Dropout: A Simple Way to Prevent Neural Networks from Overfitting, Srivastava, Hinton, Krizhevsky, Sutskever, Salakhutdinov; 2014 - Summary
author: DartingMelody
score: 10 / 10

What is the core idea?

The paper introduces a new way to regularize models namely dropout. Dropout is a technique to randomly drop units and their connection with a probability (p) leading to “thinned” models. For testing, a single “unthinned” model with smaller weight (pw) is used which is an approximation of averaging the predictions of all the different “thinned” architectures.

Without and with dropout network

Dropout has the following features:

  1. It prevents overfitting by using different “thinned” architectures.
  2. It approximates to combining various different architectures by sampling from an exponential set of architectures.
  3. It adds noise that allows the optimization process to explore different regions of weight space.
  4. It reduces co-adaptations by making other hidden units unreliable. Therefore, any unit should become self robust in different contexts and does not rely on particular units to rectify their mistakes. This can be seen in the following figure.
  5. The Activation of hidden units become sparse.

Without and with dropout first layer features

How is it realized (technically)?

Dropout is generally applied after the non-linear activation function on a layer which then acts as the input to the next layer. Dropout is realised by the following feed forward equations (* denotes element wise product) :

Training equations

In case of Stochastic Gradient Descent(SGD), in a mini-batch each parameter’s gradient are averaged over the training cases. During test, the weights are scaled as :

\[{W_{test}}^{l} = pW^{l}\]

How well does the paper perform?

The paper rigorously tests dropout on various architectures and diverse datasets ranging from different domains like vision, speech and text. There is significant improvement in generalization and accuracy with dropout in all these cases with state of art in SVHN, ImageNet, CIFAR-100 and MNIST. Even with pre-training, dropout improves generalization with a small learning rate. For scare datasets, dropout outperforms all other models apart from the bayesian model. Dropout restricted boltzmann machine (RBM) also performs better than standard RBM.

The performance of dropout was compared with various regularization methods with the conclusion that dropout combined with max-norm regularization ( \(\left \| W \right \|_{2} \leq c\) ) gives the lowest generalization error. For almost all the models, the default value of p is 0.5 for hidden layers and 0.8 for input layer.

What interesting variants are explored?

The paper discusses the gaussian dropout method which is a variation of Bernoulli dropout where each hidden layer is multiplied by a random variable drawn from \(\\N(1,\sigma ^{2})\) instead of multiplying it by p.

One disadvantage of dropout is it slows down training by a factor of 2x to 3x as each training is trying to train a different architecture. Hence, the tradeoff of accuracy to training time should be taken into consideration.