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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2025-05-01
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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 |
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| 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. |
| format | Article |
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| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| 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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