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Recent advancements in neural network optimization are focusing on enhancing efficiency and reducing computational costs, addressing key challenges in deploying deep learning models. Hierarchical zeroth-order optimization introduces a divide-and-conquer strategy that significantly lowers query complexity, making it a viable alternative to traditional gradient methods. Meanwhile, spiking layer-adaptive pruning offers a tailored approach for spiking neural networks, balancing connectivity reduction with performance stability, which is crucial for energy-efficient applications. The discovery of sparse subnetworks through continuously relaxed Bernoulli gates presents a differentiable method for identifying optimal network configurations, achieving substantial sparsity with minimal accuracy loss. Additionally, the PRISM framework accelerates the computation of matrix functions, streamlining training processes without the need for explicit spectral estimates. Lastly, the SCORE method reimagines layer stacking with a recurrent approach, enhancing convergence speed and reducing parameter count. Collectively, these innovations are paving the way for more efficient, deployable neural network architectures across various applications.