Lingxiao Li

Lingxiao Li, Samuel Hurault, Justin Solomon

We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main observation is that the time-varying velocity field of the PDE solution needs to be self-consistent: it must satisfy a fixed-point equation involving the probability flow characterized by the same velocity field. Instead of directly minimizing the residual of the fixed-point equation with neural parameterization, we use an iterative formulation with a biased gradient estimator that bypasses significant computational obstacles with strong empirical performance. Compared to existing approaches, our method does not suffer from temporal or spatial discretization, covers a wider range of PDEs, and scales to high dimensions. Experimentally, our method recovers analytical solutions accurately when they are available and achieves superior performance in high dimensions with less training time compared to alternatives.

Lingxiao Li, Qiang Liu, Anna Korba et al.

Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.

Ryan Burgert, Yuancheng Xu, Wenqi Xian et al.

Generative modeling aims to transform random noise into structured outputs. In this work, we enhance video diffusion models by allowing motion control via structured latent noise sampling. This is achieved by just a change in data: we pre-process training videos to yield structured noise. Consequently, our method is agnostic to diffusion model design, requiring no changes to model architectures or training pipelines. Specifically, we propose a novel noise warping algorithm, fast enough to run in real time, that replaces random temporal Gaussianity with correlated warped noise derived from optical flow fields, while preserving the spatial Gaussianity. The efficiency of our algorithm enables us to fine-tune modern video diffusion base models using warped noise with minimal overhead, and provide a one-stop solution for a wide range of user-friendly motion control: local object motion control, global camera movement control, and motion transfer. The harmonization between temporal coherence and spatial Gaussianity in our warped noise leads to effective motion control while maintaining per-frame pixel quality. Extensive experiments and user studies demonstrate the advantages of our method, making it a robust and scalable approach for controlling motion in video diffusion models. Video results are available on our webpage: https://eyeline-labs.github.io/Go-with-the-Flow. Source code and model checkpoints are available on GitHub: https://github.com/Eyeline-Labs/Go-with-the-Flow.

Zeqi Xiao, Yiwei Zhao, Lingxiao Li et al.

We investigate whether video generative models can exhibit visuospatial intelligence, a capability central to human cognition, using only visual data. To this end, we present Video4Spatial, a framework showing that video diffusion models conditioned solely on video-based scene context can perform complex spatial tasks. We validate on two tasks: scene navigation - following camera-pose instructions while remaining consistent with 3D geometry of the scene, and object grounding - which requires semantic localization, instruction following, and planning. Both tasks use video-only inputs, without auxiliary modalities such as depth or poses. With simple yet effective design choices in the framework and data curation, Video4Spatial demonstrates strong spatial understanding from video context: it plans navigation and grounds target objects end-to-end, follows camera-pose instructions while maintaining spatial consistency, and generalizes to long contexts and out-of-domain environments. Taken together, these results advance video generative models toward general visuospatial reasoning.

Yitong Deng, Winnie Lin, Lingxiao Li et al.

Adapting pretrained image-based diffusion models to generate temporally consistent videos has become an impactful generative modeling research direction. Training-free noise-space manipulation has proven to be an effective technique, where the challenge is to preserve the Gaussian white noise distribution while adding in temporal consistency. Recently, Chang et al. (2024) formulated this problem using an integral noise representation with distribution-preserving guarantees, and proposed an upsampling-based algorithm to compute it. However, while their mathematical formulation is advantageous, the algorithm incurs a high computational cost. Through analyzing the limiting-case behavior of their algorithm as the upsampling resolution goes to infinity, we develop an alternative algorithm that, by gathering increments of multiple Brownian bridges, achieves their infinite-resolution accuracy while simultaneously reducing the computational cost by orders of magnitude. We prove and experimentally validate our theoretical claims, and demonstrate our method's effectiveness in real-world applications. We further show that our method readily extends to the 3-dimensional space.

Yihao Wang, Lingxiao Li, Yifan Tang et al.

Intelligent transportation systems (ITS) use advanced technologies such as artificial intelligence to significantly improve traffic flow management efficiency, and promote the intelligent development of the transportation industry. However, if the data in ITS is attacked, such as tampering or forgery, it will endanger public safety and cause social losses. Therefore, this paper proposes a watermarking that can verify the integrity of copyright in response to the needs of ITS, termed ITSmark. ITSmark focuses on functions such as extracting watermarks, verifying permission, and tracing tampered locations. The scheme uses the copyright information to build the multi-bit space and divides this space into multiple segments. These segments will be assigned to tokens. Thus, the next token is determined by its segment which contains the copyright. In this way, the obtained data contains the custom watermark. To ensure the authorization, key parameters are encrypted during copyright embedding to obtain cipher data. Only by possessing the correct cipher data and private key, can the user entirely extract the watermark. Experiments show that ITSmark surpasses baseline performances in data quality, extraction accuracy, and unforgeability. It also shows unique capabilities of permission verification and tampered location tracing, which ensures the security of extraction and the reliability of copyright verification. Furthermore, ITSmark can also customize the watermark embedding position and proportion according to user needs, making embedding more flexible.

Lingxiao Li, Raaz Dwivedi, Lester Mackey · harvard, mit

Modern compression methods can summarize a target distribution $\mathbb{P}$ more succinctly than i.i.d. sampling but require access to a low-bias input sequence like a Markov chain converging quickly to $\mathbb{P}$. We introduce a new suite of compression methods suitable for compression with biased input sequences. Given $n$ points targeting the wrong distribution and quadratic time, Stein kernel thinning (SKT) returns $\sqrt{n}$ equal-weighted points with $\widetilde{O}(n^{-1/2})$ maximum mean discrepancy (MMD) to $\mathbb{P}$. For larger-scale compression tasks, low-rank SKT achieves the same feat in sub-quadratic time using an adaptive low-rank debiasing procedure that may be of independent interest. For downstream tasks that support simplex or constant-preserving weights, Stein recombination and Stein Cholesky achieve even greater parsimony, matching the guarantees of SKT with as few as $\text{poly-log}(n)$ weighted points. Underlying these advances are new guarantees for the quality of simplex-weighted coresets, the spectral decay of kernel matrices, and the covering numbers of Stein kernel Hilbert spaces. In our experiments, our techniques provide succinct and accurate posterior summaries while overcoming biases due to burn-in, approximate Markov chain Monte Carlo, and tempering.

Yihao Wang, Ruiqi Song, Lingxiao Li et al.

Existing linguistic steganography schemes often overlook the conditional probability (CP) of tokens in the candidate pool, allocating the one coding to all tokens, which results in identical selection likelihoods. This approach leads to the selection of low-CP tokens, degrading the quality of stegos and making them more detectable. This paper proposes a scheme based on the interval allocated, called DAIRstega. DAIRstega first uses a portion of the read secret to build the roulette area. Then, this scheme uses the idea of the roulette wheel and takes the CPs of tokens as the main basis for allocating the roulette area (i.e., the interval length). Thus, tokens with larger CPs are allocated more area. The secret will have an increased likelihood of selecting a token with a higher CP. During allocation, we designed some allocation functions and three constraints to optimize the process. Additionally, DAIRstega supports prompt-based controllable generation of stegos. Rich experiments show that the proposed embedding way and DAIRstega perform better than the existing ways and baselines, which shows strong perceptual, statistical, and semantic concealment, as well as anti-steganalysis ability. It can also generate high-quality longer stegos, addressing the deficiencies in this task. DAIRstega is confirmed to have potential as a secure watermarking, offering insights for its development.

Wei Hao, Zixi Wang, Lauren Hong et al.

ML models are increasingly being pushed to mobile devices, for low-latency inference and offline operation. However, once the models are deployed, it is hard for ML operators to track their accuracy, which can degrade unpredictably (e.g., due to data drift). We design the first end-to-end system for continuously monitoring and adapting models on mobile devices without requiring feedback from users. Our key observation is that often model degradation is due to a specific root cause, which may affect a large group of devices. Therefore, once the system detects a consistent degradation across a large number of devices, it employs a root cause analysis to determine the origin of the problem and applies a cause-specific adaptation. We evaluate the system on two computer vision datasets, and show it consistently boosts accuracy compared to existing approaches. On a dataset containing photos collected from driving cars, our system improves the accuracy on average by 15%.

Alexander Korotin, Lingxiao Li, Aude Genevay et al.

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport -- specifically, computation of the Wasserstein-2 distance, a commonly-used formulation of optimal transport in machine learning. To overcome the challenge of computing ground truth transport maps between continuous measures needed to assess these solvers, we use input-convex neural networks (ICNN) to construct pairs of measures whose ground truth OT maps can be obtained analytically. This strategy yields pairs of continuous benchmark measures in high-dimensional spaces such as spaces of images. We thoroughly evaluate existing optimal transport solvers using these benchmark measures. Even though these solvers perform well in downstream tasks, many do not faithfully recover optimal transport maps. To investigate the cause of this discrepancy, we further test the solvers in a setting of image generation. Our study reveals crucial limitations of existing solvers and shows that increased OT accuracy does not necessarily correlate to better results downstream.

Li Zhang, Han Wang, Lingxiao Li

Pair-based metric learning has been widely adopted to learn sentence embedding in many NLP tasks such as semantic text similarity due to its efficiency in computation. Most existing works employed a sequence encoder model and utilized limited sentence pairs with a pair-based loss to learn discriminating sentence representation. However, it is known that the sentence representation can be biased when the sampled sentence pairs deviate from the true distribution of all sentence pairs. In this paper, our theoretical analysis shows that existing works severely suffered from a good pair sampling and instance weighting strategy. Instead of one time pair selection and learning on equal weighted pairs, we propose a unified locality weighting and learning framework to learn task-specific sentence embedding. Our model, SentPWNet, exploits the neighboring spatial distribution of each sentence as locality weight to indicate the informative level of sentence pair. Such weight is updated along with pair-loss optimization in each round, ensuring the model keep learning the most informative sentence pairs. Extensive experiments on four public available datasets and a self-collected place search benchmark with 1.4 million places clearly demonstrate that our model consistently outperforms existing sentence embedding methods with comparable efficiency.