MeetingNotes

Reference

Main goal of this tutorial (official view)

The main goal of this tutorial is to teach the fundamentals of graph rewiring and its current challenges. We will motivate the need for mathematically sound graph rewiring methods as a solution to address the main limitations of GNNs: under-reaching, over-smoothing and over-squashing. We will explain the two main approaches proposed in the literature to achieve graph rewiring:

Transductive methods compute a new convolution matrix of each graph as a pre-processing step in order to improve the performance of the task at hand. Examples are parameterized diffusion or curvature-based approaches.
Inductive methods learn new convolution matrices from training on subgraphs/graphs and then predict those in unseen graphs. Ideally, this process is fully differentiable and parameter free. We will delve into the implementation of this methods. Hands-on section.

In addition, we will discuss the potential that graph rewiring has to address social and ethical challenges posed by AI, and particularly as a tool to achieve algorithmic fairness.

Section	Content
Motivation	Graph Classification and Expressiveness
Node Classification and Over-smoothingDesiderates
Introduction to Spectral Theory	Average Cut Problem
Fiedler Vector
Graph Laplacian and Dirichlet Energies
Laplacian Eigenfunctions and Spectrum
Spectral Theorem
Spectral Commute Times
Transductive Rewiring	Diffusive Rewiring
Cheeger Constant
Curvature-Based Rewiring
Inductive Rewiring	CT and the Lovász Bound
CT and Sparsification
CT and Directional Graph Networks
CT-Layer

CT-Layer and its Loss function
Learned CT Embedding and CT distances
Experiments in Graph and Node Classification
CT-Layer as Differentiable Curvature
CT and Cheeger Constant GAP-Layer
Spectral Derivatives
Learning the Fiedler vector | | Panel | 강승완 , 남궁민상, 안혜민 , 정이태 , 최민수 |