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Computing Topological Invariants of Deep Neural Networks
Xiujun Zhang1, Nazeran Idrees2, Salma Kanwal3
1School of Computer Science, Chengdu University, Chengdu, China.
Computational Intelligence and Neuroscience
|October 17, 2022
Summary
This study computes topological indices for deep neural networks (DNNs), revealing correlations between network connectivity and performance. Understanding these properties can enhance DNN efficiency and accuracy in complex pattern recognition tasks.
Area of Science:
- Computer Science
- Mathematics
- Artificial Intelligence
Background:
- Deep neural networks (DNNs) simulate human brain activity for complex pattern learning.
- DNNs excel in image, speech, and natural language processing tasks.
- Topological indices quantify network connectivity, impacting DNN efficiency and accuracy.
Purpose of the Study:
- To compute various degree-related topological indices for DNNs.
- To analyze the relationship between topological properties and DNN performance.
Main Methods:
- Calculation of topological indices including Zagreb, Randic, atom-bond connectivity, geometric-arithmetic, forgotten, multiple Zagreb, and hyper-Zagreb indices.
- Application to deep neural networks with a finite number of hidden layers.
Main Results:
- Computed specific topological indices for DNN structures.
- Established correlations between computed indices and network efficiency/accuracy.
Conclusions:
- Topological indices offer insights into DNN architecture and functionality.
- This analysis provides a quantitative framework for understanding DNNs through their topological properties.
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