Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large. The generalization bound is derived from a uniform convergence result, that shows that any MPNN, applied on a graph, approximates the MPNN applied on the geometric model that the graph discretizes.

Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems.

Designing Public Transport (PT) networks able to satisfy mobility needs of people is essential to reduce the number of individual vehicles on the road, and thus pollution and congestion. Urban sustainability is thus tightly coupled to an efficient PT. Current approaches on Transport Network Design (TND) generally aim to optimize generalized cost, i.e., a unique number including operator and users' costs. Since we intend quality of PT as the capability of satisfying mobility needs, we focus instead on PT accessibility, i.e., the ease of reaching surrounding points of interest via PT. PT accessibility is generally unequally distributed in urban regions: suburbs generally suffer from poor PT accessibility, which condemns residents therein to be dependent on their private cars. We thus tackle the problem of designing bus lines so as to minimize the inequality in the geographical distribution of accessibility. We combine state-of-the-art Message Passing Neural Networks (MPNN) and Reinforcement Learning. We show the efficacy of our method against metaheuristics (classically used in TND) in a use case representing in simplified terms the city of Montreal.

Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems. We study the generalization error of MPNNs in graph classification and regression. We assume that graphs of different classes are sampled from different random graph models. We show that, when training a MPNN on a dataset sampled from such a distribution, the generalization gap increases in the complexity of the MPNN, and decreases, not only with respect to the number of training samples, but also with the average number of nodes in the graphs. This shows how a MPNN with high complexity can generalize from a small dataset of graphs, as long as the graphs are large.

This work investigates neural algorithmic reasoning to develop neural networks capable of learning from classical algorithms. The main challenge is to develop graph neural networks that are expressive enough to predict the given algorithm outputs while generalizing well to out-of-distribution data. In this work, we introduce a new graph neural network layer called Triplet Edge Attention (TEA), an edge-aware graph attention layer. Our algorithm works by precisely computing edge latent, aggregating multiple triplet messages using edge-based attention. We empirically validate our TEA layer in the CLRS benchmark and demonstrate a $5%$ improvement on average. In particular, we achieve a $30%$ improvement for the string algorithms compared to the state-of-the-art model.

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing hypergraph-structured data. We show that the proposed model defines a design space for neural network models for hypergraphs, thus generalizing existing models for hypergraphs. We report experiments on a benchmark dataset for node classification, highlighting the effectiveness of the proposed model with respect to other state-of-the-art methods for graphs and hypergraphs. We also discuss the benefits of using hypergraph representations and, at the same time, highlight the limitation of using equivalent graph representations when the underlying problem has relations among more than two objects.

This thesis explores the benefits machine learning algorithms can bring to online planning and scheduling for autonomous vehicles in off-road situations. Mainly, we focus on typical problems of interest which include computing itineraries that meet certain objectives, as well as computing scheduling strategies to execute synchronized maneuvers with other vehicles. We present a range of learning-based heuristics to assist different itinerary planners. We show that these heuristics allow a significant increase in performance for optimal planners. Furthermore, in the case of approximate planning, we show that not only does the running time decrease, the quality of the itinerary found also becomes almost always better. Finally, in order to synthesize strategies to execute synchronized maneuvers, we propose a novel type of scheduling controllability and a learning-assisted algorithm. The proposed framework achieves significant improvement on known benchmarks in this controllability type over the performance of state-of-the-art works in a related controllability type. Moreover, it is able to find strategies on complex scheduling problems for which previous works fail to do so.