Contrastive Learning
Contrastive learning explained: InfoNCE, SimCLR, SupCon, CLIP, SigLIP, alignment and uniformity, and the geometry they impose, with interactive demos.
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Latent on the Spectrum: Why Cats Sit Closer to Dogs Than to Cars
A label-similarity kernel can be turned into a target codebook by spectral embedding: retain its leading eigenmodes, scale by their square roots, and spend a finite dimension budget. Interactive experiments move that designed geometry from a simplex toward a taxonomy, then compare it with the class-mean and within-class spectra measured in trained representations.
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What Makes a Good Latent Space? The Welch Bound and the Simplex
The hidden codebook inside representation learning: why collapse happens, why opposition is a trap, why class means form a simplex, and why the Welch bound sets the best geometry when too many concepts share too few dimensions.
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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.