10 papers
Revealing After Overwriting: An Exponential POMDP OPE Lower Bound under History-Dependent Logging
Youyu Luo, Pengzhan Zhou, Zhida Qin +4
Multi-step revealing can make off-policy evaluation tractable under memoryless logging. With history-dependent logging, state decodability and target-relevant evidence can separate…
An Explicit Family of Log-Concave Counterexamples to the Gaussian Completely Monotone Conjecture
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We construct smooth, strictly log-concave counterexamples to the Gaussian completely monotone conjecture in every dimension. In one dimension, they form an explicit family wh…
The Randomized Query Complexity of Finding Minimal Elements in Bounded-Width Posets
Luyao Fan, Jiayang Zou, Jiayang Gao +1
We study the zero-error randomized query complexity of finding all minimal elements in an unknown -element poset of width at most . Previous work of Daskalakis, Karp, Mossel,…
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…
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--…
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…
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…
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…
Convexity of Mutual Information along the Fokker-Planck Flow
Jiayang Zou, Luyao Fan, Jiayang Gao +1
We study the convexity of mutual information as a function of time along the Fokker-Planck flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow,…
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…