Library Learning Doesn't: The Curious Case of the Single-Use "Library"
This work critically assesses a key assumption in AI for mathematical reasoning, revealing that current methods may not achieve their intended goal of reusable knowledge, which is incremental but important for researchers and practitioners in the field.
The study investigated whether LLM library learning systems for mathematical reasoning actually learn reusable tools, finding that function reuse is extremely infrequent on benchmarks like miniF2F and MATH, and that performance gains primarily come from self-correction and self-consistency rather than library reuse.
Advances in Large Language Models (LLMs) have spurred a wave of LLM library learning systems for mathematical reasoning. These systems aim to learn a reusable library of tools, such as formal Isabelle lemmas or Python programs that are tailored to a family of tasks. Many of these systems are inspired by the human structuring of knowledge into reusable and extendable concepts, but do current methods actually learn reusable libraries of tools? We study two library learning systems for mathematics which both reported increased accuracy: LEGO-Prover and TroVE. We find that function reuse is extremely infrequent on miniF2F and MATH. Our followup ablation experiments suggest that, rather than reuse, self-correction and self-consistency are the primary drivers of the observed performance gains. Our code and data are available at https://github.com/ikb-a/curious-case