Related papers: Investigating the Limitations of Transformers with…

In this work, we explore whether modeling recurrence into the Transformer architecture can both be beneficial and efficient, by building an extremely simple recurrent module into the Transformer. We compare our model to baselines following…

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…

Language models are increasingly capable, yet still fail at a seemingly simple task of multi-digit multiplication. In this work, we study why, by reverse-engineering a model that successfully learns multiplication via \emph{implicit…

There is an ongoing debate on whether neural networks can grasp the quasi-regularities in languages like humans. In a typical quasi-regularity task, English past tense inflections, the neural network model has long been criticized that it…

Increasing the input length has been a driver of progress in language modeling with transformers. We identify conditions where shorter inputs are not harmful, and achieve perplexity and efficiency improvements through two new methods that…

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of…

We conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the…

Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…

Despite recent successes in language models, their ability to represent numbers is insufficient. Humans conceptualize numbers based on their magnitudes, effectively projecting them on a number line; whereas subword tokenization fails to…

We study the capabilities of the transformer architecture with varying depth. Specifically, we designed a novel set of sequence learning tasks to systematically evaluate and comprehend how the depth of transformer affects its ability to…

Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…

Within numerical reasoning, understanding numbers themselves is still a challenge for existing language models. Simple generalisations, such as solving 100+200 instead of 1+2, can substantially affect model performance (Sivakumar and…

Despite the fact that Transformers perform well in NLP tasks, recent studies suggest that self-attention is theoretically limited in learning even some regular and context-free languages. These findings motivated us to think about their…

Much theoretical work has described the ability of transformers to represent formal languages. However, linking theoretical results to empirical performance is not straightforward due to the complex interplay between the architecture, the…

Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood. Arithmetic tasks provide a controlled framework to explore these capabilities, yet…

Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution. We present a self-improvement approach where models iteratively generate and learn from their own…

It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to…

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To…

Algorithmic reasoning requires capabilities which are most naturally understood through recurrent models of computation, like the Turing machine. However, Transformer models, while lacking recurrence, are able to perform such reasoning…

We investigate the capabilities of transformer models on relational reasoning tasks. In these tasks, models are trained on a set of strings encoding abstract relations, and are then tested out-of-distribution on data that contains symbols…