Understanding the Double Descent Phenomenon in Deep Learning

Combining empirical risk minimization with capacity control is a classical strategy in machine learning when trying to control the generalization gap and avoid overfitting, as the model class capacity gets larger. Yet, in modern deep learning practice, very large over-parameterized models (e.g. neural networks) are optimized to fit perfectly the training data and still obtain great generalization performance. Past the interpolation point, increasing model complexity seems to actually lower the test error. In this tutorial, we explain the concept of double descent and its mechanisms. The first section sets the classical statistical learning framework and introduces the double descent phenomenon. By looking at a number of examples, section 2 introduces inductive biases that appear to have a key role in double descent by selecting, among the multiple interpolating solutions, a smooth empirical risk minimizer. Finally, section 3 explores the double descent with two linear models, and gives other points of view from recent related works.