4 papers
Approximating Young Measures With Deep Neural Networks
Rayehe Karimi Mahabadi, Jianfeng Lu, Hossein Salahshoor
Parametrized measures (or Young measures) enable to reformulate non-convex variational problems as convex problems at the cost of enlarging the search space from space of functions…
Quantitative Hypocoercivity and Lifting of Classical and Quantum Dynamics
Jianfeng Lu
We consider quantitative convergence analysis for hypocoercive dynamics such as Langevin and Lindblad equations describing classical and quantum open systems. Our goal is to provid…
Solution Theory of Hamilton-Jacobi-Bellman Equations in Spectral Barron Spaces
Ye Feng, Jianfeng Lu
We study the solution theory of the whole-space static (elliptic) Hamilton-Jacobi-Bellman (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coef…
What does guidance do? A fine-grained analysis in a simple setting
Muthu Chidambaram, Khashayar Gatmiry, Sitan Chen +2
The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood…