Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernels

TL;DR

The paper introduces tensor-augmented CNNs (TACNNs), which replace traditional kernels with tensors to enhance expressivity, achieving deep learning performance with shallower, more interpretable models.

Contribution

Proposes a physically-guided shallow model, TACNN, using generic tensors to significantly improve expressivity over conventional CNNs with fewer layers.

Findings

TACNN achieves 93.7% accuracy on Fashion-MNIST with only two layers.

TACNN outperforms or matches deeper models like VGG-16 and GoogLeNet.

TACNN offers a more interpretable and efficient architecture.

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.