arXiv subjects

Sixu Li

Publications and source records attributed to Sixu Li.

At least 19 recordsLinked to original sources

arXiv2026

On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers

We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers. We show that in embedding dimension two, for any key, query, and value matrices, the dynamics can be reformulated as a generalized Kuramoto-type model with pure second-harmonic coupling. This formulation is amenable to Watanabe--Strogatz theory which reveals the dynamics are intrinsically low-dimensional regardless of the parameter matrices. For a class of token initializations associated with the Ott--Antonsen (OA) manifold, we show that the parameter matrices induce a diverse variety of long-time behaviors in linear transformers, including clustering, oscillations, and bifurcations. The oscillations and bifurcations are characterized by uncovering a hidden Hamiltonian structure in the dynamics. By establishing a structural stability result, we further show that dynamics initialized near the OA manifold exhibit the same long-time behavior as those initialized exactly on the manifold. Motivated by our theory in dimension two, we conduct numerical experiments for analogous parameter regimes in higher-dimensional transformers. Our numerical experiments suggest that the long-time behaviors characterized in our theoretical results persist in higher dimensions.

cs.LG↗

arXiv2026

Longitudinal-Motion-Aware Lateral Control for Autonomous Vehicles: A Robust Nonlinear Control Framework

As autonomous vehicles (AVs) operate in increasingly dynamic traffic conditions, lateral control must be performed while longitudinal speed and acceleration vary. Yet many existing lateral controllers rely on constant-speed or operating-point-based assumptions, which can degrade performance during transient longitudinal maneuvers. Moreover, most methods assume precisely known vehicle parameters, despite real-world parametric uncertainties. To address these limitations, this paper presents a longitudinal-motion-aware robust nonlinear lateral control framework for AVs. It first derives a tracking error model that depends on varying longitudinal speed and acceleration. Using this model, feedback linearization is employed to obtain a linear input-output relation for lateral error tracking while embedding longitudinal motion into the control law. The resulting internal dynamics are then analyzed to ensure overall system stability. To address parameter uncertainty, two robust control designs with distinct implementation trade-offs are proposed: (i) a Lyapunov redesign (LR) approach inspired by sliding mode control, and (ii) an incremental nonlinear dynamic inversion (INDI) method. Both are rigorously analyzed and proven to ensure ultimate boundedness, with key robustness-tuning parameters explicitly identified. Simulations demonstrate enhanced tracking accuracy, consistent performance across varying speeds and accelerations, and robustness to model uncertainties, while also examining the effects of the robustness-related parameters. Real-vehicle tests further confirm real-time implementation and practical path-tracking performance on actual hardware.

cs.RO↗

arXiv2026

Privacy-Preserving Decentralized Cooperative Localization with Range-Only Measurements: A Convex Optimization Based Approach

Cooperative localization using range-based measurements is critical for multi-robot systems operating in GPS-denied and unstructured environments. However, traditional cooperative approaches require sharing explicit spatial coordinates across the network, presenting a severe security vulnerability in privacy-sensitive missions. While recent literature has explored privacy-preserving alternatives, these methods typically rely on accuracy-degrading noise injection or computationally prohibitive cryptographic protocols. To overcome these limitations, we propose a novel, natively privacy-preserving Decentralized Cooperative Localization (DCL) framework based on convex optimization. Discarding probabilistic noise models, we assume strictly bounded measurement noise and formulate the localization problem via Semi-Definite Programming (SDP) to compute a Maximum-Volume Inscribed Ellipsoid (MVE). Our approach introduces novel intersection-plane constraints derived from landmark measurements to significantly tighten individual spatial bounds. To incorporate inter-robot range measurements securely, we uniquely decompose coupling constraints into localized Linear Matrix Inequalities (LMIs). Agents achieve fleet-wide spatial consensus by iteratively exchanging only abstract dual variables, completely avoiding the transmission of explicit primal position estimates. Extensive 3D Monte Carlo simulations demonstrate that our DCL framework outperforms existing SDP-based localization method in accuracy, while guaranteeing operational privacy and maintaining highly scalable, parallelizable computation.

cs.RO↗

arXiv2026

Lateral String Stability for Vehicle Platoons

Connected and automated vehicle (CAV) platooning promises gains in energy efficiency and traffic throughput and, most critically, in safety. These safety benefits hinge on string stability, which determines how disturbances propagate along a platoon. While longitudinal string stability is well studied, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the intended path, remains underexplored. Its importance is increasing as autonomous vehicles rely more heavily on onboard sensing and map-free navigation, where sensor occlusion and dense formations amplify safety risks. This paper presents a new framework for lateral string stability that directly addresses safety-critical path-relative tracking errors and enables consistent comparison across vehicles following the same road geometry. Central to this framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. A formal definition of lateral string stability is introduced along with two control strategies: an onboard-sensing-only controller and a novel learn-from-predecessor approach utilizing vehicle-to-vehicle (V2V) communication. We show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, whereas V2V communication enables true error attenuation.

cs.RO↗

arXiv2026

SUMO: Segment and Track Any Motion with Nonlinear State Space Models

Visual Object Tracking (VOT) and Moving Object Segmentation (MOS) are two fundamental tasks in computer vision that involve both spatial and temporal object dynamics. Existing methods rely predominantly on visual cues and thus often falter in real-world scenarios where object motions are inherently complex and nonlinear. To address this limitation, we propose SUMO, a zero-shot, training-free, unified framework integrating nonlinear dynamics with vision-based segmentation for accurate and consistent VOT and MOS. Specifically, we develop a nonlinear State Space Model (SSM) inspired by robotics principles to capture the complex object dynamics. Building on this model, we propose a Selective Unscented Filter (SUF) for accurate state estimation, which features a joint scoring mechanism and dynamically fuses multi-source predictions to identify the most plausible object state over time. Furthermore, we apply a memory selection mechanism to evaluate the reliability of memory frames. Our extensive experimental results show that SUMO achieves state-of-the-art performance on both VOT and MOS tasks.

cs.CV↗

arXiv2026

Optimal drift optimizer for non-convex optimization

We study a finite-horizon stochastic control criterion for non-convex optimization in which Brownian exploration is balanced against a quadratic control cost. Rather than emphasizing the classical Hopf--Cole representation, we isolate the exact drift selected by the criterion and reorganize it in a form adapted to optimization. The key object is the conditional terminal law of the optimal process. We show that this law is a Gibbs measure for a proximally penalized energy, yielding three exact representations of the drift: potential, averaged-gradient, and barycentric. We then analyze two asymptotic regimes relevant for optimization. As terminal time is approached, the drift recovers a scaled gradient-descent field. In the low-temperature regime, assuming a unique global minimizer, the conditional terminal law concentrates on it even in the presence of nonglobal local minima, and the drift converges to an affine attraction field toward it. In the nondegenerate case we also derive Laplace asymptotics for the drift, the value function, and the covariance of the conditional terminal law. Finally, we record a simple gradient-free discretization suggested by the barycentric formula.

math.OC↗

arXiv2026

Learning Higher-Order Structure from Incomplete Spatiotemporal Data: Multi-Scale Hypergraph Laplacians with Neural Refinement

Sensor networks increasingly govern modern infrastructure, yet the data they lose are rarely missing in the uniform-random patterns assumed by standard imputation benchmarks. Loop detectors go offline during calibration, roadside cabinets silence clusters of nearby sensors, and newly installed instruments provide no history. Such failures create structured absences whose values are constrained by higher-order relations among groups of sensors, not merely by pairwise proximity. Existing low-rank and graph-based methods often miss this collective structure and can fail when missingness becomes coherent. We introduce Multi-Scale Hypergraph Laplacians (MSHL), a two-stage framework for learning higher-order structure from incomplete spatiotemporal observations. The Discovery stage builds a multi-scale hypergraph from complementary topology and residual-correlation evidence, with an observation-only selector that adapts to the supported interaction scale. The Refinement stage adds a small hypergraph-conditioned residual network that is safe by construction: it learns nonlinear corrections where informative residual features exist and defers to the linear estimate where they do not. We prove that MSHL represents group-conservation patterns inaccessible to pairwise graph priors, adapts to the best fixed scale up to a logarithmic factor, transfers this advantage to held-out imputation error, and admits a one-sided refinement guarantee. On two real traffic networks evaluated across scattered cell missingness, contiguous block outages, and whole-sensor blackouts at five rates, MSHL improves over a pairwise-graph baseline whenever higher-order structure is identifiable and otherwise matches it within sampling noise. The results point to a broader principle for reliable infrastructure learning: missing data should be treated not as isolated entries to fill, but as evidence of structure to discover.

cs.LG↗

arXiv2026

Lateral String Stability for Vehicle Platoons: Formulation, Definition, and Analysis

Platooning of connected and automated vehicles provides significant benefits in terms of energy efficiency, traffic throughput, and, most critically, safety. These safety benefits depend on string stability, which dictates how disturbances propagate along a vehicle string. Although longitudinal string stability has been extensively examined, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the desired path, remains underexplored. Its importance is growing as autonomous vehicles increasingly depend on onboard sensing and map-free navigation, where sensor occlusions and tight formations amplify safety risks. This paper presents a framework for lateral string stability that focuses directly on safety-critical, path-relative tracking errors and enables consistent comparison across vehicles that follow the same planned path. The key element of the framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. Building on this foundation, we propose the definition of L2 lateral string stability along with two control strategies: a feedback-feedforward strategy that relies solely on onboard sensing, and a novel learn-from-predecessor strategy that makes use of vehicle-to-vehicle communication. Both strategies are analyzed for lateral string stability with respect to two error measures: tracking error vector and lateral (cross-track) error. Our results show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, while V2V communication enables true error attenuation. The analysis further identifies structural controller requirements, showing that nonzero feedback on specific measurements is essential for guaranteeing stability.

cs.RO↗

arXiv2025

CrossCheck-Bench: Diagnosing Compositional Failures in Multimodal Conflict Resolution

Multimodal Large Language Models are primarily trained and evaluated on aligned image-text pairs, which leaves their ability to detect and resolve real-world inconsistencies largely unexplored. In open-domain applications visual and textual cues often conflict, requiring models to perform structured reasoning beyond surface-level alignment. We introduce CrossCheck-Bench, a diagnostic benchmark for evaluating contradiction detection in multimodal inputs. The benchmark adopts a hierarchical task framework covering three levels of reasoning complexity and defines seven atomic capabilities essential for resolving cross-modal inconsistencies. CrossCheck-Bench includes 15k question-answer pairs sourced from real-world artifacts with synthetically injected contradictions. The dataset is constructed through a multi-stage annotation pipeline involving more than 450 expert hours to ensure semantic validity and calibrated difficulty across perception, integration, and reasoning. We evaluate 13 state-of-the-art vision-language models and observe a consistent performance drop as tasks shift from perceptual matching to logical contradiction detection. Most models perform well on isolated entity recognition but fail when multiple clues must be synthesized for conflict reasoning. Capability-level analysis further reveals uneven skill acquisition, especially in tasks requiring multi-step inference or rule-based validation. Additional probing shows that conventional prompting strategies such as Chain-of-Thought and Set-of-Mark yield only marginal gains. By contrast, methods that interleave symbolic reasoning with grounded visual processing achieve more stable improvements. These results highlight a persistent bottleneck in multimodal reasoning and suggest new directions for building models capable of robust cross-modal verification.

cs.CL↗

arXiv2025

LaCache: Ladder-Shaped KV Caching for Efficient Long-Context Modeling of Large Language Models

Recent advancements in Large Language Models (LLMs) have spurred interest in numerous applications requiring robust long-range capabilities, essential for processing extensive input contexts and continuously generating extended outputs. As sequence lengths increase, the number of Key-Value (KV) pairs in LLMs escalates, creating a significant efficiency bottleneck. In this paper, we propose a new KV cache optimization paradigm called LaCache, a training-free method for efficient and accurate generative inference of LLMs. LaCache enables LLMs to simultaneously address both of the critical challenges in long-range modeling: robust long-range capabilities and continuous generation without running out-of-memory (OOM). Specifically, LaCache integrates two key innovations: (1) a ladder-shaped KV cache pattern that stores KV pairs not only sequentially (left-to-right within each layer) but also across layers (from shallow to deep), providing an extended span for capturing long-range dependencies under a fixed storage budget, thereby boosting long-range capabilities; and (2) an iterative compaction mechanism that progressively compresses older caches, freeing up space for new tokens within a fixed cache size. This token distance-based dynamic compression enables more effective continuous generation under constrained cache budgets. Experiments across various tasks, benchmarks, and LLM models consistently validate LaCache's effectiveness in enhancing LLMs' long-range capabilities. Our code is available at https://github.com/GATECH-EIC/LaCache.

cs.LG↗

arXiv2025

Nonlinear Oscillatory Response of Automated Vehicle Car-following: Theoretical Analysis with Traffic State and Control Input Limits

This paper presents a framework grounded in the theory of describing function (DF) and incremental-input DF to theoretically analyze the nonlinear oscillatory response of automated vehicles (AVs) car-following (CF) amidst traffic oscillations, considering the limits of traffic state and control input. While prevailing approaches largely ignore these limits (i.e., saturation of acceleration/deceleration and speed) and focus on linear string stability analysis, this framework establishes a basis for theoretically analyzing the frequency response of AV systems with nonlinearities imposed by these limits. To this end, trajectories of CF pairs are decomposed into nominal and oscillatory trajectories, subsequently, the controlled AV system is repositioned within the oscillatory trajectory coordinates. Built on this base, DFs are employed to approximate the frequency responses of nonlinear saturation components by using their first harmonic output, thereby capturing the associated amplification ratio and phase shift. Considering the closed-loop nature of AV control systems, where system states and control input mutually influence each other, amplification ratios and phase shifts are balanced within the loop to ensure consistency. This balancing process may render multiple solutions, hence the incremental-input DF is further applied to identify the reasonable ones. The proposed method is validated by estimations from Simulink, and further comparisons with prevailing methods are conducted. Results confirm the alignment of our framework with Simulink results and exhibit its superior accuracy in analysis compared to the prevailing methods. Furthermore, the framework proves valuable in string stability analysis, especially when conventional linear methods offer misleading insights.

eess.SY↗

arXiv2025

AI2-Active Safety: AI-enabled Interaction-aware Active Safety Analysis with Vehicle Dynamics

This paper introduces an AI-enabled, interaction-aware active safety analysis framework that accounts for groupwise vehicle interactions. Specifically, the framework employs a bicycle model-augmented with road gradient considerations-to accurately capture vehicle dynamics. In parallel, a hypergraph-based AI model is developed to predict probabilistic trajectories of ambient traffic. By integrating these two components, the framework derives vehicle intra-spacing over a 3D road surface as the solution of a stochastic ordinary differential equation, yielding high-fidelity surrogate safety measures such as time-to-collision (TTC). To demonstrate its effectiveness, the framework is analyzed using stochastic numerical methods comprising 4th-order Runge-Kutta integration and AI inference, generating probability-weighted high-fidelity TTC (HF-TTC) distributions that reflect complex multi-agent maneuvers and behavioral uncertainties. Evaluated with HF-TTC against traditional constant-velocity TTC and non-interaction-aware approaches on highway datasets, the proposed framework offers a systematic methodology for active safety analysis with enhanced potential for improving safety perception in complex traffic environments.

cs.RO↗

arXiv2025

Virtual Roads, Smarter Safety: A Digital Twin Framework for Mixed Autonomous Traffic Safety Analysis

This paper presents a digital-twin platform for active safety analysis in mixed traffic environments. The platform is built using a multi-modal data-enabled traffic environment constructed from drone-based aerial LiDAR, OpenStreetMap, and vehicle sensor data (e.g., GPS and inclinometer readings). High-resolution 3D road geometries are generated through AI-powered semantic segmentation and georeferencing of aerial LiDAR data. To simulate real-world driving scenarios, the platform integrates the CAR Learning to Act (CARLA) simulator, Simulation of Urban MObility (SUMO) traffic model, and NVIDIA PhysX vehicle dynamics engine. CARLA provides detailed micro-level sensor and perception data, while SUMO manages macro-level traffic flow. NVIDIA PhysX enables accurate modeling of vehicle behaviors under diverse conditions, accounting for mass distribution, tire friction, and center of mass. This integrated system supports high-fidelity simulations that capture the complex interactions between autonomous and conventional vehicles. Experimental results demonstrate the platform's ability to reproduce realistic vehicle dynamics and traffic scenarios, enhancing the analysis of active safety measures. Overall, the proposed framework advances traffic safety research by enabling in-depth, physics-informed evaluation of vehicle behavior in dynamic and heterogeneous traffic environments.

cs.RO↗

arXiv2025

Early-Bird Diffusion: Investigating and Leveraging Timestep-Aware Early-Bird Tickets in Diffusion Models for Efficient Training

Training diffusion models (DMs) requires substantial computational resources due to multiple forward and backward passes across numerous timesteps, motivating research into efficient training techniques. In this paper, we propose EB-Diff-Train, a new efficient DM training approach that is orthogonal to other methods of accelerating DM training, by investigating and leveraging Early-Bird (EB) tickets -- sparse subnetworks that manifest early in the training process and maintain high generation quality. We first investigate the existence of traditional EB tickets in DMs, enabling competitive generation quality without fully training a dense model. Then, we delve into the concept of diffusion-dedicated EB tickets, drawing on insights from varying importance of different timestep regions. These tickets adapt their sparsity levels according to the importance of corresponding timestep regions, allowing for aggressive sparsity during non-critical regions while conserving computational resources for crucial timestep regions. Building on this, we develop an efficient DM training technique that derives timestep-aware EB tickets, trains them in parallel, and combines them during inference for image generation. Extensive experiments validate the existence of both traditional and timestep-aware EB tickets, as well as the effectiveness of our proposed EB-Diff-Train method. This approach can significantly reduce training time both spatially and temporally -- achieving 2.9$\times$ to 5.8$\times$ speedups over training unpruned dense models, and up to 10.3$\times$ faster training compared to standard train-prune-finetune pipelines -- without compromising generative quality. Our code is available at https://github.com/GATECH-EIC/Early-Bird-Diffusion.

cs.CV↗

arXiv2025

Time-optimal Convexified Reeds-Shepp Paths on a Sphere

This article studies the time-optimal path planning problem for a convexified Reeds-Shepp (CRS) vehicle on a unit sphere, capable of both forward and backward motion, with speed bounded in magnitude by 1 and turning rate bounded in magnitude by a given constant. For the case in which the turning-rate bound is at least 1, using Pontryagin's Maximum Principle and a phase-portrait analysis, we show that the optimal path connecting a given initial configuration to a desired terminal configuration consists of at most six segments drawn from three motion primitives: tight turns, great circular arcs, and turn-in-place motions. A complete classification yields a finite sufficient list of 23 optimal path types with closed-form segment angles derived. The complementary case in which the turning-rate bound is less than 1 is addressed via an equivalent reformulation. The proposed formulation is applicable to underactuated satellite attitude control, spherical rolling robots, and mobile robots operating on spherical or gently curved surfaces. The source code for solving the time-optimal path problem and visualization is publicly available at https://github.com/sixuli97/Optimal-Spherical-Convexified-Reeds-Shepp-Paths.

cs.RO↗

arXiv2025

Uni-Render: A Unified Accelerator for Real-Time Rendering Across Diverse Neural Renderers

Recent advancements in neural rendering technologies and their supporting devices have paved the way for immersive 3D experiences, significantly transforming human interaction with intelligent devices across diverse applications. However, achieving the desired real-time rendering speeds for immersive interactions is still hindered by (1) the lack of a universal algorithmic solution for different application scenarios and (2) the dedication of existing devices or accelerators to merely specific rendering pipelines. To overcome this challenge, we have developed a unified neural rendering accelerator that caters to a wide array of typical neural rendering pipelines, enabling real-time and on-device rendering across different applications while maintaining both efficiency and compatibility. Our accelerator design is based on the insight that, although neural rendering pipelines vary and their algorithm designs are continually evolving, they typically share common operators, predominantly executing similar workloads. Building on this insight, we propose a reconfigurable hardware architecture that can dynamically adjust dataflow to align with specific rendering metric requirements for diverse applications, effectively supporting both typical and the latest hybrid rendering pipelines. Benchmarking experiments and ablation studies on both synthetic and real-world scenes demonstrate the effectiveness of the proposed accelerator. The proposed unified accelerator stands out as the first solution capable of achieving real-time neural rendering across varied representative pipelines on edge devices, potentially paving the way for the next generation of neural graphics applications.

cs.GR↗

arXiv2025

Gaussian Blending Unit: An Edge GPU Plug-in for Real-Time Gaussian-Based Rendering in AR/VR

The rapidly advancing field of Augmented and Virtual Reality (AR/VR) demands real-time, photorealistic rendering on resource-constrained platforms. 3D Gaussian Splatting, delivering state-of-the-art (SOTA) performance in rendering efficiency and quality, has emerged as a promising solution across a broad spectrum of AR/VR applications. However, despite its effectiveness on high-end GPUs, it struggles on edge systems like the Jetson Orin NX Edge GPU, achieving only 7-17 FPS -- well below the over 60 FPS standard required for truly immersive AR/VR experiences. Addressing this challenge, we perform a comprehensive analysis of Gaussian-based AR/VR applications and identify the Gaussian Blending Stage, which intensively calculates each Gaussian's contribution at every pixel, as the primary bottleneck. In response, we propose a Gaussian Blending Unit (GBU), an edge GPU plug-in module for real-time rendering in AR/VR applications. Notably, our GBU can be seamlessly integrated into conventional edge GPUs and collaboratively supports a wide range of AR/VR applications. Specifically, GBU incorporates an intra-row sequential shading (IRSS) dataflow that shades each row of pixels sequentially from left to right, utilizing a two-step coordinate transformation. When directly deployed on a GPU, the proposed dataflow achieved a non-trivial 1.72x speedup on real-world static scenes, though still falls short of real-time rendering performance. Recognizing the limited compute utilization in the GPU-based implementation, GBU enhances rendering speed with a dedicated rendering engine that balances the workload across rows by aggregating computations from multiple Gaussians. Experiments across representative AR/VR applications demonstrate that our GBU provides a unified solution for on-device real-time rendering while maintaining SOTA rendering quality.

cs.GR↗

arXiv2025

GauRast: Enhancing GPU Triangle Rasterizers to Accelerate 3D Gaussian Splatting

3D intelligence leverages rich 3D features and stands as a promising frontier in AI, with 3D rendering fundamental to many downstream applications. 3D Gaussian Splatting (3DGS), an emerging high-quality 3D rendering method, requires significant computation, making real-time execution on existing GPU-equipped edge devices infeasible. Previous efforts to accelerate 3DGS rely on dedicated accelerators that require substantial integration overhead and hardware costs. This work proposes an acceleration strategy that leverages the similarities between the 3DGS pipeline and the highly optimized conventional graphics pipeline in modern GPUs. Instead of developing a dedicated accelerator, we enhance existing GPU rasterizer hardware to efficiently support 3DGS operations. Our results demonstrate a 23$\times$ increase in processing speed and a 24$\times$ reduction in energy consumption, with improvements yielding 6$\times$ faster end-to-end runtime for the original 3DGS algorithm and 4$\times$ for the latest efficiency-improved pipeline, achieving 24 FPS and 46 FPS respectively. These enhancements incur only a minimal area overhead of 0.2\% relative to the entire SoC chip area, underscoring the practicality and efficiency of our approach for enabling 3DGS rendering on resource-constrained platforms.

cs.GR↗