The field of neural network research is currently moving towards improving the approximation capabilities and stability of deep learning models. Recent developments have focused on reducing the bias component of approximation errors and improving the robustness of neural networks. A key area of interest is the development of new frameworks and techniques for context-aware low-rank approximation, which has shown promising results in improving metrics over traditional methods. Additionally, there is a growing interest in understanding the theoretical properties of neural networks, such as the layerwise effective dimension and the local Lipschitz bound of transformers. These advances have the potential to improve the performance and reliability of deep learning models in a wide range of applications. Noteworthy papers include: Sharp uniform approximation for spectral Barron functions by deep neural networks, which demonstrates a significant reduction in smoothness requirements for neural network approximation. COALA: Numerically Stable and Efficient Framework for Context-Aware Low-Rank Approximation, which proposes a novel inversion-free regularized framework for context-aware low-rank approximation.