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A Gentle Introduction to Graph Neural Networks (2021)
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Re: A Gentle Introduction to Graph Neural Networks (2021)
#12There are a lot of papers using GNNs for physics simulations (e.g. computational fluid dynamics) because the unstructured meshes used to discretize the problem domain for such applications map very neatly to a graph structure.
In practice, every such mesh/graph is used once to solve a particular problem. Hence it makes little sense to train a GNN for a specific graph. However, that's exactly what most papers did because no one found a way to make a GNN that can adjust well to a different mesh/graph and different simulation parameters. I wonder if there's a breakthrough waiting just around the corner to make such a generalization possible.
Re: A Gentle Introduction to Graph Neural Networks (2021)
#13There are a lot of papers using GNNs for physics simulations (e.g. computational fluid dynamics) because the unstructured meshes used to discretize the problem domain for such applications map very neatly to a graph structure. In practice, every such mesh/graph is used once to solve a particular problem. Hence it makes little sense to train a GNN for a specific graph. However, that's exactly what most papers did beca…
Naive question:
Words in sentences kinda forms graphs, referencing other words or are leafs being referenced, both inside sentences and between sentences.
Given the success of the attention mechanism in modern LLMs, how well would they do if you trained a LLM to process an actual graph?
I guess you'd need some alternate tokenizer for optimal performance.
Re: A Gentle Introduction to Graph Neural Networks (2021)
#14There are a lot of papers using GNNs for physics simulations (e.g. computational fluid dynamics) because the unstructured meshes used to discretize the problem domain for such applications map very neatly to a graph structure. In practice, every such mesh/graph is used once to solve a particular problem. Hence it makes little sense to train a GNN for a specific graph. However, that's exactly what most papers did beca…
Naive question: Words in sentences kinda forms graphs, referencing other words or are leafs being referenced, both inside sentences and between sentences. Given the success of the attention mechanism in modern LLMs, how well would they do if you trained a LLM to process an actual graph? I guess you'd need some alternate tokenizer for optimal performance.
For physics sims, I'd say it's useless.
Imagine you discretize a cube into 1000 gridpoints in each direction, that's 1000^3 = 1 billion nodes/"tokens". Plus you typically time-march some sort of equation so you need the solutions previous 3-5 timesteps as well so that's 3-5 billion tokens. If you are gonna do that in the first place, you may as well just use the traditional solver. Traditional solvers usually set up and solve a matrix equation like Ax=b with an iterative method like multigrid which is O(n) as opposed to transformer's O(n^2). It'll give you a much more accurate answer much quicker than it'll take a transformer to do attention on a sequence of length 3 billion.
The entire point of using GNNs/CNNs in this field is that people rely on their ability to make inference using local information. That means the value at each gridpoint/node can be inferred from neighbouring nodes only, which is O(n) like multigrid. Idea in most papers is that the GNN can do this faster than multigrid. Results so far are mixed, however [1].
Re: A Gentle Introduction to Graph Neural Networks (2021)
#15Earlier quoted context omitted.
Naive question: Words in sentences kinda forms graphs, referencing other words or are leafs being referenced, both inside sentences and between sentences. Given the success of the attention mechanism in modern LLMs, how well would they do if you trained a LLM to process an actual graph? I guess you'd need some alternate tokenizer for optimal performance.
For physics sims, I'd say it's useless. Imagine you discretize a cube into 1000 gridpoints in each direction, that's 1000^3 = 1 billion nodes/"tokens". Plus you typically time-march some sort of equation so you need the solutions previous 3-5 timesteps as well so that's 3-5 billion tokens. If you are gonna do that in the first place, you may as well just use the traditional solver. Traditional solvers usually set up…
Ah yes, for dense problems like that I wouldn't expect it to work well. The example graphs in the submission were mostly quite sparse, hence why I thought of LLMs. But perhaps that was just for illustrative purposes.
Re: A Gentle Introduction to Graph Neural Networks (2021)
#16There are a lot of papers using GNNs for physics simulations (e.g. computational fluid dynamics) because the unstructured meshes used to discretize the problem domain for such applications map very neatly to a graph structure. In practice, every such mesh/graph is used once to solve a particular problem. Hence it makes little sense to train a GNN for a specific graph. However, that's exactly what most papers did beca…
A general graph solver has to be a general intelligence, since it would be able to successfully model category theory.
Re: A Gentle Introduction to Graph Neural Networks (2021)
#17Very high quality work, its a pity that distill.pub did not find a sustainable way forward [1].
On GNN's, the lack of datasets [2] might be a reason they are not as talked about. This is something that has affected also the semantic web domain.
[1] https://distill.pub/2021/distill-hiatus/
[2] https://huggingface.co/datasets?task_categories=task_categor...
Re: A Gentle Introduction to Graph Neural Networks (2021)
#18There are a lot of papers using GNNs for physics simulations (e.g. computational fluid dynamics) because the unstructured meshes used to discretize the problem domain for such applications map very neatly to a graph structure. In practice, every such mesh/graph is used once to solve a particular problem. Hence it makes little sense to train a GNN for a specific graph. However, that's exactly what most papers did beca…
Naive question: Words in sentences kinda forms graphs, referencing other words or are leafs being referenced, both inside sentences and between sentences. Given the success of the attention mechanism in modern LLMs, how well would they do if you trained a LLM to process an actual graph? I guess you'd need some alternate tokenizer for optimal performance.
This is actually a good insight. It turns out that transformers are indeed a form of graph network, precisely because of the attention mechanism. Graph attention networks are actually a very popular GNN architecture. Generally, the issue with using an LLM style architecture for generic graphs is modeling the sparsity, but is possible by using the graph adjacency matrix to mask the attention matrix. There are a number of papers and articles which address this connection, and plenty of research into mechanisms for sparsifying attention in transformers.
There are also graph tokenizers for using more standard transformers on graphs for doing things like classification, generation, and community detection.
Re: A Gentle Introduction to Graph Neural Networks (2021)
#19(2021)
Re: A Gentle Introduction to Graph Neural Networks (2021)
#20Would love to see distill come back