Compositional generalization is a fundamental trait in humans, allowing us to effortlessly combine known phrases to form novel sentences. Recent works have claimed that standard seq-to-seq models severely lack the ability to compositionally generalize. In this paper, we focus on one-shot primitive generalization as introduced by the popular SCAN benchmark. We demonstrate that modifying the training distribution in simple and intuitive ways enables standard seq-to-seq models to achieve near-perfect generalization performance, thereby showing that their compositional generalization abilities were previously underestimated. We perform detailed empirical analysis of this phenomenon. Our results indicate that the generalization performance of models is highly sensitive to the characteristics of the training data which should be carefully considered while designing such benchmarks in future.

Humans can reason compositionally whilst grounding language utterances to the real world. Recent benchmarks like ReaSCAN (Wu et al., 2021) use navigation tasks grounded in a grid world to assess whether neural models exhibit similar capabilities. In this work, we present a simple transformer-based model that outperforms specialized architectures on ReaSCAN and a modified version (Qiu et al., 2021) of gSCAN (Ruis et al., 2020). On analyzing the task, we find that identifying the target location in the grid world is the main challenge for the models. Furthermore, we show that a particular split in ReaSCAN, which tests depth generalization, is unfair. On an amended version of this split, we show that transformers can generalize to deeper input structures. Finally, we design a simpler grounded compositional generalization task, RefEx, to investigate how transformers reason compositionally. We show that a single self-attention layer with a single head generalizes to novel combinations of object attributes. Moreover, we derive a precise mathematical construction of the transformer’s computations from the learned network. Overall, we provide valuable insights about the grounded compositional generalization task and the behaviour of transformers on it, which would be useful for researchers working in this area.

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-of-words 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.

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.

While recurrent models have been effective in NLP tasks, their performance on context-free languages (CFLs) has been found to be quite weak. Given that CFLs are believed to capture important phenomena such as hierarchical structure in natural languages, this discrepancy in performance calls for an explanation. We study the performance of recurrent models on Dyck-n languages, a particularly important and well-studied class of CFLs. We find that while recurrent models generalize nearly perfectly if the lengths of the training and test strings are from the same range, they perform poorly if the test strings are longer. At the same time, we observe that RNNs are expressive enough to recognize Dyck words of arbitrary lengths in finite precision if their depths are bounded. Hence, we evaluate our models on samples generated from Dyck languages with bounded depth and find that they are indeed able to generalize to much higher lengths. Since natural language datasets have nested dependencies of bounded depth, this may help explain why they perform well in modeling hierarchical dependencies in natural language data despite prior works indicating poor generalization performance on Dyck languages. We perform probing studies to support our results and provide comparisons with Transformers.

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.