The field of neural networks is experiencing significant developments in optimization and learning techniques. Researchers are exploring new methods to improve the convergence and generalization of neural networks, including the use of second-order optimization algorithms and adaptive weighted auxiliary variables. These innovations have the potential to enhance the training of neural networks, particularly in the context of deep learning. Notably, the use of ultra-fast feature learning and emergent learning curves is being investigated to improve the training of two-layer neural networks. Furthermore, gated architectures and adaptive optimization techniques are being applied to improve the performance of deep knowledge tracing models. Among the recent papers, some noteworthy contributions include:

• A study on the emergence and scaling laws in SGD learning of shallow neural networks, which provides a precise analysis of SGD dynamics and identifies sharp transition times to recover each signal direction.
• The development of AdaFisher, a novel adaptive second-order optimizer that leverages a diagonal block-Kronecker approximation of the Fisher information matrix to adaptively precondition gradients, which exhibits remarkable stability and robustness during hyperparameter tuning.