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.

翻译：向量的半张量积推广了传统内积，使得不同维度向量间的代数运算成为可能。基于此基础，我们引入一种基于域的卷积积，并将其与半张量积相结合，构建出无需填充的卷积运算。该新型运算本质上避免了零填充或其他人工填充方式，从而消除了传统卷积神经网络中普遍存在的冗余信息与边界伪影。基于此运算，我们进一步开发了基于半张量积的卷积神经网络框架，将卷积计算拓展至不规则与跨维度的数据域。在图像处理与三阶信号识别中的应用表明，所提方法能够有效处理不规则、不完整及高维数据，且不会产生由填充导致的失真。