Softmax Attention with Constant Cost per Token

• URL: http://arxiv.org/abs/2404.05843v2
• Date: Sat, 27 Apr 2024 19:03:14 GMT
• Title: Softmax Attention with Constant Cost per Token
• Abstract summary: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of exponentials. Our modification linearizes attention with exponential kernel feature maps, whose corresponding feature function is infinite dimensional.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a simple modification to the conventional attention mechanism applied by Transformers: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of exponentials. Our modification linearizes attention with exponential kernel feature maps, whose corresponding feature function is infinite dimensional. We show that our modification is expressible as a composition of log-sums of exponentials, with a latent space of constant size, enabling application with constant time and space complexity per token. We implement our modification, verify that it works in practice, and conclude that it is a promising alternative to conventional attention.

Related papers

• Self-Attention at Constant Cost per Token via Symmetry-Aware Taylor Approximation [1.7188280334580195]
  We show that self-attention is efficiently computable to arbitrary precision with constant cost per token.<n>Our work enables token generation at modest fixed cost, substantially reducing the infrastructure and energy demands of large-scale Transformer models.
  arXiv  Detail & Related papers  (2026-01-30T20:38:02Z)
• Linear combination of unitaries with exponential convergence [0.0]
  We present a general method for decomposing non-unitary operators into a linear combination of unitary operators.<n>When implemented in a quantum circuit, the subnormalisation of the resulting block encoding scales with the double logarithm of the inverse error.
  arXiv  Detail & Related papers  (2026-01-25T22:47:21Z)
• WUSH: Near-Optimal Adaptive Transforms for LLM Quantization [52.77441224845925]
  Quantization to low bitwidth is a standard approach for deploying large language models.<n>A few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer.<n>We derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization.
  arXiv  Detail & Related papers  (2025-11-30T16:17:34Z)
• Modality Agnostic Efficient Long Range Encoder [14.705955027331674]
  We address the challenge of long-context processing on a single device using generic implementations.<n>To overcome these limitations, we propose MAELRE, a unified and efficient transformer architecture.<n>We demonstrate that MAELRE achieves superior accuracy while reducing computational cost compared to existing long-context models.
  arXiv  Detail & Related papers  (2025-07-25T16:19:47Z)
• Log-Linear Attention [81.09631871212211]
  This paper develops log-linear attention, an attention mechanism that balances linear attention's efficiency and the expressiveness of softmax attention.<n>We show that with a particular growth function, log-linear attention admits a similarly matmul-rich parallel form whose compute cost is log-linear in sequence length.<n>Log-linear attention is a general framework and can be applied on top of existing linear attention variants.
  arXiv  Detail & Related papers  (2025-06-05T08:44:51Z)
• Token Statistics Transformer: Linear-Time Attention via Variational Rate Reduction [29.12836710966048]
  We propose a novel transformer attention operator whose computational complexity scales linearly with the number of tokens. Our results call into question the conventional wisdom that pairwise similarity style attention mechanisms are critical to the success of transformer architectures.
  arXiv  Detail & Related papers  (2024-12-23T18:59:21Z)
• Continual Low-Rank Scaled Dot-product Attention [67.11704350478475]
  We introduce a new formulation of the Scaled-product Attention based on the Nystr"om approximation that is suitable for Continual Inference. In experiments on Online Audio Classification and Online Action Detection tasks, the proposed Continual Scaled Dot-product Attention can lower the number of operations by up to three orders of magnitude.
  arXiv  Detail & Related papers  (2024-12-04T11:05:01Z)
• EulerFormer: Sequential User Behavior Modeling with Complex Vector Attention [88.45459681677369]
  We propose a novel transformer variant with complex vector attention, named EulerFormer. It provides a unified theoretical framework to formulate both semantic difference and positional difference. It is more robust to semantic variations and possesses moresuperior theoretical properties in principle.
  arXiv  Detail & Related papers  (2024-03-26T14:18:43Z)
• Latte: Latent Attention for Linear Time Transformers [11.524573224123905]
  We propose a probabilistic framework for attention. Our method can be seamlessly integrated as a drop-in replacement for the standard attention mechanism. The resulting Latte Transformer'' achieves performance comparable to standard attention and other state-of-the-art models.
  arXiv  Detail & Related papers  (2024-02-27T13:54:48Z)
• FAST: Factorizable Attention for Speeding up Transformers [1.3637227185793512]
  We present a linearly scaled attention mechanism that maintains the full representation of the attention matrix without compromising on sparsification. Results indicate that our attention mechanism has a robust performance and holds significant promise for diverse applications where self-attention is used.
  arXiv  Detail & Related papers  (2024-02-12T18:59:39Z)
• Ring Attention with Blockwise Transformers for Near-Infinite Context [88.61687950039662]
  We present a novel approach, Ring Attention with Blockwise Transformers (Ring Attention), which leverages blockwise computation of self-attention and feedforward to distribute long sequences across multiple devices. Our approach enables training and inference of sequences that are up to device count times longer than those achievable by prior memory-efficient Transformers.
  arXiv  Detail & Related papers  (2023-10-03T08:44:50Z)
• Linear Self-Attention Approximation via Trainable Feedforward Kernel [77.34726150561087]
  In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches. We aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture.
  arXiv  Detail & Related papers  (2022-11-08T08:14:11Z)
• Diffuser: Efficient Transformers with Multi-hop Attention Diffusion for Long Sequences [16.066338004414092]
  textitDiffuser is a new efficient Transformer for sequence-to-sequence modeling. It incorporates all token interactions within one attention layer while maintaining low computation and memory costs. We show its ability to approximate full-attention by analyzing the graph expander property from the spectral perspective.
  arXiv  Detail & Related papers  (2022-10-21T08:13:34Z)
• Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers [55.90468016961356]
  We propose an efficient token mixer that learns to mix in the Fourier domain. AFNO is based on a principled foundation of operator learning. It can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms.
  arXiv  Detail & Related papers  (2021-11-24T05:44:31Z)
• Understanding and Overcoming the Challenges of Efficient Transformer Quantization [17.05322956052278]
  Transformer-based architectures have become the de-facto standard models for a wide range of Natural Language Processing tasks. However, their memory footprint and high latency are prohibitive for efficient deployment and inference on resource-limited devices. We show that transformers have unique quantization challenges -- namely, high dynamic activation ranges that are difficult to represent with a low bit fixed-point format.
  arXiv  Detail & Related papers  (2021-09-27T10:57:18Z)
• Combiner: Full Attention Transformer with Sparse Computation Cost [142.10203598824964]
  We propose Combiner, which provides full attention capability in each attention head while maintaining low computation complexity. We show that most sparse attention patterns used in existing sparse transformers are able to inspire the design of such factorization for full attention. An experimental evaluation on both autoregressive and bidirectional sequence tasks demonstrates the effectiveness of this approach.
  arXiv  Detail & Related papers  (2021-07-12T22:43:11Z)
• Stable, Fast and Accurate: Kernelized Attention with Relative Positional Encoding [63.539333383965726]
  We propose a novel way to accelerate attention calculation for Transformers with relative positional encoding (RPE) Based upon the observation that relative positional encoding forms a Toeplitz matrix, we mathematically show that kernelized attention with RPE can be calculated efficiently using Fast Fourier Transform (FFT)
  arXiv  Detail & Related papers  (2021-06-23T17:51:26Z)
• Exponential enhancement of quantum metrology using continuous variables [15.102680713021368]
  We propose a new design of the signal-probe Hamiltonian which generates an exponential enhancement of measurement sensitivity. We show that linear scaling in both time and the number of coupling terms is sufficient to obtain exponential enhancement.
  arXiv  Detail & Related papers  (2020-04-02T18:20:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.