Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernels
This addresses the need for more interpretable and efficient deep learning models, particularly in domains like image classification, though it appears incremental as it builds on existing CNN frameworks with tensor-based enhancements.
The paper tackled the problem of deep convolutional neural networks being computationally demanding and hard to interpret by proposing tensor-augmented CNNs (TACNNs), which use generic tensor kernels to enhance expressivity; on Fashion-MNIST, a two-layer TACNN achieved 93.7% test accuracy, matching or surpassing deeper models like VGG-16 and GoogLeNet.
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.