Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic | SpinGraph: Technical framing
description: SpinGraph analysis of arXiv Machine Learning's Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic story: technical framing, The Hype, Spin Scor…
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markdown: https://stuffthatspins.com/spin/provable-edge-of-stability-for-adam-on-a-one-dimensional-quadratic.md
keywords: edge-of-stability
keywords: Adam optimizer
keywords: theoretical ML
keywords: The Hype
keywords: narrative intelligence
published: 2026-08-24T04:00:00+00:00
modified: 2026-08-24T06:58:46.594507+00:00

Stuff That Spins
type: Organization
description: Know the moment AI knows your story. Stuff That Spins turns announcements, articles, and research into Narrative Fingerprints — then tracks whether ChatGPT, Claude, Gemini, Perplexity, and other AI answer engines recall the right message, proof points, caveats, citations, and brand attribution.

Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic
type: NewsArticle
alternative headline: Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic | SpinGraph: Technical framing
description: SpinGraph analysis of arXiv Machine Learning's Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic story: technical framing, The Hype, Spin Scor…
date published: 2026-08-24T04:00:00+00:00
date modified: 2026-08-24T06:58:46.594507+00:00
main entity of page: https://stuffthatspins.com/spin/provable-edge-of-stability-for-adam-on-a-one-dimensional-quadratic
is accessible for free: true
language: en-US
article section: research
keywords: edge-of-stability, Adam optimizer, theoretical ML, dynamical systems, optimization theory
author: arXiv Machine Learning
publisher: Stuff That Spins
citation: https://arxiv.org/abs/2608.20638
about: edge-of-stability
about: Adam optimizer
about: theoretical ML
about: dynamical systems
about: optimization theory
mentions: arXiv Machine Learning
abstract: Proves Adam's edge-of-stability (EoS) arises from optimizer-induced dynamics—not loss geometry—in a controlled 1D quadratic model Derives exact stability threshold: $2(1+\beta_1)/[\eta(1-\beta_1)]$ and shows Adam restores toward it in broad parameter regimes Identifies concrete failure modes: subcritical periodic orbits and supercritical trajectories converging to optimum

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item list element: Stuff That Spins
  type: ListItem
  position: 1
  item: https://stuffthatspins.com/
item list element: Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic
  type: ListItem
  position: 2
  item: https://stuffthatspins.com/spin/provable-edge-of-stability-for-adam-on-a-one-dimensional-quadratic

Spin Analysis: technical framing
type: AnalysisNewsArticle
description: Emphasizes explanatory power and mechanistic clarity; minimizes that the setting is highly idealized (1D, quadratic, uncorrected Adam) and lacks empirical validation on real models or tasks.
about: technical framing
  type: DefinedTerm
  description: Rigorous theoretical breakthrough that demystifies a core deep learning mystery.
  term code: The Hype
additional property: Spin Score
  type: PropertyValue
  value: 40
  unit text: percent
additional property: Narrative Risk
  type: PropertyValue
  value: low
additional property: AI Repetition Risk
  type: PropertyValue
  value: moderate
additional property: Likely AI Summary
  type: PropertyValue
  value: New research proves Adam optimizer has a provable edge-of-stability mechanism, explaining why it works so well in practice.
additional property: Narrative Frame
  type: PropertyValue
  value: Rigorous theoretical breakthrough that demystifies a core deep learning mystery.
additional property: Missing Context
  type: PropertyValue
  value: No discussion of relevance to modern large-scale training; No comparison to other optimizers (e.g., SGD, Lion) in same setting; No empirical benchmarks or ablation against real-world loss landscapes
additional property: How the Spin Works
  type: PropertyValue
  value: The story uses titles, institutions, awards, rankings, partners, experts, or official language to make the subject feel more credible. Watch for loaded terms such as concrete dynamical explanation, broad regimes, restoring tendency, exposing its limitations. The distribution reads as academic distribution. A pressure point: No discussion of relevance to modern large-scale training.
author: Stuff That Spins
is part of: Provable Edge-of-Stability for Adam on a One-Dimensional Quadratic

Extracted Claims
type: ItemList
item list element: ListItem
  position: 1
  item: Claim
    text: We prove that Adam exhibits a restoring tendency toward its frozen stability threshold $2(1+\beta_1)/[\eta(1-\beta_1)]$ in broad regimes.
    appearance: We characterize the resulting dynamics across the parameter space. In broad regimes, we prove that Adam exhibits a restoring tendency toward its frozen stability threshold $2(1+\beta_1)/[\eta(1-\beta_1)]$.
    author: arXiv Machine Learning

Key Statistics
type: Dataset
description: Extracted statistics from the source narrative
variable measured: dimensionality
  type: PropertyValue
  value: 1
  description: Analysis restricted to one-dimensional quadratic loss
variable measured: optimizer variant
  type: PropertyValue
  value: uncorrected Adam
  description: Excludes bias correction, enabling analytical tractability