# A Lagrangian Approach to Information Propagation in Graph Neural Networks

Published in ECAI2020, 2020

Recommended citation: Matteo Tiezzi, Giuseppe Marra, Stefano Melacci, Marco Maggini and Marco Gori (2020). "A Lagrangian Approach to Information Propagation in Graph Neural Networks; ECAI2020 - http://ebooks.iospress.nl/publication/55057

In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph. In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to process complex patterns. In particular, inspired by the Graph Neural Network (GNN) model, different architectures have been proposed to extend the original GNN scheme. GNNs exploit a set of state variables, each assigned to a graph node, and a diffusion mechanism of the states among neighbor nodes, to implement an iterative procedure to compute the fixed point of the (learnable) state transition function. In this paper, we propose a novel approach to the state computation and the learning algorithm for GNNs, based on a constraint optimisation task solved in the Lagrangian framework. The state convergence procedure is implicitly expressed by the constraint satisfaction mechanism and does not require a separate iterative phase for each epoch of the learning procedure. In fact, the computational structure is based on the search for saddle points of the Lagrangian in the adjoint space composed of weights, neural outputs (node states), and Lagrange multipliers. The proposed approach is compared experimentally with other popular models for processing graphs.

Recommended citation:

@inproceedings{DBLP:conf/ecai/TiezziMMMG20,
author    = {Matteo Tiezzi and
Giuseppe Marra and
Stefano Melacci and
Marco Maggini and
Marco Gori},
title     = {A Lagrangian Approach to Information Propagation in Graph Neural Networks},
booktitle = {ECAI 2020 - 24th European Conference on Artificial Intelligence},
series    = {Frontiers in Artificial Intelligence and Applications},
volume    = {325},
pages     = {1539--1546},
publisher = {IOS Press},
year      = {2020},
doi       = {10.3233/FAIA200262},
}