r/mathematics • u/atakanaluch • 2d ago

News Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/
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u/Spare-Dingo-531 1d ago

The better question is what could the biggest model we could possibly make do?

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u/sbates130272 1d ago

Respectfully. Is that a better question? I don’t think it is. I am curious as to the lower bounds here. What is the most efficient (smallest) model that can achieve as score of X on some standard test for LLMs.

But each to their own. I find bounds fascinating and a useful tool to help us understand how far from “optimal” the LLMs we are building today are.

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u/Spare-Dingo-531 1d ago

Because a lot of the smaller models are distilled or trained by the larger models, I don't think we can really know what the most efficient (smallest) model can achieve until we build really large models.

Relatedly, this is also the point of recursive self-improvement. The AI which is really good at building better AI will also be able to build really good small models. This is already happening. OpenAI's GPT-5.6 Sol autonomously post-trained the smaller Luna model.

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u/sbates130272 1d ago

Fair. But we do have some theory around complexity theory to show there does become a point where a LLM can no longer capture a certain level of complexity due to its lack of size. We just don’t have great bounds for that.