The recent developments in the research area of machine learning and image processing have shown a significant shift towards leveraging advanced mathematical frameworks and novel neural network architectures to enhance feature extraction and image reconstruction. A notable trend is the integration of wavelet transforms and implicit neural representations to address the challenges in high-frequency detail restoration and arbitrary-scale super-resolution. These methods not only improve the accuracy of image classification but also offer robust solutions for numerical homogenization and multiscale feature learning. Additionally, there is a renewed interest in optimizing spectral descriptors for shape analysis, particularly through the supervised learning of the Laplace-Beltrami operator, which has shown to significantly enhance performance in various shape-related tasks. These advancements collectively push the boundaries of what is achievable in terms of precision and adaptability in machine learning applications.