The conditionLD (w)≤ Eϵi∼N (0,ρ)[LD (w +ϵ)] means that adding Gaussian perturbation should not decrease the test error

F or anyρ >0, any distribution D, with probability 1−δ over the choice of the training setS∼ D, LD (w)≤ max ∥ϵ∥2≤ρ LS (w +ϵ) + √ k log ( 1 +∥w∥2 2 ρ2 ( 1 + √ log(n) k )2) + 4 log n δ + ˜O(1) n− 1 (4) wheren =|S|,k is the number of p · 2020