Improved Lower Bounds for Five Classical Ramsey Numbers Achieved Using LLM-Based Code Mutation Agent
By
1024core
A respectable bake. You'd come back tomorrow for another.
Summary
Researchers have improved lower bounds for five classical Ramsey numbers using AlphaEvolve, an LLM-based code mutation agent. The new lower bounds are: R(3,13) from 60 to 61, R(3,18) from 99 to 100, R(4,13) from 138 to 139, R(4,14) from 147 to 148, and R(4,15) from 158 to 159. The AlphaEvolve system successfully recovered lower bounds for all known exact Ramsey numbers and matched best known lower bounds across many other cases, representing a single meta-algorithm approach to generating search algorithms for these computational mathematics problems.
Key quotes
· 4 pulledWe present improved lower bounds for five classical Ramsey numbers: R(3, 13) is increased from 60 to 61, R(3, 18) from 99 to 100, R(4, 13) from 138 to 139, R(4, 14) from 147 to 148, and R(4, 15) from 158 to 159.
These results were achieved using AlphaEvolve, an LLM-based code mutation agent.
Beyond these new results, we successfully recovered lower bounds for all Ramsey numbers known to be exact, and matched the best known lower bounds across many other cases.
AlphaEvolve is a single meta-algorithm yielding search algorithms for all of our results.
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