Princeton Lecture Explains Why Enormous Random Matrices Stop Behaving Randomly

tctjr · x · 2026-07-31

In a lecture at Harvard, Princeton probabilist Ramon van Handel explained the strong convergence phenomenon.

He points out that while weight matrices in AI models start as random numbers, their extreme behaviors—such as the largest eigenvalues and operator norm—stop fluctuating and lock onto a deterministic limit as dimensions grow.

This explains why initialization works, why spectral norms are predictable, and why large networks behave more consistently than smaller ones.

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