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The attention mechanism within the transformer architecture enables the model to weigh and combine tokens based on their relevance to the query. While self-attention has enjoyed major success, it notably treats all queries $q$ in the same…

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax…

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. However, the employment of self-attention modules results in a quadratic…

In this work, we study rapid improvements of the training loss in transformers when being confronted with multi-step decision tasks. We found that transformers struggle to learn the intermediate task and both training and validation loss…

Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling…

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns:…

Transformer-based models have demonstrated considerable potential for source code modeling tasks in software engineering. However, they are limited by their dependence solely on automatic self-attention weight learning mechanisms. Previous…

Transformers excel through content-addressable retrieval and the ability to exploit contexts of, in principle, unbounded length. We recast associative memory at the level of probability measures, treating a context as a distribution over…

Prompt-tuning is an emerging strategy to adapt large language models (LLM) to downstream tasks by learning a (soft-)prompt parameter from data. Despite its success in LLMs, there is limited theoretical understanding of the power of…

We investigate the mechanism underlying a previously identified phenomenon in Vision Transformers - the emergence of high-norm tokens that lead to noisy attention maps (Darcet et al., 2024). We observe that in multiple models (e.g., CLIP,…

We study conditions under which transformers using soft attention can simulate hard attention, that is, effectively focus all attention on a subset of positions. First, we examine several subclasses of languages recognized by hard-attention…

Click-Through Rate (CTR) prediction, a core task in recommendation systems, estimates user click likelihood using historical behavioral data. Modeling user behavior sequences as text to leverage Language Models (LMs) for this task has…

Transformer-based architectures achieve state-of-the-art performance across a wide range of tasks in natural language processing, computer vision, and speech processing. However, their immense capacity often leads to overfitting, especially…

Softmax Self-Attention (SSA) is a key component of Transformer architectures. However, when utilised within skipless architectures, which aim to improve representation learning, recent work has highlighted the inherent instability of SSA…

Softmax self-attention often assigns disproportionate weight to semantically uninformative tokens such as special tokens and punctuation, a phenomenon known as attention noise. While recent methods like Cog Attention and the Differential…

To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and…

We introduce a new discrete-time attention model, termed the localmax dynamics, which interpolates between the classic softmax dynamics and the hardmax dynamics, where only the tokens that maximize the influence toward a given token have a…

The softmax content-based attention mechanism has proven to be very beneficial in many applications of recurrent neural networks. Nevertheless it suffers from two major computational limitations. First, its computations for an attention…

In this paper, I introduce the retrieval problem, a simple yet common reasoning task that can be solved only by transformers with a minimum number of layers, which grows logarithmically with the input size. I empirically show that large…

Recently, vision transformers have become very popular. However, deploying them in many applications is computationally expensive partly due to the Softmax layer in the attention block. We introduce a simple but effective, Softmax-free…