On Fast Dropout and its Applicability to Recurrent Networks
Authors: Justin Bayer, Christian Osendorfer, Sebastian Urban, Nutan Chen, Daniela Korhammer, Patrick van der Smagt
ICLR 2014

Abstract: Recurrent Neural Networks (RNNs) are rich models for the processing of sequential data. Recent work on advancing the state of the art has been focused on the optimization or modelling of RNNs, mostly motivated by adressing the problems of the vanishing and exploding gradients.
The control of overfitting has seen considerably less attention.
This paper contributes to that by analyzing fast dropout, a recent regularization method for generalized linear models and neural networks from a back-propagation inspired perspective. We show that fast dropout implements a quadratic form of an adaptive, per-parameter regularizer, which rewards large weights in the light of underfitting, penalizes them for overconfident predictions and vanishes at minima of an unregularized training loss. One consequence of this is the absense of a global weight attractor, which is particularly appealing for RNNs, since the dynamics are not biased towards a certain regime. We positively test the hypothesis that this improves the performance of RNNs on four musical data sets and a natural language processing (NLP) task, on which we achieve state of the art results.


Peer review:
[Review]:
Overall interesting paper. I just have some reservation about your claim that:

'[...] RNN-NADE (Boulanger-Lewandowski et al., 2013), makes speciﬁc assumptions about the data (i.e. binary observables). RNNs do not attach any assumptions to the inputs.'

The RNN-RBM/RNN-NADE actually function equally well with real-valued inputs and outputs by using Gaussian RBMs or RNADE, as was done with motion capture data in the original RNN-RBM paper (ICML 2012). In fact, your paper assumes binary variables following the Bernoulli distribution (first equation of section 3.1.1) which, if anything, makes stronger assumptions about the data.