Embeddings
Embedding geometry: the modality gap, simplex codebooks, the Welch bound, and what trained features spend their dimensions on.
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Auditing Latent Space Geometry in JAX
A runnable companion to the Welch-bound latent-space post: generate GIFs and implement the JAX metrics that tell you whether embeddings are collapsing, wasting rank, forming a simplex, or pressing against the Welch floor.
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Organizing Randomness: Contrastive Learning in JAX
A block-by-block JAX + Optax implementation of six contrastive losses, each watched as a real animated GIF turning random 2D points into organized embeddings. The runnable companion to "Untangling the Moons."
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Untangling the Moons: A Visual History of Contrastive Learning
Eight contrastive losses, twenty years of history, and one geometric audit. Watch the losses organize the same 2D points while separating opposition, orthogonality, simplex packing, and statistical independence.