Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams,
and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 5,010 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .
We generalize the definition of Proof Labeling Schemes to reactive systems, that is, systems where the configuration is supposed to keep changing forever. As an example, we address the main classical test case of reactive tasks, namely, the task of t
oken passing. Different RPLSs are given for the cases that the network is assumed to be a tree or an anonymous ring, or a general graph, and the sizes of RPLSs labels are analyzed. We also address the question of whether an RPLS exists. First, on the positive side, we show that there exists an RPLS for any distributed task for a family of graphs with unique identities. For the case of anonymous networks (even for the special case of rings), interestingly, it is known that no token passing algorithm is possible even if the number n of nodes is known. Nevertheless, we show that an RPLS is possible. On the negative side, we show that if one drops the assumption that n is known, then the construction becomes impossible.
