Triple descent and the two kinds of overfitting: Where & why do they appear?

Conference on Neural Information Processing Systems (NeurIPS)


A recent line of research has highlighted the existence of a “double descent” phenomenon in deep learning, whereby increasing the number of training examples N causes the generalization error of neural networks to peak when N is of the same order as the number of parameters P. In earlier works, a similar phenomenon was shown to exist in simpler models such as linear regression, where the peak instead occurs when N is equal to the input dimension D. Since both peaks coincide with the interpolation threshold, they are often conflated in the literature. In this paper, we show that despite their apparent similarity, these two scenarios are inherently different. In fact, both peaks can co-exist when neural networks are applied to noisy regression tasks. The relative size of the peaks is then governed by the degree of nonlinearity of the activation function. Building on recent developments in the analysis of random feature models, we provide a theoretical ground for this sample-wise triple descent. As shown previously, the nonlinear peak at N = P is a true divergence caused by the extreme sensitivity of the output function to both the noise corrupting the labels and the initialization of the random features (or the weights in neural networks). This peak survives in the absence of noise, but can be suppressed by regularization. In contrast, the linear peak at N = D is solely due to overfitting the noise in the labels, and forms earlier during training. We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization. Throughout the paper, we compare analytical results obtained in the random feature model with the outcomes of numerical experiments involving deep neural networks.

Related Publications

All Publications

COLING - December 8, 2020

Best Practices for Data-Efficient Modeling in NLG: How to Train Production-Ready Neural Models with Less Data

Ankit Arun, Soumya Batra, Vikas Bhardwaj, Ashwini Challa, Pinar Donmez, Peyman Heidari, Hakan Inan, Shashank Jain, Anuj Kumar, Shawn Mei, Karthik Mohan, Michael White

NeurIPS - November 30, 2020

Adversarial Attacks on Linear Contextual Bandits

Evrard Garcelon, Baptiste Roziere, Laurent Meunier, Jean Tarbouriech, Olivier Teytaud, Alessandro Lazaric, Matteo Pirotta

NeurIPS - December 7, 2020

Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees

Shali Jiang, Daniel Jiang, Max Balandat, Brian Karrer, Jacob R. Gardner, Roman Garnett

ICPR - December 1, 2020

Ultrasound for gaze estimation

Andre Golard, Sachin Talathi

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy