in Deep-Learning Algorithms","created":"2022-08-26","cited_by_count":86,"area":null},{"id":"2207.12678","title":"Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability","created":"2022-07-26","cited_by_count":63,"area":null},{"id":"2210.03294","title":"Understanding Edge-of-Stability Training Dynamics with a Minimalist Example","created":"2022-10-07","cited_by_count":56,"area":null},{"id":"2210.01513","title":"The Dynamics of Sharpness-Aware Minimization: Bouncing Across Ravines and Drifting Towards Wide Minima","created":"2022-10-04","cited_by_count":51,"area":null},{"id":"2212.07469","title":"Learning threshold neurons via the \"edge of stability\"","created":"2022-12-14","cited_by_count":51,"area":null},{"id":"2204.11326","title":"Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes","created":"2022-04-24","cited_by_count":43,"area":null},{"id":"2305.11788","title":"Implicit Bias of Gradient Descent for Logistic Regression at the Edge of Stability","created":"2023-05-19","cited_by_count":42,"area":null},{"id":"2405.16002","title":"Does SGD really happen in tiny subspaces?","created":"2024-05-25","cited_by_count":36,"area":null},{"id":"2402.15926","title":"Large Stepsize Gradient Descent for Logistic Loss: Non-Monotonicity of the Loss Improves Optimization Efficiency","created":"2024-02-24","cited_by_count":35,"area":null},{"id":"2306.04815","title":"Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning","created":"2023-06-07","cited_by_count":31,"area":null},{"id":"2305.15287","title":"The Crucial Role of Normalization in Sharpness-Aware Minimization","created":"2023-05-24","cited_by_count":26,"area":null},{"id":"2307.04204","title":"Trajectory Alignment: Understanding the Edge of Stability Phenomenon via Bifurcation Theory","created":"2023-07-09","cited_by_count":26,"area":null},{"id":"2310.17087","title":"Good regularity creates large learning rate implicit biases: edge of stability, balancing, and catapult","created":"2023-10-26","cited_by_count":25,"area":null},{"id":"2305.12475","title":"Two Sides of One Coin: the Limits of Untuned SGD and the Power of Adaptive Methods","created":"2023-05-21","cited_by_count":23,"area":null},{"id":"2402.17457","title":"Super Consistency of Neural Network Landscapes and Learning Rate Transfer","created":"2024-02-27","cited_by_count":23,"area":null},{"id":"2311.02076","title":"Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos","created":"2023-11-03","cited_by_count":22,"area":null},{"id":"2305.13064","title":"Gradient Descent Monotonically Decreases the Sharpness of Gradient Flow Solutions in Scalar Networks and Beyond","created":"2023-05-22","cited_by_count":21,"area":null},{"id":"2306.09000","title":"When and Why Momentum Accelerates SGD:An Empirical Study","created":"2023-06-15","cited_by_count":19,"area":null},{"id":"2309.12488","title":"Sharpness-Aware Minimization and the Edge of Stability","created":"2023-09-21","cited_by_count":17,"area":null},{"id":"2310.01687","title":"From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression","created":"2023-10-02","cited_by_count":17,"area":null},{"id":"2403.04081","title":"Directional Smoothness and Gradient Methods: Convergence and Adaptivity","created":"2024-03-06","cited_by_count":17,"area":null},{"id":"2406.08654","title":"Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization","created":"2024-06-12","cited_by_count":17,"area":null},{"id":"2305.12133","title":"Loss Spike in Training Neural Networks","created":"2023-05-20","cited_by_count":16,"area":null},{"id":"2406.05033","title":"Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes","created":"2024-06-07","cited_by_count":14,"area":null},{"id":"2607.21716","title":"A Defense of the Quadratic Model","created":"2026-07-23","cited_by_count":14,"area":null},{"id":"2506.04805","title":"Adaptive Preconditioners Trigger Loss Spikes in Adam","created":"2025-06-05","cited_by_count":13,"area":null},{"id":"2212.07295","title":"Maximal Initial Learning Rates in Deep ReLU Networks","created":"2022-12-14","cited_by_count":11,"area":null},{"id":"2302.01952","title":"On a continuous time model of gradient descent dynamics and instability in deep learning","created":"2023-02-03","cited_by_count":11,"area":null},{"id":"2604.14108","title":"Momentum Further Constrains Sharpness at the Edge of Stochastic Stability","created":"2026-04-15","cited_by_count":10,"area":null},{"id":"2208.07951","title":"On the generalization of learning algorithms that do not converge","created":"2022-08-16","cited_by_count":9,"area":null},{"id":"2310.00692","title":"A Theoretical Analysis of Noise Geometry in Stochastic Gradient Descent","created":"2023-10-01","cited_by_count":9,"area":null},{"id":"2602.01480","title":"Rod Flow: A Continuous-Time Model for Gradient Descent at the Edge of Stability","created":"2026-02-01","cited_by_count":9,"area":null},{"id":"2305.14683","title":"On progressive sharpening, flat minima and generalisation","created":"2023-05-24","cited_by_count":7,"area":null},{"id":"2504.04105","title":"Minimax Optimal Convergence of Gradient Descent in Logistic Regression via Large and Adaptive Stepsizes","created":"2025-04-05","cited_by_count":7,"area":null},{"id":"2509.25351","title":"Gradient Descent with Large Step Sizes: Chaos and Fractal Convergence Region","created":"2025-09-29","cited_by_count":7,"area":null},{"id":"2604.20446","title":"The Origin of Edge of Stability","created":"2026-04-22","cited_by_count":6,"area":null},{"id":"2206.02139","title":"Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networks","created":"2022-06-05","cited_by_count":5,"area":null},{"id":"2304.12579","title":"Learning Trajectories are Generalization Indicators","created":"2023-04-25","cited_by_count":5,"area":null},{"id":"2506.06940","title":"Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More","created":"2025-06-07","cited_by_count":5,"area":null},{"id":"2503.02809","title":"A Minimalist Example of Edge-of-Stability and Progressive Sharpening","created":"2025-03-04","cited_by_count":4,"area":null},{"id":"2506.00181","title":"On the Interaction of Batch Noise, Adaptivity, and Compression, under $(L_0,L_1)$-Smoothness: An SDE Approach","created":"2025-05-30","cited_by_count":4,"area":null},{"id":"2510.17506","title":"Convergence Rates for Gradient Descent on the Edge of Stability in Overparametrised Least Squares","created":"2025-10-20","cited_by_count":4,"area":null},{"id":"2311.15051","title":"Gradient Descent with Polyak's Momentum Finds Flatter Minima via Large Catapults","created":"2023-11-25","cited_by_count":3,"area":null},{"id":"2402.13108","title":"On the Convergence of Gradient Descent for Large Learning Rates","created":"2024-02-20","cited_by_count":3,"area":null},{"id":"2507.05164","title":"A Dynamical Systems Perspective on the Analysis of Neural Networks","created":"2025-07-07","cited_by_count":3,"area":null},{"id":"2510.18120","title":"Generalization Below the Edge of Stability: The Role of Data Geometry","created":"2025-10-20","cited_by_count":3,"area":null},{"id":"2602.14789","title":"On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials","created":"2026-02-16","cited_by_count":3,"area":null},{"id":"2309.05679","title":"Good-looking but Lacking Faithfulness: Understanding Local Explanation Methods through Trend-based Testing","created":"2023-09-09","cited_by_count":2,"area":null},{"id":"2401.08426","title":"GD doesn't make the cut: Three ways that non-differentiability affects neural network training","created":"2024-01-16","cited_by_count":2,"area":null},{"id":"2604.19740","title":"Generalization at the Edge of Stability","created":"2026-04-21","cited_by_count":2,"area":null},{"id":"2604.26993","title":"State-Dependent Lyapunov Analysis of Rank-1 Matrix Factorization","created":"2026-04-28","cited_by_count":2,"area":null},{"id":"2206.02001","title":"A PDE-based Explanation of Extreme Numerical Sensitivities and Edge of Stability in Training Neural Networks","created":"2022-06-04","cited_by_count":1,"area":null},{"id":"2312.15295","title":"AdamL: A fast adaptive gradient method incorporating loss function","created":"2023-12-23","cited_by_count":1,"area":null},{"id":"2406.00127","title":"Training on the Edge of Stability Is Caused by Layerwise Jacobian Alignment","created":"2024-05-31","cited_by_count":1,"area":null},{"id":"2502.03701","title":"First-ish Order Methods: Hessian-aware Scalings of Gradient Descent","created":"2025-02-06","cited_by_count":1,"area":null},{"id":"2502.04889","title":"Any-stepsize Gradient Descent for Separable Data under Fenchel-Young Losses","created":"2025-02-07","cited_by_count":1,"area":null},{"id":"2504.12675","title":"Physics Informed Constrained Learning of Dynamics from Static Data","created":"2025-04-17","cited_by_count":1,"area":null},{"id":"2510.25800","title":"FreIE: Low-Frequency Spectral Bias in Neural Networks for Time-Series Tasks","created":"2025-10-29","cited_by_count":1,"area":null},{"id":"2602.05065","title":"Does SGD Seek Flatness or Sharpness? An Exactly Solvable Model","created":"2026-02-04","cited_by_count":1,"area":null},{"id":"2607.08380","title":"Dynamics of Gradient Descent with Large Step Size Near a Manifold of Flat Minima","created":"2026-07-09","cited_by_count":1,"area":null},{"id":"2607.21005","title":"Weight-norm Criticality: A Mechanism for Loss Spikes Induced by the Normalization and Weight Decay","created":"2026-07-23","cited_by_count":1,"area":null},{"id":"2608.18415","title":"The Road Taken: The Role of Optimizers at the Edge of Stability","created":"2026-08-19","cited_by_count":1,"area":null},{"id":"2608.20638","title":"Adam at the Edge of Stability: Adaptive Feedback, Provable Oscillation, and Gradient Reversal","created":"2026-08-21","cited_by_count":1,"area":null},{"id":"2302.09376","title":"Why is parameter averaging beneficial in SGD? An objective smoothing perspective","created":"2023-02-18","cited_by_count":0,"area":null},{"id":"2410.10690","title":"Dynamical loss functions shape landscape topography and improve learning in artificial neural networks","created":"2024-10-14","cited_by_count":0,"area":null},{"id":"2506.14806","title":"Heavy-Ball Momentum Method in Continuous Time and Discretization Error Analysis","created":"2025-06-03","cited_by_count":0,"area":null},{"id":"2510.09034","title":"Convergence of optimizers implies eigenvalues filtering at equilibrium","created":"2025-10-10","cited_by_count":0,"area":null},{"id":"2510.24466","title":"Non-Singularity of the Gradient Descent map for Neural Networks with Piecewise Analytic Activations","created":"2025-10-28","cited_by_count":0,"area":null},{"id":"2602.18946","title":"Exponential Convergence of (Stochastic) Gradient Descent for Separable Logistic Regression","created":"2026-02-21","cited_by_count":0,"area":null},{"id":"2604.14669","title":"Zeroth-Order Optimization at the Edge of Stability","created":"2026-04-16","cited_by_count":0,"area":null},{"id":"2604.16809","title":"A Mechanism Study of Delayed Loss Spikes in Batch-Normalized Linear Models","created":"2026-04-18","cited_by_count":0,"area":null},{"id":"2604.18202","title":"Centre manifold theorem for maps along manifolds of fixed points","created":"2026-04-20","cited_by_count":0,"area":null},{"id":"2605.26489","title":"The Stability of Singular Distribution: A Spectral Perspective on the Two-Phase Dynamics of Language Model Pre-training","created":"2026-05-26","cited_by_count":0,"area":null},{"id":"2606.04212","title":"Edge of Stability Selectively Shapes Learning Across the Data Distribution","created":"2026-06-02","cited_by_count":0,"area":null},{"id":"2608.04382","title":"Non-asymptotic implicit bias of logistic regression at early-stage gradient descent dynamics","created":"2026-08-05","cited_by_count":0,"area":null},{"id":"2608.21660","title":"Variational Structure at the Edge of Stability","created":"2026-08-21","cited_by_count":0,"area":null},{"id":"2609.01034","title":"The Multiple Timescales of Gradient Descent on the Edge of Stability: A Perturbative Derivation of the Central Flow","created":"2026-09-01","cited_by_count":0,"area":null},{"id":"2609.18314","title":"Beyond Quadratic Loss: The Stability Phase Diagram of Adam","created":"2026-09-16","cited_by_count":0,"area":null},{"id":"2609.32290","title":"A Journey to the Edge of Stability","created":"2026-09-26","cited_by_count":0,"area":null},{"id":"2609.34915","title":"Muon Sublates the Edge of Stability in LLM Pretraining","created":"2026-09-28","cited_by_count":0,"area":null},{"id":"2610.00538","title":"Multi-agent Auditory Scene Analysis: Improved Localization Speed and Robustness by Multi-beamformed Speech Quality Feedback","created":"2026-09-30","cited_by_count":0,"area":null}],"next_cursor":null}