Jose L. Salmeron

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.

Jose L. Salmeron, Irina Arévalo, Antonio Ruiz-Celma

The increasing requirements for data protection and privacy has attracted a huge research interest on distributed artificial intelligence and specifically on federated learning, an emerging machine learning approach that allows the construction of a model between several participants who hold their own private data. In the initial proposal of federated learning the architecture was centralised and the aggregation was done with federated averaging, meaning that a central server will orchestrate the federation using the most straightforward averaging strategy. This research is focused on testing different federated strategies in a peer-to-peer environment. The authors propose various aggregation strategies for federated learning, including weighted averaging aggregation, using different factors and strategies based on participant contribution. The strategies are tested with varying data sizes to identify the most robust ones. This research tests the strategies with several biomedical datasets and the results of the experiments show that the accuracy-based weighted average outperforms the classical federated averaging method.

Jose L. Salmeron, Irina Arévalo

Distributed Artificial Intelligence is attracting interest day by day. In this paper, the authors introduce an innovative methodology for distributed learning of Particle Swarm Optimization-based Fuzzy Cognitive Maps in a privacy-preserving way. The authors design a training scheme for collaborative FCM learning that offers data privacy compliant with the current regulation. This method is applied to a cancer detection problem, proving that the performance of the model is improved by the Federated Learning process, and obtaining similar results to the ones that can be found in the literature.

Jose L. Salmeron, Irina Arévalo

Federated learning is an emerging machine learning approach that allows the construction of a model between several participants who hold their own private data. This method is secure and privacy-preserving, suitable for training a machine learning model using sensitive data from different sources, such as hospitals. In this paper, the authors propose two innovative methodologies for Particle Swarm Optimisation-based federated learning of Fuzzy Cognitive Maps in a privacy-preserving way. In addition, one relevant contribution this research includes is the lack of an initial model in the federated learning process, making it effectively blind. This proposal is tested with several open datasets, improving both accuracy and precision.

Irina Arévalo, Jose L. Salmeron

Federated Learning is a machine learning approach that enables the training of a deep learning model among several participants with sensitive data that wish to share their own knowledge without compromising the privacy of their data. In this research, the authors employ a secured Federated Learning method with an additional layer of privacy and proposes a method for addressing the non-IID challenge. Moreover, differential privacy is compared with chaotic-based encryption as layer of privacy. The experimental approach assesses the performance of the federated deep learning model with differential privacy using both IID and non-IID data. In each experiment, the Federated Learning process improves the average performance metrics of the deep neural network, even in the case of non-IID data.