arXiv subjects

Zhiqi Li

Publications and source records attributed to Zhiqi Li.

At least 37 records · Page 2Linked to original sources

arXiv2026

A multiphase cubic MARS method for fourth- and higher-order interface tracking of two or more materials with arbitrary topology and geometry

For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) applies to any number of materials with arbitrarily complex topology and geometry, (c) maintains an $(r,h)$-regularity of the interface so that the distance between any pair of adjacent markers is within a user-specified range, (d) distributes the markers adaptively along the interface so that arcs with high curvature are resolved by densely populated markers, and (e) achieves fourth-, sixth-, and eighth-order accuracy both in time and in space.} In particular, all possible types of junctions, which pose challenges to VOF methods and level-set methods, are handled with ease. Results of a variety of benchmark tests confirm the analysis and demonstrate the superior accuracy, efficiency, and versatility of the proposed method.

math.NA↗

arXiv2026

VideoITG: Multimodal Video Understanding with Instructed Temporal Grounding

While Video Large Language Models (Video-LLMs) have shown significant potential in multimodal understanding and reasoning tasks, how to efficiently select the most informative frames from videos remains a critical challenge. Existing methods attempt to optimize frame sampling by reducing inter-frame redundancy or employing unsupervised event localization. However, these approaches often fall short in handling complex instruction-following tasks and scenarios that demand precise temporal modeling, resulting in limited performance in both semantic alignment and temporal reasoning. To address the above challenges, we introduce Instructed Temporal Grounding for Videos (VideoITG), a framework aiming to adaptively customize frame sampling strategies based on user instructions. Specifically, we design the VidThinker pipeline, which automates annotation by generating instruction-conditioned captions, retrieving relevant video segments, and selecting key frames to enable efficient supervision. Using VidThinker, we build the VideoITG-40K dataset with 40K videos and 500K temporal grounding annotations. Our plug-and-play VideoITG model leverages Video-LLMs' visual-language alignment and reasoning for discriminative frame selection. VideoITG consistently boosts the performance on multiple multimodal video understanding benchmarks, demonstrating its effectiveness and potential.

cs.CV↗

arXiv2026

Towards Multimodal Lifelong Understanding: A Dataset and Agentic Baseline

While datasets for video understanding have scaled to hour-long durations, they typically consist of densely concatenated clips that differ from natural, unscripted daily life. To bridge this gap, we introduce MM-Lifelong, a dataset designed for Multimodal Lifelong Understanding. Comprising 181.1 hours of footage, it is structured across Day, Week, and Month scales to capture varying temporal densities. Extensive evaluations reveal two critical failure modes in current paradigms: end-to-end MLLMs suffer from a Working Memory Bottleneck due to context saturation, while representative agentic baselines experience Global Localization Collapse when navigating sparse, month-long timelines. To address this, we propose the Recursive Multimodal Agent (ReMA), which employs dynamic memory management to iteratively update a recursive belief state, significantly outperforming existing methods. Finally, we establish dataset splits designed to isolate temporal and domain biases, providing a rigorous foundation for future research in supervised learning and out-of-distribution generalization.

cs.CV↗

arXiv2026

QuadGPT: Native Quadrilateral Mesh Generation with Autoregressive Models

The generation of quadrilateral-dominant meshes is a cornerstone of professional 3D content creation. However, existing generative models generate quad meshes by first generating triangle meshes and then merging triangles into quadrilaterals with some specific rules, which typically produces quad meshes with poor topology. In this paper, we introduce QuadGPT, the first autoregressive framework for generating quadrilateral meshes in an end-to-end manner. QuadGPT formulates this as a sequence prediction paradigm, distinguished by two key innovations: a unified tokenization method to handle mixed topologies of triangles and quadrilaterals, and a specialized Reinforcement Learning fine-tuning method tDPO for better generation quality. Extensive experiments demonstrate that QuadGPT significantly surpasses previous triangle-to-quad conversion pipelines in both geometric accuracy and topological quality. Our work establishes a new benchmark for native quad-mesh generation and showcases the power of combining large-scale autoregressive models with topology-aware RL refinement for creating structured 3D assets.

cs.CV↗

arXiv2026

A Long-Short Flow-Map Perspective for Drifting Models

This paper provides a reinterpretation of the Drifting Model~\cite{deng2026generative} through a semigroup-consistent long-short flow-map factorization. We show that a global transport process can be decomposed into a long-horizon flow map followed by a short-time terminal flow map admitting a closed-form optimal velocity representation, and that taking the terminal interval length to zero recovers exactly the drifting field together with a conservative impulse term required for flow-map consistency. Based on this perspective, we propose a new likelihood learning formulation that aligns the long-short flow-map decomposition with density evolution under transport. We validate the framework through both theoretical analysis and empirical evaluations on benchmark tests, and further provide a theoretical interpretation of the feature-space optimization while highlighting several open problems for future study.

cs.LG↗

arXiv2026

LocateAnything3D: Vision-Language 3D Detection with Chain-of-Sight

To act in the world, a model must name what it sees and know where it is in 3D. Today's vision-language models (VLMs) excel at open-ended 2D description and grounding, yet multi-object 3D detection remains largely missing from the VLM toolbox. We present LocateAnything3D, a VLM-native recipe that casts 3D detection as a next-token prediction problem. The key is a short, explicit Chain-of-Sight (CoS) sequence that mirrors how human reason from images: find an object in 2D, then infer its distance, size, and pose. The decoder first emits 2D detections as a visual chain-of-thought, then predicts 3D boxes under an easy-to-hard curriculum: across objects, a near-to-far order reduces early ambiguity and matches ego-centric utility; within each object, a center-from-camera, dimensions, and rotation factorization ranks information by stability and learnability. This VLM-native interface preserves open-vocabulary and visual-prompting capability without specialized heads. On the challenging Omni3D benchmark, our model achieves state-of-the-art results, with 38.90 AP_3D, surpassing the previous best by +13.98 absolute improvement even when the baseline is given ground-truth 2D boxes. It also generalizes zero-shot to held-out categories with strong robustness. By turning 3D detection into a disciplined next-token problem, LocateAnything3D offers a practical foundation for models to perceive in 3D.

cs.CV↗

arXiv2026

An Impulse-formed Navier-Stokes Solver based on Long-range Particle Flow Maps

We present a particle-grid characteristic-mapping framework that extends long-range characteristic mapping from inviscid flows to general Navier-Stokes dynamics with viscosity, body forces, and complex boundaries. Unlike traditional grid-based and vorticity-centered characteristic methods, our method is built on the observation that particle trajectories naturally provide the long-range flow map, enabling geometric quantities and their gradients to be transported in a direct and effective manner. We identify the impulse, the gauge variable of the velocity field, as the primary quantity mapped along characteristics while remaining compatible with standard velocity-based incompressible solvers. Using the 1-form representation of the impulse equation, we derive an integral formulation that decomposes the impulse evolution into a component transported geometrically along the particle flow map and a complementary component generated by viscosity and body forces evaluated through path integrals accumulated along particle trajectories. These components together yield a unified characteristic-mapping solver capable of handling incompressible Navier-Stokes flows with viscosity and body forces while maintaining the accuracy and geometric fidelity of characteristic transport.

cs.CE↗

arXiv2026

Trajectory Consistency for One-Step Generation on Euler Mean Flows

We propose \emph{Euler Mean Flows (EMF)}, a flow-based generative framework for one-step and few-step generation that enforces long-range trajectory consistency with minimal sampling cost. The key idea of EMF is to replace the trajectory consistency constraint, which is difficult to supervise and optimize over long time scales, with a principled linear surrogate that enables direct data supervision for long-horizon flow-map compositions. We derive this approximation from the semigroup formulation of flow-based models and show that, under mild regularity assumptions, it faithfully approximates the original consistency objective while being substantially easier to optimize. This formulation leads to a unified, JVP-free training framework that supports both $u$-prediction and $x_1$-prediction variants, avoiding explicit Jacobian computations and significantly reducing memory and computational overhead. Experiments on image synthesis, particle-based geometry generation, and functional generation demonstrate improved optimization stability and sample quality under fixed sampling budgets, together with approximately $50\%$ reductions in training time and memory consumption compared to existing one-step methods for image generation.

cs.LG↗

arXiv2026

Language Models are Symbolic Learners in Arithmetic

The prevailing question in LM performing arithmetic is whether these models learn to truly compute or if they simply master superficial pattern matching. In this paper, we argues for the latter, presenting evidence that LMs act as greedy symbolic learners, prioritizing the simplest possible shortcuts to fit the stats of dataset to solve arithmetic tasks. To investigate this, we introduce subgroup induction, a practical framework adapted from Solomonoff Induction (SI), one of the most powerful universal predictors. Our framework analyzes arithmetic problems by breaking them down into subgroups-minimal mappings between a few input digits and a single output digit. Our primary metric, subgroup quality, measures the viability of these shortcuts. Experiments reveal a distinct U-shaped accuracy pattern in multi-digit multiplication: LMs quickly master the first and last output digits while struggling with those in the middle. We demonstrate this U-shape is not coincidental; it perfectly mirrors the quality of the simplest possible subgroups, those requiring the fewest input tokens. This alignment suggests a core learning mechanism: LMs first learn easy, low-token shortcuts and only incorporate more complex, multi-token patterns as training progresses. They do not learn the algorithm of multiplication but rather a hierarchy of increasingly complex symbol-to-symbol mappings. Ultimately, our findings suggest that the path to arithmetic mastery for LMs is not paved with algorithms, but with a cascade of simple, hierarchically-learned symbolic shortcuts.

cs.LG↗

arXiv2026

A Fourth-Order Cut-cell Multigrid Method for Solving Elliptic Equations on Arbitrary Domains

To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional constant-coefficient elliptic equations with both divergence and non-divergence forms and all types of boundary conditions, (2) the versatility of handling both regular and irregular domains with arbitrarily complex topology and geometry, (3) the fourth-order accuracy even at the presence of ${\cal C}^1$ discontinuities on the domain boundary, and (4) the optimal complexity of $O(h^{-2})$.Test results demonstrate the generality, accuracy, efficiency, robustness, and excellent conditioning of the proposed method.

math.NA↗

arXiv2025

DriveMLM: Aligning Multi-Modal Large Language Models with Behavioral Planning States for Autonomous Driving

Large language models (LLMs) have opened up new possibilities for intelligent agents, endowing them with human-like thinking and cognitive abilities. In this work, we delve into the potential of large language models (LLMs) in autonomous driving (AD). We introduce DriveMLM, an LLM-based AD framework that can perform close-loop autonomous driving in realistic simulators. To this end, (1) we bridge the gap between the language decisions and the vehicle control commands by standardizing the decision states according to the off-the-shelf motion planning module. (2) We employ a multimodal LLM (MLLM) to model the behavior planning module of a module AD system, which uses driving rules, user commands, and inputs from various sensors (e.g., camera, lidar) as input and makes driving decisions and provide explanations; This model can plug-and-play in existing AD systems such as Autopilot and Apollo for close-loop driving. (3) We design an effective data engine to collect a dataset that includes decision state and corresponding explanation annotation for model training and evaluation. We conduct extensive experiments and show that replacing the decision-making modules of the Autopilot and Apollo with DriveMLM resulted in significant improvements of 3.2 and 4.7 points on the CARLA Town05 Long respectively, demonstrating the effectiveness of our model. We hope this work can serve as a baseline for autonomous driving with LLMs.

cs.CV↗

arXiv2025

MoCA: Mixture-of-Components Attention for Scalable Compositional 3D Generation

Compositionality is critical for 3D object and scene generation, but existing part-aware 3D generation methods suffer from poor scalability due to quadratic global attention costs when increasing the number of components. In this work, we present MoCA, a compositional 3D generative model with two key designs: (1) importance-based component routing that selects top-k relevant components for sparse global attention, and (2) unimportant components compression that preserve contextual priors of unselected components while reducing computational complexity of global attention. With these designs, MoCA enables efficient, fine-grained compositional 3D asset creation with scalable number of components. Extensive experiments show MoCA outperforms baselines on both compositional object and scene generation tasks. Project page: https://lizhiqi49.github.io/MoCA

cs.CV↗

arXiv2025

Functional Mean Flow in Hilbert Space

We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional Flow Matching and a practical implementation for efficient training and sampling. We also introduce an $x_1$-prediction variant that improves stability over the original $u$-prediction form. The resulting framework is a practical one-step Flow Matching method applicable to a wide range of functional data generation tasks such as time series, images, PDEs, and 3D geometry.

cs.LG↗

arXiv2025

NVIDIA Nemotron Nano V2 VL

We introduce Nemotron Nano V2 VL, the latest model of the Nemotron vision-language series designed for strong real-world document understanding, long video comprehension, and reasoning tasks. Nemotron Nano V2 VL delivers significant improvements over our previous model, Llama-3.1-Nemotron-Nano-VL-8B, across all vision and text domains through major enhancements in model architecture, datasets, and training recipes. Nemotron Nano V2 VL builds on Nemotron Nano V2, a hybrid Mamba-Transformer LLM, and innovative token reduction techniques to achieve higher inference throughput in long document and video scenarios. We are releasing model checkpoints in BF16, FP8, and FP4 formats and sharing large parts of our datasets, recipes and training code.

cs.LG↗

arXiv2025

An Adjoint Method for Differentiable Fluid Simulation on Flow Maps

This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as the forward simulation. In the forward pass, this map transports fluid impulse variables from the initial frame to the current frame to simulate vortical dynamics. In the backward pass, the same map propagates adjoint variables from the current frame back to the initial frame to compute gradients. This shared long-range map allows the accuracy of gradient computation to benefit directly from improvements in flow map construction. Building on this insight, we introduce a novel adjoint solver that solves the adjoint equations directly on the flow map, enabling long-range and accurate differentiation of incompressible flows without differentiating intermediate numerical steps or storing intermediate variables, as required in conventional adjoint methods. To further improve efficiency, we propose a long-short time-sparse flow map representation for evolving adjoint variables. Our approach has low memory usage, requiring only 6.53GB of data at a resolution of $192^3$ while preserving high accuracy in tracking vorticity, enabling new differentiable simulation tasks that require precise identification, prediction, and control of vortex dynamics.

cs.GR↗

arXiv2025

Improving Model Fusion by Training-time Neuron Alignment with Fixed Neuron Anchors

Model fusion aims to integrate several deep neural network (DNN) models' knowledge into one by fusing parameters, and it has promising applications, such as improving the generalization of foundation models and parameter averaging in federated learning. However, models under different settings (data, hyperparameter, etc.) have diverse neuron permutations; in other words, from the perspective of loss landscape, they reside in different loss basins, thus hindering model fusion performances. To alleviate this issue, previous studies highlighted the role of permutation invariance and have developed methods to find correct network permutations for neuron alignment after training. Orthogonal to previous attempts, this paper studies training-time neuron alignment, improving model fusion without the need for post-matching. Training-time alignment is cheaper than post-alignment and is applicable in various model fusion scenarios. Starting from fundamental hypotheses and theorems, a simple yet lossless algorithm called TNA-PFN is introduced. TNA-PFN utilizes partially fixed neuron weights as anchors to reduce the potential of training-time permutations, and it is empirically validated in reducing the barriers of linear mode connectivity and multi-model fusion. It is also validated that TNA-PFN can improve the fusion of pretrained models under the setting of model soup (vision transformers) and ColD fusion (pretrained language models). Based on TNA-PFN, two federated learning methods, FedPFN and FedPNU, are proposed, showing the prospects of training-time neuron alignment. FedPFN and FedPNU reach state-of-the-art performances in federated learning under heterogeneous settings and can be compatible with the server-side algorithm.

cs.LG↗

arXiv2025

STORM: Token-Efficient Long Video Understanding for Multimodal LLMs

Recent advances in video-based multimodal large language models (Video-LLMs) have significantly improved video understanding by processing videos as sequences of image frames. However, many existing methods treat frames independently in the vision backbone, lacking explicit temporal modeling, which limits their ability to capture dynamic patterns and efficiently handle long videos. To address these limitations, we introduce STORM (Spatiotemporal TOken Reduction for Multimodal LLMs), a novel architecture incorporating a dedicated temporal encoder between the image encoder and the LLM. Our temporal encoder leverages the Mamba State Space Model to integrate temporal information into image tokens, generating enriched representations that preserve inter-frame dynamics across the entire video sequence. This enriched encoding not only enhances video reasoning capabilities but also enables effective token reduction strategies, including test-time sampling and training-based temporal and spatial pooling, substantially reducing computational demands on the LLM without sacrificing key temporal information. By integrating these techniques, our approach simultaneously reduces training and inference latency while improving performance, enabling efficient and robust video understanding over extended temporal contexts. Extensive evaluations show that STORM achieves state-of-the-art results across various long video understanding benchmarks (more than 5% improvement on MLVU and LongVideoBench) while reducing the computation costs by up to $8\times$ and the decoding latency by 2.4-2.9$\times$ for the fixed numbers of input frames. Project page is available at https://research.nvidia.com/labs/lpr/storm

cs.CV↗

arXiv2025

SPARK: Adaptive Low-Rank Knowledge Graph Modeling in Hybrid Geometric Spaces for Recommendation

Knowledge Graphs (KGs) enhance recommender systems but face challenges from inherent noise, sparsity, and Euclidean geometry's inadequacy for complex relational structures, critically impairing representation learning, especially for long-tail entities. Existing methods also often lack adaptive multi-source signal fusion tailored to item popularity. This paper introduces SPARK, a novel multi-stage framework systematically tackling these issues. SPARK first employs Tucker low-rank decomposition to denoise KGs and generate robust entity representations. Subsequently, an SVD-initialized hybrid geometric GNN concurrently learns representations in Euclidean and Hyperbolic spaces; the latter is strategically leveraged for its aptitude in modeling hierarchical structures, effectively capturing semantic features of sparse, long-tail items. A core contribution is an item popularity-aware adaptive fusion strategy that dynamically weights signals from collaborative filtering, refined KG embeddings, and diverse geometric spaces for precise modeling of both mainstream and long-tail items. Finally, contrastive learning aligns these multi-source representations. Extensive experiments demonstrate SPARK's significant superiority over state-of-the-art methods, particularly in improving long-tail item recommendation, offering a robust, principled approach to knowledge-enhanced recommendation. Implementation code is available at https://github.com/Applied-Machine-Learning-Lab/SPARK.

cs.IR↗