Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernels
2026-04-09 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors introduce a new type of neural network called TACNN that uses tensors instead of regular convolutional filters. This approach allows the network to capture more complex patterns with fewer layers, making it easier to understand and less computationally heavy. On a clothing image test, their shallow TACNN matched or beat deeper, more traditional CNN models. This suggests their design can provide strong results with simpler, more interpretable architectures.
Convolutional Neural Networkstensorsquantum superpositionHilbert spacemultilinear formsFashion-MNISTVGG-16GoogLeNetshallow networksmodel expressivity
Authors
Chia-Wei Hsing, Wei-Lin Tu
Abstract
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.