title: Kolmogorov-Arnold Transformer
summary: Transformers stand as the cornerstone of mordern deep learning.
  Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix
  the information between channels. In this paper, we introduce the
  Kolmogorov-Arnold Transformer (KAT), a novel architecture that replaces MLP
  layers with Kolmogorov-Arnold Network (KAN) layers to enhance the
  expressiveness and performance of the model. Integrating KANs into
  transformers, however, is no easy feat, especially when scaled up.
  Specifically, we identify three key challenges: (C1) Base function. The
  standard B-spline function used in KANs is not optimized for parallel computing
  on modern hardware, resulting in slower inference speeds. (C2) Parameter and
  Computation Inefficiency. KAN requires a unique function for each input-output
  pair, making the computation extremely large. (C3) Weight initialization. The
  initialization of weights in KANs is particularly challenging due to their
  learnable activation functions, which are critical for achieving convergence in
  deep neural networks. To overcome the aforementioned challenges, we propose
  three key solutions: (S1) Rational basis. We replace B-spline functions with
  rational functions to improve compatibility with modern GPUs. By implementing
  this in CUDA, we achieve faster computations. (S2) Group KAN. We share the
  activation weights through a group of neurons, to reduce the computational load
  without sacrificing performance. (S3) Variance-preserving initialization. We
  carefully initialize the activation weights to make sure that the activation
  variance is maintained across layers. With these designs, KAT scales
  effectively and readily outperforms traditional MLP-based transformers.
paper_authors._id: 66ea2a369f86fb71682da054
paper_authors.name: Xingyi Yang
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-09-18T07:06:28.364Z
paper_authors._id: 634cfebc350bcee9bed20a4d
paper_authors.avatarUrl: https://cdn-avatars.huggingface.co/v1/production/uploads/634cfebc350bcee9bed20a4d/fN47nN5rhw-HJaFLBZWQy.png
paper_authors.fullname: Xingyi Yang
paper_authors.type: user
paper_authors.user: adamdad
paper_authors._id: 66ea2a369f86fb71682da055
paper_authors.name: Xinchao Wang
paper_authors.status: admin_assigned
paper_authors.statusLastChangedAt: 2024-09-18T07:07:23.415Z
paper_authors._id: 63fc03a50aab060792ffef39
paper_authors.avatarUrl: /avatars/9d5b1bb2a41928e08176b703935133ab.svg
paper_authors.fullname: Wangxinchao
paper_authors.type: user
paper_authors.user: wxcTest
paper_title: Kolmogorov-Arnold Transformer
paper_summary: Transformers stand as the cornerstone of mordern deep learning.
  Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix
  the information between channels. In this paper, we introduce the
  Kolmogorov-Arnold Transformer (KAT), a novel architecture that replaces MLP
  layers with Kolmogorov-Arnold Network (KAN) layers to enhance the
  expressiveness and performance of the model. Integrating KANs into
  transformers, however, is no easy feat, especially when scaled up.
  Specifically, we identify three key challenges: (C1) Base function. The
  standard B-spline function used in KANs is not optimized for parallel computing
  on modern hardware, resulting in slower inference speeds. (C2) Parameter and
  Computation Inefficiency. KAN requires a unique function for each input-output
  pair, making the computation extremely large. (C3) Weight initialization. The
  initialization of weights in KANs is particularly challenging due to their
  learnable activation functions, which are critical for achieving convergence in
  deep neural networks. To overcome the aforementioned challenges, we propose
  three key solutions: (S1) Rational basis. We replace B-spline functions with
  rational functions to improve compatibility with modern GPUs. By implementing
  this in CUDA, we achieve faster computations. (S2) Group KAN. We share the
  activation weights through a group of neurons, to reduce the computational load
  without sacrificing performance. (S3) Variance-preserving initialization. We
  carefully initialize the activation weights to make sure that the activation
  variance is maintained across layers. With these designs, KAT scales
  effectively and readily outperforms traditional MLP-based transformers.
paper_ai_summary: The Kolmogorov-Arnold Transformer replaces MLP layers with Kolmogorov-Arnold Network layers to enhance transformers, overcoming challenges related to inference speed, computation efficiency, and weight initialization through rational basis, group learning, and variance-preserving techniques.
paper_ai_keywords: Kolmogorov-Arnold Transformer KAT Kolmogorov-Arnold Network KAN multi-layer perceptron MLP B-spline function rational function CUDA computational load activation weights variance-preserving initialization parallel computing