Legal$\Delta$: Enhancing Legal Reasoning in LLMs via Reinforcement Learning with Chain-of-Thought Guided Information Gain

TL;DR

Legal$ ext{ extDelta}$ introduces a reinforcement learning framework that improves legal reasoning in LLMs by guiding the model to generate more meaningful, multi-step explanations, leading to more accurate and interpretable legal judgments.

Contribution

It presents a novel RL-based method that distills reasoning from a large model and refines it through differential comparisons, enhancing legal reasoning capabilities of LLMs.

Findings

Outperforms baselines in accuracy and interpretability

Produces more robust and trustworthy legal judgments

Does not rely on labeled preference data

Abstract

Legal Artificial Intelligence (LegalAI) has achieved notable advances in automating judicial decision-making with the support of Large Language Models (LLMs). However, existing legal LLMs still struggle to generate reliable and interpretable reasoning processes. They often default to fast-thinking behavior by producing direct answers without explicit multi-step reasoning, limiting their effectiveness in complex legal scenarios that demand rigorous justification. To address this challenge, we propose Legal$\Delta$, a reinforcement learning framework designed to enhance legal reasoning through chain-of-thought guided information gain. During training, Legal$\Delta$ employs a dual-mode input setup-comprising direct answer and reasoning-augmented modes-and maximizes the information gain between them. This encourages the model to acquire meaningful reasoning patterns rather than generating superficial or redundant explanations. Legal$\Delta$ follows a two-stage approach: (1) distilling latent reasoning capabilities from a powerful Large Reasoning Model (LRM), DeepSeek-R1, and (2) refining reasoning quality via differential comparisons, combined with a multidimensional reward mechanism that assesses both structural coherence and legal-domain specificity. Experimental results on multiple legal reasoning tasks demonstrate that Legal$\Delta$ outperforms strong baselines in both accuracy and interpretability. It consistently produces more robust and trustworthy legal judgments without relying on labeled preference data. All code and data will be released at https://github.com/NEUIR/LegalDelta.