Autoencoder

Deep learning

Euclidean space

Mathematics

Hyperbolic space

Algorithm

Mathematical optimization

Euclidean geometry

Epistemology

Submanifold

Mathematical analysis

Philosophy

Artificial intelligence

Hyperbolic geometry

Differential geometry

Curvature

Geometry

Computer science

Simple (philosophy)

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value.

Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks