💡GPT-5.6 Closes Convex Optimization Gap With Formal Proof
AI closes a decades-old math gap with formal proof
TL;DR
OpenAI's GPT-5.6 has supplied a formal proof in Lean to close a longstanding complexity gap in deterministic zeroth-order convex optimization, potentially shifting the landscape of AI capabilities in solving complex problems.
GPT-5.6 has formally verified a new theorem in Lean, closing a 30-year gap in deterministic zeroth-order convex optimization. This breakthrough impacts how we understand algorithmic efficiency and computational limits for finding optimal solutions. The proof shows that order d² function evaluations are sufficient to find an ε-optimal point of f, with Q(d, ε) = O(d²). While the result hasn't been peer-reviewed yet, it opens up new possibilities in AI's ability to solve complex optimization problems.
Key Points
GPT-5.6 provided a ten-page prompt to formally verify the theorem in Lean, closing the complexity gap.
The new result shows order d² function evaluations are sufficient for finding ε-optimal points of f, with Q(d, ε) = O(d²).
This breakthrough impacts optimization algorithms and computational limits, potentially changing how we approach complex problem-solving.
While not peer-reviewed yet, the proof's mechanics rely on existing results from convex geometry and complexity theory.
The preprint is available at https://github.com/PhillipKerger/zero-order-bounds-lean-verification
Why It Matters
If you're working with optimization algorithms in machine learning or operations research, this proof could change how you approach computational limits and algorithmic efficiency. The result shows that order d² function evaluations are sufficient for finding ε-optimal points of f, which can significantly impact the design and analysis of optimization methods.
Frequently Asked Questions
Why does this matter?
If you're working with optimization algorithms in machine learning or operations research, this proof could change how you approach computational limits and algorithmic efficiency. The result shows that order d² function evaluations are sufficient for finding ε-optimal points of f, which can significantly impact the design and analysis of optimization methods.
What happened?
OpenAI's GPT-5.6 has supplied a formal proof in Lean to close a longstanding complexity gap in deterministic zeroth-order convex optimization, potentially shifting the landscape of AI capabilities in solving complex problems.
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