4 papers
Sample continuation in Bayesian hierarchical model via variational inference
Yucong Liu, Zilai Si, Alexander Strang
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim…
A Bootstrap Perspective on Stochastic Gradient Descent
Hongjian Lan, Yucong Liu, Florian Schäfer
Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we st…
Attention is a smoothed cubic spline
Zehua Lai, Lek-Heng Lim, Yucong Liu
We highlight a perhaps important but hitherto unobserved insight: The attention module in a transformer is a smoothed cubic spline. Viewed in this manner, this mysterious but criti…
Neural Networks are Integrable
Yucong Liu
In this study, we explore the integration of Neural Networks, a powerful class of functions known for their exceptional approximation capabilities. Our primary emphasis is on the i…