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Ulderico Fugacci

Ulderico Fugacci contributes to research discovery and scholarly infrastructure.

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Published work

6 published item(s)

preprint2026arXiv

LARAG: Link-Aware Retrieval Strategy for RAG Systems in Hyperlinked Technical Documentation

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.

preprint2022arXiv

Compression for 2-Parameter Persistent Homology

Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large inputs, and computational tasks in this area tend to be expensive. We propose two compression methods for chain complexes of free 2-parameter persistence modules. The first method extends the multi-chunk algorithm for one-parameter persistent homology, returning the smallest chain complex among all the ones quasi-isomorphic to the input. The second method produces minimal presentations of the homology of the input; it is based on an algorithm of Lesnick and Wright, but incorporates several improvements that lead to substantial performance gains. The two methods are complementary, and can be combined to compute minimal presentations for complexes with millions of generators in a few seconds. The methods have been implemented, and the software is publicly available. We report on experimental evaluations, which demonstrate substantial improvements in performance compared to previously available compression strategies.

preprint2021arXiv

Homological Scaffold via Minimal Homology Bases

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.

preprint2020arXiv

Critical Sets of PL and Discrete Morse Theory: a Correspondence

Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical points have been given in the literature for the discrete setting, making a clear understanding of the relationships occurring between them not obvious. This paper aims at providing equivalence results about critical points of the two discretized Morse theories. First of all, we prove the equivalence of the existing notions of PL critical points. Next, under an optimality condition called relative perfectness, we show a dimension agnostic correspondence between the set of PL critical points and that of discrete critical simplices of the combinatorial approach. Finally, we show how a relatively perfect discrete gradient vector field can be algorithmically built up to dimension 3. This way, we guarantee a formal and operative connection between critical sets in the PL and discrete theories.

preprint2020arXiv

On the notion of weak isometry for finite metric spaces

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.

preprint2020arXiv

Topology-Preserving Terrain Simplification

We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operations are edge flips and removals of interior vertices, re-triangulating the link of the removed vertex. This problem is motivated by topological terrain simplification, which means removing as many critical vertices of a terrain as possible while maintaining geometric closeness to the original surface. Existing methods manage to reduce the maximal possible number of critical vertices, but increase thereby the number of regular vertices. Our method can be used to post-process a simplified terrain, drastically reducing its size and preserving its favorable properties.