OpenAI and Anthropic Claim AI Models Refute Exponential Time Hypothesis
OpenAI released solutions to three math problems, including a claimed refutation of the Exponential Time Hypothesis; Anthropic issued its own refutation hours later as computer scientists organized a review.
The release drew a mixed response. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions on pre-existing work, and hours later Anthropic released its own refutation of ETH, according to TechCrunch. The report said OpenAI structured its releases differently for each of the three disciplines involved: mathematicians received the work on GitHub; computer scientists formed a working group and asked for the proofs to be shared publicly and for OpenAI to fund a conference to discuss them; physicists formed a working group that will determine how their result will be released.
MIT Professor Ryan Williams is organizing the computer science response. Williams, whose work focuses on computational complexity, criticized an earlier OpenAI proof release this October as a “DDOS attack on mathematicians,” but he told TechCrunch he agreed to collaborate with the frontier labs to help evaluate ideas important to the field. OpenAI asked him to help interpret the solution along with UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published the ETH in 1999. Their first step was to release an open letter calling for feedback from scientists interested in the problems and for discussion of norms around AI contributions to their work.
“Some parts [of OpenAI’s proof] are, maybe you could say routine, but then yes, there are two or three alien-looking parts, and it’s exactly these parts that that I saw that made me think, wow, this is something that the whole community needs to work on together,” Williams told TechCrunch.
The ETH is part of the broader P vs NP question, which asks whether every problem whose solution can be quickly verified can also be quickly solved. A Sudoku puzzle is a simple example: a completed solution can be checked quickly, but finding it can take a long time. Scientists have not proved whether that asymmetry always holds. Most assume that P does not equal NP, and ETH provides evidence for that assumption by saying that even the fastest algorithm needs exponentially more time as the number of variables grows in a specific class of logic puzzles.
OpenAI and Anthropic claim their models have produced algorithms that solve those puzzles in “sub-exponential” time, faster than previously thought possible. If true, the results would refute ETH and might open a path toward algorithms that generally perform P = NP. “Every computer scientist should probably put a little more weight on the plausibility of P = NP, but one’s weight may vary,” Williams told TechCrunch. “I do think that it kind of calls into question a lot of the intuitions that we thought we had about … how tractable [hard NP problems] are. I also think that this is probably not the final answer either. I don’t think that OpenAI’s algorithm could possibly be the best algorithm you can get.”
Williams said ETH’s durability has led to its inclusion in many scientific papers over the past decade, and those papers will need to be revisited if the AI labs’ claims hold up. He said that was part of why he pushed OpenAI to support a conference. He also said cybersecurity questions come before scientific concerns, because an improved algorithm could imply that cryptographic systems relying on certain key sizes could be affected.