IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 28(10) 2282-2293 2017年10月 [査読有り]
We present a theoretical analysis of singular points of artificial deep neural networks, resulting in providing deep neural network models having no critical points introduced by a hierarchical structure. It is considered that such deep neural net...
Proceedings of the 23rd International Conference on Neural Information Processing, ICONIP2016-Kyoto, Part IV, LNCS 9950 389-396 2016年 [査読有り]
In this paper, we analyze a deep neural network model from the viewpoint of singularities. First, we show that there exist a large number of critical points introduced by a hierarchical structure in the deep neural network as straight lines. Next,...
Yili Xia   Cyrus Jahanchahi   Tohru Nitta   Danilo P. Mandic   
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 26(12) 3287-3292 2015年12月 [査読有り]
The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exi...
ARCHIVES OF NEUROSCIENCE 2(4) 2015年10月 [査読有り][招待有り]
Context: Recently, the singular points of neural networks have attracted attention from the artificial intelligence community, and their interesting properties have been demonstrated. The objective of this study is to provide an overview of studie...