The field of neural network compression and pruning is rapidly advancing, with a focus on developing efficient and effective methods for reducing model complexity while maintaining accuracy. Recent research has explored the use of smooth regularization, influence functions, and transposable N:M sparse masks to improve model compression and pruning techniques. These innovations have led to significant gains in task performance and reduced computational requirements, making them promising solutions for deploying neural networks in real-world applications. Notably, some papers have proposed novel frameworks for incremental verification of compressed deep neural networks, ensuring their safety and reliability. Others have introduced new methods for pruning different structures within a model, achieving highly sparse models that preserve predictive ability and reduce carbon emissions. Noteworthy papers include: LayerIF, which proposes a data-driven framework for estimating layer-wise training quality in large language models. TSENOR, which introduces an efficient solver for transposable N:M sparse masks that scales to billion-parameter models. MUC-G4, which presents a novel framework for incremental verification of compressed deep neural networks. Pruning Everything, Everywhere, All at Once, which proposes a new method for pruning different structures within a model, achieving highly sparse models that preserve predictive ability and reduce carbon emissions.