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The maximum element of the vector output by the Softmax function approaches zero as the input vector size increases. Transformer-based language models rely on Softmax to compute attention scores, causing the attention distribution to…

The softmax function is crucial in Transformer attention, which normalizes each row of the attention scores with summation to one, achieving superior performances over other alternative functions. However, the softmax function can face a…

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…

Recent advances in transformer-based Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks. However, their quadratic computational complexity concerning sequence length remains a significant bottleneck…

Large language models rely on attention mechanisms with a softmax activation. Yet the dominance of softmax over alternatives (e.g., component-wise or linear) remains poorly understood, and many theoretical works have focused on the…

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…

Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of…

Linear attention Transformers and their gated variants, celebrated for enabling parallel training and efficient recurrent inference, still fall short in recall-intensive tasks compared to traditional Transformers and demand significant…

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…

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

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…

Transformers have had tremendous impact for several sequence related tasks, largely due to their ability to retrieve from any part of the sequence via softmax based dot-product attention. This mechanism plays a crucial role in Transformer's…

Transformers have demonstrated remarkable in-context learning (ICL) capabilities. The strong ICL performance of transformers is commonly believed to arise from their ability to implicitly execute certain algorithms on the context, thereby…

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage…

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates \emph{global competition}, a…

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer…

A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with…

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…

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 architectures traditionally employ softmax to compute attention weights, which produces dense distributions over all tokens in a sequence. While effective in many settings, this density has been shown to be detrimental for…