7 papers
Mitigating Gradient Pathology in PINNs through Aligned Constraint
Yichen Luo, Peiyu Zhu, Dongxiao Hu +5
While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology. The gradient…
CFG: Control Classifier-Free Guidance via Score Discrepancy Analysis
Jiayang Gao, Tianyi Zheng, Jiayang Zou +9
Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirica…
A Hexagonal Counterexample to Log-Convexity of Fisher Information Along the Heat Flow
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We construct a smooth, strictly positive, Gaussian-decaying density on for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--…
Rate-distortion Theory with Lower Semi-continuous Distortion on Noncompact Alphabets
Jiayang Zou, Luyao Fan, Jiayang Gao +1
In this paper, we study rate-distortion theory for general sources with an emphasis on the existence of optimal reconstruction distributions on noncompact alphabets. Classical atta…
Differential Properties of Information in Jump-diffusion Channels
Luyao Fan, Jiayang Zou, Jiayang Gao +1
We propose a channel modeling using jump-diffusion processes, and study the differential properties of entropy and mutual information. By utilizing the Kramers-Moyal and Kolmogorov…
A Revisit to Rate-distortion Theory via Optimal Weak Transport
Jiayang Zou, Luyao Fan, Jiayang Gao +1
This paper revisits the rate-distortion theory from the perspective of optimal weak transport, as recently introduced by Gozlan et al. While the conditions for optimality and the e…