Maxout Networks (original) (raw)
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Dropout: A Simple Way to Prevent Neural Networks from Overfitting
Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem.
Improving the Capacity of Very Deep Networks with Maxout Units
2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2018
Deep neural networks inherently have large representational power for approximating complex target functions. However, models based on rectified linear units can suffer reduction in representation capacity due to dead units. Moreover, approximating very deep networks trained with dropout at test time can be more inexact due to the several layers of nonlinearities. To address the aforementioned problems, we propose to learn the activation functions of hidden units for very deep networks via maxout. However, maxout units increase the model parameters, and therefore model may suffer from overfitting; we alleviate this problem by employing elastic net regularization. In this paper, we propose very deep networks with maxout units and elastic net regularization and show that the features learned are quite linearly separable. We perform extensive experiments and reach state-of-the-art results on the USPS and MNIST datasets. Particularly, we reach an error rate of 2.19% on the USPS dataset, surpassing the human performance error rate of 2.5% and all previously reported results, including those that employed training data augmentation. On the MNIST dataset, we reach an error rate of 0.36% which is competitive with the state-of-the-art results.
Adaptive dropout for training deep neural networks
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.
On Dropout, Overfitting, and Interaction Effects in Deep Neural Networks
ArXiv, 2020
We examine Dropout through the perspective of interactions: learned effects that combine multiple input variables. Given NNN variables, there are O(N2)O(N^2)O(N2) possible pairwise interactions, O(N3)O(N^3)O(N3) possible 3-way interactions, etc. We show that Dropout implicitly sets a learning rate for interaction effects that decays exponentially with the size of the interaction, corresponding to a regularizer that balances against the hypothesis space which grows exponentially with number of variables in the interaction. This understanding of Dropout has implications for the optimal Dropout rate: higher Dropout rates should be used when we need stronger regularization against spurious high-order interactions. This perspective also issues caution against using Dropout to measure term saliency because Dropout regularizes against terms for high-order interactions. Finally, this view of Dropout as a regularizer of interaction effects provides insight into the varying effectiveness of Dropout for diffe...
Deep Maxout Networks Applied to Noise-Robust Speech Recognition
Lecture Notes in Computer Science, 2014
Deep Neural Networks (DNN) have become very popular for acoustic modeling due to the improvements found over traditional Gaussian Mixture Models (GMM). However, not many works have addressed the robustness of these systems under noisy conditions. Recently, the machine learning community has proposed new methods to improve the accuracy of DNNs by using techniques such as dropout and maxout. In this paper, we investigate Deep Maxout Networks (DMN) for acoustic modeling in a noisy automatic speech recognition environment. Experiments show that DMNs improve substantially the recognition accuracy over DNNs and other traditional techniques in both clean and noisy conditions on the TIMIT dataset.
Max-min convolutional neural networks for image classification
2016 IEEE International Conference on Image Processing (ICIP), 2016
Convolutional neural networks (CNN) are widely used in computer vision, especially in image classification. However, the way in which information and invariance properties are encoded through in deep CNN architectures is still an open question. In this paper, we propose to modify the standard convo- lutional block of CNN in order to transfer more information layer after layer while keeping some invariance within the net- work. Our main idea is to exploit both positive and negative high scores obtained in the convolution maps. This behav- ior is obtained by modifying the traditional activation func- tion step before pooling. We are doubling the maps with spe- cific activations functions, called MaxMin strategy, in order to achieve our pipeline. Extensive experiments on two classical datasets, MNIST and CIFAR-10, show that our deep MaxMin convolutional net outperforms standard CNN.
An empirical analysis of dropout in piecewise linear networks
The recently introduced dropout training criterion for neural networks has been the subject of much attention due to its simplicity and remarkable effectiveness as a regularizer, as well as its interpretation as a training procedure for an exponentially large ensemble of networks that share parameters. In this work we empirically investigate several questions related to the efficacy of dropout, specifically as it concerns networks employing the popular rectified linear activation function. We investigate the quality of the test time weight-scaling inference procedure by evaluating the geometric average exactly in small models, as well as compare the performance of the geometric mean to the arithmetic mean more commonly employed by ensemble techniques. We explore the effect of tied weights on the ensemble interpretation by training ensembles of masked networks without tied weights. Finally, we investigate an alternative criterion based on a biased estimator of the maximum likelihood ensemble gradient.
Deterministic dropout for deep neural networks using composite random forest
Pattern Recognition Letters, 2020
Dropout prevents overfitting in deep neural networks. Typical strategy of dropout involves random termination of connections irrespective of their importance. Termination blocks the propagation of class discriminative information across the network. As a result, dropout may lead to inferior performance. We propose a deterministic dropout where only unimportant connections are dropped ensuring propagation of class discriminative information. We identify the unimportant connections using a novel composite random forest, integrated into the network. We prove that better generalization is achieved by terminating these unimportant connections. The proposed algorithm is useful in preventing overfitting in noisy datasets. The proposal is equally good for datasets with smaller number of training examples. Experiments on several benchmark datasets show up to 8% improvement in classification accuracy.
2019 International Conference on Document Analysis and Recognition (ICDAR), 2019
Global pooling layers are an essential part of Convolutional Neural Networks (CNN). They are used to aggregate activations of spatial locations to produce a fixed-size vector in several state-of-the-art CNNs. Global average pooling or global max pooling are commonly used for converting convolutional features of variable size images to a fix-sized embedding. However, both pooling layer types are computed spatially independent: each individual activation map is pooled and thus activations of different locations are pooled together. In contrast, we propose Deep Generalized Max Pooling that balances the contribution of all activations of a spatially coherent region by re-weighting all descriptors so that the impact of frequent and rare ones is equalized. We show that this layer is superior to both average and max pooling on the classification of Latin medieval manuscripts (CLAMM'16, CLAMM'17), as well as writer identification (Historical-WI'17).