In recent years, deeper and wider neural networks have shown excellent performance in computer vision tasks, while their enormous amount of parameters results in increased computational cost and overfitting. Several methods have been proposed to compress the size of the networks without reducing network performance. Network pruning can reduce redundant and unnecessary parameters from a network. Knowledge distillation can transfer the knowledge of deeper and wider networks to smaller networks. The performance of the smaller network obtained by these methods is bounded by the predefined network. Neural architecture search has been proposed, which can search automatically the architecture of the networks to break the structure limitation. Also, there is a dynamic configuration method to train networks incrementally as sub-networks. In this paper, we present a novel incremental training algorithm for deep neural networks called planting. Our planting can search the optimal network architecture with smaller number of parameters for improving the network performance by augmenting channels incrementally to layers of the initial networks while keeping the earlier trained parameters fixed. Also, we propose using the knowledge distillation method for training the channels planted. By transferring the knowledge of deeper and wider networks, we can grow the networks effectively and efficiently. We evaluate the effectiveness of the proposed method on different datasets such as CIFAR-10/100 and STL-10. For the STL-10 dataset, we show that we are able to achieve comparable performance with only 7% parameters compared to the larger network and reduce the overfitting caused by a small amount of the data.

Since the convolutional neural networks are often trained with redundant parameters, it is possible to reduce redundant kernels or filters to obtain a compact network without dropping the classification accuracy. In this paper, we propose a filter pruning method using the hierarchical group sparse regularization. It is shown in our previous work that the hierarchical group sparse regularization is effective in obtaining sparse networks in which filters connected to unnecessary channels are automatically close to zero. After training the convolutional neural network with the hierarchical group sparse regularization, the unnecessary filters are selected based on the increase of the classification loss of the randomly selected training samples to obtain a compact network. It is shown that the proposed method can reduce more than 50% parameters of ResNet for CIFAR-10 with only 0.3% decrease in the accuracy of test samples. Also, 34% parameters of ResNet are reduced for TinyImageNet-200 with higher accuracy than the baseline network.

The dimensionality reduction has been widely introduced to use the high-dimensional data for regression, classification, feature analysis, and visualization. As the one technique of dimensionality reduction, a stochastic neighbor embedding (SNE) was introduced. The SNE leads powerful results to visualize high-dimensional data by considering the similarity between the local Gaussian distributions of high and low-dimensional space. To improve the SNE, a t-distributed stochastic neighbor embedding (t-SNE) was also introduced. To visualize high-dimensional data, the t-SNE leads to more powerful and flexible visualization on 2 or 3-dimensional mapping than the SNE by using a t-distribution as the distribution of low-dimensional data. Recently, Uniform manifold approximation and projection (UMAP) is proposed as a dimensionality reduction technique. We present a novel technique called a q-Gaussian distributed stochastic neighbor embedding (q-SNE). The q-SNE leads to more powerful and flexible visualization on 2 or 3-dimensional mapping than the t-SNE and the SNE by using a q-Gaussian distribution as the distribution of low-dimensional data. The q-Gaussian distribution includes the Gaussian distribution and the t-distribution as the special cases with q=1.0 and q=2.0. Therefore, the q-SNE can also express the t-SNE and the SNE by changing the parameter q, and this makes it possible to find the best visualization by choosing the parameter q. We show the performance of q-SNE as visualization on 2-dimensional mapping and classification by k-Nearest Neighbors (k-NN) classifier in embedded space compared with SNE, t-SNE, and UMAP by using the datasets MNIST, COIL-20, OlivettiFaces, FashionMNIST, and Glove.