Applied Intelligence

, Volume 49, Issue 2, pp 376–395 | Cite as

Trainable back-propagated functional transfer matrices

  • Cheng-Hao Cai
  • Yanyan XuEmail author
  • Dengfeng Ke
  • Kaile Su
  • Jing Sun


Functional transfer matrices consist of real functions with trainable parameters. In this work, functional transfer matrices are used to model functional connections in neural networks. Different from linear connections in conventional weight matrices, the functional connections can represent nonlinear relations between two neighbouring layers. Neural networks with the functional connections, which are called functional transfer neural networks, can be trained via back-propagation. On the two spirals problem, the functional transfer neural networks are able to show considerably better performance than conventional multi-layer perceptrons. On the MNIST handwritten digit recognition task, the performance of the functional transfer neural networks is comparable to that of the conventional model. This study has demonstrated that the functional transfer matrices are able to perform better than the conventional weight matrices in specific cases, so that they can be alternatives of the conventional ones.


Functional transfer neural networks Functional connections Back-propagation 



This work is supported by the Fundamental Research Funds for the Central Universities (No. 2016JX06) and the National Natural Science Foundation of China (No. 61472369).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceThe University of AucklandAucklandNew Zealand
  2. 2.School of Information Science and TechnologyBeijing Forestry UniversityHaidian DistrictChina
  3. 3.Institute of AutomationChinese Academy of SciencesHaidian DistrictChina
  4. 4.School of Information and Communication TechnologyGriffith UniversityBrisbaneAustralia

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