Towards the Optimal Control Perspective of ResNet Training

Jens Püttschneider, Simon Heilig, Asja Fischer, Timm Faulwasser

Keywords: ResNets, optimal control, regularization, network depth

Abstract: We propose a training formulation for ResNets reflecting an optimal control problem that is applicable for standard architectures and general loss functions. We suggest bridging both worlds via penalizing intermediate outputs of hidden states corresponding to stage cost terms in optimal control. For standard ResNets, we obtain intermediate outputs by propagating the state through the subsequent skip connections and the output layer. We demonstrate that our training dynamic biases the weights of the unnecessary deeper residual layers to vanish. This indicates the potential for a theory-grounded layer pruning strategy.

Student Paper: Yes

Submission Number: 75