arXiv subjects

Xiaoyu Li

Publications and source records attributed to Xiaoyu Li.

At least 127 records · Page 7Linked to original sources

arXiv2025

GeometryCrafter: Consistent Geometry Estimation for Open-world Videos with Diffusion Priors

Despite remarkable advancements in video depth estimation, existing methods exhibit inherent limitations in achieving geometric fidelity through the affine-invariant predictions, limiting their applicability in reconstruction and other metrically grounded downstream tasks. We propose GeometryCrafter, a novel framework that recovers high-fidelity point map sequences with temporal coherence from open-world videos, enabling accurate 3D/4D reconstruction, camera parameter estimation, and other depth-based applications. At the core of our approach lies a point map Variational Autoencoder (VAE) that learns a latent space agnostic to video latent distributions for effective point map encoding and decoding. Leveraging the VAE, we train a video diffusion model to model the distribution of point map sequences conditioned on the input videos. Extensive evaluations on diverse datasets demonstrate that GeometryCrafter achieves state-of-the-art 3D accuracy, temporal consistency, and generalization capability.

cs.GR↗

arXiv2025

Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding

The key-value (KV) cache in the tensor version of transformers presents a significant bottleneck during inference. While previous work analyzes the fundamental space complexity barriers in standard attention mechanisms [Haris and Onak, 2025], our work generalizes the space complexity barriers result to tensor attention version. Our theoretical contributions rely on a reduction from communication complexity and deduce the memory lower bound for tensor-structured attention mechanisms when $d = Ω(\log n)$. Furthermore, we introduce two types of tensor attention cache and present a trade-off between time and memory for two scenarios. Overall, our work provides a theoretical foundation for us to understand the time-memory tradeoff of KV-Cache compression in tensor attention decoding and offers more perspectives in developing more memory-efficient tensor attention Transformer architectures.

cs.LG↗

arXiv2025

DiTCtrl: Exploring Attention Control in Multi-Modal Diffusion Transformer for Tuning-Free Multi-Prompt Longer Video Generation

Sora-like video generation models have achieved remarkable progress with a Multi-Modal Diffusion Transformer MM-DiT architecture. However, the current video generation models predominantly focus on single-prompt, struggling to generate coherent scenes with multiple sequential prompts that better reflect real-world dynamic scenarios. While some pioneering works have explored multi-prompt video generation, they face significant challenges including strict training data requirements, weak prompt following, and unnatural transitions. To address these problems, we propose DiTCtrl, a training-free multi-prompt video generation method under MM-DiT architectures for the first time. Our key idea is to take the multi-prompt video generation task as temporal video editing with smooth transitions. To achieve this goal, we first analyze MM-DiT's attention mechanism, finding that the 3D full attention behaves similarly to that of the cross/self-attention blocks in the UNet-like diffusion models, enabling mask-guided precise semantic control across different prompts with attention sharing for multi-prompt video generation. Based on our careful design, the video generated by DiTCtrl achieves smooth transitions and consistent object motion given multiple sequential prompts without additional training. Besides, we also present MPVBench, a new benchmark specially designed for multi-prompt video generation to evaluate the performance of multi-prompt generation. Extensive experiments demonstrate that our method achieves state-of-the-art performance without additional training.

cs.CV↗

arXiv2025

Mani-GS: Gaussian Splatting Manipulation with Triangular Mesh

Neural 3D representations such as Neural Radiance Fields (NeRF), excel at producing photo-realistic rendering results but lack the flexibility for manipulation and editing which is crucial for content creation. Previous works have attempted to address this issue by deforming a NeRF in canonical space or manipulating the radiance field based on an explicit mesh. However, manipulating NeRF is not highly controllable and requires a long training and inference time. With the emergence of 3D Gaussian Splatting (3DGS), extremely high-fidelity novel view synthesis can be achieved using an explicit point-based 3D representation with much faster training and rendering speed. However, there is still a lack of effective means to manipulate 3DGS freely while maintaining rendering quality. In this work, we aim to tackle the challenge of achieving manipulable photo-realistic rendering. We propose to utilize a triangular mesh to manipulate 3DGS directly with self-adaptation. This approach reduces the need to design various algorithms for different types of Gaussian manipulation. By utilizing a triangle shape-aware Gaussian binding and adapting method, we can achieve 3DGS manipulation and preserve high-fidelity rendering after manipulation. Our approach is capable of handling large deformations, local manipulations, and soft body simulations while keeping high-quality rendering. Furthermore, we demonstrate that our method is also effective with inaccurate meshes extracted from 3DGS. Experiments conducted demonstrate the effectiveness of our method and its superiority over baseline approaches.

cs.GR↗

arXiv2025

SMILE: a Scale-aware Multiple Instance Learning Method for Multicenter STAS Lung Cancer Histopathology Diagnosis

Spread through air spaces (STAS) represents a newly identified aggressive pattern in lung cancer, which is known to be associated with adverse prognostic factors and complex pathological features. Pathologists currently rely on time consuming manual assessments, which are highly subjective and prone to variation. This highlights the urgent need for automated and precise diag nostic solutions. 2,970 lung cancer tissue slides are comprised from multiple centers, re-diagnosed them, and constructed and publicly released three lung cancer STAS datasets: STAS CSU (hospital), STAS TCGA, and STAS CPTAC. All STAS datasets provide corresponding pathological feature diagnoses and related clinical data. To address the bias, sparse and heterogeneous nature of STAS, we propose an scale-aware multiple instance learning(SMILE) method for STAS diagnosis of lung cancer. By introducing a scale-adaptive attention mechanism, the SMILE can adaptively adjust high attention instances, reducing over-reliance on local regions and promoting consistent detection of STAS lesions. Extensive experiments show that SMILE achieved competitive diagnostic results on STAS CSU, diagnosing 251 and 319 STAS samples in CPTAC andTCGA,respectively, surpassing clinical average AUC. The 11 open baseline results are the first to be established for STAS research, laying the foundation for the future expansion, interpretability, and clinical integration of computational pathology technologies. The datasets and code are available at https://anonymous.4open.science/r/IJCAI25-1DA1.

cs.CV↗

arXiv2025

Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows

Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While prior work established the worst case optimality of standard flow matching under Wasserstein distances, the theoretical guarantees for higher-order flow matching - which incorporates acceleration terms to refine sample trajectories - remain unexplored. In this paper, we bridge this gap by proving that higher-order flow matching preserves worst case optimality as a distribution estimator. We derive upper bounds on the estimation error for second-order flow matching, demonstrating that the convergence rates depend polynomially on the smoothness of the target distribution (quantified via Besov spaces) and key parameters of the ODE dynamics. Our analysis employs neural network approximations with carefully controlled depth, width, and sparsity to bound acceleration errors across both small and large time intervals, ultimately unifying these results into a general worst case optimal bound for all time steps.

cs.LG↗

arXiv2025

Grams: Gradient Descent with Adaptive Momentum Scaling

We introduce $\mathbf{G}$radient Descent with $\mathbf{A}$daptive $\mathbf{M}$omentum $\mathbf{S}$caling ($\mathbf{Grams}$), a novel optimization algorithm that decouples the direction and magnitude of parameter updates in deep learning. Unlike traditional optimizers that directly integrate momentum into updates, Grams separates the update direction, derived from current gradients, from momentum, which is used solely for adaptive magnitude scaling. This approach enables Grams to achieve improved loss descent compared to state-of-the-art cautious and momentum-based optimizers. We theoretically demonstrate that Grams descents faster than other state-of-the-art optimizers and establish a global convergence guarantee for Grams. We also validate its effectiveness through extensive empirical evaluations. The results demonstrate Grams' superior performance, including faster convergence and better generalization, compared to widely-used optimizers such as Adam, Lion, and their cautious variants. Our results highlight Grams' potential as a transformative approach for efficiently training and fine-tuning large language models. Code is available at https://github.com/Gunale0926/Grams.

cs.LG↗

arXiv2025

Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approaches

Recently, Large Language Models (LLMs) have achieved remarkable success. A key factor behind this success is the scaling law observed by OpenAI. Specifically, for models with Transformer architecture, the test loss exhibits a power-law relationship with model size, dataset size, and the amount of computation used in training, demonstrating trends that span more than seven orders of magnitude. This scaling law challenges traditional machine learning wisdom, notably the Oscar Scissors principle, which suggests that an overparametrized algorithm will overfit the training datasets, resulting in poor test performance. Recent research has also identified the scaling law in simpler machine learning contexts, such as linear regression. However, fully explaining the scaling law in large practical models remains an elusive goal. In this work, we advance our understanding by demonstrating that the scaling law phenomenon extends to multiple regression and kernel regression settings, which are significantly more expressive and powerful than linear methods. Our analysis provides deeper insights into the scaling law, potentially enhancing our understanding of LLMs.

cs.LG↗

arXiv2025

Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent

In-context learning has been recognized as a key factor in the success of Large Language Models (LLMs). It refers to the model's ability to learn patterns on the fly from provided in-context examples in the prompt during inference. Previous studies have demonstrated that the Transformer architecture used in LLMs can implement a single-step gradient descent update by processing in-context examples in a single forward pass. Recent work has further shown that, during in-context learning, a looped Transformer can implement multi-step gradient descent updates in forward passes. However, their theoretical results require an exponential number of in-context examples, $n = \exp(Ω(T))$, where $T$ is the number of loops or passes, to achieve a reasonably low error. In this paper, we study linear looped Transformers in-context learning on linear vector generation tasks. We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, e.g., $n = O(d)$, the linear looped Transformers can achieve a small error by multi-step gradient descent during in-context learning. Furthermore, our preliminary experiments validate our theoretical analysis. Our findings reveal that the Transformer architecture possesses a stronger in-context learning capability than previously understood, offering new insights into the mechanisms behind LLMs and potentially guiding the better design of efficient inference algorithms for LLMs.

cs.LG↗

arXiv2025

Fast John Ellipsoid Computation with Differential Privacy Optimization

Determining the John ellipsoid - the largest volume ellipsoid contained within a convex polytope - is a fundamental problem with applications in machine learning, optimization, and data analytics. Recent work has developed fast algorithms for approximating the John ellipsoid using sketching and leverage score sampling techniques. However, these algorithms do not provide privacy guarantees for sensitive input data. In this paper, we present the first differentially private algorithm for fast John ellipsoid computation. Our method integrates noise perturbation with sketching and leverages score sampling to achieve both efficiency and privacy. We prove that (1) our algorithm provides $(ε,δ)$-differential privacy and the privacy guarantee holds for neighboring datasets that are $ε_0$-close, allowing flexibility in the privacy definition; (2) our algorithm still converges to a $(1+ξ)$-approximation of the optimal John ellipsoid in $Θ(ξ^{-2}(\log(n/δ_0) + (Lε_0)^{-2}))$ iterations where $n$ is the number of data point, $L$ is the Lipschitz constant, $δ_0$ is the failure probability, and $ε_0$ is the closeness of neighboring input datasets. Our theoretical analysis demonstrates the algorithm's convergence and privacy properties, providing a robust approach for balancing utility and privacy in John ellipsoid computation. This is the first differentially private algorithm for fast John ellipsoid computation, opening avenues for future research in privacy-preserving optimization techniques.

cs.DS↗

arXiv2025

The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexity

In this paper, we analyze the computational limitations of Mamba and State-space Models (SSMs) by using the circuit complexity framework. Despite Mamba's stateful design and recent attention as a strong candidate to outperform Transformers, we have demonstrated that both Mamba and SSMs with $\mathrm{poly}(n)$-precision and constant-depth layers reside within the $\mathsf{DLOGTIME}$-uniform $\mathsf{TC}^0$ complexity class. This result indicates Mamba has the same computational capabilities as Transformer theoretically, and it cannot solve problems like arithmetic formula problems, boolean formula value problems, and permutation composition problems if $\mathsf{TC}^0 \neq \mathsf{NC}^1$. Therefore, it challenges the assumption Mamba is more computationally expressive than Transformers. Our contributions include rigorous proofs showing that Selective SSM and Mamba architectures can be simulated by $\mathsf{DLOGTIME}$-uniform $\mathsf{TC}^0$ circuits, and they cannot solve problems outside $\mathsf{TC}^0$.

cs.CC↗

arXiv2025

Force Matching with Relativistic Constraints: A Physics-Inspired Approach to Stable and Efficient Generative Modeling

This paper introduces Force Matching (ForM), a novel framework for generative modeling that represents an initial exploration into leveraging special relativistic mechanics to enhance the stability of the sampling process. By incorporating the Lorentz factor, ForM imposes a velocity constraint, ensuring that sample velocities remain bounded within a constant limit. This constraint serves as a fundamental mechanism for stabilizing the generative dynamics, leading to a more robust and controlled sampling process. We provide a rigorous theoretical analysis demonstrating that the velocity constraint is preserved throughout the sampling procedure within the ForM framework. To validate the effectiveness of our approach, we conduct extensive empirical evaluations. On the \textit{half-moons} dataset, ForM significantly outperforms baseline methods, achieving the lowest Euclidean distance loss of \textbf{0.714}, in contrast to vanilla first-order flow matching (5.853) and first- and second-order flow matching (5.793). Additionally, we perform an ablation study to further investigate the impact of our velocity constraint, reaffirming the superiority of ForM in stabilizing the generative process. The theoretical guarantees and empirical results underscore the potential of integrating special relativity principles into generative modeling. Our findings suggest that ForM provides a promising pathway toward achieving stable, efficient, and flexible generative processes. This work lays the foundation for future advancements in high-dimensional generative modeling, opening new avenues for the application of physical principles in machine learning.

cs.LG↗

arXiv2025

Universal Approximation of Visual Autoregressive Transformers

We investigate the fundamental limits of transformer-based foundation models, extending our analysis to include Visual Autoregressive (VAR) transformers. VAR represents a big step toward generating images using a novel, scalable, coarse-to-fine ``next-scale prediction'' framework. These models set a new quality bar, outperforming all previous methods, including Diffusion Transformers, while having state-of-the-art performance for image synthesis tasks. Our primary contributions establish that, for single-head VAR transformers with a single self-attention layer and single interpolation layer, the VAR Transformer is universal. From the statistical perspective, we prove that such simple VAR transformers are universal approximators for any image-to-image Lipschitz functions. Furthermore, we demonstrate that flow-based autoregressive transformers inherit similar approximation capabilities. Our results provide important design principles for effective and computationally efficient VAR Transformer strategies that can be used to extend their utility to more sophisticated VAR models in image generation and other related areas.

cs.LG↗

arXiv2025

On Computational Limits and Provably Efficient Criteria of Visual Autoregressive Models: A Fine-Grained Complexity Analysis

Recently, Visual Autoregressive ($\mathsf{VAR}$) Models introduced a groundbreaking advancement in the field of image generation, offering a scalable approach through a coarse-to-fine ``next-scale prediction'' paradigm. Suppose that $n$ represents the height and width of the last VQ code map generated by $\mathsf{VAR}$ models, the state-of-the-art algorithm in [Tian, Jiang, Yuan, Peng and Wang, NeurIPS 2024] takes $O(n^{4+o(1)})$ time, which is computationally inefficient. In this work, we analyze the computational limits and efficiency criteria of $\mathsf{VAR}$ Models through a fine-grained complexity lens. Our key contribution is identifying the conditions under which $\mathsf{VAR}$ computations can achieve sub-quadratic time complexity. We have proved that assuming the Strong Exponential Time Hypothesis ($\mathsf{SETH}$) from fine-grained complexity theory, a sub-quartic time algorithm for $\mathsf{VAR}$ models is impossible. To substantiate our theoretical findings, we present efficient constructions leveraging low-rank approximations that align with the derived criteria. This work initiates the study of the computational efficiency of the $\mathsf{VAR}$ model from a theoretical perspective. Our technique will shed light on advancing scalable and efficient image generation in $\mathsf{VAR}$ frameworks.

cs.LG↗

arXiv2025

RichSpace: Enriching Text-to-Video Prompt Space via Text Embedding Interpolation

Text-to-video generation models have made impressive progress, but they still struggle with generating videos with complex features. This limitation often arises from the inability of the text encoder to produce accurate embeddings, which hinders the video generation model. In this work, we propose a novel approach to overcome this challenge by selecting the optimal text embedding through interpolation in the embedding space. We demonstrate that this method enables the video generation model to produce the desired videos. Additionally, we introduce a simple algorithm using perpendicular foot embeddings and cosine similarity to identify the optimal interpolation embedding. Our findings highlight the importance of accurate text embeddings and offer a pathway for improving text-to-video generation performance.

cs.CV↗

arXiv2025

High-Order Matching for One-Step Shortcut Diffusion Models

One-step shortcut diffusion models [Frans, Hafner, Levine and Abbeel, ICLR 2025] have shown potential in vision generation, but their reliance on first-order trajectory supervision is fundamentally limited. The Shortcut model's simplistic velocity-only approach fails to capture intrinsic manifold geometry, leading to erratic trajectories, poor geometric alignment, and instability-especially in high-curvature regions. These shortcomings stem from its inability to model mid-horizon dependencies or complex distributional features, leaving it ill-equipped for robust generative modeling. In this work, we introduce HOMO (High-Order Matching for One-Step Shortcut Diffusion), a game-changing framework that leverages high-order supervision to revolutionize distribution transportation. By incorporating acceleration, jerk, and beyond, HOMO not only fixes the flaws of the Shortcut model but also achieves unprecedented smoothness, stability, and geometric precision. Theoretically, we prove that HOMO's high-order supervision ensures superior approximation accuracy, outperforming first-order methods. Empirically, HOMO dominates in complex settings, particularly in high-curvature regions where the Shortcut model struggles. Our experiments show that HOMO delivers smoother trajectories and better distributional alignment, setting a new standard for one-step generative models.

cs.CV↗

arXiv2025

Dissecting Submission Limit in Desk-Rejections: A Mathematical Analysis of Fairness in AI Conference Policies

As AI research surges in both impact and volume, conferences have imposed submission limits to maintain paper quality and alleviate organizational pressure. In this work, we examine the fairness of desk-rejection systems under submission limits and reveal that existing practices can result in substantial inequities. Specifically, we formally define the paper submission limit problem and identify a critical dilemma: when the number of authors exceeds three, it becomes impossible to reject papers solely based on excessive submissions without negatively impacting innocent authors. Thus, this issue may unfairly affect early-career researchers, as their submissions may be penalized due to co-authors with significantly higher submission counts, while senior researchers with numerous papers face minimal consequences. To address this, we propose an optimization-based fairness-aware desk-rejection mechanism and formally define two fairness metrics: individual fairness and group fairness. We prove that optimizing individual fairness is NP-hard, whereas group fairness can be efficiently optimized via linear programming. Through case studies, we demonstrate that our proposed system ensures greater equity than existing methods, including those used in CVPR 2025, offering a more socially just approach to managing excessive submissions in AI conferences.

cs.LG↗

arXiv2025

On the Computational Capability of Graph Neural Networks: A Circuit Complexity Bound Perspective

Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have achieved significant empirical success, their theoretical limitations remain an active area of research. Existing studies primarily focus on characterizing GNN expressiveness through Weisfeiler-Lehman (WL) graph isomorphism tests. In this paper, we take a fundamentally different approach by exploring the computational limitations of GNNs through the lens of circuit complexity. Specifically, we analyze the circuit complexity of common GNN architectures and prove that under constraints of constant-depth layers, linear or sublinear embedding sizes, and polynomial precision, GNNs cannot solve key problems such as graph connectivity and graph isomorphism unless $\mathsf{TC}^0 = \mathsf{NC}^1$. These results reveal the intrinsic expressivity limitations of GNNs behind their empirical success and introduce a novel framework for analyzing GNN expressiveness that can be extended to a broader range of GNN models and graph decision problems.

cs.LG↗