9 papers · 1 filter
Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space
Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exh…
SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving
Yesom Park, Annie C. Lu, Shao-Ching Huang +3
We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth express…
VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction
Yadi Cao, Yuxuan Liu, Liu Yang +3
In-Context Operator Networks (ICONs) have demonstrated the ability to learn operators across diverse partial differential equations using few-shot, in-context learning. However, ex…
Dynamical Implicit Neural Representations
Yesom Park, Kelvin Kan, Thomas Flynn +4
Implicit Neural Representations (INRs) provide a powerful continuous framework for modeling complex visual and geometric signals, but spectral bias remains a fundamental challenge,…
Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiency
Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3
We study Transformers through the perspective of optimal control theory, using tools from continuous-time formulations to derive actionable insights into training and architecture…
Sparse Transformer Architectures via Regularized Wasserstein Proximal Operator with Prior
Fuqun Han, Stanley Osher, Wuchen Li
In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the…