Related papers: Transformers in Uniform TC$^0$

Recently Transformers have provided state-of-the-art performance in sparse matching, crucial to realize high-performance 3D vision applications. Yet, these Transformers lack efficiency due to the quadratic computational complexity of their…

Linear attention reduces the quadratic cost of softmax attention to $\mathcal{O}(T)$, but its memory state grows as $\mathcal{O}(T)$ in Frobenius norm, causing progressive interference between stored associations. We introduce…

Transformers have demonstrated strong performance across a wide range of sequence modeling tasks, but their quadratic attention complexity limits scalability to long sequences. Linear models such as Mamba and sliding-window attention (SWA)…

The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original…

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the…

A common lens to theoretically study neural net architectures is to analyze the functions they can approximate. However, constructions from approximation theory may be unrealistic and therefore less meaningful. For example, a common…

Despite their central role in the success of foundational models and large-scale language modeling, the theoretical foundations governing the operation of Transformers remain only partially understood. Contemporary research has largely…

Transformer language models have driven significant progress across various fields, including natural language processing and computer vision. A central component of these models is the self-attention (SA) mechanism, which learns rich…

Previous work on the learnability of transformers \textemdash\ focused primarily on examining their ability to approximate specific algorithmic patterns through training \textemdash\ has largely been data-driven, offering only probabilistic…

Transformer-based approaches have revolutionized image super-resolution by modeling long-range dependencies. However, the quadratic computational complexity of vanilla self-attention mechanisms poses significant challenges, often leading to…

Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than…

To overcome the quadratic cost of self-attention, recent works have proposed various sparse attention modules, most of which fall under one of two groups: 1) sparse attention under a hand-crafted patterns and 2) full attention followed by a…

Transformers have achieved great success in machine translation, but transformer-based NMT models often require millions of bilingual parallel corpus for training. In this paper, we propose a novel architecture named as attention link (AL)…

We propose an innovative, learnable two-sided short-time Laplace transform (STLT) mechanism to supplant the traditional self attention in transformer-based LLMs. Our STLT introduces trainable parameters for each Laplace node, enabling…

The transformer architecture predominates across various models. As the heart of the transformer, attention has a computational complexity of $O(N^2)$, compared to $O(N)$ for linear transformations. When handling large sequence lengths,…

Recent advances in efficient Transformers have exploited either the sparsity or low-rank properties of attention matrices to reduce the computational and memory bottlenecks of modeling long sequences. However, it is still challenging to…

The quadratic complexity of the attention mechanism represents one of the biggest hurdles for processing long sequences using Transformers. Current methods, relying on sparse representations or stateful recurrence, sacrifice token-to-token…

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…

Large Language Models (LLMs) have emerged as a pivotal research area, yet the attention module remains a critical bottleneck in LLM inference, even with techniques like KVCache to mitigate redundant computations. While various top-$k$…

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…