Gaps : geometry-aware problem solver

Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems. Additionally, the current research predominantly focuses on geometry calculation problems, while overlooking other essential aspects like proving. In this study, we address these limitations by proposing the Geometry-Aware Problem Solver (GAPS) model. GAPS is specifically designed to generate solution programs for geometry math problems of various types with the help of its unique problem-type classifier. To achieve this, GAPS treats the solution program as a composition of operators and operands, segregating their generation processes. Furthermore, we introduce the geometry elements enhancement method, which enhances the ability of GAPS to recognize geometry elements accurately. By leveraging these improvements, GAPS showcases remarkable performance in resolving geometry math problems. Our experiments conducted on the UniGeo dataset demonstrate the superiority of GAPS over the state-of-the-art model, Geoformer. Specifically, GAPS achieves an accuracy improvement of more than 5.3% for calculation tasks and an impressive 41.1% for proving tasks. Notably, GAPS achieves an impressive accuracy of 97.5% on proving problems, representing a significant advancement in solving geometry proving tasks

Synthesis With Hypergraphs

Many problems related to synthesis with intelligent tutoring may be phrased as program synthesis problems using AI-style search and formal reasoning techniques. The _x000C_first two results in this dissertation focus on problem synthesis as an aspect of intelligent tutoring systems applied to STEM-based education frameworks, specifically high school geometry. Given a geometric _x000C_figure as input, our technique constructs a hypergraph representing logical deduction of facts, and then traverses the hypergraph to synthesize problems and their corresponding solutions. Using similar techniques, our third result is focused on exhaustive synthesis of molecules. This synthesis process involves bonding sets of basic, molecular `fragments\u27 according to chemical constraints to create molecules of increasing size. For each input set of fragments, synthesis results in a significant set of molecules. Due to big data constraints we give special consideration in how to construct a corresponding molecular hypergraph based on a target, template molecule. Synthesis of the target molecule in a laboratory environment then corresponds to any path in the molecular hypergraph from the set of fragments to the target molecule