  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 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 large-scale Unified Geometry problem benchmark,
UniGeo, which contains 4,998 calculation problems and 9,543 proving problems.
Each proving problem is annotated 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 annotated program sequence for
calculation problems. Naturally, we also present a unified multi-task 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 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.
