Computing the Testing Error Without a Testing Set

X = x i ,y i n i=1 TRAINING DATA Z = x i ,y i m i=n+1 iteration iteration (a) (b) λ, µ g(λ, µ) λ * ,µ * (λ k ,µ k , ∆ ρk ) ρtest = ρ train -∆ρ ∆ρ Figure 1: (a) We compute the test performance 1 of any Deep Neural Network (DNN) on any computer vision problem using no testing samples (top); neither labelled nor unlabelled samples are necessary. This in sharp contrast to the classical computer vision approach, where model performance is calculated using a curated test dataset (bottom). (b) The persistent algebraic topological summary (λ * , µ * ) given by our algorithm (x-axis) against the performance gap ∆ρ between training and testing performance (y-axis).