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

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 A...

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Main Authors: Yaser Shahbazi, Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi, Siamak Pedrammehr
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/9/1513
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author Yaser Shahbazi
Mohsen Mokhtari Kashavar
Abbas Ghaffari
Mohammad Fotouhi
Siamak Pedrammehr
author_facet Yaser Shahbazi
Mohsen Mokhtari Kashavar
Abbas Ghaffari
Mohammad Fotouhi
Siamak Pedrammehr
author_sort Yaser Shahbazi
collection DOAJ
description 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 R<sup>2</sup> = 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 R<sup>2</sup> = 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 (R<sup>2</sup> = 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 (~2300) 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.
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spelling doaj-art-c8de2f386d0345e8857c22ed26461e8d2025-08-20T01:49:28ZengMDPI AGMathematics2227-73902025-05-01139151310.3390/math13091513CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear RegressionYaser Shahbazi0Mohsen Mokhtari Kashavar1Abbas Ghaffari2Mohammad Fotouhi3Siamak Pedrammehr4Faculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, IranFaculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, IranFaculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, IranFaculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CN Delft, The NetherlandsFaculty of Design, Tabriz Islamic Art University, Tabriz 5164736931, IranModeling 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 R<sup>2</sup> = 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 R<sup>2</sup> = 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 (R<sup>2</sup> = 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 (~2300) 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.https://www.mdpi.com/2227-7390/13/9/1513Chaos-Integrated Synaptic-Memory Network (CISMN)chaos theoryartificial neural networksdynamic learningmachine learningcomplex systems
spellingShingle Yaser Shahbazi
Mohsen Mokhtari Kashavar
Abbas Ghaffari
Mohammad Fotouhi
Siamak Pedrammehr
CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
Mathematics
Chaos-Integrated Synaptic-Memory Network (CISMN)
chaos theory
artificial neural networks
dynamic learning
machine learning
complex systems
title CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
title_full CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
title_fullStr CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
title_full_unstemmed CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
title_short CISMN: A Chaos-Integrated Synaptic-Memory Network with Multi-Compartment Chaotic Dynamics for Robust Nonlinear Regression
title_sort cismn a chaos integrated synaptic memory network with multi compartment chaotic dynamics for robust nonlinear regression
topic Chaos-Integrated Synaptic-Memory Network (CISMN)
chaos theory
artificial neural networks
dynamic learning
machine learning
complex systems
url https://www.mdpi.com/2227-7390/13/9/1513
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