arXiv subjects

Xinran Liu

Publications and source records attributed to Xinran Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

High-precision quadrature via local Fourier extension: analytic integration, uniform sampling, and correction for piecewise smooth integrands

We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an extended periodic domain, and then evaluates the integral \emph{analytically} from the resulting Fourier coefficients. Under uniform sampling, the discrete LFE matrix and its TSVD factors are precomputed once and reused across all windows, yielding an efficient offline/online implementation that remains compatible with classical composite rules. We provide an error bound that reduces the quadrature error to the LFE approximation error and derive algebraic convergence rates for Sobolev-regular integrands. Numerical experiments demonstrate that, on smooth functions, the proposed quadrature reaches near machine precision with substantially fewer nodes than the composite Simpson rule. The advantage persists for oscillatory and variable-frequency integrands and becomes more pronounced for nonuniform phase structures. For continuous piecewise smooth integrands, we develop a correction strategy driven by coefficient-energy outliers to identify singularity-containing windows, followed by a localized procedure that brackets the singular point within one grid cell and corrects only the affected window contribution. The corrected quadrature restores near-spectral accuracy in the reported tests, including cases where the singularity is not aligned with the window endpoints.

math.NA↗

arXiv2026

Online Navigation Refinement: Achieving Lane-Level Guidance by Associating Standard-Definition and Online Perception Maps

Lane-level navigation is critical for geographic information systems and navigation-based tasks, offering finer-grained guidance than road-level navigation by standard definition (SD) maps. However, it currently relies on expansive global HD maps that cannot adapt to dynamic road conditions. Recently, online perception (OP) maps have become research hotspots, providing real-time geometry as an alternative, but lack the global topology needed for navigation. To address these issues, Online Navigation Refinement (ONR), a new mission is introduced that refines SD-map-based road-level routes into accurate lane-level navigation by associating SD maps with OP maps. The map-to-map association to handle many-to-one lane-to-road mappings under two key challenges: (1) no public dataset provides lane-to-road correspondences; (2) severe misalignment from spatial fluctuations, semantic disparities, and OP map noise invalidates traditional map matching. For these challenges, We contribute: (1) Online map association dataset (OMA), the first ONR benchmark with 30K scenarios and 2.6M annotated lane vectors; (2) MAT, a transformer with path-aware attention to aligns topology despite spatial fluctuations and semantic disparities and spatial attention for integrates noisy OP features via global context; and (3) NR P-R, a metric evaluating geometric and semantic alignment. Experiments show that MAT outperforms existing methods at 34 ms latency, enabling low-cost and up-to-date lane-level navigation.

cs.CV↗

arXiv2026

Recovering Counterfactual Distributions via Wasserstein GANs

Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack informative gradients under support mismatch and produce structural artifacts when outcomes are multimodal. This paper proposes a robust estimator grounded in Optimal Transport (OT). We construct the synthetic control by minimizing the Wasserstein-1 distance between probability measures, implemented via a Wasserstein Generative Adversarial Network (WGAN). We establish the formal point identification of synthetic weights under an affine independence condition on the donor pool. Monte Carlo simulations confirm that while standard estimators exhibit catastrophic variance explosions under heavy-tailed contamination and support mismatch, our WGAN-based approach remains consistent and stable. Furthermore, we show that our measure-based method correctly recovers complex bimodal mixtures where traditional quantile averaging fails structurally.

econ.EM↗

arXiv2025

LUNA: Linear Universal Neural Attention with Generalization Guarantees

Scaling attention faces a critical bottleneck: the $\mathcal{O}(n^2)$ quadratic computational cost of softmax attention, which limits its application in long-sequence domains. While linear attention mechanisms reduce this cost to $\mathcal{O}(n)$, they typically rely on fixed random feature maps, such as random Fourier features or hand-crafted functions. This reliance on static, data-agnostic kernels creates a fundamental trade-off, forcing practitioners to sacrifice significant model accuracy for computational efficiency. We introduce \textsc{LUNA}, a kernelized linear attention mechanism that eliminates this trade-off, retaining linear cost while matching and surpassing the accuracy of quadratic attention. \textsc{LUNA} is built on the key insight that the kernel feature map itself should be learned rather than fixed a priori. By parameterizing the kernel, \textsc{LUNA} learns a feature basis tailored to the specific data and task, overcoming the expressive limitations of fixed-feature methods. \textsc{Luna} implements this with a learnable feature map that induces a positive-definite kernel and admits a streaming form, yielding linear time and memory scaling in the sequence length. Empirical evaluations validate our approach across diverse settings. On the Long Range Arena (LRA), \textsc{Luna} achieves state-of-the-art average accuracy among efficient Transformers under compute parity, using the same parameter count, training steps, and approximate FLOPs. \textsc{Luna} also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints and briefly fine-tuning recovers most of the original performance, substantially outperforming fixed linearizations.

cs.LG↗

arXiv2025

PriorDrive: Enhancing Online HD Mapping with Unified Vector Priors

High-Definition Maps (HD maps) are essential for the precise navigation and decision-making of autonomous vehicles, yet their creation and upkeep present significant cost and timeliness challenges. The online construction of HD maps using on-board sensors has emerged as a promising solution; however, these methods can be impeded by incomplete data due to occlusions and inclement weather, while their performance in distant regions remains unsatisfying. This paper proposes PriorDrive to address these limitations by directly harnessing the power of various vectorized prior maps, significantly enhancing the robustness and accuracy of online HD map construction. Our approach integrates a variety of prior maps uniformly, such as OpenStreetMap's Standard Definition Maps (SD maps), outdated HD maps from vendors, and locally constructed maps from historical vehicle data. To effectively integrate such prior information into online mapping models, we introduce a Hybrid Prior Representation (HPQuery) that standardizes the representation of diverse map elements. We further propose a Unified Vector Encoder (UVE), which employs fused prior embedding and a dual encoding mechanism to encode vector data. To improve the UVE's generalizability and performance, we propose a segment-level and point-level pre-training strategy that enables the UVE to learn the prior distribution of vector data. Through extensive testing on the nuScenes, Argoverse 2 and OpenLane-V2, we demonstrate that PriorDrive is highly compatible with various online mapping models and substantially improves map prediction capabilities. The integration of prior maps through PriorDrive offers a robust solution to the challenges of single-perception data, paving the way for more reliable autonomous vehicle navigation. Code is available at https://github.com/MIV-XJTU/PriorDrive.

cs.CV↗

arXiv2025

Policy Search, Retrieval, and Composition via Task Similarity in Collaborative Agentic Systems

Agentic AI aims to create systems that set their own goals, adapt proactively to change, and refine behavior through continuous experience. Recent advances suggest that, when facing multiple and unforeseen tasks, agents could benefit from sharing machine-learned knowledge and reusing policies that have already been fully or partially learned by other agents. However, how to query, select, and retrieve policies from a pool of agents, and how to integrate such policies remains a largely unexplored area. This study explores how an agent decides what knowledge to select, from whom, and when and how to integrate it in its own policy in order to accelerate its own learning. The proposed algorithm, \emph{Modular Sharing and Composition in Collective Learning} (MOSAIC), improves learning in agentic collectives by combining (1) knowledge selection using performance signals and cosine similarity on Wasserstein task embeddings, (2) modular and transferable neural representations via masks, and (3) policy integration, composition and fine-tuning. MOSAIC outperforms isolated learners and global sharing approaches in both learning speed and overall performance, and in some cases solves tasks that isolated agents cannot. The results also demonstrate that selective, goal-driven reuse leads to less susceptibility to task interference. We also observe the emergence of self-organization, where agents solving simpler tasks accelerate the learning of harder ones through shared knowledge.

cs.LG↗

arXiv2025

FutureSightDrive: Thinking Visually with Spatio-Temporal CoT for Autonomous Driving

Vision-Language-Action (VLA) models offer significant potential for end-to-end driving, yet their reasoning is often constrained by textual Chains-of-Thought (CoT). This symbolic compression of visual information creates a modality gap between perception and planning by blurring spatio-temporal relations and discarding fine-grained cues. We introduce FSDrive, a framework that empowers VLAs to "think visually" using a novel visual spatio-temporal CoT. FSDrive first operates as a world model, generating a unified future frame that combines a predicted background with explicit, physically-plausible priors like future lane dividers and 3D object boxes. This imagined scene serves as the visual spatio-temporal CoT, capturing both spatial structure and temporal evolution in a single representation. The same VLA then functions as an inverse-dynamics model to plan trajectories conditioned on current observations and this visual CoT. We enable this with a unified pre-training paradigm that expands the model's vocabulary with visual tokens and jointly optimizes for semantic understanding (VQA) and future-frame prediction. A progressive curriculum first generates structural priors to enforce physical laws before rendering the full scene. Evaluations on nuScenes and NAVSIM show FSDrive improves trajectory accuracy and reduces collisions, while also achieving competitive FID for video generation with a lightweight autoregressive model and advancing scene understanding on DriveLM. These results confirm that our visual spatio-temporal CoT bridges the perception-planning gap, enabling safer, more anticipatory autonomous driving. Code is available at https://github.com/MIV-XJTU/FSDrive.

cs.CV↗

arXiv2025

PlanarTrack: A high-quality and challenging benchmark for large-scale planar object tracking

Planar tracking has drawn increasing interest owing to its key roles in robotics and augmented reality. Despite recent great advancement, further development of planar tracking, particularly in the deep learning era, is largely limited compared to generic tracking due to the lack of large-scale platforms. To mitigate this, we propose PlanarTrack, a large-scale high-quality and challenging benchmark for planar tracking. Specifically, PlanarTrack consists of 1,150 sequences with over 733K frames, including 1,000 short-term and 150 new long-term videos, which enables comprehensive evaluation of short- and long-term tracking performance. All videos in PlanarTrack are recorded in unconstrained conditions from the wild, which makes PlanarTrack challenging but more realistic for real-world applications. To ensure high-quality annotations, each video frame is manually annotated by four corner points with multi-round meticulous inspection and refinement. To enhance target diversity of PlanarTrack, we only capture a unique target in one sequence, which is different from existing benchmarks. To our best knowledge, PlanarTrack is by far the largest and most diverse and challenging dataset dedicated to planar tracking. To understand performance of existing methods on PlanarTrack and to provide a comparison for future research, we evaluate 10 representative planar trackers with extensive comparison and in-depth analysis. Our evaluation reveals that, unsurprisingly, the top planar trackers heavily degrade on the challenging PlanarTrack, which indicates more efforts are required for improving planar tracking. Our data and results will be released at https://github.com/HengLan/PlanarTrack

cs.CV↗

arXiv2025

GCDance: Genre-Controlled Music-Driven 3D Full Body Dance Generation

Music-driven dance generation is a challenging task as it requires strict adherence to genre-specific choreography while ensuring physically realistic and precisely synchronized dance sequences with the music's beats and rhythm. Although significant progress has been made in music-conditioned dance generation, most existing methods struggle to convey specific stylistic attributes in generated dance. To bridge this gap, we propose a diffusion-based framework for genre-specific 3D full-body dance generation, conditioned on both music and descriptive text. To effectively incorporate genre information, we develop a text-based control mechanism that maps input prompts, either explicit genre labels or free-form descriptive text, into genre-specific control signals, enabling precise and controllable text-guided generation of genre-consistent dance motions. Furthermore, to enhance the alignment between music and textual conditions, we leverage the features of a music foundation model, facilitating coherent and semantically aligned dance synthesis. Last, to balance the objectives of extracting text-genre information and maintaining high-quality generation results, we propose a novel multi-task optimization strategy. This effectively balances competing factors such as physical realism, spatial accuracy, and text classification, significantly improving the overall quality of the generated sequences. Extensive experimental results obtained on the FineDance and AIST++ datasets demonstrate the superiority of GCDance over the existing state-of-the-art approaches.

cs.GR↗

arXiv2025

EMPEROR: Efficient Moment-Preserving Representation of Distributions

We introduce EMPEROR (Efficient Moment-Preserving Representation of Distributions), a mathematically rigorous and computationally efficient framework for representing high-dimensional probability measures arising in neural network representations. Unlike heuristic global pooling operations, EMPEROR encodes a feature distribution through its statistical moments. Our approach leverages the theory of sliced moments: features are projected onto multiple directions, lightweight univariate Gaussian mixture models (GMMs) are fit to each projection, and the resulting slice parameters are aggregated into a compact descriptor. We establish determinacy guarantees via Carleman's condition and the Cramér-Wold theorem, ensuring that the GMM is uniquely determined by its sliced moments, and we derive finite-sample error bounds that scale optimally with the number of slices and samples. Empirically, EMPEROR captures richer distributional information than common pooling schemes across various data modalities, while remaining computationally efficient and broadly applicable.

cs.LG↗

arXiv2025

Fast numerical derivatives based on multi-interval Fourier extension

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain partitioning strategy: a global precomputation of local Fourier sampling matrices and their thin SVDs is reused throughout a recursive bisection procedure that selects locally-resolved Fourier fits. Each accepted subinterval stores a compact set of Fourier coefficients that are subsequently used to reconstruct the derivative via a precomputed differentiation operator. The stopping criterion balances fitting error and an explicit noise-level bound, and the algorithm automatically refines the partition where the function exhibits rapid oscillations or boundary activity. Numerical experiments demonstrate significant improvements over existing methods, achieving accurate derivative reconstruction for challenging functions. The approach provides a robust framework for ill-posed differentiation problems while maintaining computational efficiency.

math.NA↗

arXiv2025

ESPFormer: Doubly-Stochastic Attention with Expected Sliced Transport Plans

While self-attention has been instrumental in the success of Transformers, it can lead to over-concentration on a few tokens during training, resulting in suboptimal information flow. Enforcing doubly-stochastic constraints in attention matrices has been shown to improve structure and balance in attention distributions. However, existing methods rely on iterative Sinkhorn normalization, which is computationally costly. In this paper, we introduce a novel, fully parallelizable doubly-stochastic attention mechanism based on sliced optimal transport, leveraging Expected Sliced Transport Plans (ESP). Unlike prior approaches, our method enforces doubly stochasticity without iterative Sinkhorn normalization, significantly enhancing efficiency. To ensure differentiability, we incorporate a temperature-based soft sorting technique, enabling seamless integration into deep learning models. Experiments across multiple benchmark datasets, including image classification, point cloud classification, sentiment analysis, and neural machine translation, demonstrate that our enhanced attention regularization consistently improves performance across diverse applications. Our implementation code can be found at https://github.com/dariansal/ESPFormer.

cs.LG↗

arXiv2025

SeqGrowGraph: Learning Lane Topology as a Chain of Graph Expansions

Accurate lane topology is essential for autonomous driving, yet traditional methods struggle to model the complex, non-linear structures-such as loops and bidirectional lanes-prevalent in real-world road structure. We present SeqGrowGraph, a novel framework that learns lane topology as a chain of graph expansions, inspired by human map-drawing processes. Representing the lane graph as a directed graph $G=(V,E)$, with intersections ($V$) and centerlines ($E$), SeqGrowGraph incrementally constructs this graph by introducing one vertex at a time. At each step, an adjacency matrix ($A$) expands from $n \times n$ to $(n+1) \times (n+1)$ to encode connectivity, while a geometric matrix ($M$) captures centerline shapes as quadratic Bézier curves. The graph is serialized into sequences, enabling a transformer model to autoregressively predict the chain of expansions, guided by a depth-first search ordering. Evaluated on nuScenes and Argoverse 2 datasets, SeqGrowGraph achieves state-of-the-art performance.

cs.CV↗

arXiv2025

Constrained Sliced Wasserstein Embedding

Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions has proven challenging, often necessitating a large number of slices to achieve desirable performance and thereby increasing computational complexity. We introduce a constrained learning approach to optimize the slicing directions for SW distances. Specifically, we constrain the 1D transport plans to approximate the optimal plan in the original space, ensuring meaningful slicing directions. By leveraging continuous relaxations of these transport plans, we enable a gradient-based primal-dual approach to train the slicer parameters, alongside the remaining model parameters. We demonstrate how this constrained slicing approach can be applied to pool high-dimensional embeddings into fixed-length permutation-invariant representations. Numerical results on foundation models trained on images, point clouds, and protein sequences showcase the efficacy of the proposed constrained learning approach in learning more informative slicing directions. Our implementation code can be found at https://github.com/Stranja572/constrainedswe.

cs.LG↗

arXiv2025

Driving by the Rules: A Benchmark for Integrating Traffic Sign Regulations into Vectorized HD Map

Ensuring adherence to traffic sign regulations is essential for both human and autonomous vehicle navigation. While current online mapping solutions often prioritize the construction of the geometric and connectivity layers of HD maps, overlooking the construction of the traffic regulation layer within HD maps. Addressing this gap, we introduce MapDR, a novel dataset designed for the extraction of Driving Rules from traffic signs and their association with vectorized, locally perceived HD Maps. MapDR features over $10,000$ annotated video clips that capture the intricate correlation between traffic sign regulations and lanes. Built upon this benchmark and the newly defined task of integrating traffic regulations into online HD maps, we provide modular and end-to-end solutions: VLE-MEE and RuleVLM, offering a strong baseline for advancing autonomous driving technology. It fills a critical gap in the integration of traffic sign rules, contributing to the development of reliable autonomous driving systems. Code is available at https://github.com/MIV-XJTU/MapDR.

cs.CV↗

arXiv2025

Partial Gromov-Wasserstein Metric

The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal mass requirements of the classical GW problem, researchers have begun exploring its application in unbalanced settings. However, Unbalanced GW (UGW) can only be regarded as a discrepancy rather than a rigorous metric/distance between two metric measure spaces (mm-spaces). In this paper, we propose a particular case of the UGW problem, termed Partial Gromov-Wasserstein (PGW). We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others. We then propose two variants of the Frank-Wolfe algorithm for solving the PGW problem and show that they are mathematically and computationally equivalent. Moreover, based on our PGW metric, we introduce the analogous concept of barycenters for mm-spaces. Finally, we validate the effectiveness of our PGW metric and related solvers in applications such as shape matching, shape retrieval, and shape interpolation, comparing them against existing baselines. Our code is available at https://github.com/mint-vu/PGW_Metric.

cs.LG↗

arXiv2025

Accelerated Quasi-Static FEM for Real-Time Modeling of Continuum Robots with Multiple Contacts and Large Deformation

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains challenging. Current methods for solving the deformation of these robots, such as the Model Order Reduction and Gauss-Seidel (GS) methods, suffer from significant drawbacks. They experience reduced computational speed as the number of contact points increases and struggle to balance speed with model accuracy. To overcome these limitations, we introduce a novel finite element method (FEM) named Acc-FEM. Acc-FEM employs a large deformation quasi-static finite element model and integrates an accelerated solver scheme to handle multi-contact simulations efficiently. Additionally, it utilizes parallel computing with Graphics Processing Units (GPU) for real-time updates of the finite element models and collision detection. Extensive numerical experiments demonstrate that Acc-FEM significantly improves computational efficiency in modeling continuum robots with multiple contacts while achieving satisfactory accuracy, addressing the deficiencies of existing methods.

cs.RO↗

arXiv2025

DGFM: Full Body Dance Generation Driven by Music Foundation Models

In music-driven dance motion generation, most existing methods use hand-crafted features and neglect that music foundation models have profoundly impacted cross-modal content generation. To bridge this gap, we propose a diffusion-based method that generates dance movements conditioned on text and music. Our approach extracts music features by combining high-level features obtained by music foundation model with hand-crafted features, thereby enhancing the quality of generated dance sequences. This method effectively leverages the advantages of high-level semantic information and low-level temporal details to improve the model's capability in music feature understanding. To show the merits of the proposed method, we compare it with four music foundation models and two sets of hand-crafted music features. The results demonstrate that our method obtains the most realistic dance sequences and achieves the best match with the input music.

cs.SD↗