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Transformer models have emerged as fundamental tools across various scientific and engineering disciplines, owing to their outstanding performance in diverse applications. Despite this empirical success, the theoretical foundations of…

Self-attention, an architectural motif designed to model long-range interactions in sequential data, has driven numerous recent breakthroughs in natural language processing and beyond. This work provides a theoretical analysis of the…

The self-attention module is a key component of Transformer-based models, wherein each token pays attention to every other token. Recent studies have shown that these heads exhibit syntactic, semantic, or local behaviour. Some studies have…

Attention is a key part of the transformer architecture. It is a sequence-to-sequence mapping that transforms each sequence element into a weighted sum of values. The weights are typically obtained as the softmax of dot products between…

Transformer-based models have emerged as one of the most widely used architectures for natural language processing, natural language generation, and image generation. The size of the state-of-the-art models has increased steadily reaching…

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at…

Transformer-based models, even though achieving super-human performance on several downstream tasks, are often regarded as a black box and used as a whole. It is still unclear what mechanisms they have learned, especially their core module:…

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

Self-attention modules have demonstrated remarkable capabilities in capturing long-range relationships and improving the performance of point cloud tasks. However, point cloud objects are typically characterized by complex, disordered, and…

The great success of Transformer-based models benefits from the powerful multi-head self-attention mechanism, which learns token dependencies and encodes contextual information from the input. Prior work strives to attribute model decisions…

We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential collection with application to the Transformer and its token space. Our methods are catered to the…

Self-attention is essential to Transformer architectures, yet how information is embedded in the self-attention matrices and how different objective functions impact this process remains unclear. We present a mathematical framework to…

Recent research on the multi-head attention mechanism, especially that in pre-trained models such as BERT, has shown us heuristics and clues in analyzing various aspects of the mechanism. As most of the research focus on probing tasks or…

We revisit a basic question in sequence modeling: is explicit self-attention actually necessary for strong performance and reasoning? We argue that standard multi-head attention is best seen as a form of tensor lifting: hidden vectors are…

Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens. This representation is then exploited by the attention function, which learns dependencies between tokens and…

The Transformer architecture aggregates input information through the self-attention mechanism, but there is no clear understanding of how this information is mixed across the entire model. Additionally, recent works have demonstrated that…

Vision transformers using self-attention or its proposed alternatives have demonstrated promising results in many image related tasks. However, the underpinning inductive bias of attention is not well understood. To address this issue, this…

The recently proposed physics-based framework by Huo and Johnson~\cite{huo2024capturing} models the attention mechanism of Large Language Models (LLMs) as an interacting two-body spin system, offering a first-principles explanation for…

Self-attention, as the key block of transformers, is a powerful mechanism for extracting features from the inputs. In essence, what self-attention does is to infer the pairwise relations between the elements of the inputs, and modify the…

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…