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Paolo Di Lorenzo

Publications and source records attributed to Paolo Di Lorenzo.

At least 19 recordsLinked to original sources
arXiv2026

Inverse Cross-spectral Neural Networks for Multivariate Time Series

CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.

stat.ML↗
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

Game-Theoretic Latent Space Alignment for Multi-user Semantic MIMO Communications

Semantic communications enable AI-native wireless systems by mapping raw data into compressed task-oriented latent representations. However, independently trained agents often rely on heterogeneous latent spaces and background knowledge, leading to semantic mismatch that degrades mutual understanding and downstream task execution, especially in interferencelimited multi-user wireless networks. This paper investigates distributed latent-space alignment in multi-user semantic MIMO interference networks with cognitive radio constraints. We consider primary users and semantic-aware secondary users sharing the same wireless resources, where secondary agents must simultaneously mitigate interference and align heterogeneous semantic representations. To address this problem, we formulate semantic alignment as a non-cooperative game and derive a closed-form solution for the joint optimization of linear semantic MIMO transceivers under power and interference constraints. Exploiting the structure of the problem, we recast the original matrix valued optimization into a lower-dimensional power-allocation game, leading to an iterative semantic water-filling algorithm. We establish sufficient conditions for existence, uniqueness, and global convergence to a Nash equilibrium, explicitly relating semantic alignment properties and physical-channel interactions. Numerical results assess the performance of the proposed framework, revealing key trade-offs among semantic compression, task performance, and hierarchical spectrum access.

cs.GT↗
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

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

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↗
arXiv2026

Toward Integrated Sensing, Communications, and Edge Intelligence Networks

Wireless systems are expanding their purposes, from merely connecting humans and things to connecting intelligence and opportunistically sensing of the environment through radio-frequency signals. In this paper, we introduce the concept of triple-functional networks in which the same infrastructure and resources are shared for integrated sensing, communications, and (edge) Artificial Intelligence (AI) inference. This concept opens up several opportunities, such as devising non-orthogonal resource deployment and power consumption to concurrently update multiple services, but also challenges related to resource management and signaling cross-talk, among others. The core idea of this work is that computation-related aspects, including computing resources and AI models availability, should be explicitly considered when taking resource allocation decisions, to address the conflicting goals of the services coexistence. After showing the natural coupling between theoretical performance bounds of the three services, we formulate a service coexistence optimization problem that is solved optimally, and showcase the advantages against a disjoint allocation strategy.

eess.SP↗
arXiv2026

Distributed Semantic Alignment over Interference Channels: A Game-Theoretic Approach

Semantic communication acts as a key enabler for effective task execution in AI-driven systems, prioritizing the extraction of the underlying meaning before transmission. However, when devices rely on different logic and internal representations, semantic mismatches may arise, potentially hindering mutual understanding and effectiveness of communication. Furthermore, in interference channel environments, the coexistence of multiple devices introduce a significant degradation due to the presence of multi-user-interference. To address these challenges, in this paper we formulate the joint optimization of linear Multiple-Input-Multiple-Output (MIMO) transceivers as a distributed non-cooperative game, enabling a closed-form solution that effectively addresses semantic coexistence and latent space misalignment. We derive sufficient conditions for the existence of a Nash Equilibrium (NE), considering multiple point-to-point MIMO channels, with corresponding users modeled as selfish players optimizing their transmission and semantic alignment strategies. Numerical results substantiate the proposed approach in goal-oriented semantic communication by highlighting crucial trade-offs between information compression, interference mitigation, semantic alignment, and task performance.

cs.IT↗
arXiv2026

Metasurfaces-Integrated Wireless Neural Networks for Lightweight Over-The-Air Edge Inference

The upcoming sixth Generation (6G) of wireless networks envisions ultra-low latency and energy efficient Edge Inference (EI) for diverse Internet of Things (IoT) applications. However, traditional digital hardware for machine learning is power intensive, motivating the need for alternative computation paradigms. Over-The-Air (OTA) computation is regarded as an emerging transformative approach assigning the wireless channel to actively perform computational tasks. This article introduces the concept of Metasurfaces-Integrated Neural Networks (MINNs), a physical-layer-enabled deep learning framework that leverages programmable multi-layer metasurface structures and Multiple-Input Multiple-Output (MIMO) channels to realize computational layers in the wave propagation domain. The MINN system is conceptualized as three modules: Encoder, Channel (uncontrollable propagation features and metasurfaces), and Decoder. The first and last modules, realized respectively at the multi-antenna transmitter and receiver, consist of conventional digital or purposely designed analog Deep Neural Network (DNN) layers, and the metasurfaces responses of the Channel module are optimized alongside all modules as trainable weights. This architecture enables computation offloading into the end-to-end physical layer, flexibly among its constituent modules, achieving performance comparable to fully digital DNNs while significantly reducing power consumption. The training of the MINN framework, two representative variations, and performance results for indicative applications are presented, highlighting the potential of MINNs as a lightweight and sustainable solution for future EI-enabled wireless systems. The article is concluded with a list of open challenges and promising research directions.

cs.ET↗
arXiv2026

Federated Latent Space Alignment for Multi-user Semantic Communications

Semantic communication aims to convey meaning for effective task execution, but differing latent representations in AI-native devices can cause semantic mismatches that hinder mutual understanding. This paper introduces a novel approach to mitigating latent space misalignment in multi-agent AI- native semantic communications. In a downlink scenario, we consider an access point (AP) communicating with multiple users to accomplish a specific AI-driven task. Our method implements a protocol that shares a semantic pre-equalizer at the AP and local semantic equalizers at user devices, fostering mutual understanding and task-oriented communication while considering power and complexity constraints. To achieve this, we employ a federated optimization for the decentralized training of the semantic equalizers at the AP and user sides. Numerical results validate the proposed approach in goal-oriented semantic communication, revealing key trade-offs among accuracy, com- munication overhead, complexity, and the semantic proximity of AI-native communication devices.

cs.IT↗
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

Over-the-Air Goal-Oriented Communications

Goal-oriented communications offer an attractive alternative to the Shannon-based communication paradigm, where the data is never reconstructed at the Receiver (RX) side. Rather, focusing on the case of edge inference, the Transmitter (TX) and the RX cooperate to exchange features of the input data that will be used to predict an unseen attribute of them, leveraging information from collected data sets. This chapter demonstrates that the wireless channel can be used to perform computations over the data, when equipped with programmable metasurfaces. The end-to-end system of the TX, RX, and MS-based channel is treated as a single deep neural network which is trained through backpropagation to perform inference on unseen data. Using Stacked Intelligent Metasurfaces (SIM), it is shown that this Metasurfaces-Integrated Neural Network (MINN) can achieve performance comparable to fully digital neural networks under various system parameters and data sets. By offloading computations onto the channel itself, important benefits may be achieved in terms of energy consumption, arising from reduced computations at the transceivers and smaller transmission power required for successful inference.

eess.SP↗
arXiv2025

Over-the-Air Semantic Alignment with Stacked Intelligent Metasurfaces

Semantic communication systems aim to transmit task-relevant information between devices capable of artificial intelligence, but their performance can degrade when heterogeneous transmitter-receiver models produce misaligned latent representations. Existing semantic alignment methods typically rely on additional digital processing at the transmitter or receiver, increasing overall device complexity. In this work, we introduce the first over-the-air semantic alignment framework based on stacked intelligent metasurfaces (SIM), which enables latent-space alignment directly in the wave domain, reducing substantially the computational burden at the device level. We model SIMs as trainable linear operators capable of emulating both supervised linear aligners and zero-shot Parseval-frame-based equalizers. To realize these operators physically, we develop a gradient-based optimization procedure that tailors the metasurface transfer function to a desired semantic mapping. Experiments with heterogeneous vision transformer (ViT) encoders show that SIMs can accurately reproduce both supervised and zero-shot semantic equalizers, achieving up to 90% task accuracy in regimes with high signal-to-noise ratio (SNR), while maintaining strong robustness even at low SNR values.

eess.SP↗
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↗