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This study demonstrates that LLM-guided evolutionary search can successfully solve a 70-year-old open problem in information theory by constructing optimal deletion-correcting codes for short lengths. While the approach yields empirical improvements for multiple deletions, it currently lacks new theoretical insights and is constrained by exponential evaluation costs that limit scalability. Key engineering findings suggest prioritizing function sampling over long reasoning traces and avoiding co-evolution of natural language descriptions to maintain search diversity.
LLM-Guided Search for Deletion-Correcting Codes
arXiv:2504.00613v2 Announce Type: replace Abstract: Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. We adapt FunSearch, a large language model (LLM)-guided evolutionary search, to discover functions that construct deletion-correcting codes at short code lengths. For a single deletion, our search finds a function that we prove constructs the conjectured-optimal Varshamov-Tenengolts code. For multiple deletions and quaternary edit codes, the discovered functions improve on prior explicit, search-based, and neural constructions but remain empirical heuristics without new theoretical insights. We study design choices for LLM-guided evolutionary search and find that, for our problem, compute is better allocated to sampling more functions than to longer reasoning traces per function, and that co-evolving natural language descriptions with code hurts search quality. We propose deduplicating logically identical functions during evolution, which we find critical for search diversity. Our results demonstrate the potential of LLM-guided evolutionary search for information theory and code design and represent the first application of such methods for constructing error-correcting codes. However, in our current formulation, evaluating a function scales exponentially with code length, limiting the approach to short codes.
Abstract:Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. We adapt FunSearch, a large language model (LLM)-guided evolutionary search, to discover functions that construct deletion-correcting codes at short code lengths. For a single deletion, our search finds a function that we prove constructs the conjectured-optimal Varshamov-Tenengolts code. For multiple deletions and quaternary edit codes, the discovered functions improve on prior explicit, search-based, and neural constructions but remain empirical heuristics without new theoretical insights. We study design choices for LLM-guided evolutionary search and find that, for our problem, compute is better allocated to sampling more functions than to longer reasoning traces per function, and that co-evolving natural language descriptions with code hurts search quality. We propose deduplicating logically identical functions during evolution, which we find critical for search diversity. Our results demonstrate the potential of LLM-guided evolutionary search for information theory and code design and represent the first application of such methods for constructing error-correcting codes. However, in our current formulation, evaluating a function scales exponentially with code length, limiting the approach to short codes.
Artificial Intelligence (cs.AI); Information Theory (cs.IT); Neural and Evolutionary Computing (cs.NE)
arXiv:2504.00613 [cs.AI]
(or arXiv:2504.00613v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2504.00613 Focus to learn more arXiv-issued DOI via DataCite
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