8 papers
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,…
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…