Haoxuan Chen

Xun Tang, Haoxuan Chen, Yuehaw Khoo et al. · stanford

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

Haoxuan Chen, Xianqin Liu, Jian-Fang Hu

Spatio-Temporal Video Grounding aims to localize object tubes based on textual queries. While recent methods have achieved remarkable success, they mainly focus on high-quality(HQ) inputs, neglecting the widespread presence of low-quality(LQ) videos in real-world scenarios. Although tuning methods like LoRA can adapt to degraded inputs, they inevitably disrupt pre-trained knowledge. To address this, we propose Null-Space Tuning (NST). This framework exploits the geometric property that adding vectors within the null-space of frozen weights to the layer input does not affect the output. Leveraging this, NST injects learnable residuals into input features that can be selectively invisible to the pre-trained backbone. Specifically, NST combines the Quality-Adaptive Unit and Dual-Space Reparameterization to synthesize these residuals by confining components for HQ inputs to the null-space, while directing restoration components for LQ inputs to the non-null space. As the frozen weights eliminate null-space components, we effectively rectify degraded inputs while preserving pre-trained knowledge for HQ inputs. Extensive experiments show that NST outperforms state-of-the-art methods on our Mixed-Quality benchmark.

Yi Zhang, Yulei Kang, Haoxuan Chen et al.

Parameter-efficient fine-tuning methods have gained considerable popularity for adapting large-scale models to downstream tasks, particularly LoRA and its variants. Existing methods perform low-rank adaptation over the full parameter space. However, fine-tuning within a subspace can achieve comparable effectiveness. Inspired by the observation that pre-trained models possess non-trivial null spaces, we propose Null-space based Low-Rank Adaptation (Null-LoRA). Null-LoRA effectively reduces redundancy and enhances effective rank by freezing portions of the low-rank matrices. To further improve parameter efficiency, Null-LoRA constrains the entire incremental update within the null space, maximizing the utilization of incremental updates to adapt to new task paradigms. Null-LoRA surpasses the state of the art with fewer parameters in extensive experiments across image-text retrieval and visual question answering tasks.

Haoxuan Chen, Tianming Liang, Wei-Shi Zheng et al.

Reinforcement learning with verifiers (RLVR) has become a central paradigm for improving LLM reasoning, yet popular group-based optimization algorithms like GRPO often suffer from exploration collapse, where the models prematurely converge on a narrow set of high-scoring patterns, lacking the ability to explore new solutions. Recent efforts attempt to alleviate this by adding entropy regularization or diversity bonus. However, these approaches do not change the \textit{winner-takes-all} nature, where rollouts still compete for individual advantage rather than cooperating for maximizing global diversity. In this work, we propose Group Cooperative Policy Optimization (GCPO), which shifts the training paradigm from rollout competition to team cooperation. Specifically, GCPO replaces independent rollout scoring with team-level credit assignment: a rollout is rewarded by how much it contributes to the team's valid solution coverage, rather than its individual accuracy. This coverage is described as a determinant volume over reward-weighted semantic embeddings, where only correct and non-redundant rollouts contribute to this volume. During advantage estimation, GCPO redistributes the collective team reward to each single rollout according to its average marginal contribution to the team. This cooperative training paradigm routes optimization toward non-redundant correct reasoning paths. Experiments across multiple reasoning benchmarks demonstrate that GCPO significantly improves both reasoning accuracy and solution diversity over existing approaches. Code will be released at $\href{https://github.com/bradybuddiemarch/gcpo}{this}$.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Yinuo Ren, Haoxuan Chen, Yuchen Zhu et al. · gatech, stanford

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $τ$-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, $τ$-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $θ$-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

Haoxuan Chen, Yinuo Ren, Martin Renqiang Min et al. · stanford

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior sampling methods proposed for solving common BIPs rely on heuristic approximations to the generative process. To exploit the generative capability of DMs and avoid the usage of such approximations, we propose an ensemble-based algorithm that performs posterior sampling without the use of heuristic approximations. Our algorithm is motivated by existing works that combine DM-based methods with the sequential Monte Carlo (SMC) method. By examining how the prior evolves through the diffusion process encoded by the pre-trained score function, we derive a modified partial differential equation (PDE) governing the evolution of the corresponding posterior distribution. This PDE includes a modified diffusion term and a reweighting term, which can be simulated via stochastic weighted particle methods. Theoretically, we prove that the error between the true posterior distribution can be bounded in terms of the training error of the pre-trained score function and the number of particles in the ensemble. Empirically, we validate our algorithm on several inverse problems in imaging to show that our method gives more accurate reconstructions compared to existing DM-based methods.

Haoxuan Chen, Lexing Ying · stanford

Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this paper, we propose an ensemble-based version of AIS by combining it with population-based Monte Carlo methods to improve its efficiency. By keeping track of an ensemble instead of a single particle along some continuation path between the starting distribution and the target distribution, we take advantage of the interaction within the ensemble to encourage the exploration of undiscovered modes. Specifically, our main idea is to utilize either the snooker algorithm or the genetic algorithm used in Evolutionary Monte Carlo. We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit. We also test the efficiency of the proposed algorithm on various continuous and discrete distributions.

Jinxuan Li, Chaolei Tan, Haoxuan Chen et al.

Image-Language Foundation Models (ILFM) have demonstrated remarkable success in image-text understanding/generation tasks, providing transferable multimodal representations that generalize across diverse downstream image-based tasks. The advancement of video-text research has spurred growing interest in extending image-based models to the video domain. This paradigm, known as image-to-video transfer learning, succeeds in alleviating the substantial data and computational requirements associated with training video-language foundation models from scratch for video-text learning. This survey provides the first comprehensive review of this emerging field, which begins by summarizing the widely used ILFM and their capabilities. We then systematically classify existing image-to-video transfer learning strategies into two categories: frozen features and modified features, depending on whether the original representations from ILFM are preserved or undergo modifications. Building upon the task-specific nature of image-to-video transfer, this survey methodically elaborates these strategies and details their applications across a spectrum of video-text learning tasks, ranging from fine-grained (e.g., spatio-temporal video grounding) to coarse-grained (e.g., video question answering). We further present a detailed experimental analysis to investigate the efficacy of different image-to-video transfer learning paradigms on a range of downstream video understanding tasks. Finally, we identify prevailing challenges and highlight promising directions for future research. By offering a comprehensive and structured overview, this survey aims to establish a structured roadmap for advancing video-text learning based on existing ILFM, and to inspire future research directions in this rapidly evolving domain.

Luan Vejsiu, Qianyu Zheng, Haoxuan Chen et al.

Despite ASR technology being full-scale adopted by industry and for large portions of the population, ASR systems often have errors that require editors to post-edit text quality. While LLMs are powerful post-editing tools, baseline full rewrite models have inference inefficiencies because they often generate the same redundant text over and over again. Compact edit representations have existed but often lack the efficacy and context required for optimal accuracy. This paper introduces CEGER (Context-Enhanced Granular Edit Representation), a compact edit representation that was generated for highly accurate, efficient ASR post-editing. CEGER allows LLMs to generate a sequence of structured, fine-grained, contextually rich commands to modify the original ASR output. A separate expansion module deterministically reconstructs the corrected text based on the commands. Extensive experiments on the LibriSpeech dataset that were conducted, CEGER achieves state-of-the-art accuracy, achieving the lowest word error rate (WER) versus full rewrite and prior compact representations.

Zongyi Li, Hongkai Zheng, Nikola Kovachki et al.

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families and shows no degradation in accuracy even under zero-shot super-resolution, i.e., being able to predict beyond the resolution of training data. PINO uses the Fourier neural operator (FNO) framework that is guaranteed to be a universal approximator for any continuous operator and discretization-convergent in the limit of mesh refinement. By adding PDE constraints to FNO at a higher resolution, we obtain a high-fidelity reconstruction of the ground-truth operator. Moreover, PINO succeeds in settings where no training data is available and only PDE constraints are imposed, while previous approaches, such as the Physics-Informed Neural Network (PINN), fail due to optimization challenges, e.g., in multi-scale dynamic systems such as Kolmogorov flows.

Yiping Lu, Haoxuan Chen, Jianfeng Lu et al.

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the Schrödinger equation on a hypercube with zero Dirichlet boundary condition, which has wide application in the quantum-mechanical systems. We establish upper and lower bounds for both methods, which improves upon concurrently developed upper bounds for this problem via a fast rate generalization bound. We discover that the current Deep Ritz Methods is sub-optimal and propose a modified version of it. We also prove that PINN and the modified version of DRM can achieve minimax optimal bounds over Sobolev spaces. Empirically, following recent work which has shown that the deep model accuracy will improve with growing training sets according to a power law, we supply computational experiments to show a similar behavior of dimension dependent power law for deep PDE solvers.