Fourier Regularity and Energy-Landscape Roughness under Gaussian Smoothing
Analytic bounds linking smoothing scale to Fourier decay and optimization geometry, motivated by energy-based and score-based generative models.
Supported by a Summer Undergraduate Research Grant and advised by Xiumin Du, this project studies how Gaussian smoothing reshapes the Fourier regularity and roughness of energy landscapes, with motivation from energy-based models and score-based generative methods. I am developing analytic bounds that connect the smoothing scale to Fourier decay, gradient regularity, and the optimization geometry of the smoothed energy.