The field of rational approximation and deep learning is witnessing significant developments, with a focus on improving the efficiency and accuracy of algorithms. Researchers are exploring new variants of existing algorithms, such as the AAA algorithm, to enhance their performance and applicability. Additionally, there is a growing interest in integrating different techniques, like Kolmogorov-Arnold Networks and Chebyshev polynomials, into deep learning frameworks to improve their representation capabilities. The use of hybrid models, combining convolutional neural networks and transformers, is also being investigated for applications like skin cancer classification. Furthermore, the importance of optimal scaling and compute allocation in deep reinforcement learning is being recognized, with studies aiming to provide guidelines for maximizing performance per unit of compute. Noteworthy papers include: Two intriguing variants of the AAA algorithm for rational approximation, which presents two new variants of the AAA algorithm, AAAsmooth and AAAbudget, that improve the convergence and efficiency of the original algorithm. Beyond ReLU: Chebyshev-DQN for Enhanced Deep Q-Networks, which introduces a novel architecture that integrates Chebyshev polynomials into the DQN framework to create a more effective feature representation.