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This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…

Large Transformer models routinely achieve state-of-the-art results on a number of tasks but training these models can be prohibitively costly, especially on long sequences. We introduce two techniques to improve the efficiency of…

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models…

Neural networks are often highly sensitive to input and weight perturbations. This sensitivity has been linked to pathologies such as vulnerability to adversarial examples, divergent training, and overfitting. To combat these problems, past…

Self-supervised pre-training of large-scale transformer models on text corpora followed by finetuning has achieved state-of-the-art on a number of natural language processing tasks. Recently, Lu et al. (2021, arXiv:2103.05247) claimed that…

Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…

While transformers have proven enormously successful in a range of tasks, their fundamental properties as models of computation are not well understood. This paper contributes to the study of the expressive capacity of transformers,…

Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data, especially in next-token prediction (NTP) tasks. However, the theoretical understanding of their…

Despite the widespread success of Transformers across various domains, their optimization guarantees in large-scale model settings are not well-understood. This paper rigorously analyzes the convergence properties of gradient flow in…

Despite their ubiquity in core AI fields like natural language processing, the mechanics of deep attention-based neural networks like the Transformer model are not fully understood. In this article, we present a new perspective towards…

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is…

Embedding layers in transformer-based NLP models typically account for the largest share of model parameters, scaling with vocabulary size but not yielding performance gains proportional to scale. We propose an alternative approach in which…

The remarkable capability of Transformers to do reasoning and few-shot learning, without any fine-tuning, is widely conjectured to stem from their ability to implicitly simulate a multi-step algorithms -- such as gradient descent -- with…

Recent research has shown the existence of significant redundancy in large Transformer models. One can prune the redundant parameters without significantly sacrificing the generalization performance. However, we question whether the…

Transformer networks have achieved remarkable empirical success across a wide range of applications, yet their theoretical expressive power remains insufficiently understood. In this paper, we study the expressive capabilities of…

Transformers excel at discovering patterns in sequential data, yet their fundamental limitations and learning mechanisms remain crucial topics of investigation. In this paper, we study the ability of Transformers to learn pseudo-random…

Transformers have revolutionized natural language processing, but their use for numerical computation has received less attention. We study the approximation of matrix functions, which map scalar functions to matrices, using neural networks…

Randomized Hadamard Transforms (RHTs) have emerged as a computationally efficient alternative to the use of dense unstructured random matrices across a range of domains in computer science and machine learning. For several applications such…

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem…

Modern Foundation Models (FMs) are typically trained on corpora spanning a wide range of different data modalities, topics and downstream tasks. Utilizing these models can be very computationally expensive and is out of reach for most…