用半张量积构建无填充卷积，处理不规则数据更精准
Semi-Tensor-Product Based Convolutional Neural Networks
- 基于半张量积设计无填充卷积操作，避免维度不匹配问题
- 在图像和三阶信号任务中实现零填充干扰下的高精度识别
- 适合处理不完整、高维或结构不规则的数据场景
向量的半张量积（STP）推广了传统内积，支持不同维度向量间的代数运算。基于此，我们提出一种基于域的卷积乘积，并与STP结合，构建无需填充的卷积操作。该方法天然避免了零值或其他人工填充，从而消除传统CNN中常见的冗余信息与边界伪影。在此基础上，我们进一步发展出一种基于STP的卷积神经网络框架，将卷积计算拓展至不规则和跨维度数据域。在图像处理与三阶信号识别中的应用表明，该方法可在无填充畸变的前提下有效处理不规则、不完整及高维数据。
原文摘要 · Abstract (English)
The semi-tensor product 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 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. 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.
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