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.

Mathematical reasoning skills are essential for general-purpose intelligentsystems to perform tasks from grocery shopping to climate modeling.Towards evaluating and improving AI systems in this domain, we proposeLILA, a unified mathematical reasoning benchmark consisting of 23 diversetasks along four dimensions:(i) mathematical abilities e.g., arithmetic, calculus (ii) language format e.g., question-answering, fill-in-the-blanks (iii) language diversity e.g., no language, simple language (iv) external knowledge e.g., commonsense, physics. We construct our benchmark by extending 20 datasets benchmark by collecting task instructions and solutions in the form of Python programs,thereby obtaining explainable solutions in addition to the correct answer.We additionally introduce two evaluation datasets to measure out-of-distribution performance and robustness to language perturbation.Finally, we introduce BHASKARA,a general-purpose mathematical reasoning model trained on LILA. Importantly, we find that multi-tasking leads to significant improvements (average relative improvement of 21.83% F1 score vs. single-task models),while the best performing model only obtains 60.40%,indicating the room for improvement in general mathematical reasoning and understanding.

Building a socially intelligent agent involves many challenges. One of which is to track the agent’s mental state transition and teach the agent to make decisions guided by its value like a human. Towards this end, we propose to incorporate mental state simulation and value modeling into dialogue agents. First, we build a hybrid mental state parser that extracts information from both the dialogue and event observations and maintains a graphical representation of the agent’s mind; Meanwhile, the transformer-based value model learns human preferences from the human value dataset, ValueNet. Empirical results show that the proposed model attains state-of-the-art performance on the dialogue/action/emotion prediction task in the fantasy text-adventure game dataset, LIGHT. We also show example cases to demonstrate: (i) how the proposed mental state parser can assist the agent’s decision by grounding on the context like locations and objects, and (ii) how the value model can help the agent make decisions based on its personal priorities.

Inferring social relations from dialogues is vital for building emotionally intelligent robots to interpret human language better and act accordingly. We model the social network as an And-or Graph, named SocAoG, for the consistency of relations among a group and leveraging attributes as inference cues. Moreover, we formulate a sequential structure prediction task, and propose an 𝛼-𝛽-𝛾 strategy to incrementally parse SocAoG for the dynamic inference upon any incoming utterance: (i) an 𝛼 process predicting attributes and relations conditioned on the semantics of dialogues, (ii) a 𝛽 process updating the social relations based on related attributes, and (iii) a 𝛾 process updating individual’s attributes based on interpersonal social relations. Empirical results on DialogRE and MovieGraph show that our model infers social relations more accurately than the state-of-the-art methods. Moreover, the ablation study shows the three processes complement each other, and the case study demonstrates the dynamic relational inference.

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.