论文阅读笔记（五十五）：Self-Normalizing Neural Networks

Abstract
Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are “scaled exponential linear units” (SELUs), which induce self-normalizing properties. Using the Banach fixed-point theorem, we prove that activations close to zero mean and unit variance that are propagated through many network layers will converge towards zero mean and unit variance — even under the presence of noise and perturbations. This convergence property of SNNs allows to (1) train deep networks with many layers, (2) employ strong regularization schemes, and (3) to make learning highly robust. Furthermore, for activations not close to unit variance, we prove an upper and lower bound on the variance, thus, vanishing and exploding gradients are impossible. We compared SNNs on (a) 121 tasks from the UCI machine learning repository, on (b) drug discovery benchmarks, and on (c) astronomy tasks with standard FNNs, and other machine learning methods such as random forests and support vector machines. For FNNs we considered (i) ReLU networks without normalization, (ii) batch normalization, (iii) layer normalization, (iv) weight normalization, (v) highway networks, and (vi) residual networks. SNNs significantly outperformed all competing FNN methods at 121 UCI tasks, outperformed all competing methods at the Tox21 dataset, and set a new record at an astronomy data set. The winning SNN architectures are often very deep. Implementations are available at: github.com/bioinf-jku/SNNs.

Introduction
Deep Learning has set new records at different benchmarks and led to various commercial applications [25, 33]. Recurrent neural networks (RNNs) [18] achieved new levels at speech and natural language processing, for example at the TIMIT benchmark [12] or at language translation [36], and are already employed in mobile devices [31]. RNNs have won handwriting recognition challenges (Chinese and Arabic handwriting) [33, 13, 6] and Kaggle challenges, such as the “Grasp-and Lift EEG” competition. Their counterparts, convolutional neural networks (CNNs) [24] excel at vision and video tasks. CNNs are on par with human dermatologists at the visual detection of skin cancer [9]. The visual processing for self-driving cars is based on CNNs [19], as is the visual input to AlphaGo which has beaten one of the best human GO players [34]. At vision challenges, CNNs are constantly winning, for example at the large ImageNet competition [23, 16], but also almost all Kaggle vision challenges, such as the “Diabetic Retinopathy” and the “Right Whale” challenges [8, 14].

However, looking at Kaggle challenges that are not related to vision or sequential tasks, gradient boosting, random forests, or support vector machines (SVMs) are winning most of the competitions. Deep Learning is notably absent, and for the few cases where FNNs won, they are shallow. For example, the HIGGS challenge, the Merck Molecular Activity challenge, and the Tox21 Data challenge were all won by FNNs with at most four hidden layers. Surprisingly, it is hard to find success stories with FNNs that have many hidden layers, though they would allow for different levels of abstract representations of the input [3].

To robustly train very deep CNNs, batch normalization evolved into a standard to normalize neuron activations to zero mean and unit variance [20]. Layer normalization [2] also ensures zero mean and unit variance, while weight normalization [32] ensures zero mean and unit variance if in the previous layer the activations have zero mean and unit variance.

However, training with normalization techniques is perturbed by stochastic gradient descent (SGD), stochastic regularization (like dropout), and the estimation of the normalization parameters. Both RNNs and CNNs can stabilize learning via weight sharing, therefore they are less prone to these perturbations. In contrast, FNNs trained with normalization techniques suffer from these perturbations and have high variance in the training error (see Figure 1). This high variance hinders learning and slows it down.

Furthermore, strong regularization, such as dropout, is not possible as it would further increase the variance which in turn would lead to divergence of the learning process. We believe that this sensitivity to perturbations is the reason that FNNs are less successful than RNNs and CNNs.

Self-normalizing neural networks (SNNs) are robust to perturbations and do not have high variance in their training errors (see Figure 1). SNNs push neuron activations to zero mean and unit variance thereby leading to the same effect as batch normalization, which enables to robustly learn many layers. SNNs are based on scaled exponential linear units “SELUs” which induce self-normalizing properties like variance stabilization which in turn avoids exploding and vanishing gradients.

Conclusion
We have introduced self-normalizing neural networks for which we have proved that neuron activations are pushed towards zero mean and unit variance when propagated through the network. Additionally, for activations not close to unit variance, we have proved an upper and lower bound on the variance mapping. Consequently, SNNs do not face vanishing and exploding gradient problems. Therefore, SNNs work well for architectures with many layers, allowed us to introduce a novel regularization scheme, and learn very robustly. On 121 UCI benchmark datasets, SNNs have outperformed other FNNs with and without normalization techniques, such as batch, layer, and weight normalization, or specialized architectures, such as Highway or Residual networks. SNNs also yielded the best results on drug discovery and astronomy tasks. The best performing SNN architectures are typically very deep in contrast to other FNNs.