arXiv subjects

Jialun Li

Publications and source records attributed to Jialun Li.

At least 19 recordsLinked to original sources

arXiv2026

Dimensions of surface repellers and attractors of non-linear planar IFSs

We establish that for a $C^r$-generic surface repeller ($1 < r \leq \infty$), its Hausdorff and box dimensions are exactly the unique zero of the sub-additive topological pressure function. As an application of our framework, we show that the attractor of a uniformly non-conformal and weakly irreducible planar non-linear iterated function system (IFS) satisfying the strong separation condition (SSC) attains its expected Hausdorff and box dimensions. Furthermore, as a direct consequence of our generic repeller theorem, we deduce that this dimension formula also holds for a generic $C^r$ planar IFS satisfying the SSC. Using this approach, we also extend the dichotomy result for graphs of Weierstrass-type functions of Ren and Shen (2021) by weakening their real-analytic requirement to arbitrary $C^r$ regularity for $r > 1$.

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arXiv2026

Beyond Greedy Chunking: SLO-Aware Sliding-Window Scheduling for LLM Inference

With the rapid growth of interactive applications in large language model (LLM) online services, maintaining high system throughput while ensuring user-perceived latency has become a key issue in inference scheduling. Existing LLM service systems rely on coarse-grained output constraints, making it difficult to effectively handle resource contention among multiple requests, resulting in low resource utilization efficiency and limited support for fine-grained quality of service (QoS) differentiation. We present SlidingServe, a sliding-window-driven SLO-Aware scheduling system for online LLM inference. SlidingServe designed a lightweight batch latency predictor to estimate the execution time of a batch. Based on this, SlidingServe uses SlidingChunker to combine information from the current iteration and the next iteration to achieve dynamic chunking and improve the overall system throughput while maintaining strict QoS guarantees. SlidingServe introduces Multi-Level Priority Sorter to sort candidate requests in order to balance fairness and efficiency. Additionally, when multiple requests within the same batch are at risk of SLO violating,SlidingServe introduces BatchConstructor, which uses dynamic programming to select the set of requests to execute in the current round, mitigating the SLO violation risk of critical requests.Our evaluation demonstrates that SlidingServe can improve service capacity by up to 30% compared to advanced scheduling systems under various load conditions, and further reduces the rate of SLO violation by 16%-53% under heavy-load inference mode.

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arXiv2025

A Predictive and Synergistic Two-Layer Scheduling Framework for LLM Serving

LLM inference serving typically scales out with a two-tier architecture: a cluster router distributes requests to multiple inference engines, each of which then in turn performs its own internal scheduling. However, this commonly used paradigm suffers from critical, systemic inefficiency caused by the information gaps across two layers. At the cluster-layer, the router mainly relies on lagging, coarse-grained metrics, such as average latency and queue length to make decisions, resulting in "decision lag" that leads to suboptimal request routing. At the engine-layer, static heuristic scheduling policies cannot effectively handle the dynamic workloads, leading a poor balance between latency and throughput. Besides, these gaps may cause SLO violations and resource waste, especially in heterogeneous cloud environments. To bridge such gaps, we propose NexusSched, a cross-layer framework that shifts LLM serving system from reactive load balancing to predictive orchestration. The core of NexusSched lies in a structurally-informed online performance model that provides accurate, forward-looking per-step latency and capacity estimations. This model empowers two key components. At the engine-layer, LENS performs SLO-aware, adaptive scheduling, dynamically optimizing batching to meet SLOs under real-time loads. At the cluster-layer, PRISM uses predictive signals to perform state-driven routing, maximizing cluster-wide performance and SLO attainment. Performance evaluations show that NexusSched improves SLO attainment by 43% on average and achieves up to 3x throughput speedup in long-context and heterogeneous scenarios. Besides, we also deploy NexusSched on FlowGPT's clusters to demonstrate its advantages in production environment.

cs.DC↗

arXiv2025

Towards Paradigm-General Suicide Risk Detection via Speech LLM

Suicide risk among adolescents remains a critical public health concern, and speech provides a non-invasive and scalable approach for its detection. Speech-based suicide risk assessment commonly relies on carefully designed speech elicitation paradigms (\textit{e.g.,} verbal fluency, reading, or question answering) to probe cognitive and affective states. Existing approaches, however, typically focus on one single paradigm at a time. This paper, for the first time, investigates cross-paradigm approaches that unify diverse speech elicitation paradigms within a single model. Specifically, we use a speech LLM as backbone with a mixture of DoRA experts (MoDE) to capture complementary cues across assessments dynamically, tested on 1,223 participants across ten speech elicitation paradigms. Results show that MoDE outperforms both paradigm-specific and conventional joint-learning models. Moreover, it can generalise to unseen paradigms and provide better confidence calibration.

eess.AS↗

arXiv2025

Optimal Unpredictable Control for Linear Systems

In this paper, we investigate how to achieve the unpredictability against malicious inferences for linear systems. The key idea is to add stochastic control inputs, named as unpredictable control, to make the outputs irregular. The future outputs thus become unpredictable and the performance of inferences is degraded. The major challenges lie in: i) how to formulate optimization problems to obtain an optimal distribution of stochastic input, under unknown prediction accuracy of the adversary; and ii) how to achieve the trade-off between the unpredictability and control performance. We first utilize both variance and confidence probability of prediction error to quantify unpredictability, then formulate two two-stage stochastic optimization problems, respectively. Under variance metric, the analytic optimal distribution of control input is provided. With probability metric, it is a non-convex optimization problem, thus we present a novel numerical method and convert the problem into a solvable linear optimization problem. Last, we quantify the control performance under unpredictable control, and accordingly design the unpredictable LQR and cooperative control. Simulations demonstrate the unpredictability of our control algorithm. The obtained optimal distribution outperforms Gaussian and Laplace distributions commonly used in differential privacy under proposed metrics.

eess.SY↗

arXiv2025

Density of shapes of periodic tori in the cubic case

Consider the compact orbits of the $\mathbb{R}^2$ action of the diagonal group on $\operatorname{SL}(3,\mathbb{R})/\operatorname{SL}(3,\mathbb{Z})$, the so-called periodic tori. For any periodic torus, the set of periods of the orbit forms a lattice in $\mathbb{R}^2$. Such a lattice, re-scaled to covolume one, gives a shape point in $\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$. We prove that the shapes of all periodic tori are dense in $\operatorname{SL}(2,\mathbb{R})/\operatorname{SL}(2,\mathbb{Z})$. This implies the density of shapes of the unit groups of totally real cubic orders.

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arXiv2025

Checkerboard Target Measurement in Unordered Point Clouds with Coloured ICP

In this work, we investigate the problem of measuring a the centre checkerboard target in an 3D point cloud. This is an important problem which has applications in registration, long term monitoring and linking to other sensor systems. We use a 3D template matching approach based on the coloured ICP algorithm to solve the problem. We tackle the problem under the additional constraints that we assume no structure in the 3D data in order to be able to handle unordered point clouds. This gives us the capability to process data from the new generation of low-cost LIDAR sensors. This category of sensors also suffers from increased noise in range and reflectivity measurement. We provide extensive simulation results using synthetic data to capture the potential of the approach. We then give the detailed steps for handling real sensor data.

cs.CE↗

arXiv2024

Selberg, Ihara and Berkovich

We use the Selberg zeta function to study the limit behavior of resonances in a degenerating family of Kleinian Schottky groups. We prove that, after a suitable rescaling, the Selberg zeta functions converge to the Ihara zeta function of a limiting finite graph associated to the relevant non-Archimedean Schottky group acting on the Berkovich projective line. Moreover, we show that these techniques can be used to get an exponential error term in a result of McMullen (recently extended by Dang and Mehmeti) about the asymptotics for the vanishing rate of the Hausdorff dimension of limit sets of certain degenerating Schottky groups generating symmetric three-funnel surfaces. Here, one key idea is to introduce an intermediate zeta function capturing \emph{both} non-Archimedean and Archimedean information (while the traditional Selberg, resp. Ihara zeta functions concern only Archimedean, resp. non-Archimedean properties).

math.DS↗

arXiv2024

GRUtopia: Dream General Robots in a City at Scale

Recent works have been exploring the scaling laws in the field of Embodied AI. Given the prohibitive costs of collecting real-world data, we believe the Simulation-to-Real (Sim2Real) paradigm is a crucial step for scaling the learning of embodied models. This paper introduces project GRUtopia, the first simulated interactive 3D society designed for various robots. It features several advancements: (a) The scene dataset, GRScenes, includes 100k interactive, finely annotated scenes, which can be freely combined into city-scale environments. In contrast to previous works mainly focusing on home, GRScenes covers 89 diverse scene categories, bridging the gap of service-oriented environments where general robots would be initially deployed. (b) GRResidents, a Large Language Model (LLM) driven Non-Player Character (NPC) system that is responsible for social interaction, task generation, and task assignment, thus simulating social scenarios for embodied AI applications. (c) The benchmark, GRBench, supports various robots but focuses on legged robots as primary agents and poses moderately challenging tasks involving Object Loco-Navigation, Social Loco-Navigation, and Loco-Manipulation. We hope that this work can alleviate the scarcity of high-quality data in this field and provide a more comprehensive assessment of Embodied AI research. The project is available at https://github.com/OpenRobotLab/GRUtopia.

cs.RO↗

arXiv2024

On the dimension of limit sets on $\mathbb{P}(\mathbb{R}^3)$ via stationary measures: the theory and applications

This paper investigates the (semi)group action of $\mathrm{SL}_3(\mathbb{R})$ on $\mathbb{P}(\mathbb{R}^3)$, a primary example of non-conformal, non-linear, and non-strictly contracting action. We study the Hausdorff dimension of a dynamically defined limit set in $\mathbb{P}(\mathbb{R}^3)$ and generalize the classical Patterson-Sullivan formula using the approach of stationary measures. The two main examples are Anosov representations in $\mathrm{SL}_3(\mathbb{R})$ and the Rauzy gasket. 1. For Anosov representations in $\mathrm{SL}_3(\mathbb{R})$, we establish a sharp lower bound for the dimension of their limit sets in $\mathbb{P}(\mathbb{R}^3)$. Coupled with the upper bound in Pozzetti-Sambarino-Wienhard, it shows that their Hausdorff dimensions equal the affinity exponents. The merit of our approach is that it works uniformly for all the components of irreducible Anosov representations in $\mathrm{SL}_3(\mathbb{R})$. As an application, it reveals a surprising dimension jump phenomenon in the Barbot component, which is a local generalization of Bowen's dimension rigidity result. 2. For the Rauzy gasket, we confirm a folklore conjecture about the Hausdorff dimension of the gasket and improve the numerical lower bound to $3/2$. These results originate from a dimension formula of stationary measures on $\mathbb{P}(\mathbb{R}^3)$. Let $ν$ be a probability measure on $\mathrm{SL}_3(\mathbb{R})$ whose support is finite and spans a Zariski dense subgroup. Let $μ$ be the associated stationary measure for the action on $\mathbb{P}(\mathbb{R}^3)$. Under the exponential separation condition on $ν$, we prove that the Hausdorff dimension of $μ$ equals its Lyapunov dimension, which extends Hochman-Solomyak and Bárány-Hochman-Rapaport to non-conformal and projective settings respectively.

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arXiv2023

On the dimension of limit sets on $\mathbb{P}(\mathbb{R}^3)$ via stationary measures: variational principles and applications

In this article, we establish the variational principle of the affinity exponent of Borel Anosov representations. We also establish such a principle of the Rauzy gasket. In Li-Pan-Xu, they obtain a dimension formula of the stationary measures on $\mathbb{P}(\mathbb{R}^3)$. Combined with our result, it allows us to study the Hausdorff dimension of limit sets of Anosov representations in $\mathrm{SL}_3(\mathbb{R})$ and the Rauzy gasket. It yields the equality between the Hausdorff dimensions and the affinity exponents in both settings. In the appendix, we improve the numerical lower bound of the Hausdorff dimension of Rauzy gasket to $1.5$.

math.DS↗

arXiv2023

Equidistribution and counting of periodic tori in the space of Weyl chambers

Let G be a semisimple Lie group without compact factor and $Γ$ < G a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on tori. We prove that these periodic tori equidistribute exponentially fast towards the quotient of the Haar measure. From the equidistribution formula, we deduce a higher rank prime geodesic theorem.

math.DS↗

arXiv2022

Stationary measures for $\mathrm{SL}_2(\mathbb{R})$-actions on homogeneous bundles over flag varieties

Let $G$ be a real semisimple Lie group with finite centre and without compact factors, $Q<G$ a parabolic subgroup and $X$ a homogeneous space of $G$ admitting an equivariant projection on the flag variety $G/Q$ with fibres given by copies of lattice quotients of a semisimple factor of $Q$. Given a probability measure $μ$, Zariski-dense in a copy of $H=\mathrm{SL}_2(\mathbb{R})$ in $G$, we give a description of $μ$-stationary probability measures on $X$ and prove corresponding equidistribution results. Contrary to the results of Benoist-Quint corresponding to the case $G=Q$, the type of stationary measures that $μ$ admits depends strongly on the position of $H$ relative to $Q$. We describe possible cases and treat all but one of them, among others using ideas from the works of Eskin-Mirzakhani and Eskin-Lindenstrauss.

math.DS↗

arXiv2022

Spatio-temporal Motion Planning for Autonomous Vehicles with Trapezoidal Prism Corridors and Bézier Curves

Safety-guaranteed motion planning is critical for self-driving cars to generate collision-free trajectories. A layered motion planning approach with decoupled path and speed planning is widely used for this purpose. This approach is prone to be suboptimal in the presence of dynamic obstacles. Spatial-temporal approaches deal with path planning and speed planning simultaneously; however, the existing methods only support simple-shaped corridors like cuboids, which restrict the search space for optimization in complex scenarios. We propose to use trapezoidal prism-shaped corridors for optimization, which significantly enlarges the solution space compared to the existing cuboidal corridors-based method. Finally, a piecewise Bézier curve optimization is conducted in our proposed corridors. This formulation theoretically guarantees the safety of the continuous-time trajectory. We validate the efficiency and effectiveness of the proposed approach in numerical and CommonRoad simulations.

cs.RO↗

arXiv2022

Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps

Let $Γ$ be a geometrically finite discrete subgroup in $\operatorname{SO}(d+1,1)^{\circ}$ with parabolic elements. We establish exponential mixing of the geodesic flow on the unit tangent bundle $\operatorname{T}^1(Γ\backslash \mathbb{H}^{d+1})$ with respect to the Bowen-Margulis-Sullivan measure, which is the unique probability measure on $\operatorname{T}^1(Γ\backslash \mathbb{H}^{d+1})$ with maximal entropy. As an application, we obtain a resonance free region for the resolvent of the Laplacian on $Γ\backslash \mathbb{H}^{d+1}$. Our approach is to construct a coding for the geodesic flow and then prove a Dolgopyat-type spectral estimate for the corresponding transfer operator.

math.DS↗

arXiv2022

Multi-period Optimal Control for Mobile Agents Considering State Unpredictability

The optimal control for mobile agents is an important and challenging issue. Recent work shows that using randomized mechanism in agents' control can make the state unpredictable, and thus improve the security of agents. However, the unpredictable design is only considered in single period, which can lead to intolerable control performance in long time horizon. This paper aims at the trade-off between the control performance and state unpredictability of mobile agents in long time horizon. Utilizing random perturbations consistent with uniform distributions to maximize the attackers' prediction errors of future states, we formulate the problem as a multi-period convex stochastic optimization problem and solve it through dynamic programming. Specifically, we design the optimal control strategy considering both unconstrained and input constrained systems. The analytical iterative expressions of the control are further provided. Simulation illustrates that the algorithm increases the prediction errors under Kalman filter while achieving the control performance requirements successfully.

eess.SY↗

arXiv2022

Moving Target Interception Considering Dynamic Environment

The interception of moving targets is a widely studied issue. In this paper, we propose an algorithm of intercepting the moving target with a wheeled mobile robot in a dynamic environment. We first predict the future position of the target through polynomial fitting. The algorithm then generates an interception trajectory with path and speed decoupling. We use Hybrid A* search to plan a path and optimize it via gradient decent method. To avoid the dynamic obstacles in the environment, we introduce ST graph for speed planning. The speed curve is represented by piecewise Bézier curves for further optimization. Compared with other interception algorithms, we consider a dynamic environment and plan a safety trajectory which satisfies the kinematic characteristics of the wheeled robot while ensuring the accuracy of interception. Simulation illustrates that the algorithm successfully achieves the interception tasks and has high computational efficiency.

cs.RO↗

arXiv2022

Equidistribution and counting of periodic flat tori

Let $G$ be a semisimple Lie group without compact factor and $Γ< G$ a torsion-free, cocompact, irreducible lattice. According to Selberg, periodic orbits of regular Weyl chamber flows live on maximal flat periodic tori of the space of Weyl chambers. We prove that these flat periodic tori equidistribute exponentially fast towards the quotient of the Haar measure. From the equidistribution formula, we deduce a higher rank prime geodesic theorem. These counting and equidistribution results also hold in the non cocompact, finite covolume case for $G=\mathrm{SL}(d,\mathbb{R})$ and $Γ<\mathrm{SL}(d,\mathbb{Z})$ a finite index subgroup.

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