## 1 Introduction  
Over the past five years, there has been an unprecedented surge in interest in Artificial Intelligence (AI) across various sectors, including industry, research, and modern society [1]. AI applications have become pervasive, encompassing fields such as healthcare, commerce, transportation, logistics, automated manufacturing, finance, entertainment, security, space navigation, and internet services, among many others [2, 3, 4]. In these applications, Machine Learning stands out as the dominant research area, where Deep Learning models have emerged as the most successful [2, 5, 6]. The resurgence of neural networks with many hidden layers began in 2006 when a breakthrough combining supervised and unsupervised learning [7] challenged the belief about the great difficulty of training deep networks [8]. This advance sparked renewed research efforts, which led to the development of mechanisms that enabled fully supervised learning. These mechanisms took advantage of backpropagation and gradient descent for the training process [7, 8, 9]. Since then, novel algorithms have surfaced, primarily emphasizing the refinement of gradient gain for synaptic weight updates. While these optimizers boast advantages over traditional methods, yielding remarkable results in specific scenarios, they need extensive training datasets and many iterations to attain the desired learning thresholds. Moreover, their efficacy often diminishes when confronted with intricately complex problems. Thus, research in this field remains open and ongoing [10]. In addition to these algorithms based on gradient descent, there are learning methods that incorporate second-order information that has shown superior accuracy compared to first-order algorithms, often achieving satisfactory results in fewer training epochs. However, its considerable computational demands pose a challenge, especially when dealing with deep networks, due to the large number of adjustable parameters. Consequently, they are applied in small neural networks [9; 11; 12]. The Extended Kalman Filter (EKF) incorporates second-order information through the estimation error covariance. This method was introduced to neural network training in 1988 by [PERSON] and [PERSON] [13]. Their pioneering work demonstrated that the EKF converges in fewer iterations and with higher accuracy than backpropagation. Subsequently, two publications [11; 14] provided evidence of these advantages but pointed out the greater computational complexity. Then new versions of the EKF appeared, the most immediate in [14], with the idea of multiple EKF units (MEKA), where each MEKA unit is applied to a specific group of weights of the neural network, operating independently. Meanwhile, in [11], [PERSON] and [PERSON] developed a scheme with a single EKF for the entire neural network, which is compatible with scenarios where uncorrelated weights exist in the neural model. This approach, unlike MEKA, aligns with the original EKF and offers substantial computational relief without compromising accuracy. The general model is known as the decoupled extended Kalman filter (DEKF). The authors of the DEKF propose different decoupling levels: the global extended Kalman filter (GEKF) considers that all weights are correlated; layer-decoupled extended Kalman filter (LDEKF) assumes that the weights within each layer are correlated but not with weights in other layers; node-decoupled extended Kalman filter (NDEKF) correlates the weights of the afferent connections of each neuron; and fully decoupled extended Kalman filter (FDEKF) omits any correlation between weights [11]. In the early development of the EKF as a training algorithm, it was applied to multilayer perceptron neural networks for pattern classification problems. However, the networks that were used in these cases consisted of just a few layers and neurons [13; 15]. Nowadays, taking advantage of modern computational hardware, the algorithms based on the EKF seem interesting for training neural networks with many weights.