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Article

CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression

by
Yaser Shahbazi
1,*,
Mohsen Mokhtari Kashavar
1,
Abbas Ghaffari
1,
Mohammad Fotouhi
2,* and
Siamak Pedrammehr
3
1
Faculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, Iran
2
Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CN Delft, The Netherlands
3
Faculty of Design, Tabriz Islamic Art University, Tabriz 5164736931, Iran
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(9), 1513; https://doi.org/10.3390/math13091513 (registering DOI)
Submission received: 6 April 2025 / Revised: 29 April 2025 / Accepted: 30 April 2025 / Published: 4 May 2025
(This article belongs to the Special Issue Advances in Machine Learning and Graph Neural Networks)

Abstract

Modeling complex, non-stationary dynamics remains challenging for deterministic neural networks. We present the Chaos-Integrated Synaptic-Memory Network (CISMN), which embeds controlled chaos across four modules—Chaotic Memory Cells, Chaotic Plasticity Layers, Chaotic Synapse Layers, and a Chaotic Attention Mechanism—supplemented by a logistic-map learning-rate schedule. Rigorous stability analyses (Lyapunov exponents, boundedness proofs) and gradient-preservation guarantees underpin our design. In experiments, CISMN-1 on a synthetic acoustical regression dataset (541 samples, 22 features) achieved R2 = 0.791 and RMSE = 0.059, outpacing physics-informed and attention-augmented baselines. CISMN-4 on the PMLB sonar benchmark (208 samples, 60 bands) attained R2 = 0.424 and RMSE = 0.380, surpassing LSTM, memristive, and reservoir models. Across seven standard regression tasks with 5-fold cross-validation, CISMN led on diabetes (R2 = 0.483 ± 0.073) and excelled in high-dimensional, low-sample regimes. Ablations reveal a scalability–efficiency trade-off: lightweight variants train in < 10 s with > 95% peak accuracy, while deeper configurations yield marginal gains. CISMN sustains gradient norms (~2 300) versus LSTM collapse (<3), and fixed-seed protocols ensure < 1.2% MAE variation. Interpretability remains challenging (feature-attribution entropy ≈ 2.58 bits), motivating future hybrid explanation methods. CISMN recasts chaos as a computational asset for robust, generalizable modeling across scientific, financial, and engineering domains.
Keywords: Chaos-Integrated Synaptic-Memory Network (CISMN); chaos theory; artificial neural networks; dynamic learning; machine learning; complex systems; nonlinear dynamics Chaos-Integrated Synaptic-Memory Network (CISMN); chaos theory; artificial neural networks; dynamic learning; machine learning; complex systems; nonlinear dynamics

Share and Cite

MDPI and ACS Style

Shahbazi, Y.; Mokhtari Kashavar, M.; Ghaffari, A.; Fotouhi, M.; Pedrammehr, S. CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression. Mathematics 2025, 13, 1513. https://doi.org/10.3390/math13091513

AMA Style

Shahbazi Y, Mokhtari Kashavar M, Ghaffari A, Fotouhi M, Pedrammehr S. CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression. Mathematics. 2025; 13(9):1513. https://doi.org/10.3390/math13091513

Chicago/Turabian Style

Shahbazi, Yaser, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi, and Siamak Pedrammehr. 2025. "CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression" Mathematics 13, no. 9: 1513. https://doi.org/10.3390/math13091513

APA Style

Shahbazi, Y., Mokhtari Kashavar, M., Ghaffari, A., Fotouhi, M., & Pedrammehr, S. (2025). CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression. Mathematics, 13(9), 1513. https://doi.org/10.3390/math13091513

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