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At the core of the popular Transformer architecture is the self-attention mechanism, which dynamically assigns softmax weights to each input token so that the model can focus on the most salient information. However, the softmax structure…

Training stable biological foundation models requires rethinking attention mechanisms: we find that using sigmoid attention as a drop in replacement for softmax attention a) produces better learned representations: on six diverse…

Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token…

The original softmax-based attention mechanism (regular attention) in the extremely successful Transformer architecture computes attention between $N$ tokens, each embedded in a $D$-dimensional head, with a time complexity of $O(N^2D)$.…

We prove that with linear transformations, both (i) two-layer self-attention and (ii) one-layer self-attention followed by a softmax function are universal approximators for continuous sequence-to-sequence functions on compact domains. Our…

Transformers have achieved state-of-the-art performance across various tasks, but suffer from a notable quadratic complexity in sequence length due to the attention mechanism. In this work, we propose MonarchAttention -- a novel approach to…

Attention is a core component of transformer architecture, whether encoder-only, decoder-only, or encoder-decoder model. However, the standard softmax attention often produces noisy probability distribution, which can impair effective…

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…

This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the…

The transformer's attention mechanism has revolutionized AI and machine learning, with its efficient computation being crucial to its performance. However, calculating attention involves matrix operations interspersed with softmax…

Transformer attention is typically implemented using softmax normalization, which enforces attention weights with unit sum normalization. While effective in many settings, this constraint can limit flexibility in controlling attention…

The transformer architecture is central to the success of modern Large Language Models (LLMs), in part due to its surprising ability to perform a wide range of tasks - including mathematical reasoning, memorization, and retrieval - using…

Linear attentions have shown potential for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2)…

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on…

An essential component of modern recurrent sequence models is the forget gate. While Transformers do not have an explicit recurrent form, we show that a forget gate can be naturally incorporated into Transformers by down-weighting the…

Various forms of sparse attention have been explored to mitigate the quadratic computational and memory cost of the attention mechanism in transformers. We study sparse transformers not through a lens of efficiency but rather in terms of…

We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but critical component of a transformer becomes a natural development…

We present a theoretical analysis of the performance of transformer with softmax attention in in-context learning with linear regression tasks. While the existing literature predominantly focuses on the convergence of transformers with…

The powerful modeling capabilities of all-attention-based transformer architectures often cause overfitting and - for natural language processing tasks - lead to an implicitly learned internal language model in the autoregressive…

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear…