Paolo Boldi

Osvaldo Velarde, Lucas Parra, Paolo Boldi et al.

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the current formulation of GDL is limited to global symmetries that are not often found in real-world problems. We propose to relax GDL to allow for local symmetries, specifically fibration symmetries in graphs, to leverage regularities of realistic instances. We show that GNNs apply the inductive bias of fibration symmetries and derive a tighter upper bound for their expressive power. Additionally, by identifying symmetries in networks, we collapse network nodes, thereby increasing their computational efficiency during both inference and training of deep neural networks. The mathematical extension introduced here applies beyond graphs to manifolds, bundles, and grids for the development of models with inductive biases induced by local symmetries that can lead to better generalization.

Paolo Boldi, Andrea Marino, Massimo Santini et al.

Although web crawlers have been around for twenty years by now, there is virtually no freely available, opensource crawling software that guarantees high throughput, overcomes the limits of single-machine systems and at the same time scales linearly with the amount of resources available. This paper aims at filling this gap, through the description of BUbiNG, our next-generation web crawler built upon the authors' experience with UbiCrawler [Boldi et al. 2004] and on the last ten years of research on the topic. BUbiNG is an opensource Java fully distributed crawler; a single BUbiNG agent, using sizeable hardware, can crawl several thousands pages per second respecting strict politeness constraints, both host- and IP-based. Unlike existing open-source distributed crawlers that rely on batch techniques (like MapReduce), BUbiNG job distribution is based on modern high-speed protocols so to achieve very high throughput.

Paolo Boldi, Flavio Furia, Sebastiano Vigna

We study the problem of score and rank monotonicity for spectral ranking methods, such as eigenvector centrality and PageRank, in the case of undirected networks. Score monotonicity means that adding an edge increases the score at both ends of the edge. Rank monotonicity means that adding an edge improves the relative position of both ends of the edge with respect to the remaining nodes. It is known that common spectral rankings are both score and rank monotone on directed, strongly connected graphs. We show that, surprisingly, the situation is very different for undirected graphs, and in particular that PageRank is neither score nor rank monotone.

Corrado Monti, Paolo Boldi

Real-world complex networks describe connections between objects; in reality, those objects are often endowed with some kind of features. How does the presence or absence of such features interplay with the network link structure? Although the situation here described is truly ubiquitous, there is a limited body of research dealing with large graphs of this kind. Many previous works considered homophily as the only possible transmission mechanism translating node features into links. Other authors, instead, developed more sophisticated models, that are able to handle complex feature interactions, but are unfit to scale to very large networks. We expand on the MGJ model, where interactions between pairs of features can foster or discourage link formation. In this work, we will investigate how to estimate the latent feature-feature interactions in this model. We shall propose two solutions: the first one assumes feature independence and it is essentially based on Naive Bayes; the second one, which relaxes the independence assumption assumption, is based on perceptrons. In fact, we show it is possible to cast the model equation in order to see it as the prediction rule of a perceptron. We analyze how classical results for the perceptrons can be interpreted in this context; then, we define a fast and simple perceptron-like algorithm for this task, which can process $10^8$ links in minutes. We then compare these two techniques, first with synthetic datasets that follows our model, gaining evidence that the Naive independence assumptions are detrimental in practice. Secondly, we consider a real, large-scale citation network where each node (i.e., paper) can be described by different types of characteristics; there, our algorithm can assess how well each set of features can explain the links, and thus finding meaningful latent feature-feature interactions.

Paolo Boldi, Corrado Monti, Massimo Santini et al.

Most modern recommendation systems use the approach of collaborative filtering: users that are believed to behave alike are used to produce recommendations. In this work we describe an application (Liquid FM) taking a completely different approach. Liquid FM is a music recommendation system that makes the user responsible for the recommended items. Suggestions are the result of a voting scheme, employing the idea of viscous democracy. Liquid FM can also be thought of as the first testbed for this voting system. In this paper we outline the design and architecture of the application, both from the theoretical and from the implementation viewpoints.