The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-ofwords can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Inducing diversity in the task of paraphrasing is an important problem in NLP with applications in data augmentation and conversational agents. Previous paraphrasing approaches have mainly focused on the issue of generating semantically similar paraphrases, while paying little attention towards diversity. In fact, most of the methods rely solely on top-k beam search sequences to obtain a set of paraphrases. The resulting set, however, contains many structurally similar sentences. In this work, we focus on the task of obtaining highly diverse paraphrases while not compromising on paraphrasing quality. We provide a novel formulation of the problem in terms of monotone submodular function maximization, specifically targeted towards the task of paraphrasing. Additionally, we demonstrate the effectiveness of our method for data augmentation on multiple tasks such as intent classification and paraphrase recognition. In order to drive further research, we have made the source code available.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-ofwords can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs. PROBLEM: Jack had 8 pens and Mary had 5 pens. Jack gave 3 pens to Mary. How many pens does Jack have now? 8 -3 = 5 QUESTION SENSITIVITY VARIATION: Jack had 8 pens and Mary had 5 pens. Jack gave 3 pens to Mary. How many pens does Mary have now? 5 + 3 = 8 REASONING ABILITY VARIATION: Jack had 8 pens and Mary had 5 pens. Mary gave 3 pens to Jack. How many pens does Jack have now? 8 + 3 = 11 STRUCTURAL INVARIANCE VARIATION: Jack gave 3 pens to Mary. If Jack had 8 pens and Mary had 5 pens initially, how many pens does Jack have now? 8 -3 = 5

Transformers have supplanted recurrent models in a large number of NLP tasks. However, the differences in their abilities to model different syntactic properties remain largely unknown. Past works suggest that LSTMs generalize very well on regular languages and have close connections with counter languages. In this work, we systematically study the ability of Transformers to model such languages as well as the role of its individual components in doing so. We first provide a construction of Transformers for a subclass of counter languages, including well-studied languages such as n-ary Boolean Expressions, Dyck-1, and its generalizations. In experiments, we find that Transformers do well on this subclass, and their learned mechanism strongly correlates with our construction. Perhaps surprisingly, in contrast to LSTMs, Transformers do well only on a subset of regular languages with degrading performance as we make languages more complex according to a well-known measure of complexity. Our analysis also provides insights on the role of self-attention mechanism in modeling certain behaviors and the influence of positional encoding schemes on the learning and generalization abilities of the model.

Transformers are being used extensively across several sequence modeling tasks. Significant research effort has been devoted to experimentally probe the inner workings of Transformers. However, our conceptual and theoretical understanding of their power and inherent limitations is still nascent. In particular, the roles of various components in Transformers such as positional encodings, attention heads, residual connections, and feedforward networks, are not clear. In this paper, we take a step towards answering these questions. We analyze the computational power as captured by Turing-completeness. We first provide an alternate and simpler proof to show that vanilla Transformers are Turing-complete and then we prove that Transformers with only positional masking and without any positional encoding are also Turing-complete. We further analyze the necessity of each component for the Turing-completeness of the network; interestingly, we find that a particular type of residual connection is necessary. We demonstrate the practical implications of our results via experiments on machine translation and synthetic tasks.