We propose a guided dropout regularizer for deep networks based on the evidence of a network prediction: the firing of neurons in specific paths. In this work, we utilize the evidence at each neuron to determine the probability of dropout, rather than dropping out neurons uniformly at random as in standard dropout. In essence, we dropout with higher probability those neurons which contribute more to decision making at training time. This approach penalizes high saliency neurons that are most relevant for model prediction, i.e. those having stronger evidence. By dropping such high-saliency neurons, the network is forced to learn alternative paths in order to maintain loss minimization, resulting in a plasticity-like behavior, a characteristic of human brains too. We demonstrate better generalization ability, an increased utilization of network neurons, and a higher resilience to network compression using several metrics over four image video recognition benchmarks.
Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This paper demonstrates that max-pooling dropout is equivalent to randomly picking activation based on a multinomial distribution at training time. In light of this insight, we advocate employing our proposed probabilistic weighted pooling, instead of commonly used max-pooling, to act as model averaging at test time. Empirical evidence validates the superiority of probabilistic weighted pooling. We also empirically show that the effect of convolutional dropout is not trivial, despite the dramatically reduced possibility of over-fitting due to the convolutional architecture. Elaborately designing dropout training simultaneously in max-pooling and fully-connected layers, we achieve state-of-the-art performance on MNIST, and very competitive results on CIFAR-10 and CIFAR-100, relative to other approaches without data augmentation. Finally, we compare max-pooling dropout and stochastic pooling, both of which introduce stochasticity based on multinomial distributions at pooling stage. Preventing feature co-adaptation by encouraging independent contributions from different features often improves classification and regression performance. Dropout training (, 2012) does this by randomly dropping out (zeroing) hidden units and input features during training of neural networks. However, repeatedly sampling a random subset of input features makes training much slower. Based on an examination of the implied objective function of dropout training, we show how to do fast dropout training by sampling from or integrating a Gaussian approximation, instead of doing Monte Carlo optimization of this objective. This approximation, justified by the central limit theorem and empirical evidence, gives an order of magnitude speedup and more stability. We show how to do fast dropout training for classification, regression, and multilayer neural networks. Beyond dropout, our technique is extended to integrate out other types of noise and small image transformations. Recently, it was shown that deep neural networks can perform very well if the activities of hidden units are regularized during learning, e.g, by randomly dropping out 50 of their activities. We describe a method called 'standout' in which a binary belief network is overlaid on a neural network and is used to regularize of its hidden units by selectively setting activities to zero. This 'adaptive dropout network' can be trained jointly with the neural network by approximately computing local expectations of binary dropout variables, computing derivatives using back-propagation, and using stochastic gradient descent. Interestingly, experiments show that the learnt dropout network parameters recapitulate the neural network parameters, suggesting that a good dropout network regularizes activities according to magnitude. When evaluated on the MNIST and NORB datasets, we found that our method achieves lower classification error rates than other feature learning methods, including standard dropout, denoising auto-encoders, and restricted Boltzmann machines. For example, our method achieves 0.80 and 5.8 errors on the MNIST and NORB test sets, which is better than state-of-the-art results obtained using feature learning methods, including those that use convolutional architectures. Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptimal for the sake of convergence. In this paper, we propose to use multinomial sampling for dropout, i.e., sampling features or neurons according to a multinomial distribution with different probabilities for different features neurons. To exhibit the optimal dropout probabilities, we analyze the shallow learning with multinomial dropout and establish the risk bound for stochastic optimization. By minimizing a sampling dependent factor in the risk bound, we obtain a distribution-dependent dropout with sampling probabilities dependent on the second order statistics of the data distribution. To tackle the issue of evolving distribution of neurons in deep learning, we propose an efficient adaptive dropout (named ) that computes the sampling probabilities on-the-fly from a mini-batch of examples. Empirical studies on several benchmark datasets demonstrate that the proposed dropouts achieve not only much faster convergence and but also a smaller testing error than the standard dropout. For example, on the CIFAR-100 data, the evolutional dropout achieves relative improvements over 10 on the prediction performance and over 50 on the convergence speed compared to the standard dropout.