超复杂神经网络:探索深度学习中的四元数、八元数等

IF 1.9 Q2 MULTIDISCIPLINARY SCIENCES
MethodsX Pub Date : 2025-09-24 DOI:10.1016/j.mex.2025.103644
Raghavendra M Devadas , Vani Hiremani , Preethi , Sowmya T , Sapna R , Praveen Gujjar
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引用次数: 0

摘要

超复杂神经网络(HNNs)代表了深度学习的下一个前沿,它建立在四元数、八元数和高维代数的数学理论基础上,以推广传统的神经结构。本文综合了各种前沿方法及其理论基础、体系结构进展和主要应用,追溯了超复杂数学的发展及其在计算模型中的实现。我们总结了四元数和八元数网络的关键进展,强调了它们提供紧凑表示和计算效率的能力。特别要注意的是八元数的非结合性的独特挑战——其中数字相乘的顺序会影响结果——需要仔细设计网络操作。本文还讨论了训练的复杂性、可解释性和缺乏标准化框架,以及与实值和复杂值网络的性能比较。未来的方向包括可扩展的算法构建,通过张量分解的轻量级架构,以及使用高阶代数与量子启发系统的集成。通过对当前文献的系统综合,并将这些进展与实际应用联系起来,本综述旨在使研究人员和从业人员清楚地了解hnn在推进多维数据建模方面的优势、局限性和潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Hypercomplex neural networks: Exploring quaternion, octonion, and beyond in deep learning

Hypercomplex neural networks: Exploring quaternion, octonion, and beyond in deep learning
Hypercomplex Neural Networks (HNNs) represent the next frontier in deep learning, building on the mathematical theory of quaternions, octonions, and higher-dimensional algebras to generalize conventional neural architectures. This review synthesizes cutting-edge methods with their theoretical bases, architectural advancements, and primary applications, tracing the development of hypercomplex mathematics and its implementation in computational models. We distil key advances in quaternion and octonion networks, highlighting their ability to provide compact representations and computational efficiency. Particular attention is given to the unique challenge of non-associativity in octonions—where the order in which numbers are multiplied affects the result—requiring careful design of network operations. The article also discusses training complexity, interpretability, and the lack of standardized frameworks, alongside comparative performance with real- and complex-valued networks. Future directions include scalable algorithm construction, lightweight architectures through tensor decompositions, and integration with quantum-inspired systems using higher-order algebras. By presenting a systematic synthesis of current literature and linking these advances to practical applications, this review aims to equip researchers and practitioners with a clear understanding of the strengths, limitations, and potential of HNNs for advancing multidimensional data modelling.
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来源期刊
MethodsX
MethodsX Health Professions-Medical Laboratory Technology
CiteScore
3.60
自引率
5.30%
发文量
314
审稿时长
7 weeks
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