The semi-tensor product (STP) of vectors generalizes the conventional inner product, enabling algebraic operations between vectors of different dimensions. Building upon this foundation, we introduce a domain-based convolutional product (CP) and integrate it with the STP to formulate a padding-free convolutional operation. This new operation inherently avoids zero or other artificial padding, thereby eliminating redundant information and boundary artifacts commonly present in conventional convolutional neural networks (CNNs). Based on this operation, we further develop an STP-based CNN framework that extends convolutional computation to irregular and cross-dimensional data domains. Applications to image processing and third-order signal identification demonstrate the proposed method's effectiveness in handling irregular, incomplete, and high-dimensional data without the distortions caused by padding.

Publication:

SCIENCE CHINA-INFORMATION SCIENCES

http://dx.doi.org/10.1007/s11432-025-4734-4

Author:

Kang Lin

School of Management, Xi'an Jiaotong University, Xi'an, 710049, China

Kailan Tian

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS, Beijing, 100190, China

Correspondence to: K. Tian, State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.

E-mail addresses: k.tian@amss.ac.cn

Yuli Shan

School of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, B15 2TT, UK

Corresponding author

E-mail addresses:y.shan@bham.ac.uk