What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement
This work addresses a fundamental open problem in deep learning for researchers and practitioners, providing a theoretical framework and practical tool to improve model performance, though it is incremental in applying quantum physics tools to this domain.
The paper tackles the problem of determining what makes data suitable for locally connected neural networks by establishing a necessary and sufficient condition based on low quantum entanglement under specific feature partitions, and it introduces a preprocessing method to enhance data suitability, validated through experiments on various datasets.
The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data.