Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

By John Guibas, Morteza Mardani, Zong-Yi Li, Andrew Tao, Anima Anandkumar, Bryan Catanzaro. arXiv.org, 2021

388 citations recorded by the source corpus.

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible for high-resolution inputs. To cope with this challenge, we propose Adaptive Fourier Neural Operator (AFNO) as an efficient token mixer that learns to mix in the Fourier domain. AFNO is based on a principled foundation of operator learning which allows us to frame token mixing as a continuous global convolution without any dependence on the input resolution. This principle was previously used to design FNO, which solves global convolution efficiently in the Fourier domain and has shown promise in learning challenging PDEs. To handle challenges in visual representation learning such as discontinuities in images and high resolution inputs, we propose principled architectural modifications to FNO which results in memory and computational efficiency. This includes imposing a block-diagonal structure on the channel mixing weights, adaptively sharing weights across tokens, and sparsifying the frequency modes via soft-thresholding and shrinkage. The resulting model is highly parallel with a quasi-linear complexity and has linear memory in the sequence size. AFNO outperforms self-attention mechanisms for few-shot segmentation in terms of both efficiency and accuracy. For Cityscapes segmentation with the Segformer-B3 backbone, AFNO can handle a sequence size of 65k and outperforms other efficient self-attention mechanisms.

Subfields: Computer Vision and Pattern Recognition, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/427fe0e6e2e2d6f927c62e80c75706e02c2a747f

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Citations in the corpus

GraphCast: Learning skillful medium-range global weather forecasting (2022, methodology): “(2022) introduced FourCastNet(FCN), based on Fourier Neural Operators (Guibas et al., 2021; Li et al., 2020), and reported promising results on 0.”
FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators (2022, methodology): “While we refer the reader to the original AFNO paper [Guibas et al., 2022] for more details, we brieﬂy describe the ﬂow of computation in our model here.”
Earthformer: Exploring Space-Time Transformers for Earth System Forecasting (2022, methodology): “Pathak et al. [28] proposed the FourCastNet for global weather forecasting, which is based on Adaptive Fourier Neural Operators (AFNO) [14].”
FourCastNet: Accelerating Global High-Resolution Weather Forecasting Using Adaptive Fourier Neural Operators (2022, background): “More recently, the Adaptive Fourier Neural Operator (AFNO) has provided a class of transformers that can handle continuous input and high resolutions efficiently [17].”
Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere (2023, methodology): “Pathak et al. (2022) combined a Fourier-transform-based tokenmixing scheme (Guibas et al., 2021) with a vision transformer (ViT) backbone (Dosovitskiy et al., 2020) and developed FourCastNet (FCN) to model long-range dependencies.”
FuXi: a cascade machine learning forecasting system for 15-day global weather forecast (2023, methodology): “It integrates the Adaptive Fourier neural operator (AFNO) [13] with a Vision Transformer (ViT) [14].”