2024/08/20 by Litian Huang, Huang, Litian, Xinguo Yu +9 · 1 citation
Engineering · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.2408.10592
openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning scheme and develops a high-performance method for solving APGDs by using this scheme. To reach this goal, it first defines a hologram, being a kind of graph, and proposes a hologram generator to convert a given APGD into a hologram, which represents the entire information of APGD and the relations for solving the problem can be acquired from it by a uniform way. Then HGR, a hologram reasoning method employs a pool of prepared graph models to derive algebraic equations, which is consistent with the geometric theorems. This method is able to be updated by adding new graph models into the pool. Lastly, it employs deep reinforcement learning to enhance the efficiency of model selection from the pool. The entire HGR not only ensures high solution accuracy with fewer reasoning steps but also significantly enhances the interpretability of the solution process by providing descriptions of all reasoning steps. Experimental results demonstrate the effectiveness of HGR in improving both accuracy and interpretability in solving APGDs.