Scale Equivariant Graph Metanetworks
Ioannis Kalogeropoulos, Giorgos Bouritsas, Yannis Panagakis

TL;DR
This paper introduces ScaleGMNs, a framework that incorporates scaling symmetries into graph neural networks, making them equivariant to weight and bias scalings, and demonstrates improved performance across multiple datasets.
Contribution
It proposes ScaleGMNs, a novel graph neural network framework that leverages scaling symmetries to enhance expressivity and performance, with theoretical proofs and practical results.
Findings
Achieves state-of-the-art results on several datasets.
Demonstrates equivariance to weight and bias scalings.
Proves universality in simulating feedforward neural networks.
Abstract
This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, . With the growing interest in architectures that process NNs, a recurring design principle has permeated the field: adhering to the permutation symmetries arising from the connectionist structure of NNs. ? Zooming into most practical activation functions (e.g. sine, ReLU, tanh) answers this question negatively and gives rise to intriguing new symmetries, which we collectively refer to as , that is, non-zero scalar multiplications and divisions of weights and biases. In this work, we propose , a framework…
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Taxonomy
TopicsGraph Theory and Algorithms · Data Management and Algorithms · Topological and Geometric Data Analysis
