Document Type
Article
Publication Date
4-2024
Abstract
This paper explores the superior performance of quaternion multi-layer perceptron (QMLP) neural networks over real-valued multi-layer perceptron (MLP) neural networks, a phenomenon that has been empirically observed but not thoroughly investigated. The study utilizes loss surface visualization and projection techniques to examine quaternion-based optimization loss surfaces for the first time. The primary contribution of this research is the statistical evidence that QMLP models yield smoother loss surfaces than real-valued neural networks, which are measured and compared using a robust quantitative measure of loss surface “goodness” based on estimates of surface curvature. Extensive computational testing validates the effectiveness of these surface curvature estimates. The paper presents a comprehensive comparison of the average surface curvature of a tuned QMLP model and a tuned real-valued MLP model on both a regression task and a classification task. The results provide strong support for the improved optimization performance observed in QMLPs across various problem domains.
Source Publication
Advances in Applied Clifford Algebras
Recommended Citation
Bill, J., & Cox, B. (2024). Exploring quaternion neural network loss surfaces. Advances in Applied Clifford Algebras, 34(3), 19. https://doi.org/10.1007/s00006-024-01313-2
Comments
©2024 The Authors
This article is published by Springer, licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.