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

Yaser Shahbazi (), Mohsen Mokhtari Kashavar, Abbas Ghaffari, Mohammad Fotouhi () and Siamak Pedrammehr
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Yaser Shahbazi: Faculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, Iran
Mohsen Mokhtari Kashavar: Faculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, Iran
Abbas Ghaffari: Faculty of Architecture and Urbanism, Tabriz Islamic Art University, Tabriz 5164736931, Iran
Mohammad Fotouhi: Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CN Delft, The Netherlands
Siamak Pedrammehr: Faculty of Design, Tabriz Islamic Art University, Tabriz 5164736931, Iran

Mathematics, 2025, vol. 13, issue 9, 1-37

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 R 2 = 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 2 = 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 2 = 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.

Keywords: Chaos-Integrated Synaptic-Memory Network (CISMN); chaos theory; artificial neural networks; dynamic learning; machine learning; complex systems; nonlinear dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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