Visualizing Higher Dimensions

<p>This blog has offered some recent musings on the dynamics of high dimensions, particularly those aspects related to the loss manifold of a neural network, which in modern practice have begun to be implemented with parameterizations in the billions. The descriptive evaluation of most high dimensional geometries is still an open question for mathematicians. In machine learning, navigating the geometry of a loss manifold involves following a path of gradient signal in a series of updating steps known as backpropagation, which only reveals the geometry of a curved 1 dimensional path tracking towards loss manifold minima as opposed to anything in the aggregate. We have thus tried to look elsewhere and reason about meta properties of loss manifold high dimensional geometry that can be inferred independent of fine grained details.</p> <p><a href="https://medium.com/from-the-diaries-of-john-henry/visualizing-higher-dimensions-3b3f77af8962"><strong>Website</strong></a></p>