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Yong Li

Publications and source records attributed to Yong Li.

At least 613 records · Page 34Linked to original sources
arXiv2023

Towards continuity: Universal frequency-preserving KAM persistence and remaining regularity

Beyond Hölder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian system, even allows the non-integrable part being critical finitely smooth. To achieve this goal, besides investigating the Jackson approximation theorem towards only modulus of continuity, we demonstrate an abstract regularity theorem adapting to the new iterative scheme. Via these tools, we obtain a KAM theorem with sharp differentiability hypotheses, asserting that the persistent torus keeps prescribed universal Diophantine frequency unchanged. Further, the non-Hölder regularity for invariant KAM torus as well as the conjugation is explicitly shown by introducing asymptotic analysis. To our knowledge, this is the first approach to KAM on these aspects in a continuous sense, and we also provide two systems, which cannot be studied by previous KAM but by ours.

math.DS↗
arXiv2023

LoSAC: An Efficient Local Stochastic Average Control Method for Federated Optimization

Federated optimization (FedOpt), which targets at collaboratively training a learning model across a large number of distributed clients, is vital for federated learning. The primary concerns in FedOpt can be attributed to the model divergence and communication efficiency, which significantly affect the performance. In this paper, we propose a new method, i.e., LoSAC, to learn from heterogeneous distributed data more efficiently. Its key algorithmic insight is to locally update the estimate for the global full gradient after {each} regular local model update. Thus, LoSAC can keep clients' information refreshed in a more compact way. In particular, we have studied the convergence result for LoSAC. Besides, the bonus of LoSAC is the ability to defend the information leakage from the recent technique Deep Leakage Gradients (DLG). Finally, experiments have verified the superiority of LoSAC comparing with state-of-the-art FedOpt algorithms. Specifically, LoSAC significantly improves communication efficiency by more than $100\%$ on average, mitigates the model divergence problem and equips with the defense ability against DLG.

cs.DC↗
arXiv2023

Knowledge-infused Contrastive Learning for Urban Imagery-based Socioeconomic Prediction

Monitoring sustainable development goals requires accurate and timely socioeconomic statistics, while ubiquitous and frequently-updated urban imagery in web like satellite/street view images has emerged as an important source for socioeconomic prediction. Especially, recent studies turn to self-supervised contrastive learning with manually designed similarity metrics for urban imagery representation learning and further socioeconomic prediction, which however suffers from effectiveness and robustness issues. To address such issues, in this paper, we propose a Knowledge-infused Contrastive Learning (KnowCL) model for urban imagery-based socioeconomic prediction. Specifically, we firstly introduce knowledge graph (KG) to effectively model the urban knowledge in spatiality, mobility, etc., and then build neural network based encoders to learn representations of an urban image in associated semantic and visual spaces, respectively. Finally, we design a cross-modality based contrastive learning framework with a novel image-KG contrastive loss, which maximizes the mutual information between semantic and visual representations for knowledge infusion. Extensive experiments of applying the learnt visual representations for socioeconomic prediction on three datasets demonstrate the superior performance of KnowCL with over 30\% improvements on $R^2$ compared with baselines. Especially, our proposed KnowCL model can apply to both satellite and street imagery with both effectiveness and transferability achieved, which provides insights into urban imagery-based socioeconomic prediction.

cs.CV↗
arXiv2023

Nonreciprocal and chiral single-photon scattering for giant atoms

Quantum optics with giant atoms has provided a new paradigm to study photon scatterings. In this work, we investigate the nontrivial single-photon scattering properties of giant atoms being an effective platform to realize nonreciprocal and chiral quantum optics. For two-level giant atoms, we identify the condition for nonreciprocal transmission: the external atomic dissipation is further required other than the breaking of time-reversal symmetry by local coupling phases. Especially, in the non-Markovian regime, unconventional revival peaks periodically appear in the reflection spectrum. To explore more interesting scattering behaviors, we extend the two-level giant-atom system to Δ-type and {\nabla}-type three-level giant atoms coupled to double waveguides with different physical mechanisms to realize nonreciprocal and chiral scatterings. Our proposed giant-atom structures have potential applications of high-efficiency targeted routers that can transport single photons to any desired port deterministically and circulators that can transport single photons between four ports in a cyclic way.

quant-ph↗
arXiv2023

Moser's Theorem with Frequency-preserving

This paper mainly concerns the KAM persistence of the mapping $\mathscr{F}:\mathbb{T}^{n}\times E\rightarrow \mathbb{T}^{n}\times \mathbb{R}^{n}$ with intersection property, where $E\subset \mathbb{R}^{n}$ is a connected closed bounded domain with interior points. By assuming that the frequency mapping satisfies certain topological degree condition and weak convexity condition, we prove some Moser type results about the invariant torus of mapping $\mathscr{F}$ with frequency-preserving under small perturbations. To our knowledge, this is the first approach to Moser's theorem with frequency-preserving. Moreover, given perturbed mappings over $ \mathbb{T}^n $, it is shown that such persistence still holds when the frequency mapping and perturbations are only continuous about parameter beyond Lipschitz or even Hölder type. We also touch the parameter without dimension limitation problem under such settings.

math.DS↗
arXiv2023

Dual-interest Factorization-heads Attention for Sequential Recommendation

Accurate user interest modeling is vital for recommendation scenarios. One of the effective solutions is the sequential recommendation that relies on click behaviors, but this is not elegant in the video feed recommendation where users are passive in receiving the streaming contents and return skip or no-skip behaviors. Here skip and no-skip behaviors can be treated as negative and positive feedback, respectively. With the mixture of positive and negative feedback, it is challenging to capture the transition pattern of behavioral sequence. To do so, FeedRec has exploited a shared vanilla Transformer, which may be inelegant because head interaction of multi-heads attention does not consider different types of feedback. In this paper, we propose Dual-interest Factorization-heads Attention for Sequential Recommendation (short for DFAR) consisting of feedback-aware encoding layer, dual-interest disentangling layer and prediction layer. In the feedback-aware encoding layer, we first suppose each head of multi-heads attention can capture specific feedback relations. Then we further propose factorization-heads attention which can mask specific head interaction and inject feedback information so as to factorize the relation between different types of feedback. Additionally, we propose a dual-interest disentangling layer to decouple positive and negative interests before performing disentanglement on their representations. Finally, we evolve the positive and negative interests by corresponding towers whose outputs are contrastive by BPR loss. Experiments on two real-world datasets show the superiority of our proposed method against state-of-the-art baselines. Further ablation study and visualization also sustain its effectiveness. We release the source code here: https://github.com/tsinghua-fib-lab/WWW2023-DFAR.

cs.IR↗
arXiv2023

Learning to Simulate Daily Activities via Modeling Dynamic Human Needs

Daily activity data that records individuals' various types of activities in daily life are widely used in many applications such as activity scheduling, activity recommendation, and policymaking. Though with high value, its accessibility is limited due to high collection costs and potential privacy issues. Therefore, simulating human activities to produce massive high-quality data is of great importance to benefit practical applications. However, existing solutions, including rule-based methods with simplified assumptions of human behavior and data-driven methods directly fitting real-world data, both cannot fully qualify for matching reality. In this paper, motivated by the classic psychological theory, Maslow's need theory describing human motivation, we propose a knowledge-driven simulation framework based on generative adversarial imitation learning. To enhance the fidelity and utility of the generated activity data, our core idea is to model the evolution of human needs as the underlying mechanism that drives activity generation in the simulation model. Specifically, this is achieved by a hierarchical model structure that disentangles different need levels, and the use of neural stochastic differential equations that successfully captures piecewise-continuous characteristics of need dynamics. Extensive experiments demonstrate that our framework outperforms the state-of-the-art baselines in terms of data fidelity and utility. Besides, we present the insightful interpretability of the need modeling. The code is available at https://github.com/tsinghua-fib-lab/SAND.

cs.LG↗
arXiv2023

Complex decoherence-free interactions between giant atoms

Giant atoms provide a promising platform for engineering decoherence-free interactions which is a major task in modern quantum technologies. Here we study systematically how to implement complex decoherence-free interactions among giant atoms resorting to periodic coupling modulations and suitable arrangements of coupling points. We demonstrate that the phase of the modulation, which is tunable in experiments, can be encoded into the decoherence-free interactions, and thus enables phase-dependent dynamics when the giant atoms constitute an effective closed loop. Moreover, we consider the influence of non-Markovian retardation effect arising from large separations of the coupling points and study its dependence on the modulation parameters.

quant-ph↗
arXiv2023

Resonant modal approximation of time-domain elastic scattering from nano-bubbles in elastic materials

This paper is devoted to establishing the resonant modal expansion of the low-frequency part of the scattered field for acoustic bubbles embedded in elastic materials in the time domain. Due to the nano-bubble with damping, Minnaert resonance can be induced at certain discrete resonant frequencies, which forms the fundamental basis of effectively constructing elastic metamaterials via the composite material theory. There are two major contributions in this work. First, we ansatz a special form of the density, approximate the incident field with a finite number of modes, and then obtain an expansion with a finite number of modes for the acoustic-elastic wave scattering in the time-harmonic regime. Second, we show that the low-frequency part of the scattered field in the time domain can be well approximated by using the resonant modal expansion with sharp error estimates. Interestingly, we find that the $0$-th mode is the main contribution to the resonant modal expansion.

math.AP↗
arXiv2023

Universal frequency-preserving KAM persistence via modulus of continuity

In this paper, we study the persistence and remaining regularity of KAM invariant torus under sufficiently small perturbations of a Hamiltonian function together with its derivatives, in sense of finite smoothness with modulus of continuity, as a generalization of classical Hölder continuous circumstances. To achieve this goal, we extend the Jackson approximation theorem to the case of modulus of continuity, and establish a corresponding regularity theorem adapting to the new iterative scheme. Via these tools, we establish a KAM theorem with sharp differentiability hypotheses, which asserts that the persistent torus keeps prescribed universal Diophantine frequency unchanged and reaches the regularity for persistent KAM torus beyond Hölder's type.

math.DS↗
arXiv2023

KAM theorem on modulus of continuity about parameter

In this paper, we study the Hamiltonian systems $ H\left( {y,x,ξ,\varepsilon } \right) = \left\langle {ω\left( ξ\right),y} \right\rangle + \varepsilon P\left( {y,x,ξ,\varepsilon } \right) $, where $ ω$ and $ P $ are continuous about $ ξ$. We prove that persistent invariant tori possess the same frequency as the unperturbed tori, under certain transversality condition and weak convexity condition for the frequency mapping $ ω$. As a direct application, we prove a KAM theorem when the perturbation $P$ holds arbitrary Hölder continuity with respect to parameter $ ξ$. The infinite dimensional case is also considered. To our knowledge, this is the first approach to the systems with the only continuity in parameter beyond Hölder's type.

math.DS↗
arXiv2023

A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions

Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach to recommender systems. In this survey, we conduct a comprehensive review of the literature on graph neural network-based recommender systems. We first introduce the background and the history of the development of both recommender systems and graph neural networks. For recommender systems, in general, there are four aspects for categorizing existing works: stage, scenario, objective, and application. For graph neural networks, the existing methods consist of two categories, spectral models and spatial ones. We then discuss the motivation of applying graph neural networks into recommender systems, mainly consisting of the high-order connectivity, the structural property of data, and the enhanced supervision signal. We then systematically analyze the challenges in graph construction, embedding propagation/aggregation, model optimization, and computation efficiency. Afterward and primarily, we provide a comprehensive overview of a multitude of existing works of graph neural network-based recommender systems, following the taxonomy above. Finally, we raise discussions on the open problems and promising future directions in this area. We summarize the representative papers along with their code repositories in \url{https://github.com/tsinghua-fib-lab/GNN-Recommender-Systems}.

cs.IR↗
arXiv2023

Enantio-specific state transfer of chiral molecules through enantio-selective shortcut-to-adiabaticity paths

An interesting method of fast enantio-specific state transfer is proposed for cyclic three-level systems of chiral molecules. We show that the fast population transfer via shortcut to adiabaticity can be accomplished for the cyclic three-level system of a general (chiral) molecule with invariant-based inverse engineering of the coupling strengths. By choosing appropriate parameters, the two enantiomers, which are initially prepared in their ground states in the three-level systems, will evolve respectively along their enantio-selective shortcut-to-adiabaticity paths to different-energy final states simultaneously, namely achieving the fast enantio-specific state transfer.

quant-ph↗
arXiv2023

Modular Mix-and-Match Complementation of Büchi Automata (Technical Report)

Complementation of nondeterministic Büchi automata (BAs) is an important problem in automata theory with numerous applications in formal verification, such as termination analysis of programs, model checking, or in decision procedures of some logics. We build on ideas from a recent work on BA determinization by Li et al. and propose a new modular algorithm for BA complementation. Our algorithm allows to combine several BA complementation procedures together, with one procedure for a subset of the BA's strongly connected components (SCCs). In this way, one can exploit the structure of particular SCCs (such as when they are inherently weak or deterministic) and use more efficient specialized algorithms, regardless of the structure of the whole BA. We give a general framework into which partial complementation procedures can be plugged in, and its instantiation with several algorithms. The framework can, in general, produce a complement with an Emerson-Lei acceptance condition, which can often be more compact. Using the algorithm, we were able to establish an exponentially better new upper bound of $O(4n)$ for complementation of the recently introduced class of elevator automata. We implemented the algorithm in a prototype and performed a comprehensive set of experiments on a large set of benchmarks, showing that our framework complements well the state of the art and that it can serve as a basis for future efficient BA complementation and inclusion checking algorithms.

cs.FL↗
arXiv2023

KAM Theorems for Multi-scale Torus

In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with quasiperiodic force and so on. We study the persistence of invariant tori for this Hamiltonian system, and establish some KAM type results including the isoenergetic type. As consequences, we can show that Boltzmann's ergodicity hypothesis is also not true for this Hamiltonian system.

math.DS↗
arXiv2022

Finding similarity of orbits between two discrete dynamical systems via optimal principle

Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research techniques still remains an urgent challenge we face. To this end, the concepts of similarity transformation matrix and similarity degree are innovatively introduced to describe similarity of orbits between two complicated discrete dynamical systems that seem to be irrelevant. Furthermore, we present a general optimal principle, giving a strict characterization from the perspective of dynamical systems combined with optimization theory. For well-known examples of chaotic dynamical systems, such as Lorenz attractor, Chua's circuit, R$\rm\ddot{o}$ssler attractor, Chen attractor, L$\rm\ddot{u}$ attractor and hybrid system, with using of the homotopy idea, some numerical simulation results demonstrate that similarity can be found in rich characteristics and complex behaviors of chaotic dynamics via the optimal principle we presented.

math.DS↗
arXiv2022

A giant atom with modulated transition frequency

Giant atoms are known for the frequency-dependent spontaneous emission and associated interference effects. In this paper, we study the spontaneous emission dynamics of a two-level giant atom with dynamically modulated transition frequency. It is shown that the retarded feedback effect of the giant-atom system is greatly modified by a dynamical phase arising from the frequency modulation and the retardation effect itself. Interestingly, such a modification can in turn suppress the retarded feedback such that the giant atom behaves like a small one. By introducing an additional phase difference between the two atom-waveguide coupling paths, we also demonstrate the possibility of realizing chiral and tunable temporal profiles of the output fields. The results in this paper have potential applications in quantum information processing and quantum network engineering.

quant-ph↗
arXiv2022

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems

We study enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric with the two involved cavities being dissipatively coupled via the waveguide. When a weak waveguide-mediated coherent coupling is introduced, the anti-PT symmetry may break down. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the sensitivity shows resistances to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength, and has potential applications in high-precision measurements with physical systems involving Kerr-type nonlinearity.

quant-ph↗