arXiv subjects

Jiaqi Yu

Publications and source records attributed to Jiaqi Yu.

21 records · Page 2Linked to original sources

arXiv2023

Heisenberg Uniqueness Pairs and the wave equation

Given a curve $Γ$ and a set $Λ$ in the plane, the concept of the Heisenberg uniqueness pair $(Γ, Λ)$ was first introduced by Hedenmalm and Motes-Rodr\'ıgez (Ann. of Math. 173(2),1507-1527, 2011, \cite{HM}) as a variant of the uncertainty principle for the Fourier transform. The main results of Hedenmalm and Motes-Rodr\'ıgez concern the hyperbola $Γ_ε=\{(x_1, x_2)\in \mathbb{R}^2,\, x_1x_2=ε\}$ ($0\neε\in \mathbb{R}$) and lattice-crosses $Λ_{αβ}=(α\mathbb{Z}\times \{0\})\cup(\{0\}\times β\mathbb{Z})$ ($α, β>0$), where it's proved that $(Γ_ε, Λ_{αβ})$ is a Heisenberg uniqueness pair if and only if $αβ\leq 1/|ε|$. In this paper, we aim to study the endpoint case (i.e., $ε=0$ in $Γ_ε$) and investigate the following problem: what's the minimal amount of information required on $Λ$ (the zero set) to form a Heisenberg uniqueness pair? When $Λ$ is contained in the union of two curves in the plane, we give characterizations in terms of some dynamical system conditions. The situation is quite different in higher dimensions and we obtain characterizations in the case that $Λ$ is the union of two hyperplanes.

math.CA↗

arXiv2023

Saturated theorem along cubes for a measure and applications

We show that for a minimal system $(X,T)$, the set of saturated points along cubes with respect to its maximal $\infty$-step pro-nilfactor $X_\infty$ has a full measure. As an application, it is shown that if a minimal system $(X,T)$ has no non-trivial $(k+1)$-tuples with arbitrarily long finite IP-independence sets, then it has only at most $k$ ergodic measures and is an almost $k'$ to one extension of $X_\infty$ for some $k'\leqslant k$. Particularly, for $k=1$ we prove that $(X,T)$ is uniquely ergodic (even regular with respect to $X_\infty$), which answers a conjecture stated in [3].

math.DS↗

arXiv2023

DREAM: Domain-free Reverse Engineering Attributes of Black-box Model

Deep learning models are usually black boxes when deployed on machine learning platforms. Prior works have shown that the attributes ($e.g.$, the number of convolutional layers) of a target black-box neural network can be exposed through a sequence of queries. There is a crucial limitation: these works assume the dataset used for training the target model to be known beforehand and leverage this dataset for model attribute attack. However, it is difficult to access the training dataset of the target black-box model in reality. Therefore, whether the attributes of a target black-box model could be still revealed in this case is doubtful. In this paper, we investigate a new problem of Domain-agnostic Reverse Engineering the Attributes of a black-box target Model, called DREAM, without requiring the availability of the target model's training dataset, and put forward a general and principled framework by casting this problem as an out of distribution (OOD) generalization problem. In this way, we can learn a domain-agnostic model to inversely infer the attributes of a target black-box model with unknown training data. This makes our method one of the kinds that can gracefully apply to an arbitrary domain for model attribute reverse engineering with strong generalization ability. Extensive experimental studies are conducted and the results validate the superiority of our proposed method over the baselines.

cs.LG↗