Polynomial Neural Network

Polynomial neural networks (PNNs) leverage polynomial activation functions to enhance the expressiveness and efficiency of neural networks, aiming to improve approximation capabilities and model interpretability. Current research focuses on understanding the geometric properties of PNNs, analyzing their expressiveness and learning dynamics through tools like neural tangent kernels and algebraic geometry, and developing novel architectures such as polynomial convolutional networks and polynomial neural fields for various applications. This work is significant because it offers improved approximation properties for smooth and non-smooth functions, enabling advancements in areas like video processing, PDE solving, and symbolic regression, while also providing theoretical insights into neural network learning.