We propose ways to improve the performance of fully connected networks. We found that two approaches in particular have a strong effect on performance: linear bottleneck layers and unsupervised pre-training using autoencoders without hidden unit biases. We show how both approaches can be related to improving gradient flow and reducing sparsity in the network. We show that a fully connected network can yield approximately 70 classification accuracy on the permutation-invariant CIFAR-10 task, which is much higher than the current state-of-the-art. By adding deformations to the training data, the fully connected network achieves 78 accuracy, which is just 10 short of a decent convolutional network.
Currently, deep neural networks are the state of the art on problems such as speech recognition and computer vision. In this extended abstract, we show that shallow feed-forward networks can learn the complex functions previously learned by deep nets and achieve accuracies previously only achievable with deep models. Moreover, in some cases the shallow neural nets can learn these deep functions using a total number of parameters similar to the original deep model. We evaluate our method on the TIMIT phoneme recognition task and are able to train shallow fully-connected nets that perform similarly to complex, well-engineered, deep convolutional architectures. Our success in training shallow neural nets to mimic deeper models suggests that there probably exist better algorithms for training shallow feed-forward nets than those currently available. While Deep Neural Networks (DNNs) have achieved tremendous success for large vocabulary continuous speech recognition (LVCSR) tasks, training of these networks is slow. One reason is that DNNs are trained with a large number of training parameters (i.e., 10-50 million). Because networks are trained with a large number of output targets to achieve good performance, the majority of these parameters are in the final weight layer. In this paper, we propose a low-rank matrix factorization of the final weight layer. We apply this low-rank technique to DNNs for both acoustic modeling and language modeling. We show on three different LVCSR tasks ranging between 50-400 hrs, that a low-rank factorization reduces the number of parameters of the network by 30-50 . This results in roughly an equivalent reduction in training time, without a significant loss in final recognition accuracy, compared to a full-rank representation. Abstract We consider the problem of learning from examples in layered linear feed-forward neural networks using optimization methods, such as back propagation, with respect to the usual quadratic error function E of the connection weights. Our main result is a complete description of the landscape attached to E in terms of principal component analysis. We show that E has a unique minimum corresponding to the projection onto the subspace generated by the first principal vectors of a covariance matrix associated with the training patterns. All the additional critical points of E are saddle points (corresponding to projections onto subspaces generated by higher order vectors). The auto-associative case is examined in detail. Extensions and implications for the learning algorithms are discussed. Recently proposed deep neural network (DNN) obtains significant accuracy improvements in many large vocabulary continuous speech recognition (LVCSR) tasks. However, DNN requires much more parameters than traditional systems, which brings huge cost during online evaluation, and also limits the application of DNN in a lot of scenarios. In this paper we present our new effort on DNN aiming at reducing the model size while keeping the accuracy improvements. We apply singular value decomposition (SVD) on the weight matrices in DNN, and then restructure the model based on the inherent sparseness of the original matrices. After restructuring we can reduce the DNN model size significantly with negligible accuracy loss. We also fine-tune the restructured model using the regular back-propagation method to get the accuracy back when reducing the DNN model size heavily. The proposed method has been evaluated on two LVCSR tasks, with context-dependent DNN hidden Markov model (CD-DNN-HMM). Experimental results show that the proposed approach dramatically reduces the DNN model size by more than 80 without losing any accuracy. Index Terms: deep neural network, singular value decomposition, model restructuring