Riemannian Manifold

no idea what this is

https://medium.com/intuition/what-the-heck-is-a-manifold-60b8750e9690

• ML manifold ≈ smooth, low-dimensional subset of high-D space
• Riemannian manifold = same thing with geometry (lengths, curvature, geodesics) explicitly defined

Terminology popularized to me by Kyle Vedder.

A manifold is a low-dimensional surface embedded in a higher-dimensional space. In ML, we often say that high-dimensional data (like images) lies on a low-dimensional manifold.

Think: although an image has 1000s of pixels, the actual set of realistic images lives on a much smaller subspace.

Examples

• “Even though these images are 64x64, they really lie on a lower-dimensional manifold — maybe just 100 dimensions.”
• “The generative model learns to map random noise onto the data manifold.”