LeanReasoner: Enhancing Logical Reasoning with Lean Framework

Core Concepts

Using Lean framework improves logical reasoning in large language models by formalizing problems and enhancing performance.

Abstract

The article introduces LeanReasoner, a framework that leverages the Lean theorem proving framework to address logical reasoning challenges in large language models. It discusses the struggles of LLMs with complex logical reasoning tasks, the use of symbolic solvers, and the benefits of using Lean for theorem proving. The method achieves state-of-the-art performance on datasets like FOLIO and ProofWriter by fine-tuning on annotated data. The paper details the components of LeanReasoner, including formalizer, tactic generator, proof search mechanism, and result interpreter. Experimental results show improvements in premise selection accuracy and overall proof accuracy when pretraining on theorem-proving data.

Abstract:

• Large language models (LLMs) face challenges with complex logical reasoning.
• Lean framework addresses these challenges by formalizing problems.
• Achieves state-of-the-art performance on FOLIO dataset.

Introduction:

• Logical reasoning is challenging for machine learning systems.
• Recent advances split reasoning into symbolic formalization and problem-solving.
• Lean offers a solution to connect symbolic solvers with linguistic resources.

Problem Definition and Notation:

• Task involves logical reasoning based on natural language context.
• Components include context, question, options, formalized context, formalized question, goal, tactics.

LeanReasoner:

• Composed of a formalizer, tactic generator, proof search mechanism, result interpreter.
• Formalizer converts context and question to formalized form.
• Tactic generator generates tactics based on premises.
• Proof search controls search process for proofs.
• Result interpreter analyzes proof outcomes.

Experimental Setup:

• Evaluation done on ProofWriter and FOLIO datasets.
• Training data collected for domain adaptation from mathematical theorem proofs.

Stats

Our method achieves state-of-the-art performance on the FOLIO dataset by fine-tuning on annotated data.

Quotes

"LeanReasoner enhances our ability to treat complex reasoning tasks."
"Our contributions highlight an intersection between mathematical theorem proving and logical reasoning."

Key Insights Distilled From

LeanReasoner

by Dongwei Jian... at arxiv.org 03-21-2024

https://arxiv.org/pdf/2403.13312.pdf

Deeper Inquiries

How can incorporating pre-training data enhance solver development?

Incorporating pre-training data enhances solver development by providing the model with a strong foundation of reasoning "nuggets" that are crucial for logical reasoning tasks. Pre-training on theorem-proving data allows the model to learn intricate patterns and strategies used in mathematical theorem proving, which can be adapted to natural language logical reasoning. This exposure helps the model develop advanced reasoning capabilities and improves its ability to generate accurate proofs. Additionally, pre-training provides a structured approach to tackling complex problems by leveraging existing knowledge encoded in the training data.

What are the limitations faced when dealing with commonsense or factual reasoning?

When dealing with commonsense or factual reasoning, there are several limitations that arise. One major limitation is the challenge of retrieving all necessary information accurately from textual contexts and representing it effectively in Lean formalization. Complex concepts related to real-world knowledge may be difficult to capture and formalize correctly within Lean's framework. Furthermore, handling math word problems or tasks requiring numerical solutions poses challenges as Lean focuses on certifying validity through proof construction rather than deriving numeric answers directly. Additionally, more sophisticated formalization techniques may be required for nuanced tasks like LogicalDeduction from BigBench dataset.

How can LeanReasoner be improved to handle more complex datasets like TheoremQA?

To improve LeanReasoner's performance on more complex datasets like TheoremQA, several enhancements can be implemented:

Advanced Formalization Techniques: Develop specialized methods for capturing intricate logic structures present in complex datasets.
Integration of Constraint Solvers: Incorporate constraint satisfaction problem (CSP) solvers alongside theorem proving capabilities for handling constraints and variable possibilities efficiently.
Enhanced Search Algorithms: Implement optimized search algorithms tailored for exploring diverse solution paths in challenging problems.
Knowledge Graph Integration: Integrate external knowledge graphs or databases into the reasoning process to enrich contextual understanding.
Hybrid Approaches: Explore hybrid approaches combining symbolic logic with neural networks for enhanced performance on diverse problem types.
6 .Continuous Learning Mechanisms: Implement mechanisms for continuous learning and adaptation based on feedback loops during inference processes.

These improvements will enable LeanReasoner to tackle a wider range of complexities presented in datasets like TheoremQA effectively while enhancing its overall logical reasoning capabilities across various domains.