This paper studies the relationship between a graph neural network (GNN) and a manifold neural network (MNN) when the graph is constructed from a set of points sampled from the manifold, thus encoding geometric information.
We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i. e. vector fields over the manifolds.
In this paper we propose a pooling approach for convolutional information processing on graphs relying on the theory of graphons and limits of dense graph sequences.
In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator.
Deep neural network architectures have been proved as a powerful technique to solve problems based on these data residing on the manifold.
We also conclude that in Agg-GNNs the selectivity of the mapping operators is tied to the properties of the filters only in the first layer of the CNN stage.
Hence, in this paper, we analyze the stability properties of convolutional neural networks on manifolds to understand the stability of GNNs on large graphs.
We consider the broad class of decentralized optimal resource allocation problems in wireless networks, which can be formulated as a constrained statistical learning problems with a localized information structure.
We capture the asynchrony by modeling the activation pattern as a characteristic of each node and train a policy-based resource allocation method.
We then extend this analysis by interpreting the graphon neural network as a generating model for GNNs on deterministic and stochastic graphs instantiated from the original and perturbed graphons.
Phase I dose-finding trials are increasingly challenging as the relationship between efficacy and toxicity of new compounds (or combination of them) becomes more complex.