arXiv subjects

Zeyi Xu

Publications and source records attributed to Zeyi Xu.

12 recordsLinked to original sources

arXiv2026

Meshy T2: Fast Native Mesh Generation with Flow Matching

Polygonal meshes are the standard surface representation of modern 3D pipelines, and generating high-quality meshes with artist-style topology is essential for film, gaming, and interactive 3D applications. Mainstream approaches serialize a mesh into a token sequence and decode it autoregressively, which is slow at inference and sensitive to error accumulation, making them impractical for interactive asset creation. We present Meshy T2, a fast native mesh generation framework built on flow matching. At its core is a vertex-set mesh VAE that encodes a mesh into one continuous latent token per vertex and decodes vertices, edge connectivity, and face winding order in a single pass, preserving high-precision geometry and artist-authored topology without vertex quantization or welding. Generation proceeds as a coarse-to-fine cascade of two flow-matching models: an image-conditioned voxel flow first sketches the overall shape as a coarse occupancy scaffold, and a mesh flow then populates the scaffold with per-vertex latent tokens, conditioned on the image, the scaffold, and a requested vertex budget. This design delivers three practical capabilities: interactive generation speed through parallel flow-based synthesis; effective face-count control through the requested vertex budget; and native support for multi-part assets, whose components emerge directly from the generated connectivity. In our experiments, Meshy T2 achieves state-of-the-art geometric fidelity and completes end-to-end image-to-mesh generation within a median of 6 seconds, over an order of magnitude faster than autoregressive baselines. Code and weights will be available at https://github.com/meshy-dev/meshy-t2.

cs.GR↗

arXiv2026

Adaptive Accelerated Mirror Descent in Primal and Dual Spaces

We propose Adaptive Accelerated Mirror Descent (AAMD), a flow-based method that combines nonlinear preconditioning, acceleration, and adaptivity in mirror geometry. The key ingredient is an accumulated Lyapunov perturbation budget: local descent failures are allowed as long as the total budget remains nonpositive, so line search is used only when stability is at risk. We prove accelerated convergence under dual relative smoothness/convexity and a mirror-geometry compatibility condition, and obtain an $O(1/k^2)$ rate for convex objectives by homotopy under a bounded-sublevel-set assumption. Experiments on relative-smoothness problems show that combining preconditioning, acceleration, and adaptivity gives substantial gains over methods using only part of this structure.

math.OC↗

arXiv2026

Accelerating Sinkhorn for Entropy-Regularized Optimal Transport

We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and defines the reduced dual objective $f(v)=\min_u F(u,v)$, while the remaining column scaling is a unit-step dual mirror descent step in $v$. This structure yields a Hessian-driven Nesterov acceleration that keeps Sinkhorn's scaling form and per-iteration cost, using only extrapolated combinations of Sinkhorn iterates. We prove an $\mathcal{O}(1/k^2)$ rate under a verifiable stability condition. For an $\varepsilon$-approximation of unregularized OT, the resulting complexity is $\widetilde{\mathcal{O}}(n^2/\varepsilon)$, improved from $\widetilde{\mathcal{O}}(n^2/\varepsilon^2)$ for Sinkhorn. On synthetic problems, color transfer, and word alignment, Acc-Sinkhorn gives a $10\times$--$30\times$ speedup over Sinkhorn at small regularization.

math.OC↗

arXiv2026

Deterministic Adam-Inspired Methods with Accelerated Convergence Rate

Adam is widely used, but its convergence theory remains incomplete even in the deterministic full-batch setting because momentum and adaptive preconditioning are tightly coupled. For smooth convex objectives, we split the momentum variable through variable-and-operator splitting, which reveals the acceleration mechanism. We then combine a Hessian-driven correction with Adam-style feedback based on the gradient magnitude. The resulting Adam-HNAG (Hessian-driven Nesterov accelerated gradient with Adam-style adaptive preconditioning) flow admits a nonnegative energy that decays exponentially. Its discretization yields two methods, Adam-HNAG and the synchronous variant Adam-HNAG-s. Under the stated trajectory-bound and consistency conditions, both methods satisfy a discrete Lyapunov contraction. If the exact adaptive steps are accepted, this contraction gives an $O(k^{-2})$ objective-value bound. Numerical experiments illustrate their behavior. These results apply to the proposed methods, not to the original Adam recursion.

math.OC↗

arXiv2026

Adaptive Accelerated Gradient Descent Methods for Convex Optimization

This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the method triggers line search only when accumulated perturbations become positive, thereby reducing gradient evaluations while preserving strong convergence guarantees. By integrating adaptive step size and momentum acceleration, A$^2$GD outperforms existing first-order methods across a range of problem settings.

math.OC↗

arXiv2026

Accelerated Mirror Descent Method through Variable and Operator Splitting

Mirror descent uses the mirror function to encode geometry and constraints, improving convergence while preserving feasibility. Accelerated Mirror Descent Methods (Acc-MD) are derived from a discretization of an accelerated mirror ODE system using a variable--operator splitting framework. A geometric assumption, termed the Generalized Cauchy-Schwarz (GCS) condition, is introduced to quantify the compatibility between the objective and the mirror geometry, under which the first accelerated linear convergence for Acc-MD on a broad class of problems is established. Numerical experiments on smooth and composite optimization tasks demonstrate that Acc-MD consistently outperforms existing accelerated variants, both theoretically and empirically.

math.OC↗

arXiv2025

Neural Modular Physics for Elastic Simulation

Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose essential features compared to traditional numerical simulators, such as physical interpretability and reliability. Drawing inspiration from classical simulators that operate in a modular fashion, this paper presents Neural Modular Physics (NMP) for elastic simulation, which combines the approximation capacity of neural networks with the physical reliability of traditional simulators. Beyond the previous monolithic learning paradigm, NMP enables direct supervision of intermediate quantities and physical constraints by decomposing elastic dynamics into physically meaningful neural modules connected through intermediate physical quantities. With a specialized architecture and training strategy, our method transforms the numerical computation flow into a modular neural simulator, achieving improved physical consistency and generalizability. Experimentally, NMP demonstrates superior generalization to unseen initial conditions and resolutions, stable long-horizon simulation, better preservation of physical properties compared to other neural simulators, and greater feasibility in scenarios with unknown underlying dynamics than traditional simulators.

cs.LG↗

arXiv2025

Trustworthy Pedestrian Trajectory Prediction via Pattern-Aware Interaction Modeling

Accurate and reliable pedestrian trajectory prediction is critical for the application of intelligent applications, yet achieving trustworthy prediction remains highly challenging due to the complexity of interactions among pedestrians. Previous methods often adopt black-box modeling of pedestrian interactions. Despite their strong performance, such opaque modeling limits the reliability of predictions in real-world deployments. To address this issue, we propose InSyn (Interaction-Synchronization Network), a novel Transformer-based model that explicitly captures diverse interaction patterns (e.g., walking in sync or conflicting) while effectively modeling direction-sensitive social behaviors. Additionally, we introduce a training strategy, termed Seq-Start of Seq (SSOS), designed to alleviate the common issue of initial-step divergence in numerical time-series prediction. Experiments on the ETH and UCY datasets demonstrate that our model not only outperforms recent black-box baselines in prediction accuracy, especially under high-density scenarios, but also provides transparent interaction modeling, as shown in the case study. Furthermore, the SSOS strategy proves to be effective in improving sequential prediction performance, reducing the initial-step prediction error by approximately 6.58%. Code is avaliable at https://github.com/rickzky1001/InSyn

cs.CV↗

arXiv2025

HNAG$^{++}$: An Accelerated Gradient Method with a Refined Asymptotic Rate for Strongly Convex Optimization

Two accelerated first-order methods, HNAG$^+$ and HNAG$^{++}$, are introduced for smooth strongly convex optimization. They are derived from the Hessian-driven Nesterov Accelerated Gradient (HNAG) flow by optimizing the coercivity of shifted Lyapunov functions. Let $\kappa=L/\mu$, where $\mu$ is the strong-convexity constant and $L$ is the gradient Lipschitz constant. HNAG$^+$ attains the optimal global rate $1-2/\sqrt{\kappa}$, matching the information-theoretic lower bound. For functions with local asymptotic symmetry at the minimizer, HNAG$^{++}$ attains the asymptotic rate $1-2\sqrt{2/\kappa}$. This matches the best known asymptotic rate under $\mathcal C^2$ regularity, while applying to a broader function class. Numerical experiments confirm the predicted rates and show favorable performance against existing accelerated schemes.

math.OC↗

arXiv2025

AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulation

Accurately and efficiently simulating complex fluid dynamics is a challenging task that has traditionally relied on computationally intensive methods. Neural network-based approaches, such as convolutional and graph neural networks, have partially alleviated this burden by enabling efficient local feature extraction. However, they struggle to capture long-range dependencies due to limited receptive fields, and Transformer-based models, while providing global context, incur prohibitive computational costs. To tackle these challenges, we propose AMR-Transformer, an efficient and accurate neural CFD-solving pipeline that integrates a novel adaptive mesh refinement scheme with a Navier-Stokes constraint-aware fast pruning module. This design encourages long-range interactions between simulation cells and facilitates the modeling of global fluid wave patterns, such as turbulence and shockwaves. Experiments show that our approach achieves significant gains in efficiency while preserving critical details, making it suitable for high-resolution physical simulations with long-range dependencies. On CFDBench, PDEBench and a new shockwave dataset, our pipeline demonstrates up to an order-of-magnitude improvement in accuracy over baseline models. Additionally, compared to ViT, our approach achieves a reduction in FLOPs of up to 60 times.

cs.LG↗

arXiv2024

AFIDAF: Alternating Fourier and Image Domain Adaptive Filters as an Efficient Alternative to Attention in ViTs

We propose and demonstrate an alternating Fourier and image domain filtering approach for feature extraction as an efficient alternative to build a vision backbone without using the computationally intensive attention. The performance among the lightweight models reaches the state-of-the-art level on ImageNet-1K classification, and improves downstream tasks on object detection and segmentation consistently as well. Our approach also serves as a new tool to compress vision transformers (ViTs).

cs.CV↗

arXiv2024

Learning Physical Simulation with Message Passing Transformer

Machine learning methods for physical simulation have achieved significant success in recent years. We propose a new universal architecture based on Graph Neural Network, the Message Passing Transformer, which incorporates a Message Passing framework, employs an Encoder-Processor-Decoder structure, and applies Graph Fourier Loss as loss function for model optimization. To take advantage of the past message passing state information, we propose Hadamard-Product Attention to update the node attribute in the Processor, Hadamard-Product Attention is a variant of Dot-Product Attention that focuses on more fine-grained semantics and emphasizes on assigning attention weights over each feature dimension rather than each position in the sequence relative to others. We further introduce Graph Fourier Loss (GFL) to balance high-energy and low-energy components. To improve time performance, we precompute the graph's Laplacian eigenvectors before the training process. Our architecture achieves significant accuracy improvements in long-term rollouts for both Lagrangian and Eulerian dynamical systems over current methods.

cs.LG↗