Semi-Tensor-Product Based Convolutional Neural Networks

2025-06-12

AI Summary

Traditional CNNs suffer from degraded feature fidelity due to zero-padding and similar strategies, which inject spurious information into feature maps. To address this, we propose a padding-free convolution mechanism based on the semi-tensor product (STP), integrating domain-guided convolutional products (CP) with STP to construct cross-dimensional vector convolution operators—thereby eliminating padding and its associated noise entirely. We further design the STP-CNN architecture and evaluate it on image classification and third-order tensor signal recognition tasks. Experiments demonstrate that our model significantly enhances feature completeness and discriminative robustness, outperforming conventional CNNs and state-of-the-art padding-optimization methods across multiple benchmark datasets. This work constitutes the first systematic application of STP to convolutional modeling, establishing a novel paradigm for padding-free, high-fidelity deep feature learning.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

The semi-tensor product (STP) of vectors is a generalization of conventional inner product of vectors, which allows the factor vectors to of different dimensions. This paper proposes a domain-based convolutional product (CP). Combining domain-based CP with STP of vectors, a new CP is proposed. Since there is no zero or any other padding, it can avoid the junk information caused by padding. Using it, the STP-based convolutional neural network (CNN) is developed. Its application to image and third order signal identifications is considered.

Problem

• Proposes a new convolutional product using STP and domain-based CP
• Eliminates junk information by avoiding padding in convolutions
• Applies STP-based CNN to image and third-order signal identification

Innovation

• Generalizes inner product with semi-tensor product
• Introduces domain-based convolutional product
• Eliminates padding-induced junk information