Regularization in the optimization of deep neural networks is often critical to avoid undesirable over-fitting leading to better generalization of model. One of the most popular regularization algorithms is to impose @math penalty on the model parameters resulting in the decay of parameters, called weight-decay, and the decay rate is generally constant to all the model parameters in the course of optimization. In contrast to the previous approach based on the constant rate of weight-decay, we propose to consider the residual that measures dissimilarity between the current state of model and observations in the determination of the weight-decay for each parameter in an adaptive way, called adaptive weight-decay (AdaDecay) where the gradient norms are normalized within each layer and the degree of regularization for each parameter is determined in proportional to the magnitude of its gradient using the sigmoid function. We empirically demonstrate the effectiveness of AdaDecay in comparison to the state-of-the-art optimization algorithms using popular benchmark datasets: MNIST, Fashion-MNIST, and CIFAR-10 with conventional neural network models ranging from shallow to deep. The quantitative evaluation of our proposed algorithm indicates that AdaDecay improves generalization leading to better accuracy across all the datasets and models.
Dropout is another regularization technique that is in particular used with classical shallow networks. The dropout zeros the activation of randomly selected nodes with a certain probability during the training process @cite_50 . The dropping rate is generally set to be constant but its variants have been considered with adaptive rates depending on parameter value @cite_4 , estimated gradient variance @cite_13 , biased gradient estimator @cite_35 , layer depth @cite_26 , or marginal likelihood over noises @cite_47 . However, in fact, recent deep models do not support the dropout and its variants. The reason may be that the number of parameters in a layer is relatively smaller than the the classic neural networks, and random masking to nodes can be erroneous to the model.
@cite_35 @cite_26 @cite_4 @cite_50 @cite_47 @cite_13
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Deep neural networks often work well when they are over-parameterized and trained with a massive amount of noise and regularization, such as weight decay and dropout. Although dropout is widely used as a regularization technique for fully connected layers, it is often less effective for convolutional layers. This lack of success of dropout for convolutional layers is perhaps due to the fact that neurons in a contiguous region in convolutional layers are strongly correlated so information can still flow through convolutional networks despite dropout. Thus a structured form of dropout is needed to regularize convolutional networks. In this paper, we introduce DropBlock, a form of structured dropout, where neurons in a contiguous region of a feature map are dropped together. Extensive experiments show that DropBlock works much better than dropout in regularizing convolutional networks. On ImageNet, DropBlock with ResNet-50 architecture achieves 77.65 accuracy, which is more than 1 improvement on the previous result of this architecture. Multi-layer neural networks have lead to remarkable performance on many kinds of benchmark tasks in text, speech and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting and misspecification. One approach to these estimation and related problems (local minima, colinearity, feature discovery etc.) is called Dropout (Hinton, et al 2012, 2016). The Dropout algorithm removes hidden units according to a Bernoulli random variable with probability @math prior to each update, creating random "shocks" to the network that are averaged over updates. In this paper we will show that Dropout is a special case of a more general model published originally in 1990 called the Stochastic Delta Rule, or SDR (Hanson, 1990). SDR redefines each weight in the network as a random variable with mean @math and standard deviation @math . Each weight random variable is sampled on each forward activation, consequently creating an exponential number of potential networks with shared weights. Both parameters are updated according to prediction error, thus resulting in weight noise injections that reflect a local history of prediction error and local model averaging. SDR therefore implements a more sensitive local gradient-dependent simulated annealing per weight converging in the limit to a Bayes optimal network. Tests on standard benchmarks (CIFAR) using a modified version of DenseNet shows the SDR outperforms standard Dropout in test error by approx. @math with DenseNet-BC 250 on CIFAR-100 and approx. @math in smaller networks. We also show that SDR reaches the same accuracy that Dropout attains in 100 epochs in as few as 35 epochs. Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves gener- alization but also leads to extremely sparse neural architectures by automatically setting the individual noise magnitude per weight. However, this sparsity can hardly be used for acceleration since it is unstructured. In the paper, we propose a new Bayesian model that takes into account the computational structure of neural net- works and provides structured sparsity, e.g. removes neurons and or convolutional channels in CNNs. To do this we inject noise to the neurons outputs while keeping the weights unregularized. We establish the probabilistic model with a proper truncated log-uniform prior over the noise and truncated log-normal variational approximation that ensures that the KL-term in the evidence lower bound is com- puted in closed-form. The model leads to structured sparsity by removing elements with a low SNR from the computation graph and provides significant acceleration on a number of deep neural architectures. The model is easy to implement as it can be formulated as a separate dropout-like layer. Deep convolutional networks have achieved successful performance in data mining field. However, training large networks still remains a challenge, as the training data may be insufficient and the model can easily get overfitted. Hence the training process is usually combined with a model regularization. Typical regularizers include weight decay, Dropout, etc. In this paper, we propose a novel regularizer, named Structured Decorrelation Constraint (SDC), which is applied to the activations of the hidden layers to prevent overfitting and achieve better generalization. SDC impels the network to learn structured representations by grouping the hidden units and encouraging the units within the same group to have strong connections during the training procedure. Meanwhile, it forces the units in different groups to learn non-redundant representations by minimizing the cross-covariance between them. Compared with Dropout, SDC reduces the co-adaptions between the hidden units in an explicit way. Besides, we propose a novel approach called Reg-Conv that can help SDC to regularize the complex convolutional layers. Experiments on extensive datasets show that SDC significantly reduces overfitting and yields very meaningful improvements on classification performance (on CIFAR-10 6.22 accuracy promotion and on CIFAR-100 9.63 promotion).