Research map / Optimization / Implicit bias and generalization

Classification at the Edge of Stability: Unifying Self-Stabilization and Convergence Rates

NeurIPS 2026 · Optimization › Implicit bias and generalization · approach: Edge-of-stability dynamics

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's abstract only. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Studies gradient descent at the edge of stability for classification, aiming to unify self-stabilization and convergence-rate analyses (abstract only; full text unavailable).

Problem

Gradient descent with step sizes above classical stability thresholds (edge of stability) makes standard convergence theory inapplicable, yet this regime often yields faster convergence and better generalization; existing theories give only partial explanations.

Approach

Unifies self-stabilization and convergence-rate perspectives for GD at the edge of stability in classification settings; the abstract does not state the specific mechanism.

Surprising findings

• Edge-of-stability GD with non-monotonic loss and oscillations often converges faster and generalizes better than classical stable-step-size training.

Closest papers by meaning

• Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability (ICLR 2021 · similarity 0.93)
• Convergence Rates for Gradient Descent on the Edge of Stability for Overparametrised Least Squares (NeurIPS 2025 · similarity 0.92)
• A Precise Characterization of SGD Stability Using Loss Surface Geometry (ICLR 2024 · similarity 0.90)
• A Unified Stability Analysis of SAM vs SGD: Role of Data Coherence and Emergence of Simplicity Bias (NeurIPS 2025 · similarity 0.89)
• On the Unstable Convergence Regime of Gradient Descent (AAAI 2024 · similarity 0.89)
• A Minimalist Example of Edge-of-Stability and Progressive Sharpening (NeurIPS 2025 · similarity 0.89)