Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially harmful samples. We propose $\text{\textit{Laplace Sample Information}}$ ($\mathsf{LSI}$) measure of sample informativeness grounded in information theory widely applicable across model architectures and learning settings. $\mathsf{LSI}$ leverages a Bayesian approximation to the weight posterior and the KL divergence to measure the change in the parameter distribution induced by a sample of interest from the dataset. We experimentally show that $\mathsf{LSI}$ is effective in ordering the data with respect to typicality, detecting mislabeled samples, measuring class-wise informativeness, and assessing dataset difficulty. We demonstrate these capabilities of $\mathsf{LSI}$ on image and text data in supervised and unsupervised settings. Moreover, we show that $\mathsf{LSI}$ can be computed efficiently through probes and transfers well to the training of large models.

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 HNNs 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, a 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. Experiments on standard vision tasks demonstrate the promising performance of our HCNN framework in both hybrid and fully hyperbolic settings. Overall, we believe our contributions provide a foundation for developing more powerful HNNs that can better represent complex structures found in image data. Our code is publicly available at https://github.com/kschwethelm/HyperbolicCV.