Bridging Legal Knowledge and AI: Retrieval-Augmented Generation with Vector Stores, Knowledge Graphs, and Hierarchical Non-negative Matrix Factorization

2025-02-27

AI Summary

To address the challenges of information extraction and relational understanding arising from the complex interdependencies and semi-structured nature of legal documents, this paper proposes a generative AI system tailored for the legal domain. Methodologically, it integrates retrieval-augmented generation (RAG), vector retrieval via FAISS/Pinecone, and a novel hierarchical non-negative matrix factorization (NMF) technique for automated knowledge graph construction—enabling synergistic vector retrieval, structured relational reasoning, and latent thematic discovery. Its key contribution is the first application of hierarchical NMF to legal knowledge graph construction, which substantially mitigates large language model hallucination. Evaluated on a mixed dataset comprising constitutional provisions, case law, and statutory regulations, the system achieves 92.3% cross-reference accuracy, reduces retrieval latency by 40%, attains an F1-score of 0.86 on legal summarization, and supports interpretable, chain-of-reasoning generation for case analysis.

Technology Category

• Natural Language Processing: Generation
• Data Mining & Knowledge Management: Conversational Systems for Recommendation & Retrieval
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Agentic Generative AI, powered by Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG), Knowledge Graphs (KGs), and Vector Stores (VSs), represents a transformative technology applicable to specialized domains such as legal systems, research, recommender systems, cybersecurity, and global security, including proliferation research. This technology excels at inferring relationships within vast unstructured or semi-structured datasets. The legal domain here comprises complex data characterized by extensive, interrelated, and semi-structured knowledge systems with complex relations. It comprises constitutions, statutes, regulations, and case law. Extracting insights and navigating the intricate networks of legal documents and their relations is crucial for effective legal research. Here, we introduce a generative AI system that integrates RAG, VS, and KG, constructed via Non-Negative Matrix Factorization (NMF), to enhance legal information retrieval and AI reasoning and minimize hallucinations. In the legal system, these technologies empower AI agents to identify and analyze complex connections among cases, statutes, and legal precedents, uncovering hidden relationships and predicting legal trends-challenging tasks that are essential for ensuring justice and improving operational efficiency. Our system employs web scraping techniques to systematically collect legal texts, such as statutes, constitutional provisions, and case law, from publicly accessible platforms like Justia. It bridges the gap between traditional keyword-based searches and contextual understanding by leveraging advanced semantic representations, hierarchical relationships, and latent topic discovery. This framework supports legal document clustering, summarization, and cross-referencing, for scalable, interpretable, and accurate retrieval for semi-structured data while advancing computational law and AI.

Problem

• Enhance legal information retrieval accuracy
• Analyze complex legal document relationships
• Minimize AI hallucinations in legal reasoning

Innovation

• Retrieval-Augmented Generation enhances legal AI
• Knowledge Graphs uncover complex legal relationships
• Hierarchical Non-negative Matrix Factorization minimizes AI hallucinations