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New research frameworks model gradient descent at the edge of stability

By PulseAugur Editorial · [3 sources] ·

Two new research papers explore the phenomenon of gradient descent operating at the edge of stability (EoS) in deep learning. The first paper introduces 'Edge Flow,' a system of differential equations that models gradient descent dynamics at EoS, decomposing them into center, oscillation direction, and magnitude. The second paper presents a bifurcation theory framework that applies to overparameterized neural networks, showing how stable EoS training arises from a flip bifurcation and proving convergence to the minimizing manifold under certain conditions. AI

IMPACT These frameworks offer new theoretical tools for understanding and potentially improving the stability and convergence of deep learning training processes.

RANK_REASON Two academic papers published on arXiv presenting new theoretical frameworks for understanding deep learning dynamics.

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 3 sources. How we write summaries →

New research frameworks model gradient descent at the edge of stability

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Two academic papers published on arXiv presenting new theoretical frameworks for understanding deep learning dynamics.
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COVERAGE [3]

  1. arXiv cs.LG TIER_1 English(EN) · Pierre Marion ·

    Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability

    arXiv:2606.18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate. Classical an…

  2. arXiv cs.LG TIER_1 English(EN) · Pierre Marion ·

    Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability

    Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/η$, where $η$ is the learning rate. Classical analysis tools such as gradient flow and the descent lem…

  3. arXiv cs.LG TIER_1 English(EN) · Eric Gan ·

    A Bifurcation Theory Framework for Gradient Descent on the Edge of Stability

    arXiv:2606.15551v1 Announce Type: new Abstract: The Edge of Stability (EoS) phenomenon, where gradient descent operates with sharpness exceeding the classical convergence threshold yet the loss decreases over long timescales, is ubiquitous in modern deep learning but remains poor…

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