LEAP: Library-driven Evolutionary Abstraction Paradigm for Large Language Models

Despite the remarkable progress of evolutionary LLM frameworks like AlphaEvolve in program and algorithm discovery, they consistently struggle with tasks requiring deep algorithmic reasoning and long-horizon planning, such as the Abstraction and Reasoning Corpus (ARC-AGI). A fundamental limitation of current evolutionary code generation is its reliance on unguided stochasticity to derive child programs from parents, lacking a systematic mechanism for knowledge accumulation, whereas human problem-solving thrives on the continuous consolidation and reuse of high-level conceptual abstractions. To bridge this gap, we propose the \textbf{Library-driven Evolutionary Abstraction Paradigm (LEAP)}, a cognitive-inspired framework that enables LLMs to autonomously construct and evolve a globally shared library of reusable algorithmic primitives. The evolution of this library is governed by two rigorous theoretical principles: First, the generation of new primitives is driven by a Minimum Description Length (MDL) objective, ensuring the system only assimilates concepts that genuinely compress the problem space. Second, the evolutionary survival and selection of these primitives are governed by a principled exploration-exploitation mechanism, dynamically regulating the library's life-cycle to strike an optimal balance between exploiting proven cognitive operators and exploring novel hypotheses while strictly bounding context entropy. Extensive experiments demonstrate that LEAP significantly outperforms existing LLM evolutionary baselines on the ARC-AGI benchmark and math optimizations problems, exhibiting robust cross-task generalization, highly efficient context utilization, and autonomous concept discovery capabilities.