arXiv subjects

Liying Li

Publications and source records attributed to Liying Li.

15 recordsLinked to original sources

arXiv2026

Polynomial mixing for stochastic viscous conservation law equation on the whole line

In this paper, we study the long-time behavior of the viscous conservation law equation on the whole real line, subject to a white-in-time force and arbitrarily small damping and viscosity constants. We establish polynomial mixing rates in two settings: (a) a general super-quadratic flux with hyperviscous dissipation, where the growth of the nonlinearity is controlled by the order of hyperviscosity, and the force is sufficiently non-degenerate on a generic L2-basis; and (b) a general quadratic flux with standard second-order dissipation, and the force is non-degenerate on some unconditional basis. Both settings include the classical Burgers-type nonlinearity. The proof is based on an abstract polynomial coupling criterion developed in arXiv:2408.00592 and a Foia\c{s}--Prodi estimate.

math.AP↗

arXiv2025

Inferring Operator Emotions from a Motion-Controlled Robotic Arm

A remote robot operator's affective state can significantly impact the resulting robot's motions leading to unexpected consequences, even when the user follows protocol and performs permitted tasks. The recognition of a user operator's affective states in remote robot control scenarios is, however, underexplored. Current emotion recognition methods rely on reading the user's vital signs or body language, but the devices and user participation these measures require would add limitations to remote robot control. We demonstrate that the functional movements of a remote-controlled robotic avatar, which was not designed for emotional expression, can be used to infer the emotional state of the human operator via a machine-learning system. Specifically, our system achieved 83.3$\%$ accuracy in recognizing the user's emotional state expressed by robot movements, as a result of their hand motions. We discuss the implications of this system on prominent current and future remote robot operation and affective robotic contexts.

cs.RO↗

arXiv2025

Yi-Lightning Technical Report

This technical report presents Yi-Lightning, our latest flagship large language model (LLM). It achieves exceptional performance, ranking 6th overall on Chatbot Arena, with particularly strong results (2nd to 4th place) in specialized categories including Chinese, Math, Coding, and Hard Prompts. Yi-Lightning leverages an enhanced Mixture-of-Experts (MoE) architecture, featuring advanced expert segmentation and routing mechanisms coupled with optimized KV-caching techniques. Our development process encompasses comprehensive pre-training, supervised fine-tuning (SFT), and reinforcement learning from human feedback (RLHF), where we devise deliberate strategies for multi-stage training, synthetic data construction, and reward modeling. Furthermore, we implement RAISE (Responsible AI Safety Engine), a four-component framework to address safety issues across pre-training, post-training, and serving phases. Empowered by our scalable super-computing infrastructure, all these innovations substantially reduce training, deployment and inference costs while maintaining high-performance standards. With further evaluations on public academic benchmarks, Yi-Lightning demonstrates competitive performance against top-tier LLMs, while we observe a notable disparity between traditional, static benchmark results and real-world, dynamic human preferences. This observation prompts a critical reassessment of conventional benchmarks' utility in guiding the development of more intelligent and powerful AI systems for practical applications. Yi-Lightning is now available through our developer platform at https://platform.lingyiwanwu.com.

cs.CL↗

arXiv2025

The State of Post-Hoc Local XAI Techniques for Image Processing: Challenges and Motivations

As complex AI systems further prove to be an integral part of our lives, a persistent and critical problem is the underlying black-box nature of such products and systems. In pursuit of productivity enhancements, one must not forget the need for various technology to boost the overall trustworthiness of such AI systems. One example, which is studied extensively in this work, is the domain of Explainable Artificial Intelligence (XAI). Research works in this scope are centred around the objective of making AI systems more transparent and interpretable, to further boost reliability and trust in using them. In this work, we discuss the various motivation for XAI and its approaches, the underlying challenges that XAI faces, and some open problems that we believe deserve further efforts to look into. We also provide a brief discussion of various XAI approaches for image processing, and finally discuss some future directions, to hopefully express and motivate the positive development of the XAI research space.

cs.CV↗

arXiv2023

Coupled-Space Attacks against Random-Walk-based Anomaly Detection

Random Walks-based Anomaly Detection (RWAD) is commonly used to identify anomalous patterns in various applications. An intriguing characteristic of RWAD is that the input graph can either be pre-existing or constructed from raw features. Consequently, there are two potential attack surfaces against RWAD: graph-space attacks and feature-space attacks. In this paper, we explore this vulnerability by designing practical coupled-space attacks, investigating the interplay between graph-space and feature-space attacks. To this end, we conduct a thorough complexity analysis, proving that attacking RWAD is NP-hard. Then, we proceed to formulate the graph-space attack as a bi-level optimization problem and propose two strategies to solve it: alternative iteration (alterI-attack) or utilizing the closed-form solution of the random walk model (cf-attack). Finally, we utilize the results from the graph-space attacks as guidance to design more powerful feature-space attacks (i.e., graph-guided attacks). Comprehensive experiments demonstrate that our proposed attacks are effective in enabling the target nodes from RWAD with a limited attack budget. In addition, we conduct transfer attack experiments in a black-box setting, which show that our feature attack significantly decreases the anomaly scores of target nodes. Our study opens the door to studying the coupled-space attack against graph anomaly detection in which the graph space relies on the feature space.

cs.CR↗

arXiv2023

Localization length of the $1+1$ continuum directed random polymer

In this paper, we study the localization length of the $1+1$ continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization length converges in distribution in the thermodynamic limit, and derive an explicit density formula of the limiting distribution. As a consequence, we prove the $\tfrac32$-power law decay of the density, confirming the physics prediction of Hwa-Fisher \cite{fisher}. Our proof uses the recent result of Das-Zhu \cite{daszhu}.

math.PR↗

arXiv2022

Strongly mixing smooth planar vector field without asymptotic directions

We use a Voronoi-type tessellation based on a compound Poisson point process to construct a polynomially mixing stationary random smooth planar vector field with bounded nonnegative components such that, with probability one, none of the associated integral curves possess an asymptotic direction.

math.DS↗

arXiv2022

Point Fields of Last Passage Percolation and Coalescing Fractional Brownian Motions

We consider large-scale point fields which naturally appear in the context of the Kardar-Parisi-Zhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass concentration, and by shocks separating the sources of these points. We introduce similarly defined point fields for processes of coalescing fractional Brownian motions (cfBm). The case of the Hurst index 2/3 is of particular interest for us since, in this case, the power law of the density decay is the same as that in the KPZ phenomenon. In this paper, we present strong numerical evidence that statistical properties of points fields in these two different settings are very similar. We also discuss theoretical arguments in support of the conjecture that they are exactly the same in the large-time limit. This would indicate that two objects may, in fact, belong to the same universality class.

math.PR↗

arXiv2021

On asymptotic behavior of iterates of piecewise constant monotone maps

In this paper we study the rate of convergence of the iterates of \iid random piecewise constant monotone maps to the time-$1$ transport map for the process of coalescing Brownian motions. We prove that the rate of convergence is given by a power law. The time-1 map for the coalescing Brownian motions can be viewed as a fixed point for a natural renormalization transformation acting in the space of probability laws for random piecewise constant monotone maps. Our result implies that this fixed point is exponentially stable.

math.PR↗

arXiv2019

Intelligent Scheduling and Power Control for Multimedia Transmission in 5G CoMP Systems: A Dynamic Bargaining Game

Intelligent terminals support a large number of multimedia, such as picture, audio, video, and so on. The coexistence of various multimedia makes it necessary to provide service for different requests. In this work, we consider interference-aware coordinated multi-point (CoMP) to mitigate inter-cell interference and improve total throughput in the fifth-generation (5G) mobile networks. To select the scheduled edge users, cluster the cooperative base stations (BSs), and determine the transmitting power, a novel dynamic bargaining approach is proposed. Based on affinity propagation, we first select the users to be scheduled and the cooperative BSs serving them respectively. Then, based on the Nash bargaining solution (NBS), we develop a power control scheme considering the transmission delay, which guarantees a generalized proportional fairness among users. Simulation results demonstrate the superiority of the user-centric scheduling and power control methods in 5G CoMP systems.

cs.NI↗

arXiv2018

Weakly mixing smooth planar vector field without asymptotic directions

We construct a planar smooth weakly mixing stationary random vector field with nonnegative components such that, with probability 1, the flow generated by this vector field does not have an asymptotic direction. Moreover, for all individual trajectories, the set of partial limiting directions coincides with those spanning the positive quadrant. A modified example shows that a particle in space-time weakly mixing positive velocity field does not necessarily have an asymptotic average velocity.

math.DS↗

arXiv2018

Integrated Tempering Enhanced Sampling Method as the Infinite Switching Limit of Simulated Tempering

Fast and accurate sampling method is in high demand, in order to bridge the large gaps between molecular dynamic simulations and experimental observations. Recently, integrated tempering enhanced sampling method (ITS) has been proposed and successfully applied to various biophysical examples, significantly accelerating conformational sampling. The mathematical validation for its effectiveness has not been elucidated yet. Here we show that the integrated tempering enhanced sampling method can be viewed as a reformulation of the infinite switching limit of simulated tempering method over a mixed potential. Moreover, we demonstrate that the efficiency of simulated tempering molecular dynamics (STMD) improves as the frequency of switching between the temperatures is increased, based on the large deviation principle of empirical distributions. Our theory provides the theoretical justification of the advantage of ITS. Finally, we illustrate the utility of the infinite switching simulated tempering method through several numerical examples.

math.NA↗

arXiv2017

Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation

We consider a space-continuous and time-discrete polymer model for positive temperature and the associated zero temperature model of last passage percolation type. In our previous work, we constructed and studied infinite-volume polymer measures and one-sided infinite minimizers for the associated variational principle, and used these objects for the study of global stationary solutions of the Burgers equation with positive or zero viscosity and random kick forcing, on the entire real line. In this paper, we prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.

math.PR↗

arXiv2017

Thermodynamic limit for directed polymers and stationary solutions of the Burgers equation

The first goal of this paper is to prove multiple asymptotic results for a time-discrete and space-continuous polymer model of a random walk in a random potential. These results include: existence of deterministic free energy density in the infinite volume limit for every fixed asymptotic slope; concentration inequalities for free energy implying a bound on its fluctuation exponent; straightness estimates implying a bound on the transversal fluctuation exponent. The culmination of this program is almost sure existence and uniqueness of polymer measures on one-sided infinite paths with given endpoint and slope, and interpretation of these infinite-volume Gibbs measures as thermodynamic limits. Moreover, we prove that marginals of polymer measures with the same slope and different endpoints are asymptotic to each other. The second goal of the paper is to develop ergodic theory of the Burgers equation with positive viscosity and random kick forcing on the real line without any compactness assumptions. Namely, we prove a One Force -- One Solution principle, using the infinite volume polymer measures to construct a family of stationary global solutions for this system, and proving that each of those solutions is a one-point pullback attractor on the initial conditions with the same spatial average. This provides a natural extension of the same program realized for the inviscid Burgers equation with the help of action minimizers that can be viewed as zero temperature limits of polymer measures.

math.PR↗

arXiv2016

Primary Channel Gain Estimation for Spectrum Sharing in Cognitive Radio Networks

In cognitive radio networks, the channel gain between primary transceivers, namely, primary channel gain, is crucial for a cognitive transmitter (CT) to control the transmit power and achieve spectrum sharing. Conventionally, the primary channel gain is estimated in the primary system and thus unavailable at the CT. To deal with this issue, two estimators are proposed by enabling the CT to sense primary signals. In particular, by adopting the maximum likelihood (ML) criterion to analyze the received primary signals, a ML estimator is first developed. After demonstrating the high computational complexity of the ML estimator, a median based (MB) estimator with proved low complexity is then proposed. Furthermore, the estimation accuracy of the MB estimation is theoretically characterized. By comparing the ML estimator and the MB estimator from the aspects of the computational complexity as well as the estimation accuracy, both advantages and disadvantages of two estimators are revealed. Numerical results show that the estimation errors of the ML estimator and the MB estimator can be as small as $0.6$ dB and $0.7$ dB, respectively.

cs.IT↗