Sheaf Hypergraph Networks

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of various fields requiring structured data. Current approaches typically represent these interactions using hypergraphs. We enhance this representation by introducing cellular sheaves for hypergraphs, a mathematical construction that adds extra structure to the conventional hypergraph while maintaining their local, higherorder connectivity. Drawing inspiration from existing Laplacians in the literature, we develop two unique formulations of sheaf hypergraph Laplacians: linear and non-linear. Our theoretical analysis demonstrates that incorporating sheaves into the hypergraph Laplacian provides a more expressive inductive bias than standard hypergraph diffusion, creating a powerful instrument for effectively modelling complex data structures. We employ these sheaf hypergraph Laplacians to design two categories of models: Sheaf Hypergraph Neural Networks and Sheaf Hypergraph Convolutional Networks. These models generalize classical Hypergraph Networks often found in the literature. Through extensive experimentation, we show that this generalization significantly improves performance, achieving top results on multiple benchmark datasets for hypergraph node classification

Denoising Probabilistic Diffusion Models for Synthetic Healthcare Image Generation

Healthcare data are an essential resource in Machine Learning (ML) and Artificial Intelligence (AI) to improve clinical practice, empower patients and enhance drug development with the aim to discover new medical knowledge. In particular, the biomedical imaging analysis plays a important role in the health- care context producing a huge amount of data that can be used to study complex diseases and their evolution in a deeper way or to predict their onsets. In this work we consider an approach based on Denoising Diffusion Probabilistic Models (DDPM) which is a type of generative model that uses a parameterized Markov chain and variational inference to generate synthetic samples that match real data. In particular, we execute a study by training on Malaria images and generating high-quality synthetic samples in order (i) to test the performance of the DDPMs, (ii) to estimate the association between original and synthetic data and (iii) to understand how the natural and human-made environmental factors impact Malaria disease. Finally, we use a well-defined convolutional neural network for classification tasks to assess the DDPM’s goodness in generating the synthetic images

Concept Distillation in Graph Neural Networks

The opaque reasoning of Graph Neural Networks induces a lack of human trust. Existing graph network explainers attempt to address this issue by providing post-hoc explanations, however, they fail to make the model itself more interpretable. To fill this gap, we intro- duce the Concept Distillation Module, the first differentiable concept- distillation approach for graph networks. The proposed approach is a layer that can be plugged into any graph network to make it explainable by design, by first distilling graph concepts from the latent space and then using these to solve the task. Our results demonstrate that this approach allows graph networks to: (i) attain model accuracy comparable with their equivalent vanilla versions, (ii) distill meaningful concepts achiev- ing 4.8% higher concept completeness and 36.5% lower purity scores on average, (iii) provide high-quality concept-based logic explanations for their prediction, and (iv) support effective interventions at test time: these can increase human trust as well as improve model performance