This paper is about regularizing deep convolutional networks (ConvNets) based on an adaptive multi-objective framework for transfer learning with limited training data in the target domain. Recent advances of ConvNets regularization in this context are commonly due to the use of additional regularization objectives. They guide the training away from the target task using some concrete tasks. Unlike those related approaches, we report that an objective without a concrete goal can serve surprisingly well as a regularizer. In particular, we demonstrate Pseudo-task Regularization (PtR) which dynamically regularizes a network by simply attempting to regress image representations to a pseudo-target during fine-tuning. Through numerous experiments, the improvements on classification accuracy by PtR are shown greater or on a par to the recent state-of-the-art methods. These results also indicate a room for rethinking on the requirements for a regularizer, i.e., if specifically designed task for regularization is indeed a key ingredient. The contributions of this paper are: a) PtR provides an effective and efficient alternative for regularization without dependence on concrete tasks or extra data; b) desired strength of regularization effect in PtR is dynamically adjusted and maintained based on the gradient norms of the target objective and the pseudo-task.
The parameter norm penalty, or weight decay more specifically, has been one of the most common ways of regularization in training deep models. Our PtR leveraged weight decay by default, but we also evaluated PtR without weight decay to study its impact on accuracy. Another method being apparently similar to weight decay is to perform feature norm penalty (FNP) on the representation layer of a network @cite_22 . Superficially, FNP would resemble to PtR if the regression target for PtR was towards a static norm of zero without involving randomness (an additional feature of PtR which should be noted is that it also balances objectives automatically). The technical difference and benefit of PtR over FNP will be elaborated in Appendix . Dropout is also one of the standard techniques to improve model regularization by temporarily shielding a part of the hidden units in the bottleneck layer and fully connected layers during training @cite_30 @cite_14 . For the VGG-16 structures which we employed in our experiments, dropout was also used after flattened hidden layers.
@cite_30 @cite_14 @cite_22
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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). 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. A major challenge in training deep neural networks is overfitting, i.e. inferior performance on unseen test examples compared to performance on training examples. To reduce overfitting, stochastic regularization methods have shown superior performance compared to deterministic weight penalties on a number of image recognition tasks. Stochastic methods such as Dropout and Shakeout, in expectation, are equivalent to imposing a ridge and elastic-net penalty on the model parameters, respectively. However, the choice of the norm of weight penalty is problem dependent and is not restricted to @math . Therefore, in this paper we propose the Bridgeout stochastic regularization technique and prove that it is equivalent to an @math penalty on the weights, where the norm @math can be learned as a hyperparameter from data. Experimental results show that Bridgeout results in sparse model weights, improved gradients and superior classification performance compared to Dropout and Shakeout on synthetic and real datasets. Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of @math regularization. Literal weight decay has been shown to outperform @math regularization for optimizers for which they differ. We empirically investigate weight decay for three optimization algorithms (SGD, Adam, and K-FAC) and a variety of network architectures. We identify three distinct mechanisms by which weight decay exerts a regularization effect, depending on the particular optimization algorithm and architecture: (1) increasing the effective learning rate, (2) approximately regularizing the input-output Jacobian norm, and (3) reducing the effective damping coefficient for second-order optimization. Our results provide insight into how to improve the regularization of neural networks.