Chart Auto-Encoders for Manifold Structured Data

Understand

Deep generative models have made tremendous advances in image and signal representation learning and generation.

• These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often too simplistic to meaningfully reflect the manifold structure of the data.
• In this work, we advocate the use of a multi-chart latent space for better data representation.
• Inspired by differential geometry, we propose a \textbf{Chart Auto-Encoder (CAE)} and prove a universal approximation theorem on its representation capability.