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.