# Library Learning Doesn't: The Curious Case of the Single-Use "Library"

arXiv: https://arxiv.org/abs/2410.20274 · HTML: https://mlsanity.com/paper/2410.20274/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 36 references that are in the map.
- First posted on arXiv 26 Oct 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 30)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [API-Bank: A Comprehensive Benchmark for Tool-Augmented LLMs](https://mlsanity.com/paper/2304.08244/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Large Language Models as Tool Makers](https://mlsanity.com/paper/2305.17126/) (2023)
- [ToolSandbox: A Stateful, Conversational, Interactive Evaluation Benchmark for LLM Tool Use Capabilities](https://mlsanity.com/paper/2408.04682/) (2024)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Tool Learning with Large Language Models: A Survey](https://mlsanity.com/paper/2405.17935/) (2024)
- [OS-Copilot: Towards Generalist Computer Agents with Self-Improvement](https://mlsanity.com/paper/2402.07456/) (2024)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [StableToolBench: Towards Stable Large-Scale Benchmarking on Tool Learning of Large Language Models](https://mlsanity.com/paper/2403.07714/) (2024)
- [CRAFT: Customizing LLMs by Creating and Retrieving from Specialized Toolsets](https://mlsanity.com/paper/2309.17428/) (2023)
- [LEGO-Prover: Neural Theorem Proving with Growing Libraries](https://mlsanity.com/paper/2310.00656/) (2023)
- [CREATOR: Tool Creation for Disentangling Abstract and Concrete Reasoning of Large Language Models](https://mlsanity.com/paper/2305.14318/) (2023)
- [TroVE: Inducing Verifiable and Efficient Toolboxes for Solving Programmatic Tasks](https://mlsanity.com/paper/2401.12869/) (2024)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [LILO: Learning Interpretable Libraries by Compressing and Documenting Code](https://mlsanity.com/paper/2310.19791/) (2023)
- [Offline Training of Language Model Agents with Functions as Learnable Weights](https://mlsanity.com/paper/2402.11359/) (2024)
- [ReGAL: Refactoring Programs to Discover Generalizable Abstractions](https://mlsanity.com/paper/2401.16467/) (2024)
- [Speech-Copilot: Leveraging Large Language Models for Speech Processing via Task Decomposition, Modularization, and Program Generation](https://mlsanity.com/paper/2407.09886/) (2024)
- [Empowering Large Language Model Agents through Action Learning](https://mlsanity.com/paper/2402.15809/) (2024)
- [Machine learning and information theory concepts towards an AI Mathematician](https://mlsanity.com/paper/2403.04571/) (2024)
- [GENOME: GenerativE Neuro-symbOlic visual reasoning by growing and reusing ModulEs](https://mlsanity.com/paper/2311.04901/) (2023)
- [REFACTOR: Learning to Extract Theorems from Proofs](https://mlsanity.com/paper/2402.17032/) (2024)
- [Can LLM find the green circle? Investigation and Human-guided tool manipulation for compositional generalization](https://mlsanity.com/paper/2312.07763/) (2023)
- [ATG: Benchmarking Automated Theorem Generation for Generative Language Models](https://mlsanity.com/paper/2405.06677/) (2024)

## Built on by (most cited first, 4 of 4)

- [LLM Library Learning Fails: A LEGO-Prover Case Study](https://mlsanity.com/paper/2504.03048/) (2025)
- [A Compute-Matched Re-Evaluation of TroVE on MATH](https://mlsanity.com/paper/2507.22069/) (2025)
- [AllocBench: Measuring Online Tool Allocation Capability in LLM Agents](https://mlsanity.com/paper/2607.23332/) (2026)
- [Let the Library Speak: Self-Advertised Method Selection for Formal Proving](https://mlsanity.com/paper/2610.09401/) (2026)

## Abstract (arXiv)

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