The recent advancements in the field of neural network optimization and pruning have significantly focused on enhancing efficiency and scalability while maintaining or even improving model performance. A notable trend is the development of novel pruning techniques that not only reduce computational costs but also address specific challenges such as vanishing activations in deep networks and biases in quadratic approximations. These methods often leverage statistical analysis and information theory to identify and remove redundant or less informative components, thereby streamlining the model without compromising its effectiveness. Additionally, there is a growing interest in subset-based training and pruning strategies that utilize smaller, representative datasets to achieve computational efficiency, which is particularly relevant for resource-constrained environments. The integration of these techniques with theoretical underpinnings ensures that the advancements are not only practical but also robust and scalable across various applications. Notably, some papers have introduced innovative approaches such as similarity-guided layer pruning and debiasing mini-batch quadratics, which stand out for their theoretical contributions and empirical success in improving model efficiency and performance.