张量增强的卷积神经网络：通过通用张量内核增强表达能力
Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernels
AI总结：
本文提出张量增强卷积神经网络（TACNN），通过通用张量替代传统卷积核提升表达能力，实验显示其在Fashion-MNIST数据集上仅用两层即可达到93.7%的准确率，优于传统深度CNN。
摘要：
卷积神经网络（CNNs）在提取局部特征方面表现出色，但其在捕捉复杂相关性方面的能力严重依赖于深度架构，这通常计算成本高且难以解释。为解决这些问题，我们提出了一种物理引导的浅层模型：张量增强的CNN（TACNN），通过通用张量替代传统卷积核来增强表示能力。这一选择的动机在于，一个阶数为N的张量自然编码了任意量子叠加态在维度为d^N的希尔伯特空间中，从而提供了更丰富的表达能力。此外，在我们的设计中，每一层的卷积输出都成为一种多线性形式，能够捕捉高阶特征相关性，从而使浅层多层架构具有与深度CNN相当的表达能力。在Fashion-MNIST基准测试中，TACNN在仅使用少量层的情况下表现出明显优势，取得了显著的准确率。特别是，仅使用两层的TACNN在测试准确率上达到93.7%，超过了或匹配了VGG-16（93.5%）和GoogLeNet（93.7%）等较深的模型。这些发现突显了TACNN作为一种有前景的框架，它在增强模型表达能力的同时保持了架构的简洁性，为更可解释和高效深度学习模型的发展铺平了道路。
英文摘要：
Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult to interpret. To address these issues, we propose a physically-guided shallow model: tensor-augmented CNN (TACNN), which replaces conventional convolution kernels with generic tensors to enhance representational capacity. This choice is motivated by the fact that an order-$N$ tensor naturally encodes an arbitrary quantum superposition state in the Hilbert space of dimension $d^N$, where $d$ is the local physical dimension, thus offering substantially richer expressivity. Furthermore, in our design the convolution output of each layer becomes a multilinear form capable of capturing high-order feature correlations, thereby equipping a shallow multilayer architecture with an expressive power competitive to that of deep CNNs. On the Fashion-MNIST benchmark, TACNN demonstrates clear advantages over conventional CNNs, achieving remarkable accuracies with only a few layers. In particular, a TACNN with only two convolution layers attains a test accuracy of 93.7$\%$, surpassing or matching considerably deeper models such as VGG-16 (93.5$\%$) and GoogLeNet (93.7$\%$). These findings highlight TACNN as a promising framework that strengthens model expressivity while preserving architectural simplicity, paving the way towards more interpretable and efficient deep learning models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
