Fractal-domain transformer based on learnable multifractal spectrum for chaotic systems classification

Gang Xiong, Wenyu Huang, Tao Zhen and Shuning Zhang

Physica A: Statistical Mechanics and its Applications, 2025, vol. 658, issue C

Abstract: Conventional deep learning in the spatiotemporal-frequency domain frequently encounter challenges in terms of slow convergence rates and limited generalization, particularly for classification of chaotic systems. To address these limitations, this paper introduces a novel fractal-inspired deep network model, specifically, the Multifractal Spectrum Transformer (MFS-Transformer), grounded in learnable multifractal analysis. Initially, we put forward the conceptual framework of fractal learning, compared with traditional fractal signal processing methodologies and spatial-temporal domain learning paradigms. Subsequently, a Learnable Multifractal Spectrum (LMFS) derived from 3D spatial gridding, coupled with fractal-domain filtering, is proposed to construct the iterative learning process within the fractal domain. Further, we formulate the MFS-Transformer, an innovative architecture that integrates multi-channel embedding, LMFS, fractal-domain filtering, residual fusion mechanisms, a mixer module, and a classifier, tailored for chaotic system classification. Ultimately, we evaluate the efficacy of our model in classifying 3D chaotic systems under stringent conditions of short-term sequences and low Signal-to-Noise Ratio (SNR). Experimental outcomes underscore the substantial performance gains achieved by the MFS-Transformer, with classification accuracy enhancements of 13.34 % and 5.00 % over existing Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs), respectively, under SNR= 0 dB and 32-sample sequences. These findings validate the superiority of the MFS-Transformer in addressing the complexities of chaotic system classification under complex scenarios. This research not only advances the frontier of fractal deep learning but also presents a novel perspective and methodology for tackling intricate spatiotemporal classification problems.

Keywords: Fractal deep learning; Learnable multifractal spectrum; Multifractal Transformer; Classification (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007866

DOI: 10.1016/j.physa.2024.130276

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