I can admit that this is the best explanation for GAT and GNN one can find. Fantastic explanation with very simple English. The quality of sound and video is great as well. Many thanks.
This was simply a fantastic explanation video, I really do hope this video gets more coverage than it already has. It would be fantastic if you were to explain the concept of multi-head attention in another video. You've earned yourself a subscriber +1.
Your work has been an absolute game-changer for me! The way you break down complex concepts into understandable and actionable insights is truly commendable. Your dedication to providing in-depth tutorials and explanations has tremendously helped me grasp the intricacies of GNNs. Keep up the phenomenal work!
A wonderful and succinct explanation with crisp visualisations about both the attention mechanism and the graph neural network. The way the learnable parameters are highlighted along with the intuition (such as a weighted adjacency matrix) and the corresponding matrix operations is very well done.
Thank you very much! This was my introduction into GAT and helped me to immediately get a good grasp of the basic concept :) I like the graphical support you provide to the explanation, it's gerat!
This is pretty amazing content. The way you explain the concept is pretty great and I especially like the visual style and very neat looking visuals and animations you make. Thank you!
Hi! Thanks! Multi-head attention simply means that several attention mechanisms are applied at the same time. It's like cloning the regular attention. What exactly is unclear here? :)
@@DeepFindr The math and code are hard to fully grasp. If you could break down the linear algebra with the matrix diagrams as you have done for single head attention, I think people would find that very helpful.
Your visual explanation is super great, help many people to learn some-hour stuff in minutes! Please make more videos on specialized topics of GNNs! Thanks in advance!
Muchas gracias por el video. Despues de haber visto muchos otros, puedo decir que el suyo es el mejor, el mas sencillo de entender. Estoy muy agradecido con usted. Saludos
Thank you so much for this beautiful video. Have been trying out too many videos on GNN and GAN but this video definitely tops. I finally understood the concept behind it. Keep up the good work :)
Just for anyone confused, in accordance to the illustration in the summary the weight matrix should have 5 rows instead of 4 that are shown in the video. Great video and I admire the fact that your topics of choice are really into the latest hot staff of ML!
Thanks a lot! Haha I use active presenter (it's free for the basic version) but I guess there are better alternatives out there. Still experimenting :)
Thank you for the great video. I have one question, what happens if weighted graphs are used with attention GNN? Do you think adding the attention-learned edge "weights" will improve the model compared to just having the input edge weights (e.g. training a GCNN with weighted graphs)?
Hi! Yes I think so. The fact that the attention weights are learnable makes them more powerful than just static weights. The model might still want to put more attention on a node, because there is valuable information in the node features, independent of the weight. A real world example of this might be the data traffic between two network nodes. If less data is sent between two nodes, you probably assign a smaller weight to the edge. Still it could be that the information coming from one nodes is very important and therefore the model pays more attention to it.
Awesome video! Quick question: do you have a video explaining Cluster-GCN? And if yes, do you know if similar clustering idea can be applied to other networks (like GAT) to be able to train the model on large graphs? Thanks!
Thanks for the great explanation! Just one thing that I do not really understand, may I ask how do you get the size of the learnable weight matrix [4,8]? I understood that there are 4 rows due to the number of features for each node. However, not sure where the 8 columns come from.
Good explanation to the key idea. One question, what is the difference between GAT and self attention constrained by a adjacency matrix(eg. Softmax(Attn*Adj) )? The memory used for GAT is D*N^2, which is D times of the intermediate ouput of SA. The node number of graph used in GAT thus cannot be too large because of memory size. But it seems that they both implement dynamic weighting of neighborhood information constrained by a adjacency matrix.
Hi, Did you have a look at the implementation iny PyG? pytorch-geometric.readthedocs.io/en/latest/_modules/torch_geometric/nn/conv/gat_conv.html#GATConv One of the key tricks in GNNs is usually to represent the adjacency matrix in COO format. Therefore you have adjacency lists and not a nxn matrix. Using functions like gather or index_select you can then do a masked selection of the local nodes. Hope this helps :)
Perfect video to understand GATs. However, I guess, you forgot to add sigmoid function when you demonstrate h1' as a sum of multiplications of hi* and attention values, in the last seconds of the video: 13:51
Yes, they are the same thing :) passing messages is in the end nothing else but multiplying with the adjacency matrix. It's just a common term to better illustrate how the information is shared :)
Thanks for the video! There's a question: at 13:03, I think the 'adjacency matrix' consists of {e_ij} could be symmetric, but after the softmax operation, the 'adjacency matrix' consists of {α_ij} should not be symmetric any more. Is that right?
At 11:30, should the denominator have k instead of j? Also, this vector w_a, is it the same vector used for all edges, there isn't a different vector to learn for each node i, right? Thank you!
Thanks a lot. Your videos are really helpful. I have a few questions regarding the case of weighted graphs. Would attention still be useful if the edges are weighted? If so, how to pass edge wights to the attention network? Can you suggest a paper doing that?
The GAT layer of PyG supports edge features but no edge weights. Therefore I would simply treat the weights as one dimensional edge features. The attention then additionally considered these weights. Probably the learned attention weights and the edge weights are sort of correlated, but I think it won't harm to include them for the attention calculation. Maybe the attention mechanism can learn even better scores for the aggregation :) I would just give it a try and see what happens. For example compare RGCN + edge weights with GAT + edge features.
Love your work and thick accent, thank you! These attention coefficients look very similar to weighted edges for me, so I want to ask a question: If my graph is unweighted attributed graph, would GATConv produce different output compared with GCNConv by Kipf and Welling?
hahah, thanks! I'm not sure if I understood the question correctly. If you have an unweighted graph, GAT will anyways learn the attention coefficients (which can be seen as edge weights) based on the embeddings. It can be seen as "learnable" edge weights. So I'm pretty sure that GATConv and GCNConv will produce different outputs. From my experience, using the attention mechanism, the output embeddings are better than using plain GCN.
Thank you for the great video! I wanted to ask - how is training of this network performed when the instances (input graphs) have varying number of nodes and/or adjacency matrix? It seems that W would not depend on the number of nodes (as its shape is 4 node features x 8 node embeddings) but shape of attention weight matrix Wa would (as its shape is proportional to the number of edges connecting node 1 with its neighbors.)
Hi! The attention weight matrix has always the same shape. The input shape is twice the node embedding size because it always takes two neighbor - combinations and predicts the attention coefficient for them. Of course if you have more connected nodes, you will have more of these combinations, but you can think of it like the batch dimension increases, but not the input dimension. For instance you have node embeddings of size 3. Then the input for the fully connected network is for instance [0.5, 1, 1, 0.6, 2, 1], so the concatenated node embeddings of two neighbors (size=3+3). It doesn't matter how many of these you input into the attention weight matrix. If you have 3 neighbors for a node it would look like this: [0.5, 1, 1, 0.6, 2, 1] [0.5, 1, 1, 0.7, 3, 2] [0.5, 1, 1, 0.8, 4, 3] The output are then 3 attention coefficients for each of the neighbors. Hope this makes sense :)
3 года назад
@@DeepFindr If graph sizes are already different, I mean if one have graph_1 that has 2200 nodes(that results in 2200,2200 adj. matrix, and graph_2 has 3000 nodes (3000,3000 adj matrix), you can zero pad graph_1 to 3000. This way you'll have fixed size of input for graph_1 and graph_2. Zero padding will create dummy nodes with no connection. So the sum with the neighboring nodes will be 0. And having dummy features for dummy nodes, you'll end up with fixed size graphs.
Hi, yes that's true! But for the attention mechanism used here no fixed graph size is required. It also works for a different number of nodes. But yes padding is a good idea to get the same shapes :)
Hi! The video in the description from this other channel explains the general attention mechanism used in transformers quite well :) or do you look for other attention mechanisms in GNNs?
OK :) In my next video (of the current GNN series) I will also Quickly talk about Graph Transformers. There the attention coefficients are calculated with a dot product of keys and queries. I hope to upload this video this or next week :)
I have come to understand attention as key, query, value multiplication/addition. Do you know why this wasn't used and if it's appropriate to call it attention?
Hi, Query / Key / Value are just a design choice of the transformer model. Attention is another technique of the architecture. There is also a GNN Transformer (look for Graphormer) that follows the query/key/value pattern. The attention mechanism is detached from this concept and is simply a way to learn importance between embeddings.
Hello ,thanks for sharing, could you plz explain how you get learnable method,is it matrix randomly chosen or there is method behind,and is this equal to lablacian method. One more question ,your embedding only on node level ,right
Hi, the learnable weight matrix is randomly initialized and then updated through back propagation. It's just a classical fully-connected neural network layer. Yes the embedding is on the node level :)
Thanks a lot for the excellent tutorial. Just a quick question, when training the single layer attention network, what are the lables of input? How this single layer network is trained?
Thanks! Typically you train it with your custom problem. So the embeddings will be specific to your use-case. For example if you want to classify molecules, then the loss of this classification problem is used to optimize the layer. The labels are then the classes. It is however also possible to train universal embeddings. This can be done by using a distance metric such as cosine distance. The idea is that similar inputs should lead to similar embeddings and the labels would then be the distance between graphs. With both options the weights in the attention layer can be optimized. It is also possible to train GNNs in an unsupervised fashion, there exist different approaches in the literature. Hope this answers the question :)
@@DeepFindr Thanks! Sorry, my question might be confusing. For the node classification task, if we use the distance metrics between nodes as labels to train the weights of attention layer, then I think the attention layer that computes attention coefficient is not needed. Because we can get the importance by computing the distance metrics. I wonder how we can train weights of the shared attentional mechanism. Thanks again!
Yes, you are right. The attention mechanism using the dot product will also lead to similar embeddings for nodes that share the same neighborhood. However the difference is that the attention mechanism is local - it only calculates the attention coefficient for the neighboring nodes. Using the distance as targets can however be applied to all nodes in the input graph. But I agree, the various GNN layers might be differently useful depending on the application.
Very helpful video! Thank you for your great work! Two questions, 1. Could you please explain the Laplacian Matrix in GCN, the GNN explained in this video is spatial-based, and I hope I can get a better understanding of those spectral-based ones. 2. How to draw those beautiful pictures? Could you share the source files? Thanks again!
Hi! The Laplacian is simply the degree matrix of a graph subtracted by the adjacency matrix. Is there anything in particular you are interested in? :) My presentations are typically a mix of PowerPoint and active presenter, so I can send you the slides. For that please send an email to deepfindr@gmail.com :)
why would the attention adjacency matrix be symmetrical? If the weight vector is learnable, then it does matter which order the two input vectors are concatenated. It doesn't seem like there would be any reason to enforce symmetry.
I am following your playlist on GNN and this is the best content I get as of now. I have a CSV file and want to apply GNN on it but I don't understand how to find the edge features from the CSV file
This simply comes from dense (fully connected layers). There are lots of resources, for example here: analyticsindiamag.com/a-complete-understanding-of-dense-layers-in-neural-networks/#:~:text=The%20dense%20layer's%20neuron%20in,vector%20of%20the%20dense%20layer.
hi.. Your explanations are really nice and easy to understand and seem rooted in fundamentals. Thank you for that. I am new to reading research papers, and i find it difficult to understand them sometimes and end up wasting a lot of time on not-so-important things. But this is what I think my problem is, but it can be something else too...idk... like sometimes i don't have the pre req or have gap in my knowledge... Could you please make a video about it or help in the comments, or recommend some other resource to get better at reading papers and understanding from the bottom up? thank you very much 🙏🙏
Hi hope you're doing well Is there any graph neural network architecture that receives multivariate dataset instead of graph-structured data as an input? I'll be very thankful if you answer me i really nead it Thanks in advanced
Hi! As the name implies, graph neural networks expect graph structured input. Please see my latest videos on how to convert a dataset to a graph. It's not that difficult :)
Good video, but you should have mentioned how in NLP, a sequence of words is used to build a fully connected adjacency graph. This is why attention can can be used in graph data; because even in NLP, it's already ON graph data!
