The field of numerical analysis and deep learning is moving towards the development of more efficient and expressive methods for solving complex problems. Researchers are exploring new techniques for approximating high-dimensional partial differential equations, such as using shallow neural networks and deep kernel methods. These approaches have shown promise in capturing complex solutions and avoiding the curse of dimensionality. Additionally, there is a growing interest in using nonlinear filtering methods, such as those based on density approximation and deep backward stochastic differential equations, for solving filtering problems. Noteworthy papers include: Solving Approximation Tasks with Greedy Deep Kernel Methods, which introduces a new framework for deep kernel greedy models and demonstrates their advantages in terms of approximation accuracies. Nonlinear filtering based on density approximation and deep BSDE prediction, which introduces a novel approximate Bayesian filter based on backward stochastic differential equations and neural networks.