Algorithm-Dependent Generalization Bounds for Overparameterized Deep Residual Networks
This provides a theoretical explanation for the improved generalization in residual networks, which is incremental but addresses a key bottleneck in deep learning theory.
The authors tackled the theoretical understanding of why deep residual networks generalize better than non-residual ones, showing that gradient descent on overparameterized residual networks leads to a small generalization gap and test error with only logarithmic overparameterization in depth.
The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased training stability and generalization performance with this architecture, although there has been limited theoretical understanding for this improvement. In this work, we analyze overparameterized deep residual networks trained by gradient descent following random initialization, and demonstrate that (i) the class of networks learned by gradient descent constitutes a small subset of the entire neural network function class, and (ii) this subclass of networks is sufficiently large to guarantee small training error. By showing (i) we are able to demonstrate that deep residual networks trained with gradient descent have a small generalization gap between training and test error, and together with (ii) this guarantees that the test error will be small. Our optimization and generalization guarantees require overparameterization that is only logarithmic in the depth of the network, while all known generalization bounds for deep non-residual networks have overparameterization requirements that are at least polynomial in the depth. This provides an explanation for why residual networks are preferable to non-residual ones.