SIGNATURE WORK
CONFERENCE & EXHIBITION 2024

My SW aims to enhance the robustness and stability of Hyperbolic Neural Networks (HNNs) by implementing Lipschitz regularization within the Poincaré ball model framework. It employs various datasets like WIBB, Actor, Cora, and Pubmed to assess the efficacy of HNNs in node classification tasks, highlighting the significance of the geometric properties of hyperbolic spaces in handling hierarchical and sparse data structures.

The methodology encompasses verifying Lipschitz bound calculations by introducing Gaussian noise to data features and comparing experimental with theoretical values across different standard deviations. A novel regularization method is introduced, adding the sum of the Lipschitz bounds as a regularization term to the classification loss function, optimizing the model’s training process and its generalization capabilities. The experimental framework evaluates the impact of different regularization strategies on HNN performance, each employing distinct computational approaches for calculating the Lipschitz bound within the hyperbolic space.

The study concludes by emphasizing the potential of Lipschitz regularization in enhancing HNN performance, suggesting future directions for extending the applicability and flexibility of HNNs through in-depth study of alternative hyperbolic operators and extending the framework to hybrid architectures, like hyperbolic graph neural networks, for modeling complex hierarchical data structures.