Kolmogorov-Arnold Networks (KANs) are a new alternative to traditional neural networks, replacing linear weights with nonlinear functions. Since their introduction, these models have been adapted to a wide range of machine learning settings. Among them is federated learning (FL), a privacy-oriented paradigm in which clients train on their local data and collaborate around a global model by sharing their models rather than their data. This combination of KANs and FL has shown considerable promise through several early works on the topic, including one that forms part of this dissertation. However, to date, all these works have provided only empirical analyses of federated KANs, without offering any theoretical guarantees. This dissertation, based on a neural network analysis technique known as the Neural Tangent Kernel, and by combining approaches from centralized KANs and federated neural networks, describes the first theoretical convergence proof for the federated optimization of KANs. The theoretical requirements for the proposed convergence guarantee prove to be highly competitive with those already established for classical neural networks, further highlighting the potential of KANs and the need for further investigation.
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