An analysis of training and generalization errors in shallow and deep networks

Understand

This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data.

• In this paper, we analyze this phenomenon in the case of regression problems when each unit evaluates a periodic activation function.
• We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure.
• Instead, we measure the generalization error in the sense of maximum loss, and sometimes, as a pointwise error.