In this work we study the problem of network morphism, an effective learning scheme to morph a well-trained neural network to a new one with the network function completely preserved. Different from existing work where basic morphing types on the layer level were addressed, we target at the central problem of network morphism at a higher level, i.e., how a convolutional layer can be morphed into an arbitrary module of a neural network. To simplify the representation of a network, we abstract a module as a graph with blobs as vertices and convolutional layers as edges, based on which the morphing process is able to be formulated as a graph transformation problem. Two atomic morphing operations are introduced to compose the graphs, based on which modules are classified into two families, i.e., simple morphable modules and complex modules. We present practical morphing solutions for both of these two families, and prove that any reasonable module can be morphed from a single convolutional layer. Extensive experiments have been conducted based on the state-of-the-art ResNet on benchmark datasets, and the effectiveness of the proposed solution has been verified.
. The evolution of convolutional neural networks has been from sequential to modularized. For example, LeNet @cite_14 , AlexNet @cite_2 , and VGG net @cite_3 are sequential networks, and their difference is primarily on the number of layers, which is 5, 8, and up to 19 respectively. However, recently proposed networks, such as GoogLeNet @cite_9 @cite_13 and ResNet @cite_10 , follow a modularized architecture design, and have achieved the state-of-the-art performance. This is why we wish to study network morphism at the module level, so that its operations are able to directly apply to these modularized network architectures.
@cite_14 @cite_10 @cite_9 @cite_3 @cite_2 @cite_13
2778955544 2520760693 2754989491 2748788739
In this paper, we present a simple and modularized neural network architecture, named interleaved group convolutional neural networks (IGCNets). The main point lies in a novel building block, a pair of two successive interleaved group convolutions: primary group convolution and secondary group convolution. The two group convolutions are complementary: (i) the convolution on each partition in primary group convolution is a spatial convolution, while on each partition in secondary group convolution, the convolution is a point-wise convolution; (ii) the channels in the same secondary partition come from different primary partitions. We discuss one representative advantage: Wider than a regular convolution with the number of parameters and the computation complexity preserved. We also show that regular convolutions, group convolution with summation fusion, and the Xception block are special cases of interleaved group convolutions. Empirical results over standard benchmarks, CIFAR-10, CIFAR-100, SVHN and ImageNet demonstrate that our networks are more efficient in using parameters and computation complexity with similar or higher accuracy. To attain a favorable performance on large-scale datasets, convolutional neural networks (CNNs) are usually designed to have very high capacity involving millions of parameters. In this work, we aim at optimizing the number of neurons in a network, thus the number of parameters. We show that, by incorporating sparse constraints into the objective function, it is possible to decimate the number of neurons during the training stage. As a result, the number of parameters and the memory footprint of the neural network are also reduced, which is also desirable at the test time. We evaluated our method on several well-known CNN structures including AlexNet, and VGG over different datasets including ImageNet. Extensive experimental results demonstrate that our method leads to compact networks. Taking first fully connected layer as an example, our compact CNN contains only (30 , ) of the original neurons without any degradation of the top-1 classification accuracy. With the rapid development of Deep Convolutional Neural Networks (DCNNs), numerous works focus on designing better network architectures (i.e., AlexNet, VGG, Inception, ResNet and DenseNet etc.). Nevertheless, all these networks have the same characteristic: each convolutional layer is followed by an activation layer, a Rectified Linear Unit (ReLU) layer is the most used among them. In this work, we argue that the paired module with 1:1 convolution and ReLU ratio is not the best choice since it may result in poor generalization ability. Thus, we try to investigate the more suitable convolution and ReLU ratio for exploring the better network architectures. Specifically, inspired by Leaky ReLU, we focus on adopting the proportional module with N:M (N @math M) convolution and ReLU ratio to design the better networks. From the perspective of ensemble learning, Leaky ReLU can be considered as an ensemble of networks with different convolution and ReLU ratio. We find that the proportional module with N:M (N @math M) convolution and ReLU ratio can help networks acquire the better performance, through the analysis of a simple Leaky ReLU model. By utilizing the proportional module with N:M (N @math M) convolution and ReLU ratio, many popular networks can form more rich representations in models, since the N:M (N @math M) proportional module can utilize information more effectively. Furthermore, we apply this module in diverse DCNN models to explore whether is the N:M (N @math M) convolution and ReLU ratio indeed more effective. From our experimental results, we can find that such a simple yet effective method achieves better performance in different benchmarks with various network architectures and the experimental results verify that the superiority of the proportional module. In this paper, we present a simple and modularized neural network architecture, named interleaved group convolutional neural networks (IGCNets). The main point lies in a novel building block, a pair of two successive interleaved group convolutions: primary group convolution and secondary group convolution. The two group convolutions are complementary: (i) the convolution on each partition in primary group convolution is a spatial convolution, while on each partition in secondary group convolution, the convolution is a point-wise convolution; (ii) the channels in the same secondary partition come from different primary partitions. We discuss one representative advantage: Wider than a regular convolution with the number of parameters and the computation complexity preserved. We also show that regular convolutions, group convolution with summation fusion, and the Xception block are special cases of interleaved group convolutions. Empirical results over standard benchmarks, CIFAR- @math , CIFAR- @math , SVHN and ImageNet demonstrate that our networks are more efficient in using parameters and computation complexity with similar or higher accuracy.