Equation 11 · FunSearch Found New Mathematics Without Ever Understanding the Problem
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Appendix A.2 of FunSearch’s supplementary material runs precisely the test this article’s framing has been building toward: strip the language model out of the identical loop, replace it with a hand-designed random mutation operator — the paper’s own researchers built a library of arithmetic operations and array functions, and had the mutation step insert or modify one operation at a random location in the program’s syntax tree — and run all three variants, the default Codey-based model, an open alternative called StarCoder, and the no-LLM random-mutation control, on the same target problem under the same evaluator [ 2 ] . The target was a harder relative of the dimension-8 cap set problem:…
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Appendix A.2 of FunSearch’s supplementary material runs precisely the test this article’s framing has been building toward: strip the language model out of the identical loop, replace it with a hand-designed random mutation operator — the paper’s own researchers built a library of arithmetic operations and array functions, and had the mutation step insert or modify one operation at a random location in the program’s syntax tree — and run all three variants, the default Codey-based model, an open alternative called StarCoder, and the no-LLM random-mutation control, on the same target problem under the same evaluator [ 2 ] . The target was a harder relative of the dimension-8 cap set problem: constructing a specific combinatorial object called a symmetric admissible set at size (15,10) , a structure whose full form the paper’s own ablation figure tracks generation by generation.
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