Hyperbolic Geometry in Computer Vision: A Novel Framework for Convolutional Neural Networks

Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces. However, current methods in computer vision rely on Euclidean backbones and only project features to the hyperbolic space in the task heads, limiting their ability to fully leverage the benefits of hyperbolic geometry. To address this, we present HCNN, the first fully hyperbolic convolutional neural network (CNN) designed for computer vision tasks. Based on the Lorentz model, we generalize fundamental components of CNNs and propose novel formulations of the convolutional layer, batch normalization, and multinomial logistic regression (MLR). Experimentation on standard vision tasks demonstrates the effectiveness of our HCNN framework and the Lorentz model in both hybrid and fully hyperbolic settings. Overall, we aim to pave the way for future research in hyperbolic computer vision by offering a new paradigm for interpreting and analyzing visual data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV

Attention, Filling in The Gaps for Generalization in Routing Problems

Machine Learning (ML) methods have become a useful tool for tackling vehicle routing problems, either in combination with popular heuristics or as standalone models. However, current methods suffer from poor generalization when tackling problems of different sizes or different distributions. As a result, ML in vehicle routing has witnessed an expansion phase with new methodologies being created for particular problem instances that become infeasible at larger problem sizes. This paper aims at encouraging the consolidation of the field through understanding and improving current existing models, namely the attention model by Kool et al. We identify two discrepancy categories for VRP generalization. The first is based on the differences that are inherent to the problems themselves, and the second relates to architectural weaknesses that limit the model's ability to generalize. Our contribution becomes threefold: We first target model discrepancies by adapting the Kool et al. method and its loss function for Sparse Dynamic Attention based on the alpha-entmax activation. We then target inherent differences through the use of a mixed instance training method that has been shown to outperform single instance training in certain scenarios. Finally, we introduce a framework for inference level data augmentation that improves performance by leveraging the model's lack of invariance to rotation and dilation changes.Comment: Accepted at ECML-PKDD 202