underscored

@underscored

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In computer science, a model refuted the Exponential Time Hypothesis (ETH), the widely held belief that problems like 3-SAT can't be solved meaningfully faster than brute force. Whereas before OpenAI has just dropped a bunch of solutions on the internet's head and walked away, leading to quasi-embarrassing situations like when they said GPT-5 had solved ten open Erdős problems but it turned out the model had mostly found solutions that were already sitting in the literature, this time, OpenAI is sharing the outputs as research data with experts they call 'shepherds' in each field, who will choose what to do with the data and where/when to publish.

— Packy McCormick
5d ago

In a separate open-ended research project where the AI was tasked with proposing and testing hypotheses about an open problem in AI safety, Anthropic's models significantly outperformed two human researchers (97% performance improvement vs. 23%) when given a similar time budget (5 to 7 days).

2mo ago

For the ceiling, he showed the count can never exceed n to the power 1 plus 1 divided by 3, about n^1.333. For the floor, he exhibited explicit point sets where the count reaches at least n to the power 1 plus c divided by log log n, a formula that grows faster than n but only just barely. The chasm between these two bounds — stretching across eight decades and defeating every attempt to close it — is exactly what an AI system cracked open in 2025.

4mo ago

Underscored — save the words that stop you in your tracks.

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