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@probnstat

One theorem every ML engineer should know: The Johnson–Lindenstrauss Lemma. It states that high-dimensional data can be projected into a much lower-dimensional space while approximately preserving pairwise distances. Why it matters: • Explains why random projections work • Enables scalable learning in high dimensions • Used in embeddings, compressed learning, and ANN search • Helps fight the curse of dimensionality The surprising part: You can reduce dimensions dramatically without destroying the geometry of the data. That’s why many ML systems can operate efficiently even with massive feature spaces. Modern representation learning is deeply connected to this idea: Good embeddings preserve structure while compressing information. In ML, compression is often not loss of intelligence — it’s removal of redundancy.

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