High-dimensional Gaussian samples live on a thin shell, not at the peak
CatAstro_Piyush · x · 2026-07-22
A visualization of a high-dimensional Gaussian illustrates a classic intuition trap: the densest point is not where most samples live.
- In high dimensions, probability mass concentrates in a thin shell around radius \(\sqrt{d}\), not near the origin.
- The mode has the highest density, but typical samples lie far away on that shell.
- The post says this has repeatedly surprised the author, prompting the visualization.
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