Giosuè Lo Bosco

Salvatore Calderaro, Domenico Amato, Giosuè Lo Bosco et al.

Graph Neural Networks (GNNs) are powerful models that can manage complex data sources and their interconnection links. One of GNNs' main drawbacks is their lack of interpretability, which limits their application in sensitive fields. In this paper, we introduce a new methodology involving graph communities to address the interpretability of graph classification problems. The proposed method, called GECo, exploits the idea that if a community is a subset of graph nodes densely connected, this property should play a role in graph classification. This is reasonable, especially if we consider the message-passing mechanism, which is the basic mechanism of GNNs. GECo analyzes the contribution to the classification result of the communities in the graph, building a mask that highlights graph-relevant structures. GECo is tested for Graph Convolutional Networks on six artificial and four real-world graph datasets and is compared to the main explainability methods such as PGMExplainer, PGExplainer, GNNExplainer, and SubgraphX using four different metrics. The obtained results outperform the other methods for artificial graph datasets and most real-world datasets.

Domenico Amato, Giosuè Lo Bosco, Raffaele Giancarlo

Learned Indexes are a novel approach to search in a sorted table. A model is used to predict an interval in which to search into and a Binary Search routine is used to finalize the search. They are quite effective. For the final stage, usually, the lower_bound routine of the Standard C++ library is used, although this is more of a natural choice rather than a requirement. However, recent studies, that do not use Machine Learning predictions, indicate that other implementations of Binary Search or variants, namely k-ary Search, are better suited to take advantage of the features offered by modern computer architectures. With the use of the Searching on Sorted Sets SOSD Learned Indexing benchmarking software, we investigate how to choose a Search routine for the final stage of searching in a Learned Index. Our results provide indications that better choices than the lower_bound routine can be made. We also highlight how such a choice may be dependent on the computer architecture that is to be used. Overall, our findings provide new and much-needed guidelines for the selection of the Search routine within the Learned Indexing framework.

Domenico Amato, Giosuè Lo Bosco, Raffaele Giancarlo

Machine Learning Techniques, properly combined with Data Structures, have resulted in Learned Static Indexes, innovative and powerful tools that speed-up Binary Search, with the use of additional space with respect to the table being searched into. Such space is devoted to the Machine Learning Model. Although in their infancy, they are methodologically and practically important, due to the pervasiveness of Sorted Table Search procedures. In modern applications, model space is a key factor and, in fact, a major open question concerning this area is to assess to what extent one can enjoy the speed-up of Binary Search achieved by Learned Indexes while using constant or nearly constant space models. In this paper, we investigate the mentioned question by (a) introducing two new models, i.e., the Learned k-ary Search Model and the Synoptic Recursive Model Index, respectively; (b) systematically exploring the time-space trade-offs of a hierarchy of existing models, i.e., the ones in the reference software platform Searching on Sorted Data, together with the new ones proposed here. By adhering and extending the current benchmarking methodology, we experimentally show that the Learned k-ary Search Model can speed up Binary Search in constant additional space. Our second model, together with the bi-criteria Piece-wise Geometric Model index, can achieve a speed-up of Binary Search with a model space of 0:05% more than the one taken by the table, being competitive in terms of time-space trade-off with existing proposals. The Synoptic Recursive Model Index and the bi-criteria Piece-wise Geometric Model complement each other quite well across the various levels of the internal memory hierarchy. Finally, our findings stimulate research in this area, since they highlight the need for further studies regarding the time-space relation in Learned Indexes.