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1. A non-parametric test to detect data-copying in generative models

   Meehan, C.; Chaudhuri, K.; Dasgupta, S. (July 2020, International Conference on Artificial Intelligence and Statistics)

   Detecting overfitting in generative models is an important challenge in machine learning. In this work, we formalize a form of overfitting that we call data-copying – where the gener- ative model memorizes and outputs training samples or small variations thereof. We pro- vide a three sample non-parametric test for detecting data-copying that uses the training set, a separate sample from the target dis- tribution, and a generated sample from the model, and study the performance of our test on several canonical models and datasets. 

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2. Data-Copying in Generative Models: A Formal Framework

   Bhattacharjee, Robi; Dasgupta, Sanjoy; Chaudhuri, Kamalika (July 2023, Proceedings of Machine Learning Research)

   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 data-copying, 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. 

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3. An empirical study on evaluation metrics of generative adversarial networks

   Xu, Q; Huang, G; Yan, Y; Guo, C; Sun, Y; Wu, F; Weinberger, K (April 2018, arXiv.org)

   Evaluating generative adversarial networks (GANs) is inherently challenging. In this paper, we revisit several representative sample-based evaluation metrics for GANs, and address the problem of how to evaluate the evaluation metrics. We start with a few necessary conditions for metrics to produce meaningful scores, such as distinguishing real from generated samples, identifying mode dropping and mode collapsing, and detecting overfitting. With a series of carefully designed experiments, we comprehensively investigate existing sample-based metrics and identify their strengths and limitations in practical settings. Based on these results, we observe that kernel Maximum Mean Discrepancy (MMD) and the 1-Nearest- Neighbor (1-NN) two-sample test seem to satisfy most of the desirable properties, provided that the distances between samples are computed in a suitable feature space. Our experiments also unveil interesting properties about the behavior of several popular GAN models, such as whether they are memorizing training samples, and how far they are from learning the target distribution. 

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4. Benign overfitting in leaky ReLU networks with moderate input dimension

   Karhadkar, Kedar; George, Erin; Murray, Michael; Montufar, Guido; Needell, Deanna (September 2024, 38th Conference on Neural Information Processing Systems (NeurIPS 2024))

   The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two- layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data that can be decomposed into the sum of a common signal and a random noise component, that lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign (or harmful) overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non- benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension d and training sample size n, while results in prior work require d= !(n2 log n), here we require only d= ! (n). 

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5. Benign overfitting in leaky ReLU networks with moderate input dimension

   Karhadkar, Kedar; George, Erin; Murray, Michael; Montufar, Guido; Needell, Deanna (September 2024, 38th Conference on Neural Information Processing Systems (NeurIPS 2024))

   The problem of benign overfitting asks whether it is possible for a model to perfectly fit noisy training data and still generalize well. We study benign overfitting in two- layer leaky ReLU networks trained with the hinge loss on a binary classification task. We consider input data that can be decomposed into the sum of a common signal and a random noise component, that lie on subspaces orthogonal to one another. We characterize conditions on the signal to noise ratio (SNR) of the model parameters giving rise to benign versus non-benign (or harmful) overfitting: in particular, if the SNR is high then benign overfitting occurs, conversely if the SNR is low then harmful overfitting occurs. We attribute both benign and non- benign overfitting to an approximate margin maximization property and show that leaky ReLU networks trained on hinge loss with gradient descent (GD) satisfy this property. In contrast to prior work we do not require the training data to be nearly orthogonal. Notably, for input dimension d and training sample size n, while results in prior work require d= !(n2 log n), here we require only d= ! (n). 

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