OpenAI released proposed solutions yesterday to three major mathematical problems, including a claimed refutation of the Exponential Time Hypothesis (ETH). ETH is a longstanding assumption that helps computer scientists describe computational difficulty. Scientific communities reacted with both excitement and concern. Anthropic mathematician Levent Alpöge suggested that OpenAI had drawn on existing work for the solutions. Anthropic published a separate claimed refutation of ETH hours later.
OpenAI handled publication differently across the three disciplines involved. OpenAI posted the mathematics work on GitHub. Computer scientists established a working group and requested public access to the proofs and OpenAI funding for a conference about the findings. Physicists established a working group that will decide how to publish the physics result.
MIT Professor Ryan Williams, whose research concerns computational complexity, is organizing computer scientists' response to the finding. Williams previously criticized OpenAI's proof release earlier this October as a "DDOS attack on mathematicians." However, Williams said Williams agreed to work with the frontier labs to help the field assess important ideas. OpenAI asked Williams to interpret the solution alongside UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published ETH in 1999. The researchers began by publishing an open letter seeking scientific feedback and discussion of standards for AI contributions to research. Williams said two or three unfamiliar-looking sections of OpenAI's proof convinced Williams that the broader community needed to examine the work together.
ETH relates to the broader P versus NP question, which asks whether every problem with a quickly verifiable solution can also be solved quickly. A completed Sudoku puzzle illustrates the distinction: checking a solution is quick, while finding a solution takes time. A similar distinction underlies cryptographic systems, where a key reveals an encoded message but breaking an effective code takes impractically long. Scientists have not proved whether the distinction always holds. Williams explained that P = NP would mean every problem whose solution can be checked quickly could also be solved quickly. Most scientists assume P ≠ NP, and ETH supported that assumption. ETH holds that even the fastest algorithm requires exponentially more time as the number of variables increases in a particular class of difficult logic problems.
OpenAI and Anthropic claim their models developed algorithms that solve those problems in sub-exponential time, faster than previously thought possible. Valid claims would refute ETH and might open a route toward algorithms that establish P = NP more generally. Williams said computer scientists should probably assign greater plausibility to P = NP, although individual assessments would differ. Williams said the finding challenges intuitions about the tractability of difficult NP problems. Williams also said OpenAI's algorithm is probably not the final answer and cannot be the best possible algorithm.
Williams said many papers from the past decade rely on ETH and would need reconsideration if the labs' claims withstand scrutiny. Williams said the implications for researchers' work were part of the reason Williams pressed OpenAI to support a conference. Williams said researchers need to understand both the algorithms and what foundations should replace earlier assumptions.
Williams warned that a better algorithm could render cryptographic systems using certain key sizes insecure. Williams said an early question to OpenAI science lead Dan Roberts concerned whether the finding made any cryptographic systems insecure. According to Williams, OpenAI apparently checked and was reasonably confident that the algorithm did not imply any security breaks.
Williams expressed optimism about AI-driven scientific discovery while acknowledging concerns, particularly about educating the next generation of scientists. Williams said working in computer science with advanced mathematics may have made adapting easier than for pure mathematicians. Williams said AI is pushing researchers to pursue more ambitious work and deeper scientific questions as AI makes familiar research tasks easier.
OpenAI and Anthropic Claim to Refute Exponential Time Hypothesis
FLASH AIShare
Summary
OpenAI and Anthropic claim to have refuted the Exponential Time Hypothesis, a key assumption in computational complexity. OpenAI shared its work on GitHub, with Anthropic following hours later. MIT’s Ryan Williams is gathering responses, noting parts of the proof need closer review. If valid, the claims could shift support and resistance levels in algorithmic efficiency and affect risk-to-reward ratio assessments in cryptographic systems. Both firms say their models found faster solutions to certain problems. Williams warned that many papers may need reevaluation if the claims hold.
Source:Show original
Disclaimer: The information on this page may have been obtained from third parties and does not necessarily reflect the views or opinions of KuCoin. This content is provided for general informational purposes only, without any representation or warranty of any kind, nor shall it be construed as financial or investment advice. KuCoin shall not be liable for any errors or omissions, or for any outcomes resulting from the use of this information.
Investments in digital assets can be risky. Please carefully evaluate the risks of a product and your risk tolerance based on your own financial circumstances. For more information, please refer to our Terms of Use and Risk Disclosure.