Equivariant Network尽管现阶段的神经网络还缺少理论支撑,但是许多经验及实验都验证了:卷积权值共享和网络深度对于神经网络的效果起到了重要作用。卷积权值共享的有效性依赖于其在大多数感知任务中都具有平移不变性:预测标签的函数和数据分布对于平移变换都近似于不变。得益于平移不变性,共享权重的卷积核可以从图像的局部区域提取特征,并且参数量远少于全连接网络,同时能够学习更多有效的变换信息。等变网络对卷积神经网络进行扩展,并在特定的变换(旋转、平移等,也可表示为一个特殊的群)下具有等变性。
ICLR, (2021)
Expressive anisotropic mesh convolution without having to pick arbitrary kernel orientation by using gauge equivariance
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Medical Image Anal., (2021): 101849-101849
We propose a framework to encode the geometric structure of the special Euclidean motion group SE(2) in convolutional networks to yield translation and rotation equivariance via the introduction of SE(2)-group convolution layers
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Masanobu Horie, Naoki Morita, Toshiaki Hishinuma, Yu Ihara, Naoto Mitsume
ICLR, (2021)
We developed isometric transformation invariant and equivariant graph convolutional networks, which shows high prediction performance and computational efficiency.
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Wang Rui, Walters Robin,Yu Rose
ICLR, (2021)
Integrate various symmetris into deep sequence models for forecasting turbulence and ocean currents with improved accuracy and physical consistency.
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Simon Batzner, Tess E. Smidt, Lixin Sun,Jonathan P. Mailoa,Mordechai Kornbluth, Nicola Molinari,Boris Kozinsky
We demonstrate that the Neural Equivariant Interatomic Potential, a new type of graph neural network built on SE(3)-equivariant convolutions exhibits state-of-the-art accuracy and exceptional data efficiency on data sets of small molecules and periodic materials
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Michael Hutchinson, Charline Le Lan, Sheheryar Zaidi, Emilien Dupont,Yee Whye Teh, Hyunjik Kim
ICML, pp.4533-4543, (2021)
Instead of the data augmentation approach used for vanilla Convolutional neural networks, to ‘train’ the symmetry into the model, group equivariant CNNs instead have a built in symmetry that leads to improvements in performance and data efficiency
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Gregor N. C. Simm, Robert Pinsler, Gábor Csányi,José Miguel Hernández-Lobato
ICLR, (2021)
Covariant actor-critic based on spherical harmonics that exploits symmetries to design molecules in 3D
Cited by0BibtexViews98
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Robin Walters, Jinxi Li,Rose Yu
ICLR, (2021)
Our model, ECCO, uses rotationally-equivariant continuous convolution to improve generalization in trajectory prediction.
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Leon Lang, Maurice Weiler
ICLR, (2021)
We parameterize equivariant convolution kernels by proving a generalization of the Wigner-Eckart theorem for spherical tensor operators.
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Nadav Dym,Haggai Maron
ICLR, (2021)
We provide sufficient conditions for universality of rotation equivariant point cloud networks and use these conditions to show that current models are universal as well as for devising new universal architectures.
Cited by0BibtexViews92
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David W. Romero, Jean-Baptiste Cordonnier
ICLR, (2021)
We provide a general self-attention formulation to impose group equivariance to arbitrary symmetry groups.
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Denis Boyda, Gurtej Kanwar,Sébastien Racanière,Danilo Jimenez Rezende, Michael S. Albergo, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan
Physical Review D, no. 7 (2021)
We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction
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Tess E. Smidt, Mario Geiger, Benjamin Kurt Miller
Physical Review Research, no. 1 (2021)
We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry breaking input to deform a square into a rectangle
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ICLR, (2021)
Equivariance to symmetry groups improves the generative adversarial synthesis of globally-symmetric images.
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Carlos Esteves, Christine Allen-Blanchette,Ameesh Makadia,Kostas Daniilidis
International Journal of Computer Vision, no. 3 (2020): 588-600
The network is applied to 3D object classification, retrieval, and alignment, but has potential applications in spherical images such as panoramas, or any data that can be represented as a spherical function
Cited by92BibtexViews157DOI
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Taco Cohen, Mario Geiger, Maurice Weiler
neural information processing systems, (2020): 9142-9153
In this paper we have developed a general theory of equivariant convolutional networks on homogeneous spaces using the formalism of fiber bundles and fields
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NIPS 2020, (2020)
We have presented an attention-based neural architecture designed for point cloud data
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Wirnsberger Peter, Ballard Andrew J., Papamakarios George, Abercrombie Stuart, Racanière Sébastien, Pritzel Alexander,Rezende Danilo Jimenez,Blundell Charles
The Journal of chemical physics, no. 14 (2020): 144112
We observe a pattern commonly encountered in machine learning: after an initial decrease of both training and test loss, the latter develops a minimum
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NIPS 2020, (2020)
We observe that the exponential can be computed implicitly. Using this we developed new invertible transformations named convolution exponentials and graph convolution exponentials, and showed that they retain their equivariance properties under exponentiation
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Erik J Bekkers
ICLR, (2020)
This paper presents a flexible framework for building Group convolutional neural networks for arbitrary Lie groups
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