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]:
This paper is a rather straightforward extension of fast dropout to standard RNNs. Maybe too straightforward, it is not very groundbreakingly novel. However, I like the results, and the application of the method to RNNs is useful to know about for other researchers. The authors remark that a comparison for standard RNNs (rather than LSTMs) with adaptive weight noise is lacking -- why have the authors not tried this comparison I wonder, as it seems highly appropriate in this context and doable in their setup.
There are a few points in the text that should be improved. For example, calling Graves' adaptive weight noise method MCMC is questionable in my view. Also, there are quite a few typos:
abstract: absence -> absence
first paragraph: sensitive initialisations -> sensible initialisations
first paragraph: remove 'so-called'
second paragraph: Contrary -> In contrast
last par of sec 1: reason -> discuss
first par sec 2.2.2: functionc ->function.
sec 2.2.2: 'an subsequently' -> 'and subsequently'
page six, line 11: 'were *** is defined as' -> 'where *** is defined as'