핵심 요약 • Recursive Self-Improvement in AI 서베이는 개선 신호를 신뢰도에 따라 형식 검증기, 실행 피드백, 학습된 심판, 내재 신호의 네 단계 검증 계층으로 정렬하고, 실제로 입증된 자기 개선의 강도가 이 계층을 따른다고 관찰합니다(측정된 법칙이 아닌 정성적 패턴입니다). • 자기 개선 루프의 실패 모드는 자기 확증 루프, 붕괴, 다양성 붕괴, 프레임 고착의 네 가지이며, 이 중 프레임 고착은 루프가 추적하는 지표로는 감지할 수 없습니다. • 자동 연구(139편)에서는 자동 평가기가 있는 진화적 프로그램 발견(FunSearch, AlphaEvolve)이 AI 인프라로 되돌아가는 결과를 냈지만, AI 과학자 에이전트는 SciIntegrity-Bench에서 7개 모델 전반에 $34.2%$ 의 무결성 실패율을 보이는 등 검증이 생성을 따라가지 못하고...

In this white paper, we present AlphaEvolve, an evolutionary coding agent that substantially enhances capabilities of state-of-the-art LLMs on highly challenging tasks such as tackling open scientific...

We introduce FunSearch, a method for searching for “functions” written in computer code, and find new solutions in mathematics and computer science. FunSearch works by pairing a pre-trained LLM, w...

FunSearch makes discoveries in established open problems using large language models by searching for programs describing how to solve a problem, rather than what the solution is.

YouTube video by Spot The Sneaky Ninja

Researchers from Deep Mind have developed FunSearch, a method that uses Large Language Models (LLMs) to discover new solutions in mathematics and computer science. The system pairs a pre-trained LLM with an automated evaluator to create new knowledge. FunSearch has made the first discovery for challenging open problems in science or mathematics using LLMs, finding new solutions for the cap set problem and more effective algorithms for the bin-packing problem. The system also outputs programs that reveal how its solutions are constructed, potentially inspiring further insights in scientists who use FunSearch.

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.

We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for that function. The free parameters of the ansatz are fitted using standard numerical optimisers, and a collection of such ansätze make up the population of a genetic algorithm. Unlike other symbolic regression techniques, our method does not require the specification of a set of functions to be used in regression, but with appropriate prompt engineering, we can arbitrarily condition the generative step. By using Kolmogorov Arnold Networks (KANs), we demonstrate that ``univariate is all you need'' for symbolic regression, and extend this method to multivariate functions by learning the univariate function on each edge of a trained KAN. The combined expression is then simplified by further processing with a language model.

Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. In this paper, we propose a novel approach for constructing deletion-correcting codes. A code is a set of sequences satisfying certain constraints, and we construct it by greedily adding the highest-priority sequence according to a priority function. To find good priority functions, we leverage FunSearch, a large language model (LLM)-guided evolutionary search proposed by Romera et al., 2024. FunSearch iteratively generates, evaluates, and refines priority functions to construct large deletion-correcting codes. For a single deletion, our evolutionary search finds functions that construct codes which match known maximum sizes, reach the size of the largest (conjectured optimal) Varshamov-Tenengolts codes where the maximum is unknown, and independently rediscover them in equivalent form. For two deletions, we find functions that construct codes with new best-known sizes for code lengths \\( n = 12, 13 \\), and \\( 16 \\), establishing improved lower bounds. These results demonstrate the potential of LLM-guided search for information theory and code design and represent the first application of such methods for constructing error-correcting codes.

We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our implementation is designed to be useful in practice for working mathematicians; it does not require expertise in machine learning or access to high-performance computing resources. Applying {\it funsearch} to a new problem involves modifying a small segment of Python code and selecting a large language model (LLM) from one of many third-party providers. We benchmarked our implementation on three different problems, obtaining metrics that may inform applications of {\it funsearch} to new problems. Our results demonstrate that {\it funsearch} successfully learns in a variety of combinatorial and number-theoretic settings, and in some contexts learns principles that generalize beyond the problem originally trained on.