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Ferdinando Zanchetta

Publications and source records attributed to Ferdinando Zanchetta.

10 recordsLinked to original sources
arXiv2026

Cartan flow matching

We introduce Cartan flow matching, a general framework for training flow matching models on Riemannian symmetric spaces, i.e. Riemannian manifolds with the property that at any point there exists a geodesic symmetry. This is a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate flow matching on symmetric spaces as flow matching on a subspace of the Lie algebra of their isometry group, thus linearizing the problem and avoiding the need to construct geodesic interpolation paths on the manifold. As an application, we showcase our framework on the real Grassmannians $ \operatorname{SO}(n) / \operatorname{SO}(k) \times \operatorname{SO}(n-k) $.

cs.LG↗
arXiv2026

Finite semisimplicial sets, differential graded algebras, and cellular sheaves

We develop a differential graded model for finite non-singular semisimplicial sets and their cellular sheaves. To a finite non-singular semisimplicial set \(S\), we associate an exterior DGA \(Ω^\bullet_S\), extending the classical anti-equivalence between finite simple directed graphs and first-order differential calculi to higher degrees. We characterize the essential image of this construction, obtaining an equivalence of categories that recovers the graph-FODC correspondence in dimension one. For a fixed \(S\), we then characterize a category of differential graded \(Ω^\bullet_S\)-modules equivalent to the category of cellular sheaves on $S$, thereby giving a differential refinement of the usual incidence-algebra description. Finally, we study connections and curvature in this framework. Connections are described by edgewise linear maps and their curvature on a 2-dimensional simplex is the difference between direct and composite edge transport. When the edge transports are invertible, vanishing of this curvature on every \(2\)-simplex can equivalently be seen as a gluing criterion to extend the given edge transports to a connection sheaf on \(P_S\).

math.DG↗
arXiv2026

Sheaf Neural Networks and biomedical applications

The purpose of this paper is to elucidate the theory and mathematical modelling behind the sheaf neural network (SNN) algorithm and then show how SNN can effectively answer to biomedical questions in a concrete case study and outperform the most popular graph neural networks (GNNs) as graph convolutional networks (GCNs), graph attention networks (GAT) and GraphSage.

cs.LG↗
arXiv2026

A Multi-Label Temporal Convolutional Framework for Transcription Factor Binding Characterization

Transcription factors (TFs) regulate gene expression through complex and co-operative mechanisms. While many TFs act together, the logic underlying TFs binding and their interactions is not fully understood yet. Most current approaches for TF binding site prediction focus on individual TFs and binary classification tasks, without a full analysis of the possible interactions among various TFs. In this paper we investigate DNA TF binding site recognition as a multi-label classification problem, achieving reliable predictions for multiple TFs on DNA sequences retrieved in public repositories. Our deep learning models are based on Temporal Convolutional Networks (TCNs), which are able to predict multiple TF binding profiles, capturing correlations among TFs andtheir cooperative regulatory mechanisms. Our results suggest that multi-label learning leading to reliable predictive performances can reveal biologically meaningful motifs and co-binding patterns consistent with known TF interactions, while also suggesting novel relationships and cooperation among TFs.

cs.LG↗
arXiv2026

Bioinspired CNNs for border completion in occluded images

We exploit the mathematical modeling of the border completion problem in the visual cortex to design convolutional neural network (CNN) filters that enhance robustness to image occlusions. We evaluate our CNN architecture, BorderNet, on three occluded datasets (MNIST, Fashion-MNIST, and EMNIST) under two types of occlusions: stripes and grids. In all cases, BorderNet demonstrates improved performance, with gains varying depending on the severity of the occlusions and the dataset.

cs.CV↗
arXiv2026

Sheaves on Graphs and their Differential Calculi

In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They include notions such as Laplacians and connections, important in the theory of discrete noncommutative geometry, that are here explored with sheaf theoretic methods and using the language of (semi)simplicial sets.

math.DG↗
arXiv2026

On Gluing Data, Finite Ringed Spaces and schemes

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link important geometric objects, such as differentiable manifolds or schemes, to certain finite ringed spaces arising from sheaves on 2 dimensional semisimplicial sets, thus opening the door to their applications in fields such as discrete differential geometry.

math.CT↗
arXiv2025

Comparison of Exterior Power Operations on Higher K-Theory of Schemes

Exterior power operations provide an additional structure on K-groups of schemes which lies at the heart of Grothendieck's Riemann-Roch theory. Over the past decades, various authors have constructed such operations on higher K-theory. In this paper, we prove that these constructions actually yield the same operations, ultimately matching up the explicit combinatorial description by Harris, the first author and Taelman on the one hand and the recent, conceptually clear-cut construction by Barwick, Glasman, Mathew and Nikolaus on the other hand. This also leads to the proof of a conjecture by the first author about composition of these operations in the equivariant context, completing the proof that higher equivariant K-groups satisfy all axioms of a lambda-ring.

math.KT↗
arXiv2023

Graph Neural Networks and Time Series as Directed Graphs for Quality Recognition

Graph Neural Networks (GNNs) are becoming central in the study of time series, coupled with existing algorithms as Temporal Convolutional Networks and Recurrent Neural Networks. In this paper, we see time series themselves as directed graphs, so that their topology encodes time dependencies and we start to explore the effectiveness of GNNs architectures on them. We develop two distinct Geometric Deep Learning models, a supervised classifier and an autoencoder-like model for signal reconstruction. We apply these models on a quality recognition problem.

cs.LG↗