# Tucker Decomposition Network: Expressive Power and Comparison

## TL;DR

This paper introduces a Tucker tensor decomposition-based deep neural network, demonstrating its superior expressive power over shallow networks and its effectiveness in image classification tasks.

## Contribution

It develops a Tucker decomposition network and analyzes its expressive power, showing it outperforms shallow networks and other tensor networks.

## Key findings

- Tucker network is more expressive than shallow networks.
- Exponential nodes are needed in shallow networks to match Tucker network.
- Experimental results show Tucker network's effectiveness in image classification.

## Abstract

Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its expressive power. It is shown that the expressiveness of Tucker network is more powerful than that of shallow network. In general, it is required to use an exponential number of nodes in a shallow network in order to represent a Tucker network. Experimental results are also given to compare the performance of the proposed Tucker network with hierarchical tensor network and shallow network, and demonstrate the usefulness of Tucker network in image classification problems.