Zhendong Zhang

Zhendong Zhang

Convolution utilizes a shift-equivalent prior of images, thus leading to great success in image processing tasks. However, commonly used poolings in convolutional neural networks (CNNs), such as max-pooling, average-pooling, and strided-convolution, are not shift-equivalent. Thus, the shift-equivalence of CNNs is destroyed when convolutions and poolings are stacked. Moreover, anti-aliasing is another essential property of poolings from the perspective of signal processing. However, recent poolings are neither shift-equivalent nor anti-aliasing. To address this issue, we propose a new pooling method that is shift-equivalent and anti-aliasing, named frequency pooling. Frequency pooling first transforms the features into the frequency domain, and then removes the frequency components beyond the Nyquist frequency. Finally, it transforms the features back to the spatial domain. We prove that frequency pooling is shift-equivalent and anti-aliasing based on the property of Fourier transform and Nyquist frequency. Experiments on image classification show that frequency pooling improves accuracy and robustness with respect to the shifts of CNNs.

Zhendong Zhang, Cheolkon Jung

Gradient boosted decision trees (GBDTs) are widely used in machine learning, and the output of current GBDT implementations is a single variable. When there are multiple outputs, GBDT constructs multiple trees corresponding to the output variables. The correlations between variables are ignored by such a strategy causing redundancy of the learned tree structures. In this paper, we propose a general method to learn GBDT for multiple outputs, called GBDT-MO. Each leaf of GBDT-MO constructs predictions of all variables or a subset of automatically selected variables. This is achieved by considering the summation of objective gains over all output variables. Moreover, we extend histogram approximation into multiple output case to speed up the training process. Various experiments on synthetic and real-world datasets verify that GBDT-MO achieves outstanding performance in terms of both accuracy and training speed. Our codes are available on-line.

Zhendong Zhang, Cheolkon Jung

Recurrent convolution (RC) shares the same convolutional kernels and unrolls them multiple steps, which is originally proposed to model time-space signals. We argue that RC can be viewed as a model compression strategy for deep convolutional neural networks. RC reduces the redundancy across layers. However, the performance of an RC network is not satisfactory if we directly unroll the same kernels multiple steps. We propose a simple yet effective variant which improves the RC networks: the batch normalization layers of an RC module are learned independently (not shared) for different unrolling steps. Moreover, we verify that RC can perform cost-adjustable inference which is achieved by varying its unrolling steps. We learn double independent BN layers for cost-adjustable RC networks, i.e. independent w.r.t both the unrolling steps of current cell and upstream cell. We provide insights on why the proposed method works successfully. Experiments on both image classification and image denoise demonstrate the effectiveness of our method.