The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data. In contrast, Kolmogorov-Arnold Networks have gained attention in the machine learning community for their bold claim of being unaffected by the curse of dimensionality. This paper explores the Kolmogorov-Arnold representation theorem and the mathematical principles underlying Kolmogorov-Arnold Networks, which enable their scalability and high performance in high-dimensional spaces. We begin with an introduction to foundational concepts necessary to understand Kolmogorov-Arnold Networks, including interpolation methods and Basis-splines, which form their mathematical backbone. This is followed by an overview of perceptron architectures and the Universal approximation theorem, a key principle guiding modern machine learning. This is followed by an overview of the Kolmogorov-Arnold representation theorem, including its mathematical formulation and implications for overcoming dimensionality challenges. Next, we review the architecture and error-scaling properties of Kolmogorov-Arnold Networks, demonstrating how these networks achieve true freedom from the curse of dimensionality. Finally, we discuss the practical viability of Kolmogorov-Arnold Networks, highlighting scenarios where their unique capabilities position them to excel in real-world applications. This review aims to offer insights into Kolmogorov-Arnold Networks' potential to redefine scalability and performance in high-dimensional learning tasks.

Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches tackle these issues reactively at the control stage. However, regardless of the controller, online motion execution can only be as robust as the system capabilities allow at any given state. This is why it is important to have good motion plans to begin with, where robustness is considered proactively. To this end, we propose a metric (derived from first principles) for representing robustness against external disturbances. We then use this metric within our trajectory optimization framework for solving complex loco-manipulation tasks. Through our experiments, we show that trajectories generated using our approach can resist a greater range of forces originating from any possible direction. By using our method, we can compute trajectories that solve tasks as effectively as before, with the added benefit of being able to counteract stronger disturbances in worst-case scenarios.

From the perspective of any nation, rural areas generally present a comparable set of problems, such as a lack of proper health care, education, living conditions, wages, and market opportunities. Some nations have created and developed the concept of smart villages during the previous few decades, which effectively addresses these issues. The landscape of traditional agriculture has been radically altered by digital agriculture, which has also had a positive economic impact on farmers and those who live in rural regions by ensuring an increase in agricultural production. We explored current issues in rural areas, and the consequences of smart village applications, and then illustrate our concept of smart village from recent examples of how emerging digital agriculture trends contribute to improving agricultural production in this chapter.

Understanding an information forager's actions during interaction is very important for the study of interactive information retrieval. Although information spread in uncertain information space is substantially complex due to the high entanglement of users interacting with information objects (text, image, etc.). However, an information forager, in general, accompanies a piece of information (information diet) while searching (or foraging) alternative contents, typically subject to decisive uncertainty. Such types of uncertainty are analogous to measurements in quantum mechanics which follow the uncertainty principle. In this paper, we discuss information seeking as a reinforcement learning task. We then present a reinforcement learning-based framework to model forager exploration that treats the information forager as an agent to guide their behaviour. Also, our framework incorporates the inherent uncertainty of the foragers' action using the mathematical formalism of quantum mechanics.

In the last year more than 70,000 people have been brought to the UK hospitals with serious injuries. Each time a clinician has to urgently take a patient through a screening procedure to make a reliable decision on the trauma treatment. Typically, such procedure comprises around 20 tests; however the condition of a trauma patient remains very difficult to be tested properly. What happens if these tests are ambiguously interpreted, and information about the severity of the injury will come misleading? The mistake in a decision can be fatal: using a mild treatment can put a patient at risk of dying from posttraumatic shock, while using an overtreatment can also cause death. How can we reduce the risk of the death caused by unreliable decisions? It has been shown that probabilistic reasoning, based on the Bayesian methodology of averaging over decision models, allows clinicians to evaluate the uncertainty in decision making. Based on this methodology, in this paper we aim at selecting the most important screening tests, keeping a high performance. We assume that the probabilistic reasoning within the Bayesian methodology allows us to discover new relationships between the screening tests and uncertainty in decisions. In practice, selection of the most informative tests can also reduce the cost of a screening procedure in trauma care centers. In our experiments we use the UK Trauma data to compare the efficiency of the proposed technique in terms of the performance. We also compare the uncertainty in decisions in terms of entropy.

The use of multiple Decision Models (DMs) enables to enhance the accuracy in decisions and at the same time allows users to evaluate the confidence in decision making. In this paper we explore the ability of multiple DMs to learn from a small amount of verified data. This becomes important when data samples are difficult to collect and verify. We propose an evolutionary-based approach to solving this problem. The proposed technique is examined on a few clinical problems presented by a small amount of data.

Noise, corruptions and variations in face images can seriously hurt the performance of face recognition systems. To make such systems robust, multiclass neuralnetwork classifiers capable of learning from noisy data have been suggested. However on large face data sets such systems cannot provide the robustness at a high level. In this paper we explore a pairwise neural-network system as an alternative approach to improving the robustness of face recognition. In our experiments this approach is shown to outperform the multiclass neural-network system in terms of the predictive accuracy on the face images corrupted by noise.