We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of (total functional) transductions. We do so using variants of RASP, a programming language designed to help people “think like transformers,” as an intermediate representation. We extend the existing Boolean variant B-RASP to sequence-to-sequence transductions and show that it computes exactly the first-order rational transductions (such as string rotation). Then, we introduce two new extensions. B-RASP[ pos ] enables calculations on positions (such as copying the first half of a string) and contains all first-order regular transductions. S-RASP adds prefix sum, which enables additional arithmetic operations (such as squaring a string) and contains all first-order polyregular transductions. Finally, we show that masked average-hard attention transformers can simulate S-RASP.

Despite their omnipresence in modern NLP, characterizing the computational power of transformer neural nets remains an interesting open question. We prove that transformers whose arithmetic precision is logarithmic in the number of input tokens (and whose feedforward nets are computable using space linear in their input) can be simulated by constant-depth logspace-uniform threshold circuits. This provides insight on the power of transformers using known results in complexity theory. For example, if L ≠ P (i.e., not all poly-time problems can be solved using logarithmic space), then transformers cannot even accurately solve linear equalities or check membership in an arbitrary context-free grammar with empty productions. Our result intuitively emerges from the transformer architecture’s high parallelizability. We thus speculatively introduce the idea of a fundamental parallelism tradeoff : any model architecture as parallelizable as the transformer will obey limitations similar to it. Since parallelism is key to training models at massive scale, this suggests a potential inherent weakness of the scaling paradigm.

Transformers have become a standard neural network architecture for many NLP problems, motivating theoretical analysis of their power in terms of formal languages. Recent work has shown that transformers with hard attention are quite limited in power (Hahn, 2020), as they can be simulated by constant-depth AND/OR circuits (Hao et al., 2022). However, hard attention is a strong assumption, which may complicate the relevance of these results in practice. In this work, we analyze the circuit complexity of transformers with saturated attention: a generalization of hard attention that more closely captures the attention patterns learnable in practical transformers. We first show that saturated transformers transcend the known limitations of hard-attention transformers. We then prove saturated transformers with floating-point values can be simulated by constant-depth threshold circuits, giving the class TC 0 as an upper bound on the formal languages they recognize.

Multihop reasoning remains an elusive goal as existing multihop benchmarks are known to be largely solvable via shortcuts. Can we create a question answering (QA) dataset that, by construction, requires proper multihop reasoning? To this end, we introduce a bottom–up approach that systematically selects composable pairs of single-hop questions that are connected, that is, where one reasoning step critically relies on information from another. This bottom–up methodology lets us explore a vast space of questions and add stringent filters as well as other mechanisms targeting connected reasoning. It provides fine-grained control over the construction process and the properties of the resulting k -hop questions. We use this methodology to create MuSiQue-Ans, a new multihop QA dataset with 25K 2–4 hop questions. Relative to existing datasets, MuSiQue-Ans is more difficult overall (3× increase in human–machine gap), and harder to cheat via disconnected reasoning (e.g., a single-hop model has a 30-point drop in F1). We further add unanswerable contrast questions to produce a more stringent dataset, MuSiQue-Full. We hope our datasets will help the NLP community develop models that perform genuine multihop reasoning. 1

Open-domain question answering (QA) involves many knowledge and reasoning challenges, but are successful QA models actually learning such knowledge when trained on benchmark QA tasks? We investigate this via several new diagnostic tasks probing whether multiple-choice QA models know definitions and taxonomic reasoning—two skills widespread in existing benchmarks and fundamental to more complex reasoning. We introduce a methodology for automatically building probe datasets from expert knowledge sources , allowing for systematic control and a comprehensive evaluation. We include ways to carefully control for artifacts that may arise during this process. Our evaluation confirms that transformer-based multiple-choice QA models are already predisposed to recognize certain types of structural linguistic knowledge. However, it also reveals a more nuanced picture: their performance notably degrades even with a slight increase in the number of “hops” in the underlying taxonomic hierarchy, and with more challenging distractor candidates. Further, existing models are far from perfect when assessed at the level of clusters of semantically connected probes, such as all hypernym questions about a single concept.

Given a knowledge base or KB containing (noisy) facts about common nouns or generics, such as “all trees produce oxygen” or “some animals live in forests”, we consider the problem of inferring additional such facts at a precision similar to that of the starting KB. Such KBs capture general knowledge about the world, and are crucial for various applications such as question answering. Different from commonly studied named entity KBs such as Freebase, generics KBs involve quantification, have more complex underlying regularities, tend to be more incomplete, and violate the commonly used locally closed world assumption (LCWA). We show that existing KB completion methods struggle with this new task, and present the first approach that is successful. Our results demonstrate that external information, such as relation schemas and entity taxonomies, if used appropriately, can be a surprisingly powerful tool in this setting. First, our simple yet effective knowledge guided tensor factorization approach achieves state-of-the-art results on two generics KBs (80% precise) for science, doubling their size at 74%–86% precision. Second, our novel taxonomy guided, submodular, active learning method for collecting annotations about rare entities (e.g., oriole, a bird) is 6x more effective at inferring further new facts about them than multiple active learning baselines.

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as A lges . We compare A lges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, A lges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.