The recent developments in the field of optimization for deep neural networks have seen a shift towards more efficient and innovative methods, particularly focusing on memory reduction, convergence diagnostics, and novel architectural insights. A notable trend is the exploration of alternative optimization frameworks, such as the Difference-of-Convex Algorithm (DCA), which provides a fresh perspective on understanding the effectiveness of shortcuts in neural networks. Additionally, memory-efficient preconditioned stochastic optimization techniques, leveraging quantization and error feedback, have demonstrated significant improvements in large-scale training scenarios. Convergence diagnostics for stochastic gradient descent have also advanced, with new coupling-based methods offering superior performance across various optimization problems. Furthermore, the introduction of scaled conjugate gradient methods for nonconvex optimization has shown promising results in accelerating training processes. The field is also witnessing a reevaluation of traditional optimization methods, with studies questioning the necessity of adaptive gradient methods in favor of simpler, yet effective, enhancements like learning rate scaling at initialization. Lastly, novel approaches to binary neural network optimization, incorporating historical gradient information and layer-specific embeddings, are pushing the boundaries of what is achievable with constrained computational resources. These advancements collectively indicate a move towards more efficient, robust, and theoretically grounded optimization strategies in deep learning.