Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictions

The geometry of a graph is encoded in dynamical processes on the graph. Many graph neural network (GNN) architectures are inspired by such dynamical systems, typically based on the graph Laplacian. Here, we introduce Dirac--Bianconi GNNs (DBGNNs), which are based on the topological Dirac equation recently proposed by Bianconi. Based on the graph Laplacian, we demonstrate that DBGNNs explore the geometry of the graph in a fundamentally different way than conventional message passing neural networks (MPNNs). While regular MPNNs propagate features diffusively, analogous to the heat equation, DBGNNs allow for coherent long-range propagation. Experimental results showcase the superior performance of DBGNNs over existing conventional MPNNs for long-range predictions of power grid stability and peptide properties. This study highlights the effectiveness of DBGNNs in capturing intricate graph dynamics, providing notable advancements in GNN architectures.

SkiNet: A Deep Learning Solution for Skin Lesion Diagnosis with Uncertainty Estimation and Explainability

Skin cancer is considered to be the most common human malignancy. Around 5 million new cases of skin cancer are recorded in the United States annually. Early identification and evaluation of skin lesions is of great clinical significance, but the disproportionate dermatologist-patient ratio poses significant problem in most developing nations. Therefore a deep learning based architecture, known as SkiNet, is proposed with an objective to provide faster screening solution and assistance to newly trained physicians in the clinical diagnosis process. The main motive behind Skinet's design and development is to provide a white box solution, addressing a critical problem of trust and interpretability which is crucial for the wider adoption of Computer-aided diagnosis systems by the medical practitioners. SkiNet is a two-stage pipeline wherein the lesion segmentation is followed by the lesion classification. In our SkiNet methodology, Monte Carlo dropout and test time augmentation techniques have been employed to estimate epistemic and aleatoric uncertainty, while saliency-based methods are explored to provide post-hoc explanations of the deep learning models. The publicly available dataset, ISIC-2018, is used to perform experimentation and ablation studies. The results establish the robustness of the model on the traditional benchmarks while addressing the black-box nature of such models to alleviate the skepticism of medical practitioners by incorporating transparency and confidence to the model's prediction.