Integrating Probabilistic Trees and Causal Networks for Clinical and Epidemiological Data

Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional Machine Learning (ML) models excel at predicting outcomes, such as identifying high risk patients, they are limited in addressing what-if questions about interventions. This study introduces the Probabilistic Causal Fusion (PCF) framework, which integrates Causal Bayesian Networks (CBNs) and Probability Trees (PTrees) to extend beyond predictions. PCF leverages causal relationships from CBNs to structure PTrees, enabling both the quantification of factor impacts and simulation of hypothetical interventions. PCF was validated on three real-world healthcare datasets i.e. MIMIC-IV, Framingham Heart Study, and Diabetes, chosen for their clinically diverse variables. It demonstrated predictive performance comparable to traditional ML models while providing additional causal reasoning capabilities. To enhance interpretability, PCF incorporates sensitivity analysis and SHapley Additive exPlanations (SHAP). Sensitivity analysis quantifies the influence of causal parameters on outcomes such as Length of Stay (LOS), Coronary Heart Disease (CHD), and Diabetes, while SHAP highlights the importance of individual features in predictive modeling. By combining causal reasoning with predictive modeling, PCF bridges the gap between clinical intuition and data-driven insights. Its ability to uncover relationships between modifiable factors and simulate hypothetical scenarios provides clinicians with a clearer understanding of causal pathways. This approach supports more informed, evidence-based decision-making, offering a robust framework for addressing complex questions in diverse healthcare settings.

Multi-Head Explainer: A General Framework to Improve Explainability in CNNs and Transformers

In this study, we introduce the Multi-Head Explainer (MHEX), a versatile and modular framework that enhances both the explainability and accuracy of Convolutional Neural Networks (CNNs) and Transformer-based models. MHEX consists of three core components: an Attention Gate that dynamically highlights task-relevant features, Deep Supervision that guides early layers to capture fine-grained details pertinent to the target class, and an Equivalent Matrix that unifies refined local and global representations to generate comprehensive saliency maps. Our approach demonstrates superior compatibility, enabling effortless integration into existing residual networks like ResNet and Transformer architectures such as BERT with minimal modifications. Extensive experiments on benchmark datasets in medical imaging and text classification show that MHEX not only improves classification accuracy but also produces highly interpretable and detailed saliency scores.

Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals. Most of the previous topological signal processing algorithms treat node and edge signals separately and work under the hypothesis that the true signal is smooth and/or well approximated by a harmonic eigenvector of the Hodge-Laplacian, which may be violated in practice. Here we propose Dirac-equation signal processing, a framework for efficiently reconstructing true signals on nodes and edges, also if they are not smooth or harmonic, by processing them jointly. The proposed physics-inspired algorithm is based on the spectral properties of the topological Dirac operator. It leverages the mathematical structure of the topological Dirac equation to boost the performance of the signal processing algorithm. We discuss how the relativistic dispersion relation obeyed by the topological Dirac equation can be used to assess the quality of the signal reconstruction. Finally, we demonstrate the improved performance of the algorithm with respect to previous algorithms. Specifically, we show that Dirac-equation signal processing can also be used efficiently if the true signal is a non-trivial linear combination of more than one eigenstate of the Dirac equation, as it generally occurs for real signals.

Explainable Deep Learning Framework for SERS Bio-quantification

Surface-enhanced Raman spectroscopy (SERS) is a potential fast and inexpensive method of analyte quantification, which can be combined with deep learning to discover biomarker-disease relationships. This study aims to address present challenges of SERS through a novel SERS bio-quantification framework, including spectral processing, analyte quantification, and model explainability. To this end,serotonin quantification in urine media was assessed as a model task with 682 SERS spectra measured in a micromolar range using cucurbit[8]uril chemical spacers. A denoising autoencoder was utilized for spectral enhancement, and convolutional neural networks (CNN) and vision transformers were utilized for biomarker quantification. Lastly, a novel context representative interpretable model explanations (CRIME) method was developed to suit the current needs of SERS mixture analysis explainability. Serotonin quantification was most efficient in denoised spectra analysed using a convolutional neural network with a three-parameter logistic output layer (mean absolute error = 0.15 {\mu}M, mean percentage error = 4.67%). Subsequently, the CRIME method revealed the CNN model to present six prediction contexts, of which three were associated with serotonin. The proposed framework could unlock a novel, untargeted hypothesis generating method of biomarker discovery considering the rapid and inexpensive nature of SERS measurements, and the potential to identify biomarkers from CRIME contexts.

Deep Equilibrium Algorithmic Reasoning

Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of the GNN matches an iteration of the algorithm. In this paper we study neurally solving algorithms from a different perspective: since the algorithm's solution is often an equilibrium, it is possible to find the solution directly by solving an equilibrium equation. Our approach requires no information on the ground-truth number of steps of the algorithm, both during train and test time. Furthermore, the proposed method improves the performance of GNNs on executing algorithms and is a step towards speeding up existing NAR models. Our empirical evidence, leveraging algorithms from the CLRS-30 benchmark, validates that one can train a network to solve algorithmic problems by directly finding the equilibrium. We discuss the practical implementation of such models and propose regularisations to improve the performance of these equilibrium reasoners.

Explaining Hypergraph Neural Networks: From Local Explanations to Global Concepts

Hypergraph neural networks are a class of powerful models that leverage the message passing paradigm to learn over hypergraphs, a generalization of graphs well-suited to describing relational data with higher-order interactions. However, such models are not naturally interpretable, and their explainability has received very limited attention. We introduce SHypX, the first model-agnostic post-hoc explainer for hypergraph neural networks that provides both local and global explanations. At the instance-level, it performs input attribution by discretely sampling explanation subhypergraphs optimized to be faithful and concise. At the model-level, it produces global explanation subhypergraphs using unsupervised concept extraction. Extensive experiments across four real-world and four novel, synthetic hypergraph datasets demonstrate that our method finds high-quality explanations which can target a user-specified balance between faithfulness and concision, improving over baselines by 25 percent points in fidelity on average.

SPHINX: Structural Prediction using Hypergraph Inference Network

The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore the higher-order interactions altogether or simplify them into pairwise connections. In order to facilitate higher-order processing, even when a hypergraph structure is not available, we introduce Structural Prediction using Hypergraph Inference Network (SPHINX), a model that learns to infer a latent hypergraph structure in an unsupervised way, solely from the final node-level signal. The model consists of a soft, differentiable clustering method used to sequentially predict, for each hyperedge, the probability distribution over the nodes and a sampling algorithm that converts them into an explicit hypergraph structure. We show that the recent advancement in k-subset sampling represents a suitable tool for producing discrete hypergraph structures, addressing some of the training instabilities exhibited by prior works. The resulting model can generate the higher-order structure necessary for any modern hypergraph neural network, facilitating the capture of higher-order interaction in domains where annotating them is difficult. Through extensive ablation studies and experiments conducted on two challenging datasets for trajectory prediction, we demonstrate that our model is capable of inferring suitable latent hypergraphs, that are interpretable and enhance the final performance.

Heterogeneous Sheaf Neural Networks

Heterogeneous graphs, with nodes and edges of different types, are commonly used to model relational structures in many real-world applications. Standard Graph Neural Networks (GNNs) struggle to process heterogeneous data due to oversmoothing. Instead, current approaches have focused on accounting for the heterogeneity in the model architecture, leading to increasingly complex models. Inspired by recent work, we propose using cellular sheaves to model the heterogeneity in the graph's underlying topology. Instead of modelling the data as a graph, we represent it as cellular sheaves, which allows us to encode the different data types directly in the data structure, eliminating the need to inject them into the architecture. We introduce HetSheaf, a general framework for heterogeneous sheaf neural networks, and a series of heterogeneous sheaf predictors to better encode the data's heterogeneity into the sheaf structure. Finally, we empirically evaluate HetSheaf on several standard heterogeneous graph benchmarks, achieving competitive results whilst being more parameter-efficient.

Neural Algorithmic Reasoning with Multiple Correct Solutions

Neural Algorithmic Reasoning (NAR) aims to optimize classical algorithms. However, canonical implementations of NAR train neural networks to return only a single solution, even when there are multiple correct solutions to a problem, such as single-source shortest paths. For some applications, it is desirable to recover more than one correct solution. To that end, we give the first method for NAR with multiple solutions. We demonstrate our method on two classical algorithms: Bellman-Ford (BF) and Depth-First Search (DFS), favouring deeper insight into two algorithms over a broader survey of algorithms. This method involves generating appropriate training data as well as sampling and validating solutions from model output. Each step of our method, which can serve as a framework for neural algorithmic reasoning beyond the tasks presented in this paper, might be of independent interest to the field and our results represent the first attempt at this task in the NAR literature.

Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations

We address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODE) are effective in learning node representations, they fail to quantify uncertainty. To address this, we introduce Latent Graph Neural Stochastic Differential Equations (LGNSDE), which enhance GNODE by embedding randomness through Brownian motion to quantify uncertainty. We provide theoretical guarantees for LGNSDE and empirically show better performance in uncertainty quantification.