Jing Yu, Yuh-Shyang Wang, James Anderson
Distributed linear control design is crucial for large-scale cyber-physical systems. It is generally desirable to both impose information exchange (communication) constraints on the distributed controller, and to limit the propagation of disturbances to a local region without cascading to the global network (localization). Recently proposed System Level Synthesis (SLS) theory provides a framework where such communication and localization requirements can be tractably incorporated in controller design and implementation. In this work, we derive a solution to the localized and distributed H2 state feedback control problem without resorting to Finite Impulse Response (FIR) approximation. Our proposed synthesis algorithm allows a column-wise decomposition of the resulting convex program, and is therefore scalable to arbitrary large-scale networks. We demonstrate superior cost performance and computation time of the proposed procedure over previous methods via numerical simulation.
Jing Yu, Varun Gupta, Adam Wierman
This paper studies the problem of online stabilization of an unknown discrete-time linear time-varying (LTV) system under bounded non-stochastic (potentially adversarial) disturbances. We propose a novel control algorithm based on convex body chasing (CBC). Under the assumption of infrequently changing or slowly drifting dynamics, the algorithm guarantees bounded-input-bounded-output stability in the closed loop. Our approach avoids system identification and applies, with minimal disturbance assumptions, to a variety of LTV systems of practical importance. We demonstrate the algorithm numerically on examples of LTV systems including Markov linear jump systems with finitely many jumps.
Anton Bernshteyn, Jing Yu
The Lovász Local Lemma (the LLL for short) is a powerful tool in probabilistic combinatorics that is used to verify the existence of combinatorial objects with desirable properties. Recent years saw the development of various "constructive" versions of the LLL. A major success of this research direction is the Borel version of the LLL due to Csóka, Grabowski, Máthé, Pikhurko, and Tyros, which holds under a subexponential growth assumption. A drawback of their approach is that it only applies when the underlying random variables take values in a finite set. We present an alternative proof of a Borel version of the LLL that holds even if the underlying random variables are continuous and applies to dependency graphs of limited exponential growth.
Jing Yu, Kangqiao Li, Gongxiang Liu
Let $H$ be a finite-dimensional Hopf algebra over an algebraically closed field $\Bbbk$ with the dual Chevalley property. We prove that $H$ is of finite corepresentation type if and only if it is coNakayama, if and only if the link quiver $\mathrm{Q}(H)$ of $H$ is a disjoint union of basic cycles, if and only if the link-indecomposable component $H_{(1)}$ containing $\Bbbk1$ is a pointed Hopf algebra and the link quiver of $H_{(1)}$ is a basic cycle.
Jing Yu, Xingyu Zhu
We present an alternative probabilistic proof for the sharp Assouad--Nagata dimension bound of a doubling metric space. In addition, we explore some partial rigidity results and applications to scalar curvature. A significant technical tool in our argument is the concept of padded decomposition, which originates in computer science and has been extended to general separable metric spaces by us. Along the way, we extend the sharp upper bound on the asymptotic dimension of graphs with polynomial growth to noncollapsed locally compact metric measure spaces with polynomial volume growth. This sheds light on broader applications of probabilistic methods in metric geometry.
Jing Yu, Jie-Xiang Zhu
We study the enumeration of graph orientations under local degree constraints. Given a finite graph $G = (V, E)$ and a family of admissible sets $\{\mathsf P_v \subseteq \mathbb{Z} : v \in V\}$, let $\mathcal N (G; \prod_{v \in V} \mathsf P_v)$ denote the number of orientations in which the out-degree of each vertex $v$ lies in $P_v$. We prove a general duality formula expressing $\mathcal N(G; \prod_{v \in V} \mathsf P_v)$ as a signed sum over edge subsets, involving products of coefficient sums associated with $\{\mathsf P_v\}_{v \in V}$, from a family of polynomials. Our approach employs gauge transformations, a technique rooted in statistical physics and holographic algorithms. We also present a probabilistic derivation of the same identity, interpreting the orientation-generating polynomial as the expectation of a random polynomial product. As applications, we obtain explicit formulas for the number of even orientations and for mixed Eulerian-even orientations on general graphs. Our formula generalizes a result of Borbényi and Csikvári on Eulerian orientations of graphs.
Jiayang Li, Jing Yu, Yu Marco Nie, Zhaoran Wang
In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework. To enable the backward propagation through the equilibria of games, we propose two approaches, respectively based on explicit and implicit differentiation. Specifically, we cast the equilibria as the solutions to variational inequalities (VIs). The explicit approach unrolls the projection method for solving VIs, while the implicit approach exploits the sensitivity of the solutions to VIs. At the core of both approaches is the differentiation through a projection operator. Moreover, we establish the correctness of both approaches and identify the conditions under which one approach is more desirable than the other. The analytical results are validated using several real-world problems.
Song Wang, Yu Jing
In this paper, we propose surrogate agent-environment interface (SAEI) in reinforcement learning. We also state that learning based on probability surrogate agent-environment interface provides optimal policy of task agent-environment interface. We introduce surrogate probability action and develop the probability surrogate action deterministic policy gradient (PSADPG) algorithm based on SAEI. This algorithm enables continuous control of discrete action. The experiments show PSADPG achieves the performance of DQN in certain tasks with the stochastic optimal policy nature in the initial training stage.
Jing Yu, Yibo Zhao, Jiapeng Zhu, Wenming Shao, Bo Pang, Zhao Zhang, Xiang Li
The widespread dissemination of toxic content on social media poses a serious threat to both online environments and public discourse, highlighting the urgent need for detoxification methods that effectively remove toxicity while preserving the original semantics. However, existing approaches often struggle to simultaneously achieve strong detoxification performance, semantic preservation, and robustness to out-of-distribution data. Moreover, they typically rely on costly, manually annotated parallel corpora while showing poor data efficiency. To address these challenges, we propose a two-stage training framework that jointly optimizes for data efficiency, semantic preservation, and model generalization. We first perform supervised fine-tuning on a small set of high-quality, filtered parallel data to establish a strong initialization. Then, we leverage unlabeled toxic inputs and a custom-designed reward model to train the LLM using Group Relative Policy Optimization. Experimental results demonstrate that our method effectively mitigates the trade-offs faced by previous work, achieving state-of-the-art performance with improved generalization and significantly reduced dependence on annotated data. Our code is available at: https://github.com/allacnobug/Detoxification-of-Text.
Jing Yu
Let $\mathcal{A}$ and $\mathcal{B}$ be subcategories of tensor categories $\mathcal{C}$ and $\mathcal{D}$, respectively, both of which are abelian categories with finitely many isomorphism classes of simple objects. We prove that if their derived categories $\mathbf{D}^b(\mathcal{A})$ and $\mathbf{D}^b(\mathcal{B})$ are left triangulated tensor ideals and are equivalent as triangulated $\mathbf{D}^b(\mathcal{C})$-module categories via an equivalence induced by a monoidal triangulated functor $F:\mathbf{D}^b(\mathcal{C})\rightarrow \mathbf{D}^b(\mathcal{D})$, then the original module categories $\mathcal{A}$ and $\mathcal{B}$ are themselves equivalent. We then apply this result to smash product algebras. Furthermore, the localization theory of module categories and triangulated module categories is investigated.
Jing Yu, Gongxiang Liu, Kun Zhou, Xiangjun Zhen
In this paper, we aim to study abelian extensions for some infinite group. We show that the Hopf algebra $\Bbbk^G{}^τ\#_σ\Bbbk F$ constructed through abelian extensions of $\Bbbk F$ by $\Bbbk^G$ for some (infinite) group $F$ and finite group $G$ is cosemisimple, and discuss when it admits a compact quantum group structure if $\Bbbk$ is the field of complex numbers $\mathbb{C}.$ We also find all the simple $\Bbbk^G{}^τ\#_σ\Bbbk F$-comodules and attempt to determine the Grothendieck ring of the category of finite-dimensional right $\Bbbk^G{}^τ\#_σ\Bbbk F$-comodules. Moreover, some new properties are given and some new examples are constructed.
George Brooks, Fadekemi Osaye, Anna Schenfisch, Zhiyu Wang, Jing Yu
In this paper, we show that all simple outerplanar graphs $G$ with minimum degree at least $2$ and positive Lin-Lu-Yau Ricci curvature on every edge have maximum degree at most $9$. Furthermore, if $G$ is maximally outerplanar, then $G$ has at most $10$ vertices. Both upper bounds are sharp.
Anton Bernshteyn, Jing Yu
Let $G$ be a Borel graph all of whose finite subgraphs embed into the $d$-dimensional grid with diagonals. We show that then $G$ itself admits a Borel embedding into the Schreier graph of a free Borel action of $\mathbb Z^{O(d)}$. This strengthens an earlier result of the authors, in which $O(d)$ is replaced by $O(ρ\log ρ)$, where $ρ$ is the polynomial growth rate of $G$.
Yaobin Chen, Jiaxi Nie, Jing Yu, Wentao Zhang
Let $α(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $α(\mathbb{F}_q^{d},p)$ up to a polylogarithmic factor by proving the balanced supersaturation conjecture of Balogh and Luo. Our result also resolves a conjecture implicitly posed by the first author, Liu, the second author and Zeng. In the course of our proof, we establish a lemma that demonstrates a ``structure vs. randomness'' phenomenon for point sets in finite-field linear spaces, which may be of independent interest.
Xiangjun Zhen, Gongxiang Liu, Jing Yu
Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules. Moreover, we completely determine which of them admit a finite-dimensional Nichols algebra.
Jing Yu, Chenghao Yang, Zengchang Qin, Zhuoqian Yang, Yue Hu, Weifeng Zhang
Feature modeling of different modalities is a basic problem in current research of cross-modal information retrieval. Existing models typically project texts and images into one embedding space, in which semantically similar information will have a shorter distance. Semantic modeling of textural relationships is notoriously difficult. In this paper, we propose an approach to model texts using a featured graph by integrating multi-view textual relationships including semantic relations, statistical co-occurrence, and prior relations in the knowledge base. A dual-path neural network is adopted to learn multi-modal representations of information and cross-modal similarity measure jointly. We use a Graph Convolutional Network (GCN) for generating relation-aware text representations, and use a Convolutional Neural Network (CNN) with non-linearities for image representations. The cross-modal similarity measure is learned by distance metric learning. Experimental results show that, by leveraging the rich relational semantics in texts, our model can outperform the state-of-the-art models by 3.4% and 6.3% on accuracy on two benchmark datasets.
Yu Jing, Tan Yujuan, Ren Ao, Liu Duo
The prediction of optical flow for occluded points is still a difficult problem that has not yet been solved. Recent methods use self-attention to find relevant non-occluded points as references for estimating the optical flow of occluded points based on the assumption of self-similarity. However, they rely on visual features of a single image and weak constraints, which are not sufficient to constrain the trained network to focus on erroneous and weakly relevant reference points. We make full use of online occlusion recognition information to construct occlusion extended visual features and two strong constraints, allowing the network to learn to focus only on the most relevant references without requiring occlusion ground truth to participate in the training of the network. Our method adds very few network parameters to the original framework, making it very lightweight. Extensive experiments show that our model has the greatest cross-dataset generalization. Our method achieves much greater error reduction, 18.6%, 16.2%, and 20.1% for all points, non-occluded points, and occluded points respectively from the state-of-the-art GMA-base method, MATCHFlow(GMA), on Sintel Albedo pass. Furthermore, our model achieves state-of-the-art performance on the Sintel bench-marks, ranking \#1 among all published methods on Sintel clean pass. The code will be open-source.
Jing Yu, Dimitar Ho, Adam Wierman
We investigate the problem of stabilizing an unknown networked linear system under communication constraints and adversarial disturbances. We propose the first provably stabilizing algorithm for the problem. The algorithm uses a distributed version of nested convex body chasing to maintain a consistent estimate of the network dynamics and applies system level synthesis to determine a distributed controller based on this estimated model. Our approach avoids the need for system identification and accommodates a broad class of communication delay while being fully distributed and scaling favorably with the number of subsystems.
Yu Jing, Xiaogang Li, Yang Yang, Chonghang Wu, Wenbing Fu, Wei Hu, Yuanyuan Li, Hua Xu
Jul 23, 2021·quant-ph·PDF With the rapid growth of qubit numbers and coherence times in quantum hardware technology, implementing shallow neural networks on the so-called Noisy Intermediate-Scale Quantum (NISQ) devices has attracted a lot of interest. Many quantum (convolutional) circuit ansaetze are proposed for grayscale images classification tasks with promising empirical results. However, when applying these ansaetze on RGB images, the intra-channel information that is useful for vision tasks is not extracted effectively. In this paper, we propose two types of quantum circuit ansaetze to simulate convolution operations on RGB images, which differ in the way how inter-channel and intra-channel information are extracted. To the best of our knowledge, this is the first work of a quantum convolutional circuit to deal with RGB images effectively, with a higher test accuracy compared to the purely classical CNNs. We also investigate the relationship between the size of quantum circuit ansatz and the learnability of the hybrid quantum-classical convolutional neural network. Through experiments based on CIFAR-10 and MNIST datasets, we demonstrate that a larger size of the quantum circuit ansatz improves predictive performance in multiclass classification tasks, providing useful insights for near term quantum algorithm developments.
Yu Jing, Yandong Ma, Yafei Li, Thomas Heine
We propose a two-dimensional crystal which possesses low indirect band gaps of 0.55 eV (monolayer) and 0.43 eV (bilayer) and high carrier mobilities similar to those of phosphorene: GeP3. GeP3 has a stable three-dimensional layered bulk counterpart which is metallic and is known from experiment since 1970. It has a small cleavage energy, which suggests exfoliation of bulk material as viable means for the preparation of mono- and few-layer materials. The material shows strong interlayer quantum confinement effects, resulting in a band gap reduction from mono- to bilayer, and then to a semiconductor-metal transition between bi- and triple layer. Under biaxial strain, the indirect band gap can be turned into a direct one. Pronounced light absorption in the spectral range from ~600 to 1400 nm is predicted for monolayer and bilayer and promises applications in photovoltaics.