Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps

Computer Science > Artificial Intelligence [Submitted on 6 Apr 2026] Non-monotonic causal discovery with Kolmogorov-Arnold Fuzzy Cognitive Maps Jose L. Salmeron Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by scalar synaptic weights and monotonic activation functions, is fundamentally constrained in modeling non-monotonic causal dependencies, thereby limiting its efficacy in systems governed by saturation effects or periodic dynamics. To overcome this topological restriction, this research proposes the Kolmogorov-Arnold Fuzzy Cognitive Map (KA-FCM), a novel architecture that redefines the causal transmission mechanism. Drawing upon the Kolmogorov-Arnold representation theorem, static scalar weights are replaced with learnable, univariate B-spline functions located on the model edges. This fundamental modification shifts the non-linearity from the nodes' aggregation phase directly to the causal influence phase. This modification allows for the modeling of arbitrary, non-monotonic causal relationships without increasing the graph density or introducing hidden layers. The proposed architecture is validated against both baselines (standard FCM trained with Particle Swarm Optimization) and universal black-box approximators (Multi-Layer Perceptron) across three distinct domains: non-monotonic inference (Yerkes-Dodson law), symbolic regression, and chaotic time-series forecasting. Experimental results demonstrate that KA-FCMs significantly outperform conventional architectures and achieve competitive accuracy relative to MLPs, while preserving graph- based interpretability and enabling the explicit extraction of mathematical laws from the learned edges. Comments: Fuzzy Cognitive Maps, Kolmogorov-Arnold Networks, Causal Modeling, Neuro-Symbolic AI Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2604.05136 [cs.AI]   (or arXiv:2604.05136v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2604.05136 Focus to learn more Journal reference: IEEE Transactions on Fuzzy Systems 2026 Related DOI: https://doi.org/10.1109/TFUZZ.2026.3680681 Focus to learn more Submission history From: Jose L. Salmeron PhD [view email] [v1] Mon, 6 Apr 2026 19:56:12 UTC (2,732 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)