PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels

• URL: http://arxiv.org/abs/2310.01655v3
• Date: Sun, 17 Mar 2024 23:35:24 GMT
• Title: PolySketchFormer: Fast Transformers via Sketching Polynomial Kernels
• Authors: Praneeth Kacham, Vahab Mirrokni, Peilin Zhong,
• Abstract summary: We show that attention with high degree can effectively replace softmax without sacrificing model quality. We present a block-based algorithm to apply causal masking efficiently. We validate PolySketchFormerAttention empirically by training language models capable of handling long contexts.
• Score: 23.99075223506133
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quadratic time and memory complexity inherent to self-attention mechanisms, with respect to sequence length, presents a critical computational bottleneck in the training and deployment of large-scale Transformer-based language models. Recent theoretical results indicate the intractability of sub-quadratic softmax attention approximation under reasonable complexity assumptions. This paper addresses this challenge by first demonstrating that polynomial attention with high degree can effectively replace softmax without sacrificing model quality. Next, we develop polynomial sketching techniques from numerical linear algebra to achieve linear-time polynomial attention with approximation guarantees. Crucially, our approach achieves this speedup without requiring the sparsification of attention matrices. We also present a block-based algorithm to apply causal masking efficiently. Combining these techniques, we provide \emph{PolySketchFormer}, a practical linear-time Transformer architecture for language modeling that offers provable guarantees. We validate PolySketchFormer empirically by training language models capable of handling long contexts. These experiments utilize both synthetic and real-world datasets (PG19, Wikipedia and C4) on Google Cloud TPUs. For context lengths of 32k and GPT-2 style models, our model achieves a 2.5-4x speedup in training compared to FlashAttention, with no observed degradation in quality across our experiments.

Related papers

• Learning Linear Attention in Polynomial Time [115.68795790532289]
  We provide the first results on learnability of single-layer Transformers with linear attention. We show that linear attention may be viewed as a linear predictor in a suitably defined RKHS. We show how to efficiently identify training datasets for which every empirical riskr is equivalent to the linear Transformer.
  arXiv  Detail & Related papers  (2024-10-14T02:41:01Z)
• Power-Softmax: Towards Secure LLM Inference over Encrypted Data [2.4576879793338913]
  Homomorphic Encryption (HE) requires cryptographic methods to have an encrypted form. Previous approaches have either directly approximated pre-trained models with large-degrees over tenfold. We present a new variant of self-attention that offers a stable form for training and is easy to approximate with training.
  arXiv  Detail & Related papers  (2024-10-12T09:32:42Z)
• Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time [17.086679273053853]
  We show that a novel fast approximation method can calculate the gradients in almost linear time. By improving the efficiency of gradient, we hope that this work will facilitate more effective training and deployment of long-context language models.
  arXiv  Detail & Related papers  (2024-08-23T17:16:43Z)
• Lean Attention: Hardware-Aware Scalable Attention Mechanism for the Decode-Phase of Transformers [4.674454841332859]
  Transformer-based models have emerged as one of the most widely used architectures for natural language processing. These huge models are memory hungry and incur significant inference latency even on cutting edge AI-accelerators. We propose LeanAttention, a scalable technique of computing self-attention for the token-generation phase.
  arXiv  Detail & Related papers  (2024-05-17T00:52:39Z)
• Decreasing the Computing Time of Bayesian Optimization using Generalizable Memory Pruning [56.334116591082896]
  We show a wrapper of memory pruning and bounded optimization capable of being used with any surrogate model and acquisition function. Running BO on high-dimensional or massive data sets becomes intractable due to this time complexity. All model implementations are run on the MIT Supercloud state-of-the-art computing hardware.
  arXiv  Detail & Related papers  (2023-09-08T14:05:56Z)
• Softmax-free Linear Transformers [90.83157268265654]
  Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. Existing methods are either theoretically flawed or empirically ineffective for visual recognition. We propose a family of Softmax-Free Transformers (SOFT)
  arXiv  Detail & Related papers  (2022-07-05T03:08:27Z)
• Sketching as a Tool for Understanding and Accelerating Self-attention for Long Sequences [52.6022911513076]
  Transformer-based models are not efficient in processing long sequences due to the quadratic space and time complexity of the self-attention modules. We propose Linformer and Informer to reduce the quadratic complexity to linear (modulo logarithmic factors) via low-dimensional projection and row selection. Based on the theoretical analysis, we propose Skeinformer to accelerate self-attention and further improve the accuracy of matrix approximation to self-attention.
  arXiv  Detail & Related papers  (2021-12-10T06:58:05Z)
• SOFT: Softmax-free Transformer with Linear Complexity [112.9754491864247]
  Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. Various attempts on approximating the self-attention with linear complexity have been made in Natural Language Processing. We identify that their limitations are rooted in keeping the softmax self-attention during approximations. For the first time, a softmax-free transformer or SOFT is proposed.
  arXiv  Detail & Related papers  (2021-10-22T17:57:29Z)
• Predicting Attention Sparsity in Transformers [0.9786690381850356]
  We propose Sparsefinder, a model trained to identify the sparsity pattern of entmax attention before computing it. Our work provides a new angle to study model efficiency by doing extensive analysis of the tradeoff between the sparsity and recall of the predicted attention graph.
  arXiv  Detail & Related papers  (2021-09-24T20:51:21Z)
• A Reinforcement Learning Environment for Polyhedral Optimizations [68.8204255655161]
  We propose a shape-agnostic formulation for the space of legal transformations in the polyhedral model as a Markov Decision Process (MDP) Instead of using transformations, the formulation is based on an abstract space of possible schedules. Our generic MDP formulation enables using reinforcement learning to learn optimization policies over a wide range of loops.
  arXiv  Detail & Related papers  (2021-04-28T12:41:52Z)

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.