text: The excellent performance of deep neural networks has enabled us to solve several automatization problems, opening an era of autonomous devices. However, current deep net architectures are heavy with millions of parameters and require billions of floating point operations. Several works have been developed to compress a pre-trained deep network to reduce memory footprint and, possibly, computation. Instead of compressing a pre-trained network, in this work, we propose a generic neural network layer structure employing multilinear projection as the primary feature extractor. The proposed architecture requires several times less memory as compared to the traditional Convolutional Neural Networks (CNN), while inherits the similar design principles of a CNN. In addition, the proposed architecture is equipped with two computation schemes that enable computation reduction or scalability. Experimental results show the effectiveness of our compact projection that outperforms traditional CNN, while requiring far fewer parameters.
  @cite_55: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9 top-5 validation error (and 4.8 test error), exceeding the accuracy of human raters.
  @cite_4: Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves @math accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs.
summary: As can be seen from ), the authors simplify a convolutional layer by two types of parameter sharing. The first is the sharing of right singular vectors ( @math ) across all @math input channels within the @math -th filter while the second enforces the sharing of left singular vectors ( @math ) across all @math filters. The work in @cite_4 is closely related to ours since we avoid designing a particular initialization scheme by including a Batch Normalization step @cite_55 . The resulting structure was easily trained from scratch with different network configurations.