Phase Transitions
2 long-form posts on Phase Transitions: machine-learning research by Taha Bouhsine, each built around live, in-browser interactive visualizations.
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The Three States of Information, in JAX
A runnable companion to The Three States of Information: train tiny models in JAX and measure the three states directly: the feature-covariance spectrum collapsing from high-rank (random) to a C−1-mode frame (structured), the distributional simplicity bias that fits low-order structure first (organized), the neural-collapse simplex where class-mean cosines lock onto −1/(C−1), and the alignment/uniformity split of contrastive learning running on two separate clocks. Four live JAX visualizations, every number an eigenvalue or a loss.
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The Three States of Information
Representations learned by a network pass through three states, like matter: random (high-entropy, no structure), organized (clusters, local order), and structured (a maximally-separated simplex, global order). The transitions between them are exactly the loss plateaus you see when training: the flat stretch is where the representation reorganizes before that reorganization shows up in the loss. Built from live in-browser training runs.