Topological Signal Processing for 3D Point Cloud Data

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

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.

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.

VitaGraph: Building a Knowledge Graph for Biologically Relevant Learning Tasks

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

Physics-Informed Topological Signal Processing for Water Distribution Network Monitoring

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

SQ-GAN: Semantic Image Communications Using Masked Vector Quantization

This work introduces Semantically Masked VQ-GAN (SQ-GAN), a novel approach integrating generative models to optimize image compression for semantic/task-oriented communications. SQ-GAN employs off-the-shelf semantic semantic segmentation and a new specifically developed semantic-conditioned adaptive mask module (SAMM) to selectively encode semantically significant features of the images. SQ-GAN outperforms state-of-the-art image compression schemes such as JPEG2000 and BPG across multiple metrics, including perceptual quality and semantic segmentation accuracy on the post-decoding reconstructed image, at extreme low compression rates expressed in bits per pixel.

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.

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.

Language-Oriented Semantic Latent Representation for Image Transmission

In the new paradigm of semantic communication (SC), the focus is on delivering meanings behind bits by extracting semantic information from raw data. Recent advances in data-to-text models facilitate language-oriented SC, particularly for text-transformed image communication via image-to-text (I2T) encoding and text-to-image (T2I) decoding. However, although semantically aligned, the text is too coarse to precisely capture sophisticated visual features such as spatial locations, color, and texture, incurring a significant perceptual difference between intended and reconstructed images. To address this limitation, in this paper, we propose a novel language-oriented SC framework that communicates both text and a compressed image embedding and combines them using a latent diffusion model to reconstruct the intended image. Experimental results validate the potential of our approach, which transmits only 2.09\% of the original image size while achieving higher perceptual similarities in noisy communication channels compared to a baseline SC method that communicates only through text.The code is available at https://github.com/ispamm/Img2Img-SC/ .

Opportunistic Information-Bottleneck for Goal-oriented Feature Extraction and Communication

The Information Bottleneck (IB) method is an information theoretical framework to design a parsimonious and tunable feature-extraction mechanism, such that the extracted features are maximally relevant to a specific learning or inference task. Despite its theoretical value, the IB is based on a functional optimization problem that admits a closed form solution only on specific cases (e.g., Gaussian distributions), making it difficult to be applied in most applications, where it is necessary to resort to complex and approximated variational implementations. To overcome this limitation, we propose an approach to adapt the closed-form solution of the Gaussian IB to a general task. Whichever is the inference task to be performed by a (possibly deep) neural-network, the key idea is to opportunistically design a regression sub-task, embedded in the original problem, where we can safely assume a (joint) multivariate normality between the sub-task's inputs and outputs. In this way we can exploit a fixed and pre-trained neural network to process the input data, using a tunable number of features, to trade data-size and complexity for accuracy. This approach is particularly useful every time a device needs to transmit data (or features) to a server that has to fulfil an inference task, as it provides a principled way to extract the most relevant features for the task to be executed, while looking for the best trade-off between the size of the feature vector to be transmitted, inference accuracy, and complexity. Extensive simulation results testify the effectiveness of the proposed methodhttps://info.arxiv.org/help/prep#comments and encourage to further investigate this research line.