Before revision:  In a nutshell, partially ordered relation is introduced to the basic components of each layer in the model , namely neurons in dense layers and channels in convolutional layers . Specifically, if one component participates in the forward pass , then all of its preceding components are also activated. Dynamically trained under such structural constraint, we can slice a narrower sub-model during inference whose run-time memory and computational operation consumption is roughly quadratic to the width controlled by a single parameter slice rate.
After revision:  In a nutshell, partially ordered relation is introduced to the basic components of each layer in the model , namely neurons in dense layers and channels in convolutional layers ), and then partially ordered relation is introduced to these groups by enforcing that groups participated in each forward pass always starts from the first group to the dynamically-determined rightmost group. Trained by dynamically indexing the rightmost group with a single parameter slice rate, the network is engendered to build up group-wise and residual representation. Then during inference, a sub-model during inference whose run-time memory and computational operation consumption is roughly quadratic to the width controlled by a single parameter slice rate.