Hologram Reasoning for Solving Algebra Problems with Geometry Diagrams

TL;DR

This paper introduces a hologram reasoning scheme for solving algebra problems with geometry diagrams, improving accuracy, interpretability, and efficiency through graph-based representations and deep reinforcement learning.

Contribution

It proposes a novel hologram reasoning framework that converts geometry diagrams into graph representations and employs reinforcement learning for model selection, enhancing solution accuracy and interpretability.

Findings

HGR achieves high solution accuracy with fewer reasoning steps.

The method significantly improves interpretability of algebra-geometry problem solving.

Experimental results validate the effectiveness of the hologram reasoning approach.

Abstract

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.