Periodic Function

Periodic functions, characterized by their repeating patterns, are a fundamental concept with applications across diverse scientific fields. Current research focuses on improving the representation and modeling of periodic functions within neural networks, exploring architectures like Fourier Analysis Networks (FAN) and modifications to existing implicit neural representations (INRs) using variable-periodic activation functions to overcome limitations in handling high frequencies and complex periodic signals. These advancements are crucial for enhancing the accuracy and efficiency of machine learning models in various applications, including signal processing, time series forecasting, and computer vision, where periodic phenomena are prevalent. Furthermore, theoretical work investigates the limitations of gradient-based optimization for learning high-frequency periodic functions, highlighting challenges and guiding the development of more effective algorithms.