The field of differential equations and tensor decomposition is experiencing a significant surge in innovation, driven by the intersection of deep learning and traditional numerical methods. Researchers are exploring new ways to improve the efficiency and accuracy of neural differential equations, including the development of scalable adjoint backpropagation methods and hybrid models that combine neural networks with recurrent neural networks. Additionally, tensor decomposition techniques such as canonical polyadic decomposition and interpolative decompositions are being enhanced with novel algorithms that reduce computational complexity and improve fitting accuracy. Noteworthy papers in this area include the introduction of a semigroup-homomorphic signature scheme, which provides a secure and efficient way to construct homomorphic signatures on semigroups. The development of a novel CP decomposition algorithm that significantly improves efficiency is also a highlight. Furthermore, the creation of MixFunn, a neural network architecture designed to solve differential equations with enhanced precision, interpretability, and generalization capability, demonstrates the potential for machine learning models to achieve higher accuracy and improved generalization in physics-informed settings.