Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders
arXiv:1901.06033
Abstract
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidean counterpart, and can qualitatively and quantitatively better recover hierarchical structures.
arXiv commentAdvances in Neural Information Processing Systems
References in corpus (9)
- Auto-Encoding Variational Bayes
- Stochastic Backpropagation and Approximate Inference in Deep Generative Models
- Hierarchical structure and the prediction of missing links in networks
- Variational Graph Auto-Encoders
- Poincaré GloVe: Hyperbolic Word Embeddings
- Implicit Reparameterization Gradients
- Hyperspherical Variational Auto-Encoders
- Diffusion Variational Autoencoders
- Poincaré Wasserstein Autoencoder
Cited by in corpus (28)
- Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder
- Normalizing Flows on Tori and Spheres
- Constant Curvature Graph Convolutional Networks
- Riemannian Continuous Normalizing Flows
- Probing BERT in Hyperbolic Spaces
- The Power Spherical distribution
- Latent Variable Modelling with Hyperbolic Normalizing Flows
- Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels
- Variational Autoencoders with Riemannian Brownian Motion Priors
- Fine-Grain Few-Shot Vision via Domain Knowledge as Hyperspherical Priors
- Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs
- Manifolds for Unsupervised Visual Anomaly Detection
- Mix Dimension in Poincaré Geometry for 3D Skeleton-based Action Recognition
- APo-VAE: Text Generation in Hyperbolic Space
- Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
- Convergence Analysis of Riemannian Stochastic Approximation Schemes
- Variational Autoencoder with Learned Latent Structure
- Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations
- Hyperbolic Generative Adversarial Network
- Unsupervised Embedding of Hierarchical Structure in Euclidean Space
- Hyperbolic Neural Networks++
- Causal Future Prediction in a Minkowski Space-Time
- Exponential-wrapped distributions on symmetric spaces
- Amortised Learning by Wake-Sleep
- Siamese networks for Poincaré embeddings and the reconstruction of evolutionary trees
- What Remains of Visual Semantic Embeddings
- Understanding in Artificial Intelligence
- Continuous normalizing flows on manifolds