# Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs

## TL;DR

This paper introduces a flexible graph-based layer formulation that generalizes convolutional layers to non-Euclidean domains, enabling learnable weight sharing schemes that exploit underlying graph structures.

## Contribution

It presents a novel, generic layer formulation for graphs that learns both filter weights and sharing schemes, extending convolutional concepts beyond images.

## Key findings

- Filters achieve performance comparable to traditional convolutions on image datasets
- The method effectively exploits graph structure for signal processing
- Demonstrates the potential of learnable weight sharing in graph neural networks

## Abstract

We propose a simple and generic layer formulation that extends the properties of convolutional layers to any domain that can be described by a graph. Namely, we use the support of its adjacency matrix to design learnable weight sharing filters able to exploit the underlying structure of signals in the same fashion as for images. The proposed formulation makes it possible to learn the weights of the filter as well as a scheme that controls how they are shared across the graph. We perform validation experiments with image datasets and show that these filters offer performances comparable with convolutional ones.