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Isabella Mastroianni

Publications and source records attributed to Isabella Mastroianni.

4 recordsLinked to original sources

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.

cs.IR↗

Hook-decomposable modules and their resolutions

We compare several classes of biparameter persistence modules: $γ$-products of monoparameter modules, hook-decomposable modules, modules admitting a Smith-type structure theorem, and modules of projective dimension at most 1. We determine all logical implications among these classes, providing explicit counterexamples showing that the converses fail when appropriate. In particular, $γ$-products (i.e., hook-decomposable modules) form a very small subclass of biparameter modules, precisely the ones for which a structure theorem still holds, thus making explicit the richer structural complexity of the biparameter setting compared to the monoparameter one.

math.AT↗

Retrieving biparameter persistence modules from monoparameter ones: a characterization of hook-decomposable persistence modules

Motivated by the need to relate the biparameter persistence module induced by a pair of scalar functions with the monoparameter persistence modules induced by each function separately, we introduce a construction that defines a kind of product between two monoparameter persistence modules. While originally conceived to serve this comparative purpose, our construction unexpectedly reveals a deeper structural property: it also characterizes a class of biparameter modules known as hook-decomposable modules.

math.AT↗

Topological Correlation

We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and monoparameter persistence, while the other leverages this gap to measure the interdependence of filtering functions. Our framework sheds light on the expressive advantage of multiparameter over monoparameter persistence and suggests potential applications.

math.AT↗