Scalable Transformer for PDE Surrogate Modeling

Transformer has shown state-of-the-art performance on various applications and has recently emerged as a promising tool for surrogate modeling of partial differential equations (PDEs). Despite the introduction of linear-complexity variant, applying attention to a large number of grid points can result in instability and is still expensive to compute. In this work, we propose Factorized Transformer(FactFormer), which is based on an axial factorized kernel integral. Concretely, we introduce a learnable projection operator that decomposes the input function into multiple sub-functions with one-dimensional domain. These sub-functions are then evaluated and used to compute the instance-based kernel with an axial factorized scheme. We showcase that the proposed model is able to simulate 2D Kolmogorov flow on a 256 by 256 grid and 3D smoke buoyancy on a 64 by 64 by 64 grid with good accuracy and efficiency. In addition, we find out that with the factorization scheme, the attention matrices enjoy a more compact spectrum than full softmax-free attention matrices

Rethinking Semantic Segmentation from a Sequence-to-Sequence Perspective with Transformers

Most recent semantic segmentation methods adopt a fully-convolutional network (FCN) with an encoder-decoder architecture. The encoder progressively reduces the spatial resolution and learns more abstract/semantic visual concepts with larger receptive fields. Since context modeling is critical for segmentation, the latest efforts have been focused on increasing the receptive field, through either dilated/atrous convolutions or inserting attention modules. However, the encoder-decoder based FCN architecture remains unchanged. In this paper, we aim to provide an alternative perspective by treating semantic segmentation as a sequence-to-sequence prediction task. Specifically, we deploy a pure transformer (ie, without convolution and resolution reduction) to encode an image as a sequence of patches. With the global context modeled in every layer of the transformer, this encoder can be combined with a simple decoder to provide a powerful segmentation model, termed SEgmentation TRansformer (SETR). Extensive experiments show that SETR achieves new state of the art on ADE20K (50.28% mIoU), Pascal Context (55.83% mIoU) and competitive results on Cityscapes. Particularly, we achieve the first position in the highly competitive ADE20K test server leaderboard on the day of submission.Comment: CVPR 2021. Project page at https://fudan-zvg.github.io/SETR

Mitigation of Spatial Nonstationarity with Vision Transformers

Spatial nonstationarity, the location variance of features' statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction trends, in mineral deposits grades vary due to sedimentation and concentration processes, in hydrology rainfall varies due to the atmosphere and topography interactions, and in metallurgy crystalline structures vary due to differential cooling. Conventional geostatistical modeling workflows rely on the assumption of stationarity to be able to model spatial features for the geostatistical inference. Nevertheless, this is often not a realistic assumption when dealing with nonstationary spatial data and this has motivated a variety of nonstationary spatial modeling workflows such as trend and residual decomposition, cosimulation with secondary features, and spatial segmentation and independent modeling over stationary subdomains. The advent of deep learning technologies has enabled new workflows for modeling spatial relationships. However, there is a paucity of demonstrated best practice and general guidance on mitigation of spatial nonstationarity with deep learning in the geospatial context. We demonstrate the impact of two common types of geostatistical spatial nonstationarity on deep learning model prediction performance and propose the mitigation of such impacts using self-attention (vision transformer) models. We demonstrate the utility of vision transformers for the mitigation of nonstationarity with relative errors as low as 10%, exceeding the performance of alternative deep learning methods such as convolutional neural networks. We establish best practice by demonstrating the ability of self-attention networks for modeling large-scale spatial relationships in the presence of commonly observed geospatial nonstationarity

UniHead: Unifying Multi-Perception for Detection Heads

The detection head constitutes a pivotal component within object detectors, tasked with executing both classification and localization functions. Regrettably, the commonly used parallel head often lacks omni perceptual capabilities, such as deformation perception, global perception and cross-task perception. Despite numerous methods attempt to enhance these abilities from a single aspect, achieving a comprehensive and unified solution remains a significant challenge. In response to this challenge, we have developed an innovative detection head, termed UniHead, to unify three perceptual abilities simultaneously. More precisely, our approach (1) introduces deformation perception, enabling the model to adaptively sample object features; (2) proposes a Dual-axial Aggregation Transformer (DAT) to adeptly model long-range dependencies, thereby achieving global perception; and (3) devises a Cross-task Interaction Transformer (CIT) that facilitates interaction between the classification and localization branches, thus aligning the two tasks. As a plug-and-play method, the proposed UniHead can be conveniently integrated with existing detectors. Extensive experiments on the COCO dataset demonstrate that our UniHead can bring significant improvements to many detectors. For instance, the UniHead can obtain +2.7 AP gains in RetinaNet, +2.9 AP gains in FreeAnchor, and +2.1 AP gains in GFL. The code will be publicly available. Code Url: https://github.com/zht8506/UniHead.Comment: 10 pages, 5 figure

Towards End-to-End Generative Modeling of Long Videos with Memory-Efficient Bidirectional Transformers

Autoregressive transformers have shown remarkable success in video generation. However, the transformers are prohibited from directly learning the long-term dependency in videos due to the quadratic complexity of self-attention, and inherently suffering from slow inference time and error propagation due to the autoregressive process. In this paper, we propose Memory-efficient Bidirectional Transformer (MeBT) for end-to-end learning of long-term dependency in videos and fast inference. Based on recent advances in bidirectional transformers, our method learns to decode the entire spatio-temporal volume of a video in parallel from partially observed patches. The proposed transformer achieves a linear time complexity in both encoding and decoding, by projecting observable context tokens into a fixed number of latent tokens and conditioning them to decode the masked tokens through the cross-attention. Empowered by linear complexity and bidirectional modeling, our method demonstrates significant improvement over the autoregressive Transformers for generating moderately long videos in both quality and speed. Videos and code are available at https://sites.google.com/view/mebt-cvpr2023

Visual Representation Learning with Transformer: A Sequence-to-Sequence Perspective

Visual representation learning is the key of solving various vision problems. Relying on the seminal grid structure priors, convolutional neural networks (CNNs) have been the de facto standard architectures of most deep vision models. For instance, classical semantic segmentation methods often adopt a fully-convolutional network (FCN) with an encoder-decoder architecture. The encoder progressively reduces the spatial resolution and learns more abstract visual concepts with larger receptive fields. Since context modeling is critical for segmentation, the latest efforts have been focused on increasing the receptive field, through either dilated (i.e., atrous) convolutions or inserting attention modules. However, the FCN-based architecture remains unchanged. In this paper, we aim to provide an alternative perspective by treating visual representation learning generally as a sequence-to-sequence prediction task. Specifically, we deploy a pure Transformer to encode an image as a sequence of patches, without local convolution and resolution reduction. With the global context modeled in every layer of the Transformer, stronger visual representation can be learned for better tackling vision tasks. In particular, our segmentation model, termed as SEgmentation TRansformer (SETR), excels on ADE20K (50.28% mIoU, the first position in the test leaderboard on the day of submission), Pascal Context (55.83% mIoU) and reaches competitive results on Cityscapes. Further, we formulate a family of Hierarchical Local-Global (HLG) Transformers characterized by local attention within windows and global-attention across windows in a hierarchical and pyramidal architecture. Extensive experiments show that our method achieves appealing performance on a variety of visual recognition tasks (e.g., image classification, object detection and instance segmentation and semantic segmentation).Comment: Extended version of CVPR 2021 paper arXiv:2012.1584

P2AT: Pyramid Pooling Axial Transformer for Real-time Semantic Segmentation

Recently, Transformer-based models have achieved promising results in various vision tasks, due to their ability to model long-range dependencies. However, transformers are computationally expensive, which limits their applications in real-time tasks such as autonomous driving. In addition, an efficient local and global feature selection and fusion are vital for accurate dense prediction, especially driving scene understanding tasks. In this paper, we propose a real-time semantic segmentation architecture named Pyramid Pooling Axial Transformer (P2AT). The proposed P2AT takes a coarse feature from the CNN encoder to produce scale-aware contextual features, which are then combined with the multi-level feature aggregation scheme to produce enhanced contextual features. Specifically, we introduce a pyramid pooling axial transformer to capture intricate spatial and channel dependencies, leading to improved performance on semantic segmentation. Then, we design a Bidirectional Fusion module (BiF) to combine semantic information at different levels. Meanwhile, a Global Context Enhancer is introduced to compensate for the inadequacy of concatenating different semantic levels. Finally, a decoder block is proposed to help maintain a larger receptive field. We evaluate P2AT variants on three challenging scene-understanding datasets. In particular, our P2AT variants achieve state-of-art results on the Camvid dataset 80.5%, 81.0%, 81.1% for P2AT-S, P2ATM, and P2AT-L, respectively. Furthermore, our experiment on Cityscapes and Pascal VOC 2012 have demonstrated the efficiency of the proposed architecture, with results showing that P2AT-M, achieves 78.7% on Cityscapes. The source code will be available a