Paper:
Regularizing Deep Neural Networks by Noise: Its Interpretation and Optimization
Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is known as a successful regularizer, but it is still not clear enough why such training techniques work well in practice and how we can maximize their benefit in the presence of two conflicting objectives-optimizing to true data distribution and preventing overfitting by regularization. This paper addresses the above issues by 1) interpreting that the conventional training methods with regularization by noise injection optimize the lower bound of the true objective and 2) proposing a technique to achieve a tighter lower bound using multiple noise samples per training example in a stochastic gradient descent iteration. We demonstrate the effectiveness of our idea in several computer vision applications.

Review:
This paper introduces a method for regularizing deep neural network by noise. The core of the approach is to draw connections between applying a random perturbation to layer activations and the optimization of a lower-bound objective function. Experiments for four visual tasks are carried out, and show a slight improvement of the proposed method compared to dropout.
On the positive side:
- The problem of regularization for training deep neural network is a crucial issue, which has a huge potential practical and theoretical impact.
- The connection between regularization by noise and the derivation of a lower bound of the training objective is appealing to provide a formal understanding of the impact of noise regularization techniques, e.g. dropout.
On the negative side:
- The aforementioned connection between regularization by noise and training objective lower bounding seems to be a straightforward adaptation of [9] in the case of deep neural networks. For the most important result given in Eq (6), i.e. the fact that using several noise sampling operations gives a tighter bound on the objective function than using a single random sampling (as done in dropout), the authors refer to the derivation in [9]. Therefore, the improvement and positioning with respect to ref [9] is not clear to me.
- Beyond this connection, the implementation of the model given in Section 4 for the case of dropout is also straightforward: several (random) forward passes are performed and a weighted average of the resulting gradients is computed using Eq (8), before applying the backward pass.
- Experiments are carried out in various vision tasks, which choice could be better justified. It is not clear why these tasks are highly regularization demanding: the noise seems to be applied in a few (fully connected layers). In addition, the improvement brought out by the proposed method is contrasted across tasks (e.g. small improvement in UCF-101 and below the published baseline for image captioning).
As a conclusion, although the approach is interesting, its novelty level seems to be low and the experiments should be more targeted to better illustrate the benefit of the multiple sampling operations. In their rebuttal, I would like the authors to answer my concern about positioning with respect to [9].