Abstract Improving risk stratification for coronary artery disease, the leading cause of death worldwide, continues to present a daily challenge in clinical practice, highlighting the urgent need for innovative approaches to early prediction of future cardiovascular events. In this work, we propose AngioGraphCAD, a deep learning based framework that employs graph neural networks to leverage geometry features and a masked attention to fuse geometry features from multiple coronary stenoses for future events prediction at both lesion and patient level from invasive coronary angiography. AngioGraphCAD is evaluated across two clinical cohorts at the lesion level and one datatset at the patient level, achieving superior performance compared to clinical measures. This is the first study that highlights the importance of geometry information in advancing future events prediction from invasive coronary angiography. Given the significance of the clinical question and the innovative nature of the proposed methodology, this work could pave the way for the development of an AI framework fueled by patient-specific data in cardiology, potentially revolutionizing personalized decision-making in managing coronary artery diseases for individual patients.

Separating multiple graph signals from a single observed mixture is an inherently ill-posed problem that traditionally relies on restrictive and handcrafted priors. This letter addresses this challenge by proposing an unsupervised learnable spectral filtering framework. Our approach reconstructs latent components by passing a fixed random input through learnable spectral filters, operating within the low-frequency eigenspace of each source-specific graph Laplacian. The architecture implicitly biases the recovered signals toward smooth patterns by confining reconstruction to these low-frequency subspaces. This acts as a structural prior, establishing a principled bridge between classical graph spectral analysis and modern neural decomposition. Numerical experiments confirm that this framework successfully isolates individual sources using solely the observed mixture and the underlying graph topology.

Graph generative models are essential across diverse scientific domains by capturing complex distributions over relational data. Among them, graph diffusion models achieve superior performance but face inefficient sampling and limited flexibility due to the tight coupling between training and sampling stages. We introduce DeFoG, a novel graph generative framework that disentangles sampling from training, enabling a broader design space for more effective and efficient model optimization. DeFoG employs a discrete flow-matching formulation that respects the inherent symmetries of graphs. We theoretically ground this disentangled formulation by explicitly relating the training loss to the sampling algorithm and showing that DeFoG faithfully replicates the ground truth graph distribution. Building on these foundations, we thoroughly investigate DeFoG's design space and propose novel sampling methods that significantly enhance performance and reduce the required number of refinement steps. Extensive experiments demonstrate state-of-the-art performance across synthetic, molecular, and digital pathology datasets, covering both unconditional and conditional generation settings. It also outperforms most diffusion-based models with just 5–10\% of their sampling steps.

Simplicial complexes provide a powerful framework for modeling higher-order interactions in structured data, making them particularly suitable for applications such as trajectory prediction and mesh processing. However, existing simplicial neural networks (SNNs), whether convolutional or attention-based, rely primarily on discrete filtering techniques, which can be restrictive. In contrast, partial differential equations (PDEs) on simplicial complexes offer a principled approach to capture continuous dynamics in such structures. In this work, we introduce continuous simplicial neural network (COSIMO), a novel SNN architecture derived from PDEs on simplicial complexes. We provide theoretical and experimental justifications of COSIMO's stability under simplicial perturbations. Furthermore, we investigate the over-smoothing phenomenon—a common issue in geometric deep learning—demonstrating that COSIMO offers better control over this effect than discrete SNNs. Our experiments on real-world datasets demonstrate that COSIMO achieves competitive performance compared to state-of-the-art SNNs in complex and noisy environments. The implementation codes are available in https://github.com/ArefEinizade2/COSIMO.

Graph diffusion models have emerged as state-of-the-art techniques in graph generation; yet, integrating domain knowledge into these models remains challenging. Domain knowledge is particularly important in real-world scenarios, where invalid generated graphs hinder deployment in practical applications. Unconstrained and conditioned graph diffusion models fail to guarantee such domain-specific structural properties. We present ConStruct, a novel framework that enables graph diffusion models to incorporate hard constraints on specific properties, such as planarity or acyclicity. Our approach ensures that the sampled graphs remain within the domain of graphs that satisfy the specified property throughout the entire trajectory in both the forward and reverse processes. This is achieved by introducing an edge-absorbing noise model and a new projector operator. ConStruct demonstrates versatility across several structural and edge-deletion invariant constraints and achieves state-of-the-art performance for both synthetic benchmarks and attributed real-world datasets. For example, by incorporating planarity constraints in digital pathology graph datasets, the proposed method outperforms existing baselines, improving data validity by up to 71.1 percentage points.

Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to nonEuclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to small perturbations in the input, is not yet well understood. Although there exists some results showing the stability of graph neural networks, most take the form of an upper bound on the magnitude of change due to a perturbation in the graph topology. However, the change in the graph topology captured in existing bounds tend not to be expressed in terms of structural properties, limiting our understanding of the model robustness properties. In this work, we develop an interpretable upper bound elucidating that graph neural networks are stable to rewiring between high degree nodes. This bound and further research in bounds of similar type provide further understanding of the stability properties of graph neural networks.

Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve common tasks such as denoising and anomaly detection, as well as design deep learning architectures such as graph neural networks. Despite being an important tool, there is a lack of theoretical understanding of the stability properties of spectral graph filters, which are important for designing robust machine learning models. In this paper, we study filter stability and provide a novel and interpretable upper bound on the change of filter output, where the bound is expressed in terms of the endpoint degrees of the deleted and newly added edges, as well as the spatial proximity of those edges. This upper bound allows us to reason, in terms of structural properties of the graph, when a spectral graph filter will be stable. We further perform extensive experiments to verify intuition that can be gained from the bound.

We address the difficult problem of estimating the attributes of weight and height of individuals from pictures taken in completely unconstrained settings. We present a deep learning scheme that relies on simultaneous prediction of human silhouettes and skeletal joints as strong regularizers that improve the prediction of attributes such as height and weight. Apart from imparting robustness to the prediction of attributes, our regularization also allows for better visual interpretability of the attribute prediction. For height estimation, our method shows lower mean average error compared to the state of the art despite using a simpler approach. For weight estimation, which has hardly been addressed in the literature, we set a new benchmark.

Spectral graph filters are a key component in state-of-the-art machine learning models used for graph-based learning, such as graph neural networks. For certain tasks stability of the spectral graph filters is important for learning suitable representations. Understanding the type of structural perturbation to which spectral graph filters are robust lets us reason as to when we may expect them to be well suited to a learning task. In this work, we first prove that polynomial graph filters are stable with respect to the change in the normalised graph Laplacian matrix. We then show empirically that properties of a structural perturbation, specifically the relative locality of the edges removed in a binary graph, effect the change in the normalised graph Laplacian. Together, our results have implications on designing robust graph filters and representations under structural perturbation.

In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an effective graph-based transform. We introduce a novel graph estimation algorithm, which uncovers the connectivities between the graph signal values by taking into consideration the coding of both the signal and the graph topology in rate-distortion terms. In particular, we introduce a novel coding solution for the graph by treating the edge weights as another graph signal that lies on the dual graph. Then, the cost of the graph description is introduced in the optimization problem by minimizing the sparsity of the coefficients of its graph Fourier transform (GFT) on the dual graph. In this way, we obtain a convex optimization problem whose solution defines an efficient transform coding strategy. The proposed technique is a general framework that can be applied to different types of signals, and we show two possible application fields, namely natural image coding and piecewise smooth image coding. The experimental results show that the proposed graph-based transform outperforms classical fixed transforms such as DCT for both natural and piecewise smooth images. In the case of depth map coding, the obtained results are even comparable to the state-of-the-art graph-based coding method, that are specifically designed for depth map images.

We consider the problem of inferring the hidden structure of high-dimensional time-varying data. In particular, we aim at capturing the dynamic relationships by representing data as valued nodes in a sequence of graphs. Our approach is motivated by the observation that imposing a meaningful graph topology can help solving the generally ill-posed and challenging problem of structure inference. To capture the temporal evolution in the sequence of graphs, we introduce a new prior that asserts that the graph edges change smoothly in time. We propose a primal-dual optimization algorithm that scales linearly with the number of allowed edges and can be easily parallelized. Our new algorithm is shown to outperform standard graph learning and other baseline methods both on a synthetic and a real dataset.

Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. If this is not possible, the data structure has to be inferred from the mere signal observations. This is exactly the problem that we address in this paper, under the assumption that the graph signals can be represented as a sparse linear combination of a few atoms of a structured graph dictionary. The dictionary is constructed on polynomials of the graph Laplacian, which can sparsely represent a general class of graph signals composed of localized patterns on the graph. We formulate a graph learning problem, whose solution provides an ideal fit between the signal observations and the sparse graph signal model. As the problem is non-convex, we propose to solve it by alternating between a signal sparse coding and a graph update step. We provide experimental results that outline the good graph recovery performance of our method, which generally compares favourably to other recent network inference algorithms.

In this paper, we propose a new graph-based compression scheme for image coding. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance. In particular, we model the pixels as nodes of a graph and we treat the pixel intensities as a signal living on an unknown graph topology. We then introduce a novel graph learning algorithm targeted for image compression that uncovers the connectivities between the pixels, by taking into consideration the coding of the image signal and the graph topology in rate-distortion terms. The cost of the graph description is introduced in the optimization problem by treating the edge weights as another graph signal that lies on the dual graph, and minimizing the sparsity of its graph Fourier coefficients (GFT). In this way, we obtain a convex optimization problem whose solution defines the transform of the image signal. The experimental results show that the proposed method outperforms classical fixed transforms such as DCT, and confirm the potential of graph-based methods for adaptive image coding solutions.

This paper addresses the problem of compression of 3D point cloud sequences that are characterized by moving 3D positions and color attributes. As temporally successive point cloud frames share some similarities, motion estimation is key to effective compression of these sequences. It, however, remains a challenging problem as the point cloud frames have varying numbers of points without explicit correspondence information. We represent the time-varying geometry of these sequences with a set of graphs, and consider 3D positions and color attributes of the point clouds as signals on the vertices of the graphs. We then cast motion estimation as a feature-matching problem between successive graphs. The motion is estimated on a sparse set of representative vertices using new spectral graph wavelet descriptors. A dense motion field is eventually interpolated by solving a graph-based regularization problem. The estimated motion is finally used for removing the temporal redundancy in the predictive coding of the 3D positions and the color characteristics of the point cloud sequences. Experimental results demonstrate that our method is able to accurately estimate the motion between consecutive frames. Moreover, motion estimation is shown to bring a significant improvement in terms of the overall compression performance of the sequence. To the best of our knowledge, this is the first paper that exploits both the spatial correlation inside each frame (through the graph) and the temporal correlation between the frames (through the motion estimation) to compress the color and the geometry of 3D point cloud sequences in an efficient way.

The construction of a meaningful graph plays a crucial role in the emerging field of signal processing on graphs. In this paper, we address the problem of learning graph Laplacians, which is similar to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. We adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these graph signals. We show that the Gaussian prior leads to an efficient representation that favours the smoothness property of the graph signals, and propose an algorithm for learning graphs that enforce such property. Experiments demonstrate that the proposed framework can efficiently infer meaningful graph topologies from only the signal observations.

We study the problem of learning constitutive features for the effective representation of graph signals, which can be considered as observations collected on different graph topologies. We propose to learn graph atoms and build graph dictionaries that provide sparse representations for classes of signals, which share common spectral characteristics but reside on the vertices of different graphs. In particular, we concentrate on graph atoms that are constructed on polynomials of the graph Laplacian. Such a design permits to abstract from the precise graph topology and to design dictionaries that can be trained and eventually used on different graphs. We cast the dictionary learning problem as an alternating optimization problem where the dictionary and the sparse representations of training signals are updated iteratively. Experimental results on synthetic graph signals representing common processes on graphs show that our dictionaries are able to capture the important components in graph signals. Further experiments on traffic data confirm the benefits of our dictionaries in the sparse approximation of signals capturing traffic bottlenecks.

This paper addresses the problem of motion estimation in 3D point cloud sequences that are characterized by moving 3D positions and color attributes. Motion estimation is key to effective compression of these sequences, but it remains a challenging problem as the temporally successive frames have varying sizes without explicit correspondence information. We represent the time-varying geometry of these sequences with a set of graphs, and consider 3D positions and color attributes of the points clouds as signals on the vertices of the graph. We then cast motion estimation as a feature matching problem between successive graphs. The motion is estimated on a sparse set of representative vertices using new spectral graph wavelet descriptors. A dense motion field is eventually interpolated by solving a graph-based regularization problem. The estimated motion is finally used for color compensation in the compression of 3D point cloud sequences. Experimental results demonstrate that our method is able to accurately estimate the motion and to bring significant improvement in terms of color compression performance.

We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. In particular, we exploit the increasing correlation between the exchanged values throughout the iterations of the consensus algorithm in order to design a novel quantization scheme, particularly efficient at low bit rates. We implement a low complexity, uniform quantizer in each sensor, where refined quantization is achieved by progressively reducing the quantization intervals with the convergence of the consensus algorithm. We propose a recurrence relation for computing the quantization parameters that depend on the network topology and the communication rate. Finally, simulation results demonstrate the effectiveness of the progressive quantization scheme that leads to the consensus solution even at low communication rate.

We consider the problem of classification of a pattern from multiple compressed observations that are collected in a sensor network. In particular, we exploit the properties of random projections in generic sensor devices and we take some first steps in introducing linear dimensionality reduction techniques in the compressed domain. We design a classification framework that consists in embedding the low dimensional classification space given by classical linear dimensionality reduction techniques in the compressed domain. The measurements of the multiple observations are then projected onto the new classification subspace and are finally aggregated in order to reach a classification decision. Simulation results verify the effectiveness of our scheme and illustrate that compressed measurements combined with information diversity lead to efficient dimensionality reduction in simple sensing architectures.