Recent advancements across various small research areas have collectively propelled the field of machine learning towards more efficient, scalable, and robust solutions, particularly in resource-constrained environments. A common thread among these developments is the emphasis on optimizing both computational and storage costs while maintaining or enhancing model performance. In quantization techniques, innovative strategies such as adaptive and mixed-precision quantization are tailoring bit-width allocation to specific model components, mitigating performance degradation. Notable contributions include TTAQ for stable quantization in dynamic test domains and ResQ for advanced mixed-precision quantization in large language models. In DNN optimization and acceleration, sub-6-bit quantization methods and novel systolic array architectures have demonstrated significant improvements in hardware performance and energy efficiency. The integration of asymmetric quantization and bit-slice sparsity in DNN accelerators has further pushed the boundaries of hardware efficiency. Advances in applying neural networks to differential equations and optimization problems have introduced more efficient algorithms, such as Forward-Backward Stochastic Jump Neural Networks and Neural Port-Hamiltonian Differential Algebraic Equations, enhancing scalability and accuracy. Optimization frameworks like the Difference-of-Convex Algorithm (DCA) and memory-efficient preconditioned stochastic optimization techniques are redefining traditional methods, offering new insights into training efficiency. These innovations collectively underscore a shift towards more adaptive, energy-conscious, and scalable solutions in machine learning, addressing the evolving demands of real-world applications.