Improved step-size bound in smooth convex optimization
Improved step-size bound in smooth convex optimization is graded already known on whataifound.org, with the AI's role graded ai-assisted.
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.
- Verification
- Already known
- Autonomy
- AI-assisted
- 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bound, strictly stronger than the model's 1.5/L. The model was working from an earlier version and its result was superseded before it was produced.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
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.
Sources
Community discussion
How this is graded
whataifound.org grades every entry on two axes: verification (how solid the result is, from a machine-checked proof down to refuted) and autonomy (how much the AI did versus its human collaborators). This finding is already known and ai-assisted. Full definitions are in the methodology.
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-bound