Chongyu Chen
2022
UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression
Jiaqi Chen

Tong Li

Jinghui Qin

Pan Lu

Liang Lin

Chongyu Chen

Xiaodan Liang
Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing
Geometry problem solving is a wellrecognized testbed for evaluating the highlevel multimodal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a largescale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multistep proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multitask Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains stateoftheart performance by outperforming taskspecific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.
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Coauthors
 Jiaqi Chen 1
 Tong Li 1
 Jinghui Qin 1
 Pan Lu 1
 Liang Lin 1
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