Xiaoli Dong

Yanjie Li, Weijun Li, Lina Yu et al.

Multilayer perception (MLP) has permeated various disciplinary domains, ranging from bioinformatics to financial analytics, where their application has become an indispensable facet of contemporary scientific research endeavors. However, MLP has obvious drawbacks. 1), The type of activation function is single and relatively fixed, which leads to poor `representation ability' of the network, and it is often to solve simple problems with complex networks; 2), the network structure is not adaptive, it is easy to cause network structure redundant or insufficient. In this work, we propose a novel neural network paradigm X-Net promising to replace MLPs. X-Net can dynamically learn activation functions individually based on derivative information during training to improve the network's representational ability for specific tasks. At the same time, X-Net can precisely adjust the network structure at the neuron level to accommodate tasks of varying complexity and reduce computational costs. We show that X-Net outperforms MLPs in terms of representational capability. X-Net can achieve comparable or even better performance than MLP with much smaller parameters on regression and classification tasks. Specifically, in terms of the number of parameters, X-Net is only 3% of MLP on average and only 1.1% under some tasks. We also demonstrate X-Net's ability to perform scientific discovery on data from various disciplines such as energy, environment, and aerospace, where X-Net is shown to help scientists discover new laws of mathematics or physics.

Liping Zhang, Weijun Li, Linjun Sun et al.

How to represent a face pattern? While it is presented in a continuous way in our visual system, computers often store and process the face image in a discrete manner with 2D arrays of pixels. In this study, we attempt to learn a continuous representation for face images with explicit functions. First, we propose an explicit model (EmFace) for human face representation in the form of a finite sum of mathematical terms, where each term is an analytic function element. Further, to estimate the unknown parameters of EmFace, a novel neural network, EmNet, is designed with an encoder-decoder structure and trained using the backpropagation algorithm, where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace. Experimental results show that EmFace has a higher representation performance on faces with various expressions, postures, and other factors, compared to that of other methods. Furthermore, EmFace achieves reasonable performance on several face image processing tasks, including face image restoration, denoising, and transformation.

Liping Zhang, Weijun Li, Lina Yu et al.

Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to complex physiological structures and dynamic behaviors, mathematical representation of the human face is an especially challenging task. A mathematical model for face image representation called GmFace is proposed in the form of a multi-Gaussian function in this paper. The model utilizes the advantages of two-dimensional Gaussian function which provides a symmetric bell surface with a shape that can be controlled by parameters. The GmNet is then designed using Gaussian functions as neurons, with parameters that correspond to each of the parameters of GmFace in order to transform the problem of GmFace parameter solving into a network optimization problem of GmNet. The face modeling process can be described by the following steps: (1) GmNet initialization; (2) feeding GmNet with face image(s); (3) training GmNet until convergence; (4) drawing out the parameters of GmNet (as the same as GmFace); (5) recording the face model GmFace. Furthermore, using GmFace, several face image transformation operations can be realized mathematically through simple parameter computation.

Xin Ning, Shaohui Xu, Xiaoli Dong et al.

The generative adversarial network (GAN) exhibits great superiority in the face attribute synthesis task. However, existing methods have very limited effects on the expansion of new attributes. To overcome the limitations of a single network in new attribute synthesis, a continuous learning method for face attribute synthesis is proposed in this work. First, the feature vector of the input image is extracted and attribute direction regression is performed in the feature space to obtain the axes of different attributes. The feature vector is then linearly guided along the axis so that images with target attributes can be synthesized by the decoder. Finally, to make the network capable of continuous learning, the orthogonal direction modification module is used to extend the newly-added attributes. Experimental results show that the proposed method can endow a single network with the ability to learn attributes continuously, and, as compared to those produced by the current state-of-the-art methods, the synthetic attributes have higher accuracy.