arXiv subjects

Paolo Di Lorenzo

Publications and source records attributed to Paolo Di Lorenzo.

At least 37 records · Page 2Linked to original sources

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

Semantic Channel Equalization Strategies for Deep Joint Source-Channel Coding

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.

cs.LG↗

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

Communication Efficient Split Learning of ViTs with Attention-based Double Compression

This paper proposes a novel communication-efficient Split Learning (SL) framework, named Attention-based Double Compression (ADC), which reduces the communication overhead required for transmitting intermediate Vision Transformers activations during the SL training process. ADC incorporates two parallel compression strategies. The first one merges samples' activations that are similar, based on the average attention score calculated in the last client layer; this strategy is class-agnostic, meaning that it can also merge samples having different classes, without losing generalization ability nor decreasing final results. The second strategy follows the first and discards the least meaningful tokens, further reducing the communication cost. Combining these strategies not only allows for sending less during the forward pass, but also the gradients are naturally compressed, allowing the whole model to be trained without additional tuning or approximations of the gradients. Simulation results demonstrate that Attention-based Double Compression outperforms state-of-the-art SL frameworks by significantly reducing communication overheads while maintaining high accuracy.

cs.LG↗

arXiv2025

Latent Space Alignment for AI-Native MIMO Semantic Communications

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.

cs.LG↗

arXiv2025

RIS-aided Latent Space Alignment for Semantic Channel Equalization

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.

cs.LG↗

arXiv2025

Frame-Based Zero-Shot Semantic Channel Equalization for AI-Native Communications

In future AI-native wireless networks, the presence of mismatches between the latent spaces of independently designed and trained deep neural network (DNN) encoders may impede mutual understanding due to the emergence of semantic channel noise. This undermines the receiver's ability to interpret transmitted representations, thereby reducing overall system performance. To address this issue, we propose the Parseval Frame Equalizer (PFE), a zero-shot, frame-based semantic channel equalizer that aligns latent spaces of heterogeneous encoders without requiring system retraining. PFE enables dynamic signal compression and expansion, mitigating semantic noise while preserving performance on downstream tasks. Building on this capability, we introduce a dynamic optimization strategy that coordinates communication, computation, and learning resources to balance energy consumption, end-to-end (E2E) latency, and task performance in multi-agent semantic communication scenarios. Extensive simulations confirm the effectiveness of our approach in maintaining semantic consistency and meeting long-term constraints on latency and accuracy under diverse and time-varying network conditions.

cs.NI↗

arXiv2025

Causal Abstraction Learning based on the Semantic Embedding Principle

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.

cs.LG↗

arXiv2025

Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes

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.

eess.SP↗

arXiv2025

Adaptive Semantic Token Communication for Transformer-based Edge Inference

This paper presents an adaptive framework for edge inference based on a dynamically configurable transformer-powered deep joint source channel coding (DJSCC) architecture. Motivated by a practical scenario where a resource constrained edge device engages in goal oriented semantic communication, such as selectively transmitting essential features for object detection to an edge server, our approach enables efficient task aware data transmission under varying bandwidth and channel conditions. To achieve this, input data is tokenized into compact high level semantic representations, refined by a transformer, and transmitted over noisy wireless channels. As part of the DJSCC pipeline, we employ a semantic token selection mechanism that adaptively compresses informative features into a user specified number of tokens per sample. These tokens are then further compressed through the JSCC module, enabling a flexible token communication strategy that adjusts both the number of transmitted tokens and their embedding dimensions. We incorporate a resource allocation algorithm based on Lyapunov stochastic optimization to enhance robustness under dynamic network conditions, effectively balancing compression efficiency and task performance. Experimental results demonstrate that our system consistently outperforms existing baselines, highlighting its potential as a strong foundation for AI native semantic communication in edge intelligence applications.

cs.LG↗

arXiv2025

Dynamic Relative Representations for Goal-Oriented Semantic Communications

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.

cs.NI↗

arXiv2025

Over-the-Air Edge Inference via End-to-End Metasurfaces-Integrated Artificial Neural Networks

In the Edge Inference (EI) paradigm, where a Deep Neural Network (DNN) is split across the transceivers to wirelessly communicate goal-defined features in solving a computational task, the wireless medium has been commonly treated as a source of noise. In this paper, motivated by the emerging technologies of Reconfigurable Intelligent Surfaces (RISs) and Stacked Intelligent Metasurfaces (SIM) that offer programmable propagation of wireless signals, either through controllable reflections or diffractions, we optimize the RIS/SIM-enabled smart wireless environment as a means of over-the-air computing, resembling the operations of DNN layers. We propose a framework of Metasurfaces-Integrated Neural Networks (MINNs) for EI, presenting its modeling, training through a backpropagation variation for fading channels, and deployment aspects. The overall end-to-end DNN architecture is general enough to admit RIS and SIM devices, through controllable reconfiguration before each transmission or fixed configurations after training, while both channel-aware and channel-agnostic transceivers are considered. Our numerical evaluation showcases metasurfaces to be instrumental in performing image classification under link budgets that impede conventional communications or metasurface-free systems. It is demonstrated that our MINN framework can significantly simplify EI requirements, achieving near-optimal performance with $50~$dB lower testing signal-to-noise ratio compared to training, even without transceiver channel knowledge.

cs.LG↗

arXiv2025

Topological Dictionary Learning

The aim of this paper is to introduce a novel dictionary learning algorithm for sparse representation of signals defined over combinatorial topological spaces, specifically, regular cell complexes. Leveraging Hodge theory, we embed topology into the dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, yielding localized spectral topological filter frames. The learning problem is cast to jointly infer the underlying cell complex and optimize the dictionary coefficients and the sparse signal representation. We efficiently solve the problem via iterative alternating algorithms. Numerical results on both synthetic and real data show the effectiveness of the proposed procedure in jointly learning the sparse representations and the underlying relational structure of topological signals.

eess.SP↗

arXiv2025

Semantic and Goal-oriented Wireless Network Coverage: The Area of Effectiveness

Assessing wireless coverage is a fundamental task for public network operators and private deployments, whose goal is to guarantee quality of service across the network while minimizing material waste and energy consumption. These maps are usually built through ray tracing techniques and/or channel measurements that can be consequently translated into network Key Performance Indicators (KPIs), such as capacity or throughput. However, next generation networks (e.g., 6G) typically involve beyond communication resources, towards services that require data transmission, but also processing (local and remote) to perform complex decision making in real time, with the best balance between performance, energy consumption, material waste, and privacy. In this paper, we introduce the novel concept of areas of effectiveness, which goes beyond the legacy notion of coverage, towards one that takes into account capability of the network of offering edge Artificial Intelligence (AI)-related computation. We will show that radio coverage is a poor indicator of real system performance, depending on the application and the computing capabilities of network and devices. This opens new challenges in network planning, but also resource orchestration during operation to achieve the specific goal of communication.

cs.NI↗

arXiv2025

Topological Signal Processing and Learning: Recent Advances and Future Challenges

Developing methods to process irregularly structured data is crucial in applications like gene-regulatory, brain, power, and socioeconomic networks. Graphs have been the go-to algebraic tool for modeling the structure via nodes and edges capturing their interactions, leading to the establishment of the fields of graph signal processing (GSP) and graph machine learning (GML). Key graph-aware methods include Fourier transform, filtering, sampling, as well as topology identification and spatiotemporal processing. Although versatile, graphs can model only pairwise dependencies in the data. To this end, topological structures such as simplicial and cell complexes have emerged as algebraic representations for more intricate structure modeling in data-driven systems, fueling the rapid development of novel topological-based processing and learning methods. This paper first presents the core principles of topological signal processing through the Hodge theory, a framework instrumental in propelling the field forward thanks to principled connections with GSP-GML. It then outlines advances in topological signal representation, filtering, and sampling, as well as inferring topological structures from data, processing spatiotemporal topological signals, and connections with topological machine learning. The impact of topological signal processing and learning is finally highlighted in applications dealing with flow data over networks, geometric processing, statistical ranking, biology, and semantic communication.

eess.SP↗

arXiv2025

Topological Neural Networks over the Air

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.

cs.IT↗

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↗