Paolo Di Lorenzo

Paolo Di Lorenzo, Gesualdo Scutari

We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and nonseparable) function - the agents' sum-utility - plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on successive convex approximation techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents: each agent first solves (possibly inexactly) a local convex approximation of the nonconvex original problem, and then performs local averaging operations. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Our algorithmic framework is then customized to a variety of convex and nonconvex problems in several fields, including signal processing, communications, networking, and machine learning. Numerical results show that the new method compares favorably to existing distributed algorithms on both convex and nonconvex problems.

Lorenzo Giusti, Claudio Battiloro, Lucia Testa et al.

Since their introduction, graph attention networks achieved outstanding results in graph representation learning tasks. However, these networks consider only pairwise relationships among nodes and then they are not able to fully exploit higher-order interactions present in many real world data-sets. In this paper, we introduce Cell Attention Networks (CANs), a neural architecture operating on data defined over the vertices of a graph, representing the graph as the 1-skeleton of a cell complex introduced to capture higher order interactions. In particular, we exploit the lower and upper neighborhoods, as encoded in the cell complex, to design two independent masked self-attention mechanisms, thus generalizing the conventional graph attention strategy. The approach used in CANs is hierarchical and it incorporates the following steps: i) a lifting algorithm that learns {\it edge features} from {\it node features}; ii) a cell attention mechanism to find the optimal combination of edge features over both lower and upper neighbors; iii) a hierarchical {\it edge pooling} mechanism to extract a compact meaningful set of features. The experimental results show that CAN is a low complexity strategy that compares favorably with state of the art results on graph-based learning tasks.

Claudio Battiloro, Lucia Testa, Lorenzo Giusti et al.

Graph machine learning methods excel at leveraging pairwise relations present in the data. However, graphs are unable to fully capture the multi-way interactions inherent in many complex systems. An effective way to incorporate them is to model the data on higher-order combinatorial topological spaces, such as Simplicial Complexes (SCs) or Cell Complexes. For this reason, we introduce Generalized Simplicial Attention Neural Networks (GSANs), novel neural network architectures designed to process data living on simplicial complexes using masked self-attentional layers. Hinging on topological signal processing principles, we devise a series of principled self-attention mechanisms able to process data associated with simplices of various order, such as nodes, edges, triangles, and beyond. These schemes learn how to combine data associated with neighbor simplices of consecutive order in a task-oriented fashion, leveraging on the simplicial Dirac operator and its Dirac decomposition. We also prove that GSAN satisfies two fundamental properties: permutation equivariance and simplicial-awareness. Finally, we illustrate how our approach compares favorably with other simplicial and graph models when applied to several (inductive and transductive) tasks such as trajectory prediction, missing data imputation, graph classification, and simplex prediction.

Gabriele D'Acunto, Paolo Di Lorenzo, Sergio Barbarossa

The inference of causal structures from observed data plays a key role in unveiling the underlying dynamics of the system. This paper exposes a novel method, named Multiscale-Causal Structure Learning (MS-CASTLE), to estimate the structure of linear causal relationships occurring at different time scales. Differently from existing approaches, MS-CASTLE takes explicitly into account instantaneous and lagged inter-relations between multiple time series, represented at different scales, hinging on stationary wavelet transform and non-convex optimization. MS-CASTLE incorporates, as a special case, a single-scale version named SS-CASTLE, which compares favorably in terms of computational efficiency, performance and robustness with respect to the state of the art onto synthetic data. We used MS-CASTLE to study the multiscale causal structure of the risk of 15 global equity markets, during covid-19 pandemic, illustrating how MS-CASTLE can extract meaningful information thanks to its multiscale analysis, outperforming SS-CASTLE. We found that the most persistent and strongest interactions occur at mid-term time resolutions. Moreover, we identified the stock markets that drive the risk during the considered period: Brazil, Canada and Italy. The proposed approach can be exploited by financial investors who, depending to their investment horizon, can manage the risk within equity portfolios from a causal perspective.

Nour Hello, Paolo Di Lorenzo, Emilio Calvanese Strinati

This paper investigates the advantages of representing and processing semantic knowledge extracted into graphs within the emerging paradigm of semantic communications. The proposed approach leverages semantic and pragmatic aspects, incorporating recent advances on large language models (LLMs) to achieve compact representations of knowledge to be processed and exchanged between intelligent agents. This is accomplished by using the cascade of LLMs and graph neural networks (GNNs) as semantic encoders, where information to be shared is selected to be meaningful at the receiver. The embedding vectors produced by the proposed semantic encoder represent information in the form of triplets: nodes (semantic concepts entities), edges(relations between concepts), nodes. Thus, semantic information is associated with the representation of relationships among elements in the space of semantic concept abstractions. In this paper, we investigate the potential of achieving high compression rates in communication by incorporating relations that link elements within graph embeddings. We propose sending semantic symbols solely equivalent to node embeddings through the wireless channel and inferring the complete knowledge graph at the receiver. Numerical simulations illustrate the effectiveness of leveraging knowledge graphs to semantically compress and transmit information.

Claudio Battiloro, Zhiyang Wang, Hans Riess et al.

In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based on this convolution operation, which are novel continuous architectures operating on tangent bundle signals, i.e. vector fields over the manifolds. Tangent bundle filters admit a spectral representation that generalizes the ones of scalar manifold filters, graph filters and standard convolutional filters in continuous time. We then introduce a discretization procedure, both in the space and time domains, to make TNNs implementable, showing that their discrete counterpart is a novel principled variant of the very recently introduced sheaf neural networks. We formally prove that this discretized architecture converges to the underlying continuous TNN. Finally, we numerically evaluate the effectiveness of the proposed architecture on various learning tasks, both on synthetic and real data.

Claudio Battiloro, Zhiyang Wang, Hans Riess et al.

In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tangent bundle filters and tangent bundle neural networks (TNNs), novel continuous architectures operating on tangent bundle signals, i.e. vector fields over manifolds. We discretize TNNs both in space and time domains, showing that their discrete counterpart is a principled variant of the recently introduced Sheaf Neural Networks. We formally prove that this discrete architecture converges to the underlying continuous TNN. We numerically evaluate the effectiveness of the proposed architecture on a denoising task of a tangent vector field over the unit 2-sphere.

Gabriele D'Acunto, Paolo Di Lorenzo, Francesco Bonchi et al.

Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency bands. Motivated by many applications in which this differentiation is pivotal, we overcome this limitation by learning a block-sparse, frequency-dependent, partial correlation graph, in which layers correspond to different frequency bands, and partial correlations can occur over just a few layers. To this aim, we formulate and solve two nonconvex learning problems: the first has a closed-form solution and is suitable when there is prior knowledge about the number of partial correlations; the second hinges on an iterative solution based on successive convex approximation, and is effective for the general case where no prior knowledge is available. Numerical results on synthetic data show that the proposed methods outperform the current state of the art. Finally, the analysis of financial time series confirms that partial correlations exist only within a few frequency bands, underscoring how our methods enable the gaining of valuable insights that would be undetected without discriminating along the frequency domain.

Alessio Devoto, Federico Alvetreti, Jary Pomponi et al.

Recently, foundation models based on Vision Transformers (ViTs) have become widely available. However, their fine-tuning process is highly resource-intensive, and it hinders their adoption in several edge or low-energy applications. To this end, in this paper we introduce an efficient fine-tuning method for ViTs called $\textbf{ALaST}$ ($\textit{Adaptive Layer Selection Fine-Tuning for Vision Transformers}$) to speed up the fine-tuning process while reducing computational cost, memory load, and training time. Our approach is based on the observation that not all layers are equally critical during fine-tuning, and their importance varies depending on the current mini-batch. Therefore, at each fine-tuning step, we adaptively estimate the importance of all layers and we assign what we call ``compute budgets'' accordingly. Layers that were allocated lower budgets are either trained with a reduced number of input tokens or kept frozen. Freezing a layer reduces the computational cost and memory usage by preventing updates to its weights, while discarding tokens removes redundant data, speeding up processing and reducing memory requirements. We show that this adaptive compute allocation enables a nearly-optimal schedule for distributing computational resources across layers, resulting in substantial reductions in training time (up to 1.5x), FLOPs (up to 2x), and memory load (up to 2x) compared to traditional full fine-tuning approaches. Additionally, it can be successfully combined with other parameter-efficient fine-tuning methods, such as LoRA.

Domenico Mattia Cinque, Claudio Battiloro, Paolo Di Lorenzo

The goal of this paper is to introduce pooling strategies for simplicial convolutional neural networks. Inspired by graph pooling methods, we introduce a general formulation for a simplicial pooling layer that performs: i) local aggregation of simplicial signals; ii) principled selection of sampling sets; iii) downsampling and simplicial topology adaptation. The general layer is then customized to design four different pooling strategies (i.e., max, top-k, self-attention, and separated top-k) grounded in the theory of topological signal processing. Also, we leverage the proposed layers in a hierarchical architecture that reduce complexity while representing data at different resolutions. Numerical results on real data benchmarks (i.e., flow and graph classification) illustrate the advantage of the proposed methods with respect to the state of the art.

Kyriakos Stylianopoulos, Paolo Di Lorenzo, George C. Alexandropoulos

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.

Giuseppe Di Poce, Mattia Merluzzi, Emilio Calvanese Strinati et al.

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.

Enrico Grimaldi, Mario Edoardo Pandolfo, Gabriele D'Acunto et al.

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.

Lorenzo Marinucci, Leonardo Di Nino, Gabriele D'Acunto et al.

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.

Kyriakos Stylianopoulos, Mario Edoardo Pandolfo, Paolo Di Lorenzo et al.

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.

Theodore Papamarkou, Tolga Birdal, Michael Bronstein et al.

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Simone Fiorellino, Claudio Battiloro, Emilio Calvanese Strinati et al.

In future 6G wireless networks, semantic and effectiveness aspects of communications will play a fundamental role, incorporating meaning and relevance into transmissions. However, obstacles arise when devices employ diverse languages, logic, or internal representations, leading to semantic mismatches that might jeopardize understanding. In latent space communication, this challenge manifests as misalignment within high-dimensional representations where deep neural networks encode data. This paper presents a novel framework for goal-oriented semantic communication, leveraging relative representations to mitigate semantic mismatches via latent space alignment. We propose a dynamic optimization strategy that adapts relative representations, communication parameters, and computation resources for energy-efficient, low-latency, goal-oriented semantic communications. Numerical results demonstrate our methodology's effectiveness in mitigating mismatches among devices, while optimizing energy consumption, delay, and effectiveness.

Tomás Hüttebräucker, Simone Fiorellino, Mohamed Sana et al.

In multi-user semantic communication, language mismatche poses a significant challenge when independently trained agents interact. We present a novel semantic equalization algorithm that enables communication between agents with different languages without additional retraining. Our algorithm is based on relative representations, a framework that enables different agents employing different neural network models to have unified representation. It proceeds by projecting the latent vectors of different models into a common space defined relative to a set of data samples called \textit{anchors}, whose number equals the dimension of the resulting space. A communication between different agents translates to a communication of semantic symbols sampled from this relative space. This approach, in addition to aligning the semantic representations of different agents, allows compressing the amount of information being exchanged, by appropriately selecting the number of anchors. Eventually, we introduce a novel anchor selection strategy, which advantageously determines prototypical anchors, capturing the most relevant information for the downstream task. Our numerical results show the effectiveness of the proposed approach allowing seamless communication between agents with radically different models, including differences in terms of neural network architecture and datasets used for initial training.

Alessio Devoto, Simone Petruzzi, Jary Pomponi et al.

In this paper, we propose a novel design for AI-native goal-oriented communications, exploiting transformer neural networks under dynamic inference constraints on bandwidth and computation. Transformers have become the standard architecture for pretraining large-scale vision and text models, and preliminary results have shown promising performance also in deep joint source-channel coding (JSCC). Here, we consider a dynamic model where communication happens over a channel with variable latency and bandwidth constraints. Leveraging recent works on conditional computation, we exploit the structure of the transformer blocks and the multihead attention operator to design a trainable semantic token selection mechanism that learns to select relevant tokens (e.g., image patches) from the input signal. This is done dynamically, on a per-input basis, with a rate that can be chosen as an additional input by the user. We show that our model improves over state-of-the-art token selection mechanisms, exhibiting high accuracy for a wide range of latency and bandwidth constraints, without the need for deploying multiple architectures tailored to each constraint. Last, but not least, the proposed token selection mechanism helps extract powerful semantics that are easy to understand and explain, paving the way for interpretable-by-design models for the next generation of AI-native communication systems.

Mario Edoardo Pandolfo, Simone Fiorellino, Emilio Calvanese Strinati et al.

Semantic communications focus on prioritizing the understanding of the meaning behind transmitted data and ensuring the successful completion of tasks that motivate the exchange of information. However, when devices rely on different languages, logic, or internal representations, semantic mismatches may occur, potentially hindering mutual understanding. This paper introduces a novel approach to addressing latent space misalignment in semantic communications, exploiting multiple-input multiple-output (MIMO) communications. Specifically, our method learns a MIMO precoder/decoder pair that jointly performs latent space compression and semantic channel equalization, mitigating both semantic mismatches and physical channel impairments. We explore two solutions: (i) a linear model, optimized by solving a biconvex optimization problem via the alternating direction method of multipliers (ADMM); (ii) a neural network-based model, which learns semantic MIMO precoder/decoder under transmission power budget and complexity constraints. Numerical results demonstrate the effectiveness of the proposed approach in a goal-oriented semantic communication scenario, illustrating the main trade-offs between accuracy, communication burden, and complexity of the solutions.

Simone Fiorellino, Claudio Battiloro, Paolo Di Lorenzo

Topological neural networks (TNNs) are information processing architectures that model representations from data lying over topological spaces (e.g., simplicial or cell complexes) and allow for decentralized implementation through localized communications over different neighborhoods. Existing TNN architectures have not yet been considered in realistic communication scenarios, where channel effects typically introduce disturbances such as fading and noise. This paper aims to propose a novel TNN design, operating on regular cell complexes, that performs over-the-air computation, incorporating the wireless communication model into its architecture. Specifically, during training and inference, the proposed method considers channel impairments such as fading and noise in the topological convolutional filtering operation, which takes place over different signal orders and neighborhoods. Numerical results illustrate the architecture's robustness to channel impairments during testing and the superior performance with respect to existing architectures, which are either communication-agnostic or graph-based.

Gabriele D'Acunto, Fabio Massimo Zennaro, Yorgos Felekis et al.

Structural causal models (SCMs) allow us to investigate complex systems at multiple levels of resolution. The causal abstraction (CA) framework formalizes the mapping between high- and low-level SCMs. We address CA learning in a challenging and realistic setting, where SCMs are inaccessible, interventional data is unavailable, and sample data is misaligned. A key principle of our framework is semantic embedding, formalized as the high-level distribution lying on a subspace of the low-level one. This principle naturally links linear CA to the geometry of the Stiefel manifold. We present a category-theoretic approach to SCMs that enables the learning of a CA by finding a morphism between the low- and high-level probability measures, adhering to the semantic embedding principle. Consequently, we formulate a general CA learning problem. As an application, we solve the latter problem for linear CA; considering Gaussian measures and the Kullback-Leibler divergence as an objective. Given the nonconvexity of the learning task, we develop three algorithms building upon existing paradigms for Riemannian optimization. We demonstrate that the proposed methods succeed on both synthetic and real-world brain data with different degrees of prior information about the structure of CA.

Jary Pomponi, Mattia Merluzzi, Alessio Devoto et al.

This paper presents a novel framework for goal-oriented semantic communications leveraging recursive early exit models. The proposed approach is built on two key components. First, we introduce an innovative early exit strategy that dynamically partitions computations, enabling samples to be offloaded to a server based on layer-wise recursive prediction dynamics that detect samples for which the confidence is not increasing fast enough over layers. Second, we develop a Reinforcement Learning-based online optimization framework that jointly determines early exit points, computation splitting, and offloading strategies, while accounting for wireless conditions, inference accuracy, and resource costs. Numerical evaluations in an edge inference scenario demonstrate the method's adaptability and effectiveness in striking an excellent trade-off between performance, latency, and resource efficiency.

Tomás Hüttebräucker, Mario Edoardo Pandolfo, Simone Fiorellino et al.

Semantic communication systems introduce a new paradigm in wireless communications, focusing on transmitting the intended meaning rather than ensuring strict bit-level accuracy. These systems often rely on Deep Neural Networks (DNNs) to learn and encode meaning directly from data, enabling more efficient communication. However, in multi-user settings where interacting agents are trained independently-without shared context or joint optimization-divergent latent representations across AI-native devices can lead to semantic mismatches, impeding mutual understanding even in the absence of traditional transmission errors. In this work, we address semantic mismatch in Multiple-Input Multiple-Output (MIMO) channels by proposing a joint physical and semantic channel equalization framework that leverages the presence of Reconfigurable Intelligent Surfaces (RIS). The semantic equalization is implemented as a sequence of transformations: (i) a pre-equalization stage at the transmitter; (ii) propagation through the RIS-aided channel; and (iii) a post-equalization stage at the receiver. We formulate the problem as a constrained Minimum Mean Squared Error (MMSE) optimization and propose two solutions: (i) a linear semantic equalization chain, and (ii) a non-linear DNN-based semantic equalizer. Both methods are designed to operate under semantic compression in the latent space and adhere to transmit power constraints. Through extensive evaluations, we show that the proposed joint equalization strategies consistently outperform conventional, disjoint approaches to physical and semantic channel equalization across a broad range of scenarios and wireless channel conditions.

Lorenzo Marinucci, Claudio Battiloro, Paolo Di Lorenzo

This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we present a topological LMS algorithm that efficiently processes streaming signals observed over time-varying edge subsets. We provide a detailed stochastic analysis of the algorithm, deriving its stability conditions, steady-state mean-square-error, and convergence speed, while exploring the impact of edge sampling on performance. We also propose strategies to design optimal edge sampling probabilities, minimizing rate while ensuring desired estimation accuracy. Assuming partial knowledge of the complex structure (e.g., the underlying graph), we introduce an adaptive topology inference method that integrates with the proposed LMS framework. Additionally, we propose a distributed version of the algorithm and analyze its stability and mean-square-error properties. Empirical results on synthetic and real-world traffic data demonstrate that our approach, in both centralized and distributed settings, outperforms graph-based LMS methods by leveraging higher-order topological features.

Leonardo Di Nino, Sergio Barbarossa, Paolo Di Lorenzo

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.

Giuseppe Di Poce, Mario Edoardo Pandolfo, Emilio Calvanese Strinati et al.

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.

Gabriele D'Acunto, Paolo Di Lorenzo, Sergio Barbarossa

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.

Mario Edoardo Pandolfo, Kyriakos Stylianopoulos, George C. Alexandropoulos et al.

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.

Lorenzo Marinucci, Gabriele D'Acunto, Paolo Di Lorenzo et al.

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.

Lorenzo Pannacci, Simone Fiorellino, Mario Edoardo Pandolfo et al.

Deep joint source-channel coding (DeepJSCC) has emerged as a powerful paradigm for end-to-end semantic communications, jointly learning to compress and protect task-relevant features over noisy channels. However, existing DeepJSCC schemes assume a shared latent space at transmitter (TX) and receiver (RX) - an assumption that fails in multi-vendor deployments where encoders and decoders cannot be co-trained. This mismatch introduces "semantic noise", degrading reconstruction quality and downstream task performance. In this paper, we systematize and evaluate methods for semantic channel equalization for DeepJSCC, introducing an additional processing stage that aligns heterogeneous latent spaces under both physical and semantic impairments. We investigate three classes of aligners: (i) linear maps, which admit closed-form solutions; (ii) lightweight neural networks, offering greater expressiveness; and (iii) a Parseval-frame equalizer, which operates in zero-shot mode without the need for training. Through extensive experiments on image reconstruction over AWGN and fading channels, we quantify trade-offs among complexity, data efficiency, and fidelity, providing guidelines for deploying DeepJSCC in heterogeneous AI-native wireless networks.

Claudio Battiloro, Indro Spinelli, Lev Telyatnikov et al.

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.

Kyriakos Stylianopoulos, Mattia Merluzzi, Paolo Di Lorenzo et al.

In this paper, we propose a novel algorithm for energy-efficient, low-latency, accurate inference at the wireless edge, in the context of 6G networks endowed with reconfigurable intelligent surfaces (RISs). We consider a scenario where new data are continuously generated/collected by a set of devices and are handled through a dynamic queueing system. Building on the marriage between Lyapunov stochastic optimization and deep reinforcement learning (DRL), we devise a dynamic learning algorithm that jointly optimizes the data compression scheme, the allocation of radio resources (i.e., power, transmission precoding), the computation resources (i.e., CPU cycles), and the RIS reflectivity parameters (i.e., phase shifts), with the aim of performing energy-efficient edge classification with end-to-end (E2E) delay and inference accuracy constraints. The proposed strategy enables dynamic control of the system and of the wireless propagation environment, performing a low-complexity optimization on a per-slot basis while dealing with time-varying radio channels and task arrivals, whose statistics are unknown. Numerical results assess the performance of the proposed RIS-empowered edge inference strategy in terms of trade-off between energy, delay, and accuracy of a classification task.

Paolo Di Lorenzo, Simone Scardapane

We study distributed stochastic nonconvex optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the agents' sum-utility) plus a convex (possibly nonsmooth) regularizer. The proposed method hinges on successive convex approximation (SCA) techniques, leveraging dynamic consensus as a mechanism to track the average gradient among the agents, and recursive averaging to recover the expected gradient of the sum-utility function. Almost sure convergence to (stationary) solutions of the nonconvex problem is established. Finally, the method is applied to distributed stochastic training of neural networks. Numerical results confirm the theoretical claims, and illustrate the advantages of the proposed method with respect to other methods available in the literature.

Simone Scardapane, Paolo Di Lorenzo

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA) techniques. The basic idea is to iteratively replace the original (non-convex, highly dimensional) learning problem with a sequence of (strongly convex) approximations, which are both accurate and simple to optimize. Differently from similar ideas (e.g., quasi-Newton algorithms), the approximations can be constructed using only first-order information of the neural network function, in a stochastic fashion, while exploiting the overall structure of the learning problem for a faster convergence. We discuss several use cases, based on different choices for the loss function (e.g., squared loss and cross-entropy loss), and for the regularization of the NN's weights. We experiment on several medium-sized benchmark problems, and on a large-scale dataset involving simulated physical data. The results show how the algorithm outperforms state-of-the-art techniques, providing faster convergence to a better minimum. Additionally, we show how the algorithm can be easily parallelized over multiple computational units without hindering its performance. In particular, each computational unit can optimize a tailored surrogate function defined on a randomly assigned subset of the input variables, whose dimension can be selected depending entirely on the available computational power.

Simone Scardapane, Paolo Di Lorenzo

The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly time-varying, connectivity pattern. In such distributed scenario, the training problem can be formulated as the (regularized) optimization of a non-convex social cost function, given by the sum of local (non-convex) costs, where each agent contributes with a single error term defined with respect to its local dataset. To devise a flexible and efficient solution, we customize a recently proposed framework for non-convex optimization over networks, which hinges on a (primal) convexification-decomposition technique to handle non-convexity, and a dynamic consensus procedure to diffuse information among the agents. Several typical choices for the training criterion (e.g., squared loss, cross entropy, etc.) and regularization (e.g., $\ell_2$ norm, sparsity inducing penalties, etc.) are included in the framework and explored along the paper. Convergence to a stationary solution of the social non-convex problem is guaranteed under mild assumptions. Additionally, we show a principled way allowing each agent to exploit a possible multi-core architecture (e.g., a local cloud) in order to parallelize its local optimization step, resulting in strategies that are both distributed (across the agents) and parallel (inside each agent) in nature. A comprehensive set of experimental results validate the proposed approach.

P. Di Lorenzo, P. Banelli, S. Barbarossa et al.

The aim of this paper is to propose distributed strategies for adaptive learning of signals defined over graphs. Assuming the graph signal to be bandlimited, the method enables distributed reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, some useful strategies for distributed selection of the sampling set are provided. Several numerical results validate our theoretical findings, and illustrate the performance of the proposed method for distributed adaptive learning of signals defined over graphs.

Paolo Di Lorenzo, Ali H. Sayed

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the detection of sparsity via a diffusive process over the network. The resulting algorithms endow networks with learning abilities and allow them to learn the sparse structure from the incoming data in real-time, and also to track variations in the sparsity of the model. We provide convergence and mean-square performance analysis of the proposed method and show under what conditions it outperforms the unregularized diffusion version. We also show how to adaptively select the regularization parameter. Simulation results illustrate the advantage of the proposed filters for sparse data recovery.