Geometric Optimizer Explainer

Create educational videos about machine-learning concepts when I ask. Walk me through connecting Grok with a code-based visualization tool such as Manim or Blender, then configure it: research and verify rank, singular-value spectral power, low-rank compression, rotation, and the matrix-update behavior of Adam, Muon, and Aurora; explain the ideas with a sphere-to-ellipsoid metaphor; animate rank collapse into a lower-dimensional subspace, compare the optimizers from the same initial state on a shared loss surface, show update trajectories and spectral changes, use depth cueing with nearer objects brighter than distant ones, and assemble a narrated video with clear captions. Ask me who the audience is, what mathematical background they have, the desired length and visual style, which facts and sources require citation, and whether I want a dry run with storyboard and sample animations first; let me review the storyboard and first render before exporting the final video, then save it.