Ulderico Fugacci

Giorgia Bolognesi, Claudio Estatico, Ulderico Fugacci et al.

Retrieval-Augmented Generation (RAG) enhances the factual grounding of Large Language Models by conditioning their outputs on external documents. However, standard embedding-based retrievers treat naturally structured corpora, such as technical manuals, as flat collections of passages, thereby overlooking the hyperlink topology that users rely on when navigating such content. We introduce LARAG (Link-Aware RAG): a lightweight, link-aware retrieval strategy that leverages the author-defined hyperlink structure already present in HTML documentation, encoding hyperlink relations as metadata in the chunk representations and exploiting them to perform a form of graph-like retrieval of locally relevant content. In a benchmark of twenty expert-designed queries over Rulex Platform technical documentation and four prompting strategies, LARAG consistently improves answer quality, achieving the highest BERTScore F1, while retrieving fewer chunks and generating fewer tokens than a baseline RAG architecture used for comparison. These results show that directly leveraging the existing hyperlink topology of technical documentation, even without explicit graph construction or inference, enables an implicit form of graph-like retrieval that yields a more faithful and efficient RAG pipeline, providing better grounding at lower cost.

Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli et al.

This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homology, as well as for computer scientists interested in its theoretical underpinnings. The exposition is as self-contained as possible: all the required background is recalled when needed, and only a few standard results are cited without proof. One section of the book, devoted to monodromy in biparameter persistence (Section 4.4), requires more advanced knowledge of algebraic topology. Persistent homology can be introduced from different perspectives, reflecting the variety of mathematical languages that have shaped its development over the years. Some approaches emphasize the algebraic foundations of the theory, while others highlight its topological essence. In this book, we adopt the latter viewpoint - the one that historically marked the birth of the subject - because we believe it offers both conceptual clarity and pedagogical effectiveness, making it particularly suitable for undergraduate and early graduate students. This book differs from existing introductory texts in several respects. First, it adopts a functional viewpoint: rather than representing data as finite (pseudo-)metric spaces, it treats them as functions encoding the information to be analyzed. This interpretative framework allows data to be viewed as measurable objects and highlights the role of observers and their equivariances in the analysis process. Second, this perspective provides a natural bridge between Topological Data Analysis and machine learning through the theory of Group Equivariant Non-Expansive Operators (GENEOs), which offers a mathematically grounded framework for incorporating symmetries and invariances into learning systems.

Taher Yacoub, Camille Depenveiller, Atsushi Tatsuma et al.

This SHREC 2025 track dedicated to protein surface shape retrieval involved 9 participating teams. We evaluated the performance in retrieval of 15 proposed methods on a large dataset of 11,555 protein surfaces with calculated electrostatic potential (a key molecular surface descriptor). The performance in retrieval of the proposed methods was evaluated through different metrics (Accuracy, Balanced accuracy, F1 score, Precision and Recall). The best retrieval performance was achieved by the proposed methods that used the electrostatic potential complementary to molecular surface shape. This observation was also valid for classes with limited data which highlights the importance of taking into account additional molecular surface descriptors.

René Corbet, Ulderico Fugacci, Michael Kerber et al.

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.