arXiv subjects

Sergio Barbarossa

Publications and source records attributed to Sergio Barbarossa.

At least 19 recordsLinked to original sources

arXiv2026

Structured Sheaf Learning of Consistent Connection Graphs

Connection graphs (CGs) extend classical graphs by associating vector-valued signals to nodes and orthogonal transport maps across edges, making them a natural model for synchronization and manifold-based signal processing. Despite their growing use, learning CGs directly from observations remains challenging because the network topology and the underlying geometric structure are coupled through non-Euclidean orthogonality constraints. In this work, we address this inverse problem by learning a consistent connection graph from noisy vector-valued signals. Exploiting the spectral characterization of consistent CGs, we formulate a structured learning problem that jointly estimates a denoised signal, the graph topology, and node-wise local reference frames. The proposed formulation couples the spectrum of the learned connection Laplacian to that of an underlying combinatorial Laplacian, enabling explicit spectral and topological priors while guaranteeing a nontrivial global-section space. We develop Structured Connection Graph Learning (SCGL), a block-coordinate algorithm that combines closed-form updates, manifold projections, and spectral constraints, and converges to stationary points of the resulting nonconvex problem. Numerical experiments show that SCGL improves topology and geometry recovery over competing approaches, while also yielding effective denoising and signal-compression bases.

eess.SP↗

arXiv2026

Sheaf-Based Federated Representation Learning

Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, sensing modalities, model architectures, latent dimensionalities, and local learning objectives. To address this challenge, we propose Sheaf-based Federated Representation Learning (SFRL), a general framework that jointly optimizes local objectives with a manifold-constrained geometric alignment regularizer based on learnable sheaf restriction maps. Unlike most existing approaches, SFRL does not assume a shared global latent space. Instead, global consistency emerges from the alignment of neighboring latent representations through orthogonal transformations and isometric embeddings. This alignment is enforced by a quadratic gluing regularizer induced by the sheaf Laplacian, whose learnable restriction maps adapt the geometry to the observed data. The penalty is evaluated on a small set of shared pilot samples, ensuring scalability and communication efficiency. We develop a decentralized algorithm for solving SFRL, termed Sheaf-FRL, which alternates between gradient updates of the local models and closed-form Procrustes updates of the edge-wise restriction maps. We further establish convergence of Sheaf-FRL to first-order stationary points in both deterministic and stochastic settings. As an application, we consider a cooperative classification task in the context of semantic communication, under model and data heterogeneity. Our results show that Sheaf-FRL outperforms baseline approaches in terms of local and post-communication classification accuracy across different levels of local distribution shift and exhibits greater robustness to latent-space dimensionality compression.

cs.LG↗

arXiv2026

Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling

Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure. Processing such data requires a mathematical framework capable of simultaneously modeling heterogeneous local signal spaces and the transformations relating them. Network sheaves provide such a framework by associating local vector spaces with network entities and linear restriction maps with their interactions. This is the first paper to develop a unified sheaf signal processing (SSP) framework on network sheaves, extending the fundamental operations of signal processing, namely spectral analysis, filtering, and sampling, to heterogeneous local spaces. Unlike graph and topological signal processing, where signals are modeled over a common vector space, SSP jointly models heterogeneous local signal spaces and the linear transformations relating neighboring spaces through restriction maps. We define the Sheaf Fourier Transform (SFT), whose frequencies quantify signal inconsistency induced by the network topology, the restriction maps, and the local geometry. Building on this representation, we develop polynomial sheaf filters and formulate sampling as the joint selection of network nodes and intra-node components. We derive perfect recovery conditions for bandlimited sheaf signals and propose a greedy sampling-set design algorithm. To incorporate application-dependent signal models, including different bases, dictionaries, and learned embeddings, we introduce representation sheaves and characterize the natural transformations that preserve spectral properties and guarantee interoperability across representations. Experiments on synthetic, motion-capture, and financial datasets validate the proposed framework and demonstrate consistent improvements over canonical graph signal processing baselines.

eess.SP↗

arXiv2026

A Sheaf-Theoretic Framework for Distributed Multi-Site Channel Charting

Channel charting (CC) enables data-driven user localization in wireless networks by embedding channel state information (CSI) into low-dimensional representations. In multi-cell scenarios, each base station independently learns a local chart via neural encoders, leading to misaligned representation spaces across overlapping coverage areas. This lack of consistency hinders network-level tasks such as user tracking, handover prediction, and resource allocation. To address this issue, we propose a principled framework for multi-site channel charting based on topological signal processing. We model the collection of local charts as a network sheaf, which encodes consistency constraints across the network and enables the coherent integration of locally learned representations into a shared global structure. This formulation introduces an interpretable inductive bias that promotes alignment across base stations while preserving local geometric fidelity. Building on this model, we develop a multi-site channel charting architecture and an alternating optimization algorithm that jointly updates neural encoders and inter-site orthogonal transport maps, with theoretical guarantees on consistency. Experimental results validate the effectiveness of the proposed approach, demonstrating improved cross-site alignment without degrading the quality of local embeddings.

eess.SP↗

arXiv2026

SEMASIA: A Large-Scale Dataset of Semantically Structured Latent Representations

Latent representations learned by neural networks often exhibit semantic structure, where concept similarity is reflected by geometric proximity in embedding space. However, comparing such spaces across models remains difficult: changes in architecture, pretraining data, objective, or random seed can yield embeddings with similar content but incompatible geometry. This latent space alignment problem is central to interpretability, transfer and multimodal learning, federated systems, and semantic communication; however, progress remains limited by the lack of large-scale, model-diverse, and metadata-rich benchmarks. To address this gap, we introduce SEMASIA, a large-scale collection of latent representations extracted from approximately 1,700 pretrained vision models across eight standard image-classification benchmarks. SEMASIA pairs embeddings with structured metadata describing architectures, training regimes, pretraining sources, and model scale. We demonstrate three applications of the resource. First, we analyze the conceptual organization of individual latent spaces, showing consistent prototype-like clustering and hierarchical semantic neighborhoods across models and datasets. Second, we benchmark supervised alignment mappings between latent spaces using reconstruction error and downstream task performance. Third, we perform a large-scale regression analysis of how pretraining-data complexity, specialization, transfer learning, augmentation, and model scale relate to geometric and probing properties of embeddings. By coupling representational scale with standardized metadata, SEMASIA provides a reproducible foundation for studying latent geometry, evaluating alignment methods, and developing next-generation heterogeneous and interoperable AI systems.

cs.LG↗

arXiv2026

Topological Signal Processing for 3D Point Cloud Data

Our goal in this paper is to apply the topological signal processing (TSP) framework to the analysis of 3D Point Clouds (PCs) represented on simplicial complexes. Building on Discrete Exterior Calculus (DEC) theory for vector fields, we introduce higher-order Laplacian operators that enable the processing of signals over triangular meshes. Unlike traditional approaches, the proposed approach allows us to characterize both color attributes, modeled as 3D vectors on nodes, and geometry, modeled as 3D vectors on the barycenter of each triangle. Then, we show as TSP tools may efficiently be used to sample, recover and filter PCs attributes treating them as edge signals. Numerical results on synthetic PCs demonstrate accurate color reconstruction with robustness to sparse data and geometry refinement in the case of noisy PC coordinates. The proposed approach provides a topology-based representation to characterize the geometry and attributes of PCs.

eess.SP↗

arXiv2026

Learning Dirac Spectral Transforms for Topological Signals

The Dirac operator provides a unified framework for processing signals defined over different order topological domains, such as node and edge signals. Its eigenmodes define a spectral representation that inherently captures cross-domain interactions, in contrast to conventional Hodge-Laplacian eigenmodes that operate within a single topological dimension. In this paper, we compare the two alternatives in terms of the distortion/sparsity trade-off and we show how an overcomplete basis built concatenating the two dictionaries can provide better performance with respect to each approach. Then, we propose a parameterized nonredundant transform whose eigenmodes incorporate a mode-specific mass parameter that captures the interplay between node and edge modes. Interestingly, we show that learning the mass parameters from data makes the proposed transform able to achieve the best distortion-sparsity tradeoff with respect to both complete and overcomplete bases.

eess.SP↗

arXiv2026

Learning Consistent Causal Abstraction Networks

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal knowledge. Pushing in the same direction, we tackle the learning of consistent causal abstraction network (CAN), a sheaf-theoretic framework where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs) adhering to the semantic embedding principle, and (iii) edge stalks correspond--up to permutation--to the node stalks of more detailed SCMs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex objectives. We propose an efficient search procedure, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.

cs.LG↗

arXiv2025

Colored Markov Random Fields for Probabilistic Topological Modeling

Probabilistic Graphical Models (PGMs) encode conditional dependencies among random variables using a graph -nodes for variables, links for dependencies- and factorize the joint distribution into lower-dimensional components. This makes PGMs well-suited for analyzing complex systems and supporting decision-making. Recent advances in topological signal processing highlight the importance of variables defined on topological spaces in several application domains. In such cases, the underlying topology shapes statistical relationships, limiting the expressiveness of canonical PGMs. To overcome this limitation, we introduce Colored Markov Random Fields (CMRFs), which model both conditional and marginal dependencies among Gaussian edge variables on topological spaces, with a theoretical foundation in Hodge theory. CMRFs extend classical Gaussian Markov Random Fields by including link coloring: connectivity encodes conditional independence, while color encodes marginal independence. We quantify the benefits of CMRFs through a distributed estimation case study over a physical network, comparing it with baselines with different levels of topological prior.

stat.ML↗

arXiv2025

Learning Network Sheaves for AI-native Semantic Communication

Recent advances in AI call for a paradigm shift from bit-centric communication to goal- and semantics-oriented architectures, paving the way for AI-native 6G networks. In this context, we address a key open challenge: enabling heterogeneous AI agents to exchange compressed latent-space representations while mitigating semantic noise and preserving task-relevant meaning. We cast this challenge as learning both the communication topology and the alignment maps that govern information exchange among agents, yielding a learned network sheaf equipped with orthogonal maps. This learning process is further supported by a semantic denoising end compression module that constructs a shared global semantic space and derives sparse, structured representations of each agent's latent space. This corresponds to a nonconvex dictionary learning problem solved iteratively with closed-form updates. Experiments with mutiple AI agents pre-trained on real image data show that the semantic denoising and compression facilitates AI agents alignment and the extraction of semantic clusters, while preserving high accuracy in downstream task. The resulting communication network provides new insights about semantic heterogeneity across agents, highlighting the interpretability of our methodology.

cs.MA↗

arXiv2025

Simplicial Gaussian Models: Representation and Inference

Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial Gaussian model (SGM), which extends Gaussian PGM to simplicial complexes. SGM jointly models random variables supported on vertices, edges, and triangles, within a single parametrized Gaussian distribution. Our model builds upon discrete Hodge theory and incorporates uncertainty at every topological level through independent random components. Motivated by applications, we focus on the marginal edge-level distribution while treating node- and triangle-level variables as latent. We then develop a maximum-likelihood inference algorithm to recover the parameters of the full SGM and the induced conditional dependence structure. Numerical experiments on synthetic simplicial complexes with varying size and sparsity confirm the effectiveness of our algorithm.

stat.ML↗

arXiv2025

Learning the Structure of Connection Graphs

Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization, Riemannian signal processing, and neural sheaf diffusion. In this work, we address the inverse problem of learning CGs directly from observed signals. We propose a principled framework based on maximum pseudo-likelihood under a consistency assumption, which enforces spectral properties linking the connection Laplacian to the underlying combinatorial Laplacian. Based on this formulation, we introduce the Structured Connection Graph Learning (SCGL) algorithm, a block-optimization procedure over Riemannian manifolds that jointly infers network topology, edge weights, and geometric structure. Our experiments show that SCGL consistently outperforms existing baselines in both topological recovery and geometric fidelity, while remaining computationally efficient.

cs.LG↗

arXiv2025

Networks of Causal Abstractions: A Sheaf-theoretic Framework

A core challenge in causal artificial intelligence is the principled coordination of multiple, imperfect, and subjective causal perspectives arising from distributed agents with limited and heterogeneous access to the environment. This problem has received little formal treatment, as the existing framework assumes a single shared global causal model. This work introduces the causal abstraction network (CAN), a general sheaf-theoretic framework for representing, learning, and reasoning across collections of mixture of causal models (MCMs) - a class that unifies several existing models of context-dependent causal mechanisms. Sheaf theory provides a natural foundation for this task, offering a rigorous framework to coherently align distributed causal knowledge without requiring explicit causal graphs, functional mechanisms, interventional data, or jointly sampled observations. At the theoretical level, we provide a categorical formulation of MCMs and characterize key properties of CANs, including consistency and smoothness. Under consistency, we establish necessary and sufficient conditions: (i) for the existence of global sections, linked to spectral properties of an associated connection Laplacian; and (ii) for the convergence of causal knowledge diffusion over the CAN to the space of global sections. At the methodological level, we exploit the compositionality of causal abstractions to decompose the learning of consistent CANs into local problems on network edges, extending our prior work on Gaussian variables to Gaussian mixtures via the proposed MIXTURE-CALSEP algorithm. We validate the framework on synthetic data and through a financial application involving a multi-agent trading system, demonstrating CAN recovery, CAN-based portfolio optimization, and counterfactual reasoning.

cs.AI↗

arXiv2025

SPARQ: An Optimization Framework for the Distribution of AI-Intensive Applications under Non-Linear Delay Constraints

Next-generation real-time compute-intensive applications, such as extended reality, multi-user gaming, and autonomous transportation, are increasingly composed of heterogeneous AI-intensive functions with diverse resource requirements and stringent latency constraints. While recent advances have enabled very efficient algorithms for joint service placement, routing, and resource allocation for increasingly complex applications, current models fail to capture the non-linear relationship between delay and resource usage that becomes especially relevant in AI-intensive workloads. In this paper, we extend the cloud network flow optimization framework to support queuing-delay-aware orchestration of distributed AI applications over edge-cloud infrastructures. We introduce two execution models, Guaranteed-Resource (GR) and Shared-Resource (SR), that more accurately capture how computation and communication delays emerge from system-level resource constraints. These models incorporate M/M/1 and M/G/1 queue dynamics to represent dedicated and shared resource usage, respectively. The resulting optimization problem is non-convex due to the non-linear delay terms. To overcome this, we develop SPARQ, an iterative approximation algorithm that decomposes the problem into two convex sub-problems, enabling joint optimization of service placement, routing, and resource allocation under nonlinear delay constraints. Simulation results demonstrate that the SPARQ not only offers a more faithful representation of system delays, but also substantially improves resource efficiency and the overall cost-delay tradeoff compared to existing state-of-the-art methods.

cs.NI↗

arXiv2025

VitaGraph: Building a Knowledge Graph for Biologically Relevant Learning Tasks

The intrinsic complexity of human biology presents ongoing challenges to scientific understanding. Researchers collaborate across disciplines to expand our knowledge of the biological interactions that define human life. AI methodologies have emerged as powerful tools across scientific domains, particularly in computational biology, where graph data structures effectively model biological entities such as protein-protein interaction (PPI) networks and gene functional networks. Those networks are used as datasets for paramount network medicine tasks, such as gene-disease association prediction, drug repurposing, and polypharmacy side effect studies. Reliable predictions from machine learning models require high-quality foundational data. In this work, we present a comprehensive multi-purpose biological knowledge graph constructed by integrating and refining multiple publicly available datasets. Building upon the Drug Repurposing Knowledge Graph (DRKG), we define a pipeline tasked with a) cleaning inconsistencies and redundancies present in DRKG, b) coalescing information from the main available public data sources, and c) enriching the graph nodes with expressive feature vectors such as molecular fingerprints and gene ontologies. Biologically and chemically relevant features improve the capacity of machine learning models to generate accurate and well-structured embedding spaces. The resulting resource represents a coherent and reliable biological knowledge graph that serves as a state-of-the-art platform to advance research in computational biology and precision medicine. Moreover, it offers the opportunity to benchmark graph-based machine learning and network medicine models on relevant tasks. We demonstrate the effectiveness of the proposed dataset by benchmarking it against the task of drug repurposing, PPI prediction, and side-effect prediction, modeled as link prediction problems.

cs.LG↗

arXiv2025

Physics-Informed Topological Signal Processing for Water Distribution Network Monitoring

Water management is one of the most critical aspects of our society, together with population increase and climate change. Water scarcity requires a better characterization and monitoring of Water Distribution Networks (WDNs). This paper presents a novel framework for monitoring Water Distribution Networks (WDNs) by integrating physics-informed modeling of the nonlinear interactions between pressure and flow data with Topological Signal Processing (TSP) techniques. We represent pressure and flow data as signals defined over a second-order cell complex, enabling accurate estimation of water pressures and flows throughout the entire network from sparse sensor measurements. By formalizing hydraulic conservation laws through the TSP framework, we provide a comprehensive representation of nodal pressures and edge flows that incorporate higher-order interactions captured through the formalism of cell complexes. This provides a principled way to decompose the water flows in WDNs in three orthogonal signal components (irrotational, solenoidal and harmonic). The spectral representations of these components inherently reflect the conservation laws governing the water pressures and flows. Sparse representation in the spectral domain enable topology-based sampling and reconstruction of nodal pressures and water flows from sparse measurements. Our results demonstrate that employing cell complex-based signal representations enhances the accuracy of edge signal reconstruction, due to proper modeling of both conservative and non-conservative flows along the polygonal cells.

eess.SP↗

arXiv2025

SQ-GAN: Semantic Image Communications Using Masked Vector Quantization

This work introduces Semantically Masked Vector Quantized Generative Adversarial Network (SQ-GAN), a novel approach integrating semantically driven image coding and vector quantization to optimize image compression for semantic/task-oriented communications. The method only acts on source coding and is fully compliant with legacy systems. The semantics is extracted from the image computing its semantic segmentation map using off-the-shelf software. A new specifically developed semantic-conditioned adaptive mask module (SAMM) selectively encodes semantically relevant features of the image. The relevance of the different semantic classes is task-specific, and it is incorporated in the training phase by introducing appropriate weights in the loss function. SQ-GAN outperforms state-of-the-art image compression schemes such as JPEG2000, BPG, and deep-learning based methods across multiple metrics, including perceptual quality and semantic segmentation accuracy on the reconstructed image, at extremely low compression rates.

cs.CV↗

arXiv2025

Learning Sheaf Laplacian Optimizing Restriction Maps

The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf theory, which represents an important generalization of graph signal processing. The learning problem aims to find the sheaf Laplacian that minimizes the total variation of the observed data, where the variation over each edge is also locally minimized by optimizing the associated restriction maps. Compared to alternative methods based on semidefinite programming, our solution is significantly more numerically efficient, as all its fundamental steps are resolved in closed form. The method is numerically tested on data consisting of vectors defined over subspaces of varying dimensions at each node. We demonstrate how the resulting graph is influenced by two key factors: the cross-correlation and the dimensionality difference of the data residing on the graph's nodes.

eess.SP↗