Hyperbolic Deep Neural Networks: A Survey

Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer to the model as hyperbolic deep neural network in this paper. Such a hyperbolic neural architecture potentially leads to drastically compact model withmuch more physical interpretability than its counterpart in Euclidean space. To stimulate future research, this paper presents acoherent and comprehensive review of the literature around the neural components in the construction of hyperbolic deep neuralnetworks, as well as the generalization of the leading deep approaches to the Hyperbolic space. It also presents current applicationsaround various machine learning tasks on several publicly available datasets, together with insightful observations and identifying openquestions and promising future directions

Relative gradient optimization of the Jacobian term in unsupervised deep learning

Peer reviewe

Masked Autoregressive Flow for Density Estimation

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.Comment: section 4.3 is corrected since the previous versio