175 citations · 317 across the 46 of their papers we have counts for
8 papers · 1 filter
Loss Curvature as a Sampling-Free Proxy for Memorization in Diffusion Models
Shashank Sule, Xinyue Yu, Boonam Shin +3
Understanding the mechanism behind why diffusion models memorize their training data remains an open question in generative modeling. In this paper, we examine this question from t…
Wasserstein Moment Nudging for Vlasov-Poisson Data Assimilation
Liyao Lyu, Xinyue Yu, David Schneidinger +1
We introduce a continuous data assimilation method for particle-in-cell simulations of the Vlasov-Poisson equation when only hydrodynamic moments are observed. The forecast state i…
Kernel Methods for Learning Operators with Multiple Inputs and Outputs
Adrien Weihs, Chunyang Liao, Jingmin Sun +1
Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning. We introduce a general kernel-based encoder-decoder framework for oper…
Multiscale Nudging: From Macroscopic Observations to Microscopic Dynamics
Liyao Lyu, Xinyue Yu, Hayden Schaeffer
We introduce a measure-based nudging framework for assimilating macroscopic observations into microscopic mean-field particle dynamics. The central difficulty is a representation m…
Multiple Neural Operators Achieve Near-Optimal Rates for Multi-Task Learning
Adrien Weihs, Hayden Schaeffer
We study the approximation and statistical complexity of learning collections of operators in a shared multi-task setting, with a focus on the Multiple Neural Operators (MNO) archi…
MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
Liyao Lyu, Xinyue Yu, Hayden Schaeffer
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued…
Generalization Bounds and Statistical Guarantees for Multi-Task and Multiple Operator Learning with MNO Networks
Adrien Weihs, Hayden Schaeffer
Multiple operator learning concerns learning operator families indexed by an operator descriptor . Training data are collected hierarchically by sampl…
Adam Improves Muon: Adaptive Moment Estimation with Orthogonalized Momentum
Minxin Zhang, Yuxuan Liu, Hayden Schaeffer
Efficient stochastic optimization typically integrates an update direction that performs well in the deterministic regime with a mechanism adapting to stochastic perturbations. Whi…