title: Multi-Layer Transformers Gradient Can be Approximated in Almost Linear
    Time
summary: The quadratic computational complexity in the self-attention mechanism of
  popular transformer architectures poses significant challenges for training and
  inference, particularly in terms of efficiency and memory requirements. Towards
  addressing these challenges, this paper introduces a novel fast computation
  method for gradient calculation in multi-layer transformer models. Our approach
  enables the computation of gradients for the entire multi-layer transformer
  model in almost linear time n^{1+o(1)}, where n is the input sequence
  length. This breakthrough significantly reduces the computational bottleneck
  associated with the traditional quadratic time complexity. Our theory holds for
  any loss function and maintains a bounded approximation error across the entire
  model. Furthermore, our analysis can hold when the multi-layer transformer
  model contains many practical sub-modules, such as residual connection, casual
  mask, and multi-head attention. By improving the efficiency of gradient
  computation in large language models, we hope that our work will facilitate the
  more effective training and deployment of long-context language models based on
  our theoretical results.
paper_authors._id: 66cc05aed20991c2a015a6bc
paper_authors.name: Yingyu Liang
paper_authors._id: 66cc05aed20991c2a015a6bd
paper_authors.name: Zhizhou Sha
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-08-27T07:42:34.868Z
paper_authors._id: 6335604ea01bd734f72316b0
paper_authors.avatarUrl: /avatars/4c6611dabd492106ffb2e82fd680d983.svg
paper_authors.fullname: Zhizhou Sha
paper_authors.type: user
paper_authors.user: JamesSand
paper_authors._id: 66cc05aed20991c2a015a6be
paper_authors.name: Zhenmei Shi
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-09-30T08:07:40.297Z
paper_authors._id: 64b769d7fa7eabaae5fb7f2f
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/64b769d7fa7eabaae5fb7f2f/AbxVphanApZDfj3cOI1tb.jpeg
paper_authors.fullname: Zhenmei Shi
paper_authors.type: user
paper_authors.user: Zhenmei
paper_authors._id: 66cc05aed20991c2a015a6bf
paper_authors.name: Zhao Song
paper_authors._id: 66cc05aed20991c2a015a6c0
paper_authors.name: Yufa Zhou
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2024-08-27T07:42:27.200Z
paper_authors._id: 658ab894c4b2004663dff3ae
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/658ab894c4b2004663dff3ae/oPRnFuW2Imaa2KkYWNbSf.jpeg
paper_authors.fullname: YUFA ZHOU
paper_authors.type: user
paper_authors.user: MasterZhou
paper_title: Multi-Layer Transformers Gradient Can be Approximated in Almost Linear
    Time
paper_summary: The quadratic computational complexity in the self-attention mechanism of
  popular transformer architectures poses significant challenges for training and
  inference, particularly in terms of efficiency and memory requirements. Towards
  addressing these challenges, this paper introduces a novel fast computation
  method for gradient calculation in multi-layer transformer models. Our approach
  enables the computation of gradients for the entire multi-layer transformer
  model in almost linear time n^{1+o(1)}, where n is the input sequence
  length. This breakthrough significantly reduces the computational bottleneck
  associated with the traditional quadratic time complexity. Our theory holds for
  any loss function and maintains a bounded approximation error across the entire
  model. Furthermore, our analysis can hold when the multi-layer transformer
  model contains many practical sub-modules, such as residual connection, casual
  mask, and multi-head attention. By improving the efficiency of gradient
  computation in large language models, we hope that our work will facilitate the
  more effective training and deployment of long-context language models based on
  our theoretical results.
paper_ai_summary: A novel fast computation method for gradient calculation in multi-layer transformer models reduces computational complexity from quadratic to almost linear, improving efficiency and enabling better handling of long-context language models.
paper_ai_keywords: self-attention mechanism transformer architectures gradient calculation multi-layer transformer models residual connection casual mask multi-head attention