UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression

Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing, pages 3313 - 3323 December 7-11, 2022 ©2022 Association for Computational Linguistics UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression Jiaqi Chen1,3, Tong Li2, Jinghui Qin4, Pan Lu5, Liang Lin1, Chongyu Chen6, Xiaodan Liang1,2∗ 1Sun Yat-sen University, 2Shenzhen Campus of Sun Yat-sen University, 3The University of Hong Kong, 4Guangdong University of Technology, 5University of California, Los Angeles, 6DarkMatter AI Research Abstract Geometry problem solving is a well-recognized testbed for evaluating the high-level multi- modal 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 mul- tiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can im- prove the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 prov- ing problems. Each proving problem is an- notated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the anno- tated program sequence for calculation prob- lems. Naturally, we also present a unified multi- task Geometric Transformer framework, Geo- former, to tackle calculation and proving prob- lems 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 im- proving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geo- former obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.1 1 Introduction Achieving logical reasoning abilities is still chal- lenging for neural networks, especially in some ∗Corresponding author. 1Data and code: https://github.com/chen-judge/UniGeo Equal | N0 | Double | V0 Program Sequence AB is the diameter of circle O and point C is on the circle. If�OCA=25� (N0), then�BOC=(). Calculation Unified Geometric Transformer � OA = OC � �OCA = �OAC = 25� � � BOC = 2 �OAC = 50� Solution Proving Given VX=UW and TW=UX. U is the midpoint of TV. Complete the proof that �T=�VUX. Midpoint | TU | = | UV | SSS |�TUW | � | �UVX | CPCTC | �T | = |�VUX Proving Sequence Pretraining Unified Training Unified Geometric Transformer Figure 1: The pipeline of pretraining and unified train- ing of our proposed Geoformer. We pretrain the model by predicting the mathematical expression extracted from the solution of calculation problems. After that, we consider the calculation and proving as downstream tasks, and feed both types of data to Geoformer for unified training. mathematical reasoning tasks, such as math word problems (MWP) (Zhang et al., 2020a,b; Qin et al., 2020, 2021; …

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