Matthew Lewis

Pranav Ramanathan, Thomas Prellberg, Matthew Lewis et al.

The No-Three-In-Line problem asks for the maximum number of points that can be placed on an n by n grid with no three collinear, representing a famous problem in combinatorial geometry. While classical methods like Integer Linear Programming (ILP) guarantee optimal solutions, they face exponential scaling with grid size, and recent advances in machine learning offer promising alternatives for pattern-based approximation. This paper presents the first systematic comparison of classical optimization and AI approaches to this problem, evaluating their performance against traditional algorithms. We apply PatternBoost transformer learning and reinforcement learning (PPO) to this problem for the first time, comparing them against ILP. ILP achieves provably optimal solutions up to 19 by 19 grids, while PatternBoost matches optimal performance up to 14 by 14 grids with 96% test loss reduction. PPO achieves perfect solutions on 10 by 10 grids but fails at 11 by 11 grids, where constraint violations prevent valid configurations. These results demonstrate that classical optimization remains essential for exact solutions while AI methods offer competitive performance on smaller instances, with hybrid approaches presenting the most promising direction for scaling to larger problem sizes.

Samuel Thio, Matthew Lewis, Spiros Denaxas et al.

Electronic health record (EHR) systems present clinicians with vast repositories of clinical information, creating a significant cognitive burden where critical details are easily overlooked. While Large Language Models (LLMs) offer transformative potential for data processing, they face significant limitations in clinical settings, particularly regarding context grounding and hallucinations. Current solutions typically isolate retrieval methods focusing either on structured data (SQL/Cypher) or unstructured semantic search but fail to integrate both simultaneously. This work presents MediGRAF (Medical Graph Retrieval Augmented Framework), a novel hybrid Graph RAG system that bridges this gap. By uniquely combining Neo4j Text2Cypher capabilities for structured relationship traversal with vector embeddings for unstructured narrative retrieval, MediGRAF enables natural language querying of the complete patient journey. Using 10 patients from the MIMIC-IV dataset (generating 5,973 nodes and 5,963 relationships), we generated enough nodes and data for patient level question answering (QA), and we evaluated this architecture across varying query complexities. The system demonstrated 100\% recall for factual queries which means all relevant information was retrieved and in the output, while complex inference tasks achieved a mean expert quality score of 4.25/5 with zero safety violations. These results demonstrate that hybrid graph-grounding significantly advances clinical information retrieval, offering a safer, more comprehensive alternative to standard LLM deployments.

Matthew Lewis, Samuel Thio, Richard JB Dobson et al.

This paper presents the development and evaluation of a Retrieval-Augmented Generation (RAG) system for querying the United Kingdom's National Institute for Health and Care Excellence (NICE) clinical guidelines using Large Language Models (LLMs). The extensive length and volume of these guidelines can impede their utilisation within a time-constrained healthcare system, a challenge this project addresses through the creation of a system capable of providing users with precisely matched information in response to natural language queries. The system's retrieval architecture, composed of a hybrid embedding mechanism, was evaluated against a database of 10,195 text chunks derived from three hundred guidelines. It demonstrates high performance, with a Mean Reciprocal Rank (MRR) of 0.814, a Recall of 81% at the first chunk and of 99.1% within the top ten retrieved chunks, when evaluated on 7901 queries. The most significant impact of the RAG system was observed during the generation phase. When evaluated on a manually curated dataset of seventy question-answer pairs, RAG-enhanced models showed substantial gains in performance. Faithfulness, the measure of whether an answer is supported by the source text, was increased by 64.7 percentage points to 99.5% for the RAG-enhanced O4-Mini model and significantly outperformed the medical-focused Meditron3-8B LLM, which scored 43%. This, combined with a perfect Context Precision score of 1 for all RAG-enhanced models, confirms the system's ability to prevent information fabrication by grounding its answers in relevant source material. This study thus establishes RAG as an effective, reliable, and scalable approach for applying generative AI in healthcare, enabling cost-effective access to medical guidelines.