arXiv subjects

Hanxiao Wang

Publications and source records attributed to Hanxiao Wang.

At least 19 recordsLinked to original sources

arXiv2026

Nexus: Native Mesh Generation with Diffusion

Generating high-quality triangle meshes is essential for film, gaming, and interactive 3D applications. Mainstream methods rely on mesh serialization and autoregressive processes, which stuggles in effective inference and is sensitive to error accumulation. In this paper, we present Nexus, a diffusion method that achieves holistic mesh generation via decoupled vertex and topology generation. First, we view mesh vertices as sparse voxels organized as an octree and adopt a diffusion model to generate the vertices in a coarse-to-fine manner. Second, for topology modeling, we propose Spacetime Interval, as an extension of Spacetime Distance to encode arbitrary edge and face topology into continuous per-vertex embeddings. It allows for a global and efficient recovery of complex topology. We then employ a diffusion model to generate the continuous embeddings on the generated vertices. Extensive experiments on the Objaverse and Toys4K datasets and in-the-wild images demonstrate that our method outperforms state-of-the-art autoregressive and two-stage baselines, effectively circumventing the inherent limitations of sequential mesh modeling. A blind user study from 3D practitioners confirms strong perceptual preference for our results.

cs.CV↗

arXiv2026

Sub-Infinite Horizon Stochastic Linear-Quadratic Optimal Control Problems and Delayed Backward Riccati Equations

In this paper, we investigate a class of so-called sub-infinite horizon stochastic linear-quadratic optimal control problems, in which the initial time $t$ is arbitrarily taken from $[0,\infty)$ and the running cost is defined over $[t,t+T]$ for a given $T>0$. The optimal control of this type of problem can be obtained by standard methods; however, it is shown that the resulting optimal control is generally time-inconsistent. Thus, instead of seeking an optimal control, which is time-inconsistent, we aim to find a time-consistent, locally optimal, and time-invariant equilibrium strategy, by introducing a new and very interesting type of Riccati equation. Its main feature is that the generator depends on a delay term of the unknown. In other words, this Riccati equation is a backward ordinary differential equation (ODE) with delay, which is equivalent to a forward ODE with advanced terms. Such an equation is essentially a Fredholm integral equation, whose solvability is challenging. We overcome the difficulty by deriving a sharp a priori estimate and applying the Leray--Schauder fixed point theorem. To this end, we establish a comparison theorem between two matrix-valued nonlinear algebraic equations. The convergence behavior of the solution to the Riccati equation as $T\to\infty$ is also provided.

math.OC↗

arXiv2026

Stackelberg Stochastic Linear-Quadratic Differential Games: A Closed-Loop Equilibrium Approach

This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two coupled Hamilton-Jacobi-Bellman (HJB) equations derived via time discretization and a limiting argument, whose convergence remains an open problem. We propose an alternative framework based on closed-loop equilibrium strategies. We reformulate the leader's problem as a forward-backward optimal control problem involving a coupled system of forward SDEs and backward Riccati equations. Due to the presence of controlled Riccati equations, the leader's problem becomes essentially nonlinear. Using a variational method, we characterize the leader's closed-loop equilibrium strategy and derive the associated equilibrium Riccati equation (ERE). A key conceptual distinction is that the follower adopts a globally optimal strategy against any admissible control of the leader, whereas in previous literature the follower's strategy was only locally optimal along the leader's specific equilibrium path. This makes the follower's strategy more robust and the leader's commitment more credible. In our LQ setting, the resulting ERE coincides exactly with the coupled HJB system from the literature, showing the leader's strategy is equivalent to the feedback Stackelberg solution. Thus, our framework provides not only an alternative derivation but also a rigorous justification of the limiting argument. We establish a priori estimates for the ERE, covering 1D and high-dimensional cases, ensuring global well-posedness for any finite horizon. This significantly extends existing results which require a sufficiently short time horizon or control-independent diffusion. An application to an asset management problem with numerical simulations illustrates the theoretical results.

math.OC↗

arXiv2026

FACE: A Face-based Autoregressive Representation for High-Fidelity and Efficient Mesh Generation

Autoregressive models for 3D mesh generation suffer from a fundamental limitation: they flatten meshes into long vertex-coordinate sequences. This results in prohibitive computational costs, hindering the efficient synthesis of high-fidelity geometry. We argue this bottleneck stems from operating at the wrong semantic level. We introduce FACE, a novel Autoregressive Autoencoder (ARAE) framework that reconceptualizes the task by generating meshes at the face level. Our one-face-one-token strategy treats each triangle face, the fundamental building block of a mesh, as a single, unified token. This simple yet powerful design reduces the sequence length by a factor of nine, leading to an unprecedented compression ratio of 0.11, halving the previous state-of-the-art. This dramatic efficiency gain does not compromise quality; by pairing our face-level decoder with a powerful VecSet encoder, FACE achieves state-of-the-art reconstruction quality on standard benchmarks. The versatility of the learned latent space is further demonstrated by training a latent diffusion model that achieves high-fidelity, single-image-to-mesh generation. FACE provides a simple, scalable, and powerful paradigm that lowers the barrier to high-quality structured 3D content creation.

cs.CV↗

arXiv2025

CostFilter-AD: Enhancing Anomaly Detection through Matching Cost Filtering

Unsupervised anomaly detection (UAD) seeks to localize the anomaly mask of an input image with respect to normal samples. Either by reconstructing normal counterparts (reconstruction-based) or by learning an image feature embedding space (embedding-based), existing approaches fundamentally rely on image-level or feature-level matching to derive anomaly scores. Often, such a matching process is inaccurate yet overlooked, leading to sub-optimal detection. To address this issue, we introduce the concept of cost filtering, borrowed from classical matching tasks, such as depth and flow estimation, into the UAD problem. We call this approach {\em CostFilter-AD}. Specifically, we first construct a matching cost volume between the input and normal samples, comprising two spatial dimensions and one matching dimension that encodes potential matches. To refine this, we propose a cost volume filtering network, guided by the input observation as an attention query across multiple feature layers, which effectively suppresses matching noise while preserving edge structures and capturing subtle anomalies. Designed as a generic post-processing plug-in, CostFilter-AD can be integrated with either reconstruction-based or embedding-based methods. Extensive experiments on MVTec-AD and VisA benchmarks validate the generic benefits of CostFilter-AD for both single- and multi-class UAD tasks. Code and models will be released at https://github.com/ZHE-SAPI/CostFilter-AD.

eess.IV↗

arXiv2025

Mean-Field Stochastic Linear-Quadratic Optimal Controls: Roles of Expectation and Conditional Expectation Operators

This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"ıve, and equilibrium solutions and establish the well-posedness of the associated Riccati equations. This reveals how the expectation and conditional expectation operators influence time-consistency.

math.OC↗

arXiv2025

On the Performance Analysis of Momentum Method: A Frequency Domain Perspective

Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

cs.LG↗

arXiv2025

Solvability of Equilibrium Riccati Equations: A Direct Approach

The solvability of equilibrium Riccati equations (EREs) plays a central role in the study of time-inconsistent stochastic linear-quadratic optimal control problems, because it paves the way to constructing a closed-loop equilibrium strategy. Under the standard conditions, Yong [29] established its well-posedness by introducing the well-known multi-person differential game method. However, this method depends on the dynamic programming principle (DPP) of the sophisticated problems on every subinterval, and thus is essentially a control theory approach. In this paper, we shall give a new and more direct proof, in which the DPP is no longer needed. We first establish a priori estimates for the ERE in the case of smooth coefficients. Using this estimate, we then demonstrate both the local and global solvability of the ERE by constructing an appropriate Picard iteration sequence, which actually provides a numerical algorithm. Additionally, a mollification method is employed to handle the case with non-smooth coefficients.

math.OC↗

arXiv2025

Forward-Backward Stochastic Linear-Quadratic Optimal Controls: Equilibrium Strategies and Non-Symmetric Riccati Equations

Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control systems, the corresponding optimal control problem is inherently time-inconsistent. Consequently, the optimal controls derived in existing literature represent pre-committed solutions rather than dynamically consistent strategies. In this paper, we shift focus from pre-committed solutions to addressing the time-inconsistency issue directly, adopting a dynamic game-theoretic approach to derive equilibrium strategies. Owing to the forward-backward structure, the associated equilibrium Riccati equation (ERE) constitutes a coupled system of matrix-valued, non-local ordinary differential equations with a non-symmetric structure. This non-symmetry introduces fundamental challenges in establishing the solvability of the EREs. We overcome the difficulty by establishing a priori estimates for a combination of the solutions to EREs, which, interestingly, is a representation of the equilibrium value function.

math.OC↗

arXiv2025

iFlame: Interleaving Full and Linear Attention for Efficient Mesh Generation

This paper propose iFlame, a novel transformer-based network architecture for mesh generation. While attention-based models have demonstrated remarkable performance in mesh generation, their quadratic computational complexity limits scalability, particularly for high-resolution 3D data. Conversely, linear attention mechanisms offer lower computational costs but often struggle to capture long-range dependencies, resulting in suboptimal outcomes. To address this trade-off, we propose an interleaving autoregressive mesh generation framework that combines the efficiency of linear attention with the expressive power of full attention mechanisms. To further enhance efficiency and leverage the inherent structure of mesh representations, we integrate this interleaving approach into an hourglass architecture, which significantly boosts efficiency. Our approach reduces training time while achieving performance comparable to pure attention-based models. To improve inference efficiency, we implemented a caching algorithm that almost doubles the speed and reduces the KV cache size by seven-eighths compared to the original Transformer. We evaluate our framework on ShapeNet and Objaverse, demonstrating its ability to generate high-quality 3D meshes efficiently. Our results indicate that the proposed interleaving framework effectively balances computational efficiency and generative performance, making it a practical solution for mesh generation. The training takes only 2 days with 4 GPUs on 39k data with a maximum of 4k faces on Objaverse.

cs.CV↗

arXiv2025

Autoregressive Generation of Static and Growing Trees

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer range skip connections to completent this multi-resolution approach. The key advantage of this architecture is the faster processing speed and lower memory consumption. We are therefore able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

cs.CV↗

arXiv2024

Solvability of Coupled Forward-Backward Volterra Integral Equations

Motivated by the optimality system associated with controlled (forward) Volterra integral equations (FVIEs, for short), the well-posedness of coupled forward-backward Voterra integral equations (FBVIEs, for short) is studied. The main feature of FBVIEs is that the unknown $\{(X(t,s),Y(t,s))\}$ has two arguments. By taking $t$ as a parameter and $s$ as a (time) variable, one can regard FBVIE as a system of ordinary differential equations (ODEs, for short), with infinite-dimensional space values $\{(X(\cdot,s),Y(\cdot,s));\,s\in[0,T]\}$. To establish the well-posedness of such an FBVIE, a new non-local monotonicity condition is introduced, by which a bridge in infinite-dimensional spaces is constructed. Then by generalizing the method of continuation developed by \cite{Hu-Peng1995,Yong1997,Peng-Wu1999} for differential equations, we have established the well-posedness of FBVIEs.The key is to apply the chain rule to the mapping $t\mapsto\big[\int_\cdot^T\langle Y(s,s),X(s,\cdot)\rangle ds +\langle G(X(T,T)),X(T,\cdot)\rangle\big](t)$.

math.OC↗

arXiv2024

KANs for Computer Vision: An Experimental Study

This paper presents an experimental study of Kolmogorov-Arnold Networks (KANs) applied to computer vision tasks, particularly image classification. KANs introduce learnable activation functions on edges, offering flexible non-linear transformations compared to traditional pre-fixed activation functions with specific neural work like Multi-Layer Perceptrons (MLPs) and Convolutional Neural Networks (CNNs). While KANs have shown promise mostly in simplified or small-scale datasets, their effectiveness for more complex real-world tasks such as computer vision tasks remains less explored. To fill this gap, this experimental study aims to provide extended observations and insights into the strengths and limitations of KANs. We reveal that although KANs can perform well in specific vision tasks, they face significant challenges, including increased hyperparameter sensitivity and higher computational costs. These limitations suggest that KANs require architectural adaptations, such as integration with other architectures, to be practical for large-scale vision problems. This study focuses on empirical findings rather than proposing new methods, aiming to inform future research on optimizing KANs, in particular computer vision applications or alike.

cs.CV↗

arXiv2024

E$^3$-Net: Efficient E(3)-Equivariant Normal Estimation Network

Point cloud normal estimation is a fundamental task in 3D geometry processing. While recent learning-based methods achieve notable advancements in normal prediction, they often overlook the critical aspect of equivariance. This results in inefficient learning of symmetric patterns. To address this issue, we propose E3-Net to achieve equivariance for normal estimation. We introduce an efficient random frame method, which significantly reduces the training resources required for this task to just 1/8 of previous work and improves the accuracy. Further, we design a Gaussian-weighted loss function and a receptive-aware inference strategy that effectively utilizes the local properties of point clouds. Our method achieves superior results on both synthetic and real-world datasets, and outperforms current state-of-the-art techniques by a substantial margin. We improve RMSE by 4% on the PCPNet dataset, 2.67% on the SceneNN dataset, and 2.44% on the FamousShape dataset.

cs.CV↗

arXiv2024

The Lp Polar bodies of shadow system and related inequalities

The $L_p$ versions of the support function and polar body are introduced by Berndtsson, Mastrantonis and Rubinstein in \cite{Berndtsson-Mastrantonis-Rubinstein-2023} recently. In this paper, we prove that the $L_p$-support function of the shadow system $K_t$ introduced by Rogers and Shephard in \cite{rogers-1958-02,shephard-1964} is convex and the volume of the section of $L_p$ polar bodies of $K_t$ is $\frac{1}{n}$-concave with respect to parameter $t$, and obtain some related inequalities. Finally, we present the reverse Rogers-Shephard type inequality for $L_p$-polar bodies.

math.FA↗

arXiv2024

Diffusion Deepfake

Recent progress in generative AI, primarily through diffusion models, presents significant challenges for real-world deepfake detection. The increased realism in image details, diverse content, and widespread accessibility to the general public complicates the identification of these sophisticated deepfakes. Acknowledging the urgency to address the vulnerability of current deepfake detectors to this evolving threat, our paper introduces two extensive deepfake datasets generated by state-of-the-art diffusion models as other datasets are less diverse and low in quality. Our extensive experiments also showed that our dataset is more challenging compared to the other face deepfake datasets. Our strategic dataset creation not only challenge the deepfake detectors but also sets a new benchmark for more evaluation. Our comprehensive evaluation reveals the struggle of existing detection methods, often optimized for specific image domains and manipulations, to effectively adapt to the intricate nature of diffusion deepfakes, limiting their practical utility. To address this critical issue, we investigate the impact of enhancing training data diversity on representative detection methods. This involves expanding the diversity of both manipulation techniques and image domains. Our findings underscore that increasing training data diversity results in improved generalizability. Moreover, we propose a novel momentum difficulty boosting strategy to tackle the additional challenge posed by training data heterogeneity. This strategy dynamically assigns appropriate sample weights based on learning difficulty, enhancing the model's adaptability to both easy and challenging samples. Extensive experiments on both existing and newly proposed benchmarks demonstrate that our model optimization approach surpasses prior alternatives significantly.

cs.CV↗

arXiv2024

Dynamic Coalition Portfolio Selection with Recursive Utility

In this paper, we consider a dynamic coalition portfolio selection problem, with each agent's objective given by an Epstein--Zin recursive utility. To find a Pareto optimum, the coalition's problem is formulated as an optimization problem evolved by a multi-dimensional forward-backward SDE. Since the evolution system has a forward-backward structure, the problem is intrinsically time-inconsistent. With the dynamic-game point of view, we rigorously develop an approach to finding the equilibrium Pareto investment-consumption strategy. We find that the relationship between risk aversion and EIS has more influence on the coalition's problem than that on the one-agent problem. More interestingly, we show that the equilibrium Pareto consumption strategy associated with the recursive utility is much more effective than that associated with the CRRA expected utility, which highlights the feature of recursive utilities that the marginal benefit of consumption can depend on the future consumption.

math.OC↗

arXiv2023

Present-Biased Lobbyists in Linear Quadratic Stochastic Differential Games

We investigate a linear quadratic stochastic zero-sum game where two players lobby a political representative to invest in a wind turbine farm. Players are time-inconsistent because they discount performance with a non-constant rate. Our objective is to identify a consistent planning equilibrium in which the players are aware of their inconsistency and cannot commit to a lobbying policy. We analyze the equilibrium behavior in both single player and two-player cases, and compare the behavior of the game under constant and non-constant discount rates. The equilibrium behavior is provided in closed-loop form, either analytically or via numerical approximation. Our numerical analysis of the equilibrium reveals that strategic behavior leads to more intense lobbying without resulting in overshooting.

econ.GN↗