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Graph attention network(GAN) exactly perform the same thing you are referring to . In chebnet, graphsage we have a fixed adjacency matrix that is given to us. Now, in GAN the authors try to learn the adjacency matrix via self-attention mechanism. Graph Attention Network: Let, $K$ be the number of attention heads, $h^{l+1}_i$ is the feature vector of node $i$ ...


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According to the definition of Graph Neural Networks taken from here GCN perfroms an operation of the form: $$ f (H^{(l)} ,A) = \sigma(\tilde{D}^{-1/2} \tilde{A} \tilde{D}^{-1/2} H^{(l)} W^{(l)}) $$ Where $H^{(l)}$ is the input to GCN layer, $\tilde{A} = A + I$ is the adjacency matrix with self loops added and $\tilde{D}$ is a degree matrix, corresponding to ...


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I didn't read the paper in depth, but one example of where assumptions of Euclidean space are made in the design of the networks are with ConvNets in image processing. Specifically, Euclidean spaces are transformationally invariant, meaning that $d(a,b) = d(a+c,b+c)$. Each convolution layer iterates over the image with a certain amount of stride, which ...


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It's hard to say because Euclidean space is defined with respect to some kind of metric, so without any clearer exposition on the nature of the data/problem, the phrase itself may or may not be clear. A metric $d: A \times A \rightarrow \mathbb{R}$ is a function that defines distance between any two points in the space with respect to axioms that 1. two ...


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