论文阅读 [TPAMI-2022] VolterraNet: A Higher Order Convolutional Network With Group Equivariance for Homogeneous Manifolds

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搜索论文: VolterraNet: A Higher Order Convolutional Network With Group Equivariance for Homogeneous Manifolds

搜索论文: http://www.studyai.com/search/whole-site/?q=VolterraNet:+A+Higher+Order+Convolutional+Network+With+Group+Equivariance+for+Homogeneous+Manifolds

关键字(Keywords)

Convolution; Manifolds; Correlation; Kernel; Extraterrestrial measurements; Large scale integration; Symmetric matrices; Homogeneous spaces; volterra series; convolutions; geometric deep learning; equivariance

机器学习

分组测试

摘要(Abstract)

Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property.

卷积神经网络由于其平移等变特性，在基于图像的学习任务中取得了巨大的成功。.

Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-euclidean spaces and shown group equivariance of the generalized convolution operation.

最近的工作将卷积神经网络的传统卷积层推广到非欧几里德空间，并证明了广义卷积运算的群等变性。.

In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces.

本文针对黎曼齐次空间上定义为函数样本的数据，提出了一种新的高阶Volterra卷积神经网络（VolterraNet）。.

Analagous to the result for traditional convolutions, we prove that the Volterra functional convolutions are equivariant to the action of the isometry group admitted by the Riemannian homogeneous spaces, and under some restrictions, any non-linear equivariant function can be expressed as our homogeneous space Volterra convolution, generalizing the non-linear shift equivariant characterization of Volterra expansions in euclidean space.

通过对传统卷积结果的分析，我们证明了Volterra函数卷积与黎曼齐次空间所允许的等距群的作用是等价的，并且在某些限制条件下，任何非线性等变函数都可以表示为我们的齐次空间Volterra卷积，推广欧氏空间中Volterra展开的非线性平移等变特征。.

We also prove that second order functional convolution operations can be represented as cascaded convolutions which leads to an efficient implementation.

我们还证明了二阶函数卷积运算可以表示为级联卷积，这导致了一个有效的实现。.

Beyond this, we also propose a dilated VolterraNet model.

除此之外，我们还提出了一个扩展的VolterNet模型。.

These advances lead to large parameter reductions relative to baseline non-euclidean CNNs.

这些进展导致相对于基线非欧几里德CNN的参数大幅降低。.

To demonstrate the efficacy of the VolterraNet performance, we present several real data experiments involving classification tasks on spherical-MNIST, atomic energy, Shrec17 data sets, and group testing on diffusion MRI data.

为了证明VolterNet性能的有效性，我们提供了几个真实数据实验，涉及球形MNIST、原子能、Shrec17数据集的分类任务，以及扩散MRI数据的分组测试。.

Performance comparisons to the state-of-the-art are also presented…

还将性能与最新技术进行了比较。。.

作者(Authors)

[‘Monami Banerjee’, ‘Rudrasis Chakraborty’, ‘Jose Bouza’, ‘Baba C. Vemuri’]

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