Bicomplex Neural Networks with Hypergeometric Activation Functions

Vieira, N.

doi:10.1007/s00006-023-01268-w

Adv. Appl. Clifford Algebras

2023

DOI: 10.1007/s00006-023-01268-w

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Bicomplex Neural Networks with Hypergeometric Activation Functions

N. Vieira

Abstract: Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In… Show more

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Machine Learning Clifford Invariants of ADE Coxeter Elements

Chen,

Dechant,

et al. 2024

Adv. Appl. Clifford Algebras

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There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for $$A_8$$ A 8 , $$D_8$$ D 8 and $$E_8$$ E 8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results.

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Machine Learning Clifford Invariants of ADE Coxeter Elements

Chen,

Dechant,

et al. 2024

Adv. Appl. Clifford Algebras

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Efficient and privacy-preserving image classification using homomorphic encryption and chunk-based convolutional neural network

Jia,

Cai,

Yang

et al. 2023

J Cloud Comp

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Image feature categorization has emerged as a crucial component in many domains, including computer vision, machine learning, and biometrics, in the dynamic environment of big data and cloud computing. It is extremely difficult to guarantee image data security, privacy, and computing efficiency while also lowering storage and transmission costs. This paper introduces a novel method for classifying image features that combines multilevel homomorphic encryption and image data partitioning in an integrated manner. We employ a novel partitioning strategy to reduce computational complexity, significantly reducing computational load and improving classification accuracy. In the quest for increased data security and privacy, we introduce a novel, fully homomorphic encryption approach specialized to partitioned images. To counter the inherent complexity of encryption, we devise a compound encryption strategy that exploits the full potential of homomorphic computation, with an explicit objective to curtail computational and storage overheads. Evidently superior to conventional methods, our methodology showcases pronounced benefits in computational efficiency, storage and transmission cost reduction, and robust security and privacy preservation. Hence, the methodology put forth in this paper presents a pioneering and efficacious resolution to the multifaceted challenges of image feature classification within the intricate milieu of cloud computing and big data.

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Bicomplex Neural Networks with Hypergeometric Activation Functions

Cited by 2 publications

References 23 publications

Machine Learning Clifford Invariants of ADE Coxeter Elements

Machine Learning Clifford Invariants of ADE Coxeter Elements

Efficient and privacy-preserving image classification using homomorphic encryption and chunk-based convolutional neural network

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