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19 votes

What is geometric deep learning?

To complete the first answer that is rather graph oriented, I will write a little about deep learning on manifolds, which is quite general in terms of GDL thanks to the nature of manifolds. Note ...
Blupon's user avatar
  • 301
16 votes
Accepted

What is non-Euclidean data?

I presume this question was prompted by the paper Geometric deep learning: going beyond Euclidean data (2017). If we look at its abstract: Many scientific fields study data with an underlying ...
brazofuerte's user avatar
  • 1,031
10 votes

What is non-Euclidean data?

Non-Euclidian geometry can be generally boiled down to the phrase the shortest path between 2 points isn't necessarily a straight line. Or, put in a way that lends itself very much to machine ...
Jaden Travnik's user avatar
8 votes
Accepted

What is geometric deep learning?

The article Geometric deep learning: going beyond Euclidean data (by Michael M. Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, Pierre Vandergheynst) provides an overview of this relatively new sub-...
nbro's user avatar
  • 40.8k
6 votes
Accepted

What is a filter in the context of graph convolutional networks?

Short answer Check out the paper of Shuman et al. [1], it provides some background on Graph Signal Processing, including answers to your questions in sections II.C and III.A Long Answer Question 1 Yes,...
Eduardo Montesuma's user avatar
6 votes

What is the difference between graph convolution in the spatial vs spectral domain?

Spectral Convolution In a spectral graph convolution, we perform an Eigen decomposition of the Laplacian Matrix of the graph. This Eigen decomposition helps us in understanding the underlying ...
Srivatsan Ramesh's user avatar
4 votes

Is there an open-source implementation for graph convolution networks for weighted graphs?

You can use Pytorch_Geometric library for your projects. Its supports weighted GCNs. It is a rapidly evolving open-source library with easy to use syntax. It is mentioned in the landing page of ...
user1825567's user avatar
3 votes

How does the K-dimensional WL test work?

I never used a k-WL in practice, but I did apply weisfeiler-lehman for my graph tasks. As you can know, the WL provides the coloring by interactive procedure that's assign each node a 'color' (...
Kirill Fedyanin's user avatar
3 votes
Accepted

How do graph neural networks adapt to different number of nodes and connections of different graphs?

The essence of the reason, why this approach works for graphs with a different number of nodes is the locality and node order permutation invariance. The typical form of the layer-wise signal ...
spiridon_the_sun_rotator's user avatar
3 votes
Accepted

How are GCN doing semi-supervised learning?

In the introduction, the authors write We consider the problem of classifying nodes (such as documents) in a graph (such as a citation network), where labels are only available for a small subset of ...
nbro's user avatar
  • 40.8k
3 votes
Accepted

What is the best resources to learn Graph Convolutional Neural Networks?

I believe Graph Representation Learning book by William L. Hamilton is a great resource to start
gcorso's user avatar
  • 366
3 votes

Machine learning with graph as input and output

You can flatten the graph into a matrix and then train it like a normal neural network input. Perhaps an adjacency graph or maybe simply a series of linear equations representing the nodes and convert ...
user3551708's user avatar
3 votes
Accepted

Using GraphSAGE model for multigraph datasets

My question is if GraphSAGE is suitable for this kind of data? To my knowledge, GraphSAGE is designed for very large graphs with highly connected nodes (like social networks). The neighborhood ...
Chillston's user avatar
  • 1,748
3 votes
Accepted

Node classification with random labels for GNNs

The Cora dataset is unbalanced (s. here). It's graph consists of 2708 nodes and the label distribution (for labels 1 to 7) is 818, 426, 418, 351, 298, 217, 180, i.e....
Chillston's user avatar
  • 1,748
2 votes

What is a graph neural network?

Graph Neural Networks The term Graph Neural Network, in its broadest sense, refers to any Neural Network designed to take graph structured data as its input: To cover a broader range of methods, this ...
brazofuerte's user avatar
  • 1,031
2 votes

What is the difference between graph convolution in the spatial vs spectral domain?

After I read multiple explanations from different sources I think I found the main difference between the two methods. Implementation wise the only difference is the matrix that you're multiplying the ...
razvanc92's user avatar
  • 1,138
2 votes

Are there neural networks that accept graphs or trees as inputs?

Yes, there are numerous, coming under the umbrella term Graph Neural Networks (GNN). The most common input structures accepted by these techniques are the adjacency matrix of the graph (optionally ...
brazofuerte's user avatar
  • 1,031
2 votes
Accepted

Understanding the node information score in the paper "Hierarchical Graph Pooling with Structure Learning"

Here, $H$ is a $n * d$ matrix where $n$ is the number of total nodes in the graph and $d$ is the dimension of embedding of each node. Using the notation in the question, the basic GNN formulation ...
user1825567's user avatar
2 votes
Accepted

What are some conferences for publishing papers on graph convolutional networks?

Based on past publications, here are some journals and conferences where you can possibly publish or present a research paper on geometric deep learning or graph neural networks Neural Information ...
nbro's user avatar
  • 40.8k
2 votes
Accepted

Is there an open-source implementation for graph convolution networks for weighted graphs?

A Comprehensive Survey on Graph Neural Networks (2019) presents a list of ConvGNN's. All of the following accept weighted graphs, and three accept those with edge weights as well: And below is a ...
brazofuerte's user avatar
  • 1,031
2 votes

How Graph Convolutional Neural Networks forward propagate?

I think the picture you're presenting is mostly for educational purposes and that's why they are excluding the node itself from it's neighbors and using two distinct networks (most of the papers I've ...
razvanc92's user avatar
  • 1,138
2 votes

Are Graph Neural Networks generalizations of Convolutional Neural Networks?

Excuse my lack of rigor. Although I believe this could be rigorously proven for certain definitions of GNN, the term is still too loose for me to honestly claim one way or another on this. Hopefully ...
JacKeown's user avatar
  • 125
2 votes

What is the best GNN for a NMT task?

I will start by saying that I do not have any experience with Graph2Seq networks or GGNN, but I have some knowledge about GNN in general and the other three architectures. Firstly, it is essential to ...
Jesse's user avatar
  • 31
2 votes
Accepted

Why don't we use diffusion for non-graph CNNs?

Just for completeness, here is one simple formalization of a diffusion GCN (Gasteiger et al.): $\text{D-GCN}(X) = \sum_{k=1}^K A^k X W_k$ You have a diffusion factor $k \in [1 .. K]$ and you apply ...
Chillston's user avatar
  • 1,748
2 votes
Accepted

Relevance of Weisfeiler–Lehman Graph Isomorphism Test limitation for Graph Neural Networks

Firstly, as already stated in the Wikipedia quote: Observing that a type of GNN is as expressive as the Weisfeiler–Lehman (WL) Test, means in practice that two graphs $\mathcal{G}_1$ and $\mathcal{G}...
Chillston's user avatar
  • 1,748
2 votes

Why is the output of my graph neural network not permutation equivariant?

It seems that the graph filter layer in your GNN takes information from the immediate neighbors for every node and applies a ReLU nonlinearity. However, the architecture you've shown does not ...
michael williams's user avatar
2 votes

How can I improve this toy Graph Neural Network Generative Language model

First of all, I would like to encourage you to keep trying new things, it sounds super fun! There are a few things I would like you to clarify about Graph Neural Networks (GNNs) and Graph ...
Cesar Ruiz's user avatar
2 votes
Accepted

Why is there a shared matrix W in graph attention networks instead of the query-key-value trio like in regular transformers?

To my understanding, there isn't any theoretical reason why the query, key and values weights are absent. I feel that the difference may lie in the way the additive attention is calculated vs the dot-...
Cesar Ruiz's user avatar
2 votes

How to pass batch of Graphs in GATv2Conv?

For efficiency reasons, it is the standard for graph learning libraries to use the format [n_batches x num_nodes, node_feature_dim], instead of having batches in an ...
Chillston's user avatar
  • 1,748
1 vote
Accepted

Is "node embedding" in GNN analogous to "hidden layer" of FFN?

Embeddings are vectors. Layers are functions. So, node embeddings (e.g. produced by TransE) are analogous to word embeddings or code embeddings, i.e. they are vector (and lower-dimensional) ...
nbro's user avatar
  • 40.8k

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