5,337
edits
Deep Learning: Difference between revisions
→Other heuristic/emperical defenses
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;Lemma (Lerg & Pellegrino 1951) | ;Lemma (Lerg & Pellegrino 1951) | ||
Consider a subset <math>A \subset S^{d-1}</math> | Consider a subset <math>A \subset S^{d-1} \subset \mathbb{R}^n</math> with normalized measure <math>\mu_1(A) \geq 1/2</math>. | ||
When using the geodesic metric, the <math>\epsilon</math>-expansion <math>A(\epsilon)</math> is at least as large as the <math>\epsilon</math>-expansion of a half sphere. | |||
;Lemma (Milman & Schechtman 1986) | ;Lemma (Milman & Schechtman 1986) | ||