Data-Copying in Generative Models: A Formal Framework

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying" was proposed by Meehan et. al (2020) . We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect datacopying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection. no no no no no c = 5 no no no no yes c = 10 no no no no yes c = 20 no no no yes yes Table 2. Statistical Significance of data-copying Rates over Halfmoons Algo q = p ρ = 0.1 0.2 0.3 0.4 Ours no yes yes yes yes c = 1 no no no no no c = 5 no no no no yes c = 10 no no no no yes c = 20 no no no yes yes A.3. Further Experimental Details We begin by reviewing the definitions of p and q. p is the Halfmoons dataset with Gaussian noise (σ = 0.1). To define q, we have a mixture of two distributions, q copy and q underf it , which are defined as follows.