论文标题
切线束过滤器和神经网络：从歧管到蜂窝滑轮和背部
Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back
论文作者
论文摘要
在这项工作中，我们介绍了利用连接拉普拉斯运算符的Riemannian歧管的切线束。我们使用卷积来定义切线束过滤器和切线束神经网络（TNNS），在切线束信号上运行的新型连续体系结构，即歧管上的向量字段。我们在时空领域和时间域中分散TNN，这表明它们的离散对应物是最近引入的造纸神经网络的原则性变体。我们正式证明这种离散的体系结构会收敛到基础连续TNN。我们从数值上评估了所提出的体系结构对单元2速率上切线矢量场的降解任务的有效性。
In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere.
