  Conventional research attributes the improvements of generalization ability
of deep neural networks either to powerful optimizers or the new network
design. Different from them, in this paper, we aim to link the generalization
ability of a deep network to optimizing a new objective function. To this end,
we propose a \textit{nonlinear collaborative scheme} for deep network training,
with the key technique as combining different loss functions in a nonlinear
manner. We find that after adaptively tuning the weights of different loss
functions, the proposed objective function can efficiently guide the
optimization process. What is more, we demonstrate that, from the mathematical
perspective, the nonlinear collaborative scheme can lead to (i) smaller KL
divergence with respect to optimal solutions; (ii) data-driven stochastic
gradient descent; (iii) tighter PAC-Bayes bound. We also prove that its
advantage can be strengthened by nonlinearity increasing. To some extent, we
bridge the gap between learning (i.e., minimizing the new objective function)
and generalization (i.e., minimizing a PAC-Bayes bound) in the new scheme. We
also interpret our findings through the experiments on Residual Networks and
DenseNet, showing that our new scheme performs superior to single-loss and
multi-loss schemes no matter with randomization or not.
