A Theoretical Analysis of Generalization in Graph Convolutional Neural Networks – Ron Levie from Ludwig Maximilian University of Munich

Recording:

https://us02web.zoom.us/rec/share/fHCCma3ibcwJDDysXJeiVXwJgIrZB2y6KP70r0lSoVx6f66BFk00LyWd7af-fPpy.RD5WoGdSZW92a31V?startTime=1638093861000

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Hey Everyone,

On Sunday 28.11.2021, we will host Ron Levie from Ludwig Maximilian University of Munich.

Title
A Theoretical Analysis of Generalization in Graph Convolutional Neural Networks

Abstract
In recent years, the need to accommodate non-Euclidean structures in data science has brought a boom in deep learning methods on graphs, leading to many practical applications with commercial impact. In this talk, we will review the mathematical foundations of the generalization capabilities of graph convolutional neural networks (GNNs). We will focus mainly on spectral GNNs, where convolution is defined as element-wise multiplication in the frequency domain of the graph.

In machine learning settings where the dataset consists of signals defined on many different graphs, the trained GNN should generalize to graphs outside the training set. A GNN is called transferable if, whenever two graphs represent the same underlying phenomenon, the GNN has similar repercussions on both graphs. Transferability ensures that GNNs generalize if the graphs in the test set represent the same phenomena as the graphs in the training set. We will discuss the different approaches to mathematically model the notions of transferability, and derive corresponding transferability error bounds, proving that GNNs have good generalization capabilities.