VC Theoretical Explanation of Double Descent

There has been growing interest in generalization performance of large multilayer neural networks that can be trained to achieve zero training error, while generalizing well on test data. This regime is known as'second descent' and it appears to contradict the conventional view that optimal model complexity should reflect an optimal balance between underfitting and overfitting, i.e., the bias-variance trade-off. This paper presents a VC-theoretical analysis of double descent and shows that it can be fully explained by classical VC-generalization bounds. We illustrate an application of analytic VC-bounds for modeling double descent for classification, using empirical results for several learning methods, such as SVM, Least Squares, and Multilayer Perceptron classifiers. In addition, we discuss several reasons for the misinterpretation of VC-theoretical results in Deep Learning community. There have been many recent successful applications of Deep Learning (DL). However, at present, various DL methods are driven mainly by heuristic improvements, while theoretical and conceptual understanding of this technology remains limited. For example, large neural networks can be trained to fit available data (achieving zero training error) and still achieve good generalization for test data. This contradicts the conventional statistical wisdom that overfitting leads to poor generalization. This phenomenon has been systematically described by Belkin et al. (2019) who introduced the term'double descent' and pointed out the difference between the classical regime (first descent) and the modern one (second descent).