Given the ubiquitous nature of numbers in text, reasoning with numbers to perform simple calculations is an important skill of AI systems. While many datasets and models have been developed to this end, state-of-the-art AI systems are brittle; failing to perform the underlying mathematical reasoning when they appear in a slightly different scenario. Drawing inspiration from GLUE that was proposed in the context of natural language understanding, we propose NumGLUE, a multi-task benchmark that evaluates the performance of AI systems on eight different tasks, that at their core require simple arithmetic understanding. We show that this benchmark is far from being solved with neural models including state-of-the-art large-scale language models performing significantly worse than humans (lower by 46.4 %). Further, NumGLUE promotes sharing knowledge across tasks, especially those with limited training data as evidenced by the superior performance (average gain of 3.4 % on each task) when a model is jointly trained on all the tasks as opposed to task-specific modeling. Finally, we hope that NumGLUE will encourage systems that perform robust and general arithmetic reasoning within language, a first step towards being able to perform more complex mathematical reasoning.

Successful application of Knowledge Representation and Reasoning (KR) in Natural Language Understanding (NLU) is largely limited by the availability of a robust and general purpose natural language parser. Even though several projects have been launched in the pursuit of developing a universal meaning representation language, the existence of an accurate universal parser is far from reality. This has severely limited the application of knowledge representation and reasoning (KR) in the field of NLP and also prevented a proper evaluation of KR based NLU systems. Our goal is to build KR based systems for Natural Language Understanding without relying on a parser. Towards this we propose a method named Deeply Embedded Knowledge Representation & Reasoning (DeepEKR) where we replace the parser by a neural network, soften the symbolic representation so that a deterministic mapping exists between the parser neural network and the interpretable logical form, and finally replace the symbolic solver by an equivalent neural network, so the model can be trained end-to-end. We evaluate our method with respect to the task of Qualitative Word Problem Solving on the two available datasets (QuaRTz and QuaRel). Our system achieves same accuracy as that of the state-of-the-art accuracy on QuaRTz, outperforms the state-of-the-art on QuaRel and severely outperforms a traditional KR based system. The results show that the bias introduced by a KR solution does not prevent it from doing a better job at the end task. Moreover, our method is interpretable due to the bias introduced by the KR approach.

Winograd Schema Challenge (WSC) is a pronoun resolution task which seems to require reasoning with commonsense knowledge. The needed knowledge is not present in the given text. Automatic extraction of the needed knowledge is a bottleneck in solving the challenge. The existing state-of-the-art approach uses the knowledge embedded in their pre-trained language model. However, the language models only embed part of the knowledge, the ones related to frequently co-existing concepts. This limits the performance of such models on the WSC problems. In this work, we build-up on the language model based methods and augment them with a commonsense knowledge hunting (using automatic extraction from text) module and an explicit reasoning module. Our end-to-end system built in such a manner improves on the accuracy of two of the available language model based approaches by 5.53% and 7.7% respectively. Overall our system achieves the state-of-the-art accuracy of 71.06% on the WSC dataset, an improvement of 7.36% over the previous best.

Open book question answering is a type of natural language based QA (NLQA) where questions are expected to be answered with respect to a given set of open book facts, and common knowledge about a topic. Recently a challenge involving such QA, OpenBookQA, has been proposed. Unlike most other NLQA that focus on linguistic understanding, OpenBookQA requires deeper reasoning involving linguistic understanding as well as reasoning with common knowledge. In this paper we address QA with respect to the OpenBookQA dataset and combine state of the art language models with abductive information retrieval (IR), information gain based re-ranking, passage selection and weighted scoring to achieve 72.0% accuracy, an 11.6% improvement over the current state of the art.