MULTI-LEVEL RESIDUAL NETWORKS FROM DYNAMI- CAL SYSTEMS VIEW
Deep residual networks (ResNets) and their variants are widely used in many computer vision applications and natural language processing tasks. However, the theoretical principles for designing and training ResNets are still not fully understood. Recently, several points of view have emerged to try to interpret ResNet theoretically, such as unraveled view, unrolled iterative estimation and dynamical systems view. In this paper, we adopt the dynamical systems point of view, and analyze the lesioning properties of ResNet both theoretically and experimentally. Based on these analyses, we additionally propose a novel method for accelerating ResNet training. We apply the proposed method to train ResNets and Wide ResNets for three image classification benchmarks, reducing training time by more than 40% with superior or on-par accuracy.
I enjoyed reading the paper. This is a very well written paper, the authors propose a method for speeding up the training time of Residual Networks based on the dynamical system view interpretation of ResNets. In general I have a positive opinion about the paper, however, I’d like to ask for some clarifications.
I’m not fully convinced by the interpretation of Eq. 5: “… d is inversely proportional to the norm of the residual modules G(Yj)”. Since F(Yj) is not a constant, I think that d is inversely proportional to ||G(Yj)||/||F(Yj)||, however, in the interpretation the dependence on ||F(Yj)|| is ignored. Could the authors comment on that?
Section 4. 1 “ Each cycle itself can be regarded as a training process, thus we need to reset the learning rate value at the beginning of each training cycle and anneal the learning rate during that cycle.” Is there any empirical evidence for this? What would happen if the learning rate is not reset at the beginning of each cycle? 
Questions with respect to dynamical systems point of view: Eq. 4 assumes small value of h. However, for ResNet there is no guarantee that the h would be small (e. g. in Appendix C the values between 0.25 and 1 are used). Would the authors be willing to comment on the importance of the value of h? In figure 1, pooling (strided convolutions) are not depicted between network stages. I have one question w.r.t. feature maps dimensionality changes inside a CNN: how does pooling (or strided convolution) fit into dynamical systems view?
Table 3 and 4. I assume that the training time unit is a minute, I couldn’t find this information in the paper. Is the batch size the same for all models (100 for CIFAR and 32 for STL-10)? I understand that the models with different #Blocks have different capacity, for clarity, would it be possible to add # of parameters to each model? For multilevel method, would it be possible to show intermediate results in Table 3 and 4, e. g. at the end of cycle 1 and 2? I see these results in Figure 6, however, the plots are condensed and it is difficult to see the exact number at the end of each cycle. 
The citation (E, 2017) seems to be wrong, could the authors check it?