Improved step-size bound in smooth convex optimization
GPT-5 Pro extended a guaranteed-convexity window for gradient descent from η ≤ 1/L to η ≤ 1.5/L, but the optimal 1.75/L bound had already been published months earlier.
- Lab
- OpenAI
- Model
- GPT-5 Pro
- Field
- Mathematics
- Date
- 2025-08-01
- Human collaborators
- Sébastien Bubeck
What was found
Bubeck posed an open problem from a convex optimization paper. After about 17 minutes of reasoning the model produced an improved bound using Bregman divergence inequalities and cocoercivity. Bubeck verified the proof as correct and described it as new mathematics.
Novelty check
Version 2 of the source paper, published 2 April 2025, had already established the optimal 1.75/L bound, strictly stronger than the model's 1.5/L. The model was working from an earlier version and its result was superseded before it was produced.
Caveats and known objections
The proof itself is valid; the novelty claim is not. Analysts noted the argument largely recombined known techniques in different notation. Retained as a cautionary entry: this is the single most common failure mode in this space, and the reason every entry carries a novelty check.
Nobody outside the lab has checked this yet.
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Entry history (1 event)
- AddedEntered the registry graded Already known and AI-assisted.
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Community discussion
Graded already known for verification and ai-assisted for autonomy. What these mean.
Cite this entry
whataifound.org. (2025). Improved step-size bound in smooth convex optimization. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2025-08-gpt5-convex-boundBibTeX
@misc{whataifound-openai-2025-bound,
title = {Improved step-size bound in smooth convex optimization},
author = {{whataifound.org}},
year = {2025},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by OpenAI. Verification: Already known. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2025-08-gpt5-convex-bound}
}