Weijie Su

Chenxin Tao, Xizhou Zhu, Weijie Su et al.

Self-supervised learning (SSL) has delivered superior performance on a variety of downstream vision tasks. Two main-stream SSL frameworks have been proposed, i.e., Instance Discrimination (ID) and Masked Image Modeling (MIM). ID pulls together representations from different views of the same image, while avoiding feature collapse. It lacks spatial sensitivity, which requires modeling the local structure within each image. On the other hand, MIM reconstructs the original content given a masked image. It instead does not have good semantic alignment, which requires projecting semantically similar views into nearby representations. To address this dilemma, we observe that (1) semantic alignment can be achieved by matching different image views with strong augmentations; (2) spatial sensitivity can benefit from predicting dense representations with masked images. Driven by these analysis, we propose Siamese Image Modeling (SiameseIM), which predicts the dense representations of an augmented view, based on another masked view from the same image but with different augmentations. SiameseIM uses a Siamese network with two branches. The online branch encodes the first view, and predicts the second view's representation according to the relative positions between these two views. The target branch produces the target by encoding the second view. SiameseIM can surpass both ID and MIM on a wide range of downstream tasks, including ImageNet finetuning and linear probing, COCO and LVIS detection, and ADE20k semantic segmentation. The improvement is more significant in few-shot, long-tail and robustness-concerned scenarios. Code shall be released at https://github.com/fundamentalvision/Siamese-Image-Modeling.

Weijie Su, Xizhou Zhu, Chenxin Tao et al.

To effectively exploit the potential of large-scale models, various pre-training strategies supported by massive data from different sources are proposed, including supervised pre-training, weakly-supervised pre-training, and self-supervised pre-training. It has been proved that combining multiple pre-training strategies and data from various modalities/sources can greatly boost the training of large-scale models. However, current works adopt a multi-stage pre-training system, where the complex pipeline may increase the uncertainty and instability of the pre-training. It is thus desirable that these strategies can be integrated in a single-stage manner. In this paper, we first propose a general multi-modal mutual information formula as a unified optimization target and demonstrate that all existing approaches are special cases of our framework. Under this unified perspective, we propose an all-in-one single-stage pre-training approach, named Maximizing Multi-modal Mutual Information Pre-training (M3I Pre-training). Our approach achieves better performance than previous pre-training methods on various vision benchmarks, including ImageNet classification, COCO object detection, LVIS long-tailed object detection, and ADE20k semantic segmentation. Notably, we successfully pre-train a billion-level parameter image backbone and achieve state-of-the-art performance on various benchmarks. Code shall be released at https://github.com/OpenGVLab/M3I-Pretraining.

Ke Sun, Yizhou Zhao, Jiayi Xin et al.

Context or prompt-level reweighting has emerged as a central algorithmic lever in Reinforcement Learning with Verified Rewards (RLVR) for improving the reasoning capability of large language models, yet the principle determining what constitutes an optimal weighting remains poorly understood. We address this gap by formulating prompt reweighting as a functional derivative of a utility functional defined in the pass-rate function space, yielding a unified optimality framework that accommodates existing schemes, including REINFORCE and GRPO. Building on this optimality framework, we propose a distribution-aware prompt reweighting approach, called CurveRL, based on a quantile coordinate transform, in which the weight assigned to each prompt depends not on the absolute value of pass rates but on its rank and density to reflect the distributional structure of the pass rates in the learning dynamics. Extensive experiments across multiple benchmarks demonstrate that our proposed CurveRL consistently outperforms GRPO and other RLVR baselines. Our study identifies context-distribution control as a principled axis for analyzing and designing prompt-reweighted RLVR algorithms. The code is released in https://github.com/zhyzmath/CurveRL.

Lei Wu, Mingze Wang, Weijie Su

The phenomenon that stochastic gradient descent (SGD) favors flat minima has played a critical role in understanding the implicit regularization of SGD. In this paper, we provide an explanation of this striking phenomenon by relating the particular noise structure of SGD to its \emph{linear stability} (Wu et al., 2018). Specifically, we consider training over-parameterized models with square loss. We prove that if a global minimum $θ^*$ is linearly stable for SGD, then it must satisfy $\|H(θ^*)\|_F\leq O(\sqrt{B}/η)$, where $\|H(θ^*)\|_F, B,η$ denote the Frobenius norm of Hessian at $θ^*$, batch size, and learning rate, respectively. Otherwise, SGD will escape from that minimum \emph{exponentially} fast. Hence, for minima accessible to SGD, the sharpness -- as measured by the Frobenius norm of the Hessian -- is bounded \emph{independently} of the model size and sample size. The key to obtaining these results is exploiting the particular structure of SGD noise: The noise concentrates in sharp directions of local landscape and the magnitude is proportional to loss value. This alignment property of SGD noise provably holds for linear networks and random feature models (RFMs), and is empirically verified for nonlinear networks. Moreover, the validity and practical relevance of our theoretical findings are also justified by extensive experiments on CIFAR-10 dataset.

Ruochen Jin, Bojian Hou, Jiancong Xiao et al.

In recent years, task arithmetic has garnered increasing attention. This approach edits pre-trained models directly in weight space by combining the fine-tuned weights of various tasks into a unified model. Its efficiency and cost-effectiveness stem from its training-free combination, contrasting with traditional methods that require model training on large datasets for multiple tasks. However, applying such a unified model to individual tasks can lead to interference from other tasks (lack of weight disentanglement). To address this issue, Neural Tangent Kernel (NTK) linearization has been employed to leverage a "kernel behavior", facilitating weight disentanglement and mitigating adverse effects from unrelated tasks. Despite its benefits, NTK linearization presents drawbacks, including doubled training costs, as well as reduced performance of individual models. To tackle this problem, we propose a simple yet effective and efficient method that is to finetune the attention modules only in the Transformer. Our study reveals that the attention modules exhibit kernel behavior, and fine-tuning the attention modules only significantly improves weight disentanglement. To further understand how our method improves the weight disentanglement of task arithmetic, we present a comprehensive study of task arithmetic by differentiating the role of the representation module and task-specific module. In particular, we find that the representation module plays an important role in improving weight disentanglement whereas the task-specific modules such as the classification heads can degenerate the weight disentanglement performance. (The code is available at https://github.com/kyrie-23/task_arithmetic_tangent)

Zhe Chen, Jiannan Wu, Wenhai Wang et al.

The exponential growth of large language models (LLMs) has opened up numerous possibilities for multimodal AGI systems. However, the progress in vision and vision-language foundation models, which are also critical elements of multi-modal AGI, has not kept pace with LLMs. In this work, we design a large-scale vision-language foundation model (InternVL), which scales up the vision foundation model to 6 billion parameters and progressively aligns it with the LLM, using web-scale image-text data from various sources. This model can be broadly applied to and achieve state-of-the-art performance on 32 generic visual-linguistic benchmarks including visual perception tasks such as image-level or pixel-level recognition, vision-language tasks such as zero-shot image/video classification, zero-shot image/video-text retrieval, and link with LLMs to create multi-modal dialogue systems. It has powerful visual capabilities and can be a good alternative to the ViT-22B. We hope that our research could contribute to the development of multi-modal large models. Code and models are available at https://github.com/OpenGVLab/InternVL.

Buxin Su, Jiayao Zhang, Natalie Collina et al. · princeton

We conducted an experiment during the review process of the 2023 International Conference on Machine Learning (ICML), asking authors with multiple submissions to rank their papers based on perceived quality. In total, we received 1,342 rankings, each from a different author, covering 2,592 submissions. In this paper, we present an empirical analysis of how author-provided rankings could be leveraged to improve peer review processes at machine learning conferences. We focus on the Isotonic Mechanism, which calibrates raw review scores using the author-provided rankings. Our analysis shows that these ranking-calibrated scores outperform the raw review scores in estimating the ground truth ``expected review scores'' in terms of both squared and absolute error metrics. Furthermore, we propose several cautious, low-risk applications of the Isotonic Mechanism and author-provided rankings in peer review, including supporting senior area chairs in overseeing area chairs' recommendations, assisting in the selection of paper awards, and guiding the recruitment of emergency reviewers.

Jinguo Zhu, Weiyun Wang, Zhe Chen et al.

We introduce InternVL3, a significant advancement in the InternVL series featuring a native multimodal pre-training paradigm. Rather than adapting a text-only large language model (LLM) into a multimodal large language model (MLLM) that supports visual inputs, InternVL3 jointly acquires multimodal and linguistic capabilities from both diverse multimodal data and pure-text corpora during a single pre-training stage. This unified training paradigm effectively addresses the complexities and alignment challenges commonly encountered in conventional post-hoc training pipelines for MLLMs. To further improve performance and scalability, InternVL3 incorporates variable visual position encoding (V2PE) to support extended multimodal contexts, employs advanced post-training techniques such as supervised fine-tuning (SFT) and mixed preference optimization (MPO), and adopts test-time scaling strategies alongside an optimized training infrastructure. Extensive empirical evaluations demonstrate that InternVL3 delivers superior performance across a wide range of multi-modal tasks. In particular, InternVL3-78B achieves a score of 72.2 on the MMMU benchmark, setting a new state-of-the-art among open-source MLLMs. Its capabilities remain highly competitive with leading proprietary models, including ChatGPT-4o, Claude 3.5 Sonnet, and Gemini 2.5 Pro, while also maintaining strong pure-language proficiency. In pursuit of open-science principles, we will publicly release both the training data and model weights to foster further research and development in next-generation MLLMs.

Zhehang Du, Hangfeng He, Weijie Su

Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context embeddings. We approach this problem by analyzing a constrained layer-peeled optimization program, which serves as a mathematically tractable surrogate for LLMs by treating the output projection matrix and last-layer context embeddings as optimization variables. Our analysis of this nonconvex optimization program demonstrates that symmetries in the target next-token distributions are transferred to the global minimizers of the layer-peeled model in a precise group-theoretic sense. Specifically, we prove that when the target tokens exhibit a cyclic-shift symmetry (such as the seven days of the week or the twelve months of the year), the optimal logit matrix is exactly circulant, and the Gram matrices of both the output projections and the context embeddings form circulant geometries as well. Next, for exchangeable target distributions invariant under the symmetric group and, more generally, under two-transitive group actions, we show that the global optimal output projection matrix forms a simplex equiangular tight frame, while the optimal logit matrix and context embeddings inherit the permutation symmetries present in the input data. A key technical step is to reduce the constrained nonconvex factorized problem to an explicit logit-level convex characterization for cyclic symmetry and to a symmetry-based lower bound for permutation symmetry, together with a sharp characterization of the optimal factorization. Finally, we empirically demonstrate that open-source LLMs naturally exhibit symmetries consistent with our theoretical predictions, despite being trained without any explicit regularization promoting such geometric structure.

Jianhao Huang, Zhanpeng Zhou, Renqiu Xia et al.

While next-token prediction (NTP) has been the standard objective for training language models, it often struggles to capture global structure in reasoning tasks. Multi-token prediction (MTP) has recently emerged as a promising alternative, yet its underlying mechanisms remain poorly understood. In this paper, we study how MTP facilitates reasoning, with a focus on planning. Empirically, we show that MTP consistently outperforms NTP on both synthetic graph path-finding tasks and more realistic reasoning benchmarks, such as Countdown and boolean satisfiability problems. Theoretically, we analyze a simplified two-layer Transformer on a star graph task. We prove that MTP induces a two-stage reverse reasoning process: the model first attends to the end node and then reconstructs the path by tracing intermediate nodes backward. This behavior arises from a gradient decoupling property of MTP, which provides a cleaner training signal compared to NTP. Ultimately, our results highlight how multi-token objectives inherently bias optimization toward robust and interpretable reasoning circuits.

Buxin Su, Jiayao Zhang, Natalie Collina et al.

This article is the rejoinder to ``The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review,'' to appear in the Journal of the American Statistical Association with discussion. To address the practical and theoretical points raised by the discussants, we organize our response around four core themes: (i) formulating peer review as a statistical estimation problem; (ii) mitigating equity and strategic concerns in the deployment of the Isotonic Mechanism; (iii) incorporating complementary signals such as reviewer rankings and structured metadata; and (iv) exploring a human-centered framework for peer review in the era of generative AI.

Weiyun Wang, Zhangwei Gao, Lixin Gu et al. · cmu, pku

We introduce InternVL 3.5, a new family of open-source multimodal models that significantly advances versatility, reasoning capability, and inference efficiency along the InternVL series. A key innovation is the Cascade Reinforcement Learning (Cascade RL) framework, which enhances reasoning through a two-stage process: offline RL for stable convergence and online RL for refined alignment. This coarse-to-fine training strategy leads to substantial improvements on downstream reasoning tasks, e.g., MMMU and MathVista. To optimize efficiency, we propose a Visual Resolution Router (ViR) that dynamically adjusts the resolution of visual tokens without compromising performance. Coupled with ViR, our Decoupled Vision-Language Deployment (DvD) strategy separates the vision encoder and language model across different GPUs, effectively balancing computational load. These contributions collectively enable InternVL3.5 to achieve up to a +16.0\% gain in overall reasoning performance and a 4.05$\times$ inference speedup compared to its predecessor, i.e., InternVL3. In addition, InternVL3.5 supports novel capabilities such as GUI interaction and embodied agency. Notably, our largest model, i.e., InternVL3.5-241B-A28B, attains state-of-the-art results among open-source MLLMs across general multimodal, reasoning, text, and agentic tasks -- narrowing the performance gap with leading commercial models like GPT-5. All models and code are publicly released.

Lei Bai, Zhongrui Cai, Yuhang Cao et al.

In recent years, a plethora of open-source foundation models have emerged, achieving remarkable progress in some widely attended fields, with performance being quite close to that of closed-source models. However, in high-value but more challenging scientific professional fields, either the fields still rely on expert models, or the progress of general foundation models lags significantly compared to those in popular areas, far from sufficient for transforming scientific research and leaving substantial gap between open-source models and closed-source models in these scientific domains. To mitigate this gap and explore a step further toward Artificial General Intelligence (AGI), we introduce Intern-S1, a specialized generalist equipped with general understanding and reasoning capabilities with expertise to analyze multiple science modal data. Intern-S1 is a multimodal Mixture-of-Experts (MoE) model with 28 billion activated parameters and 241 billion total parameters, continually pre-trained on 5T tokens, including over 2.5T tokens from scientific domains. In the post-training stage, Intern-S1 undergoes offline and then online reinforcement learning (RL) in InternBootCamp, where we propose Mixture-of-Rewards (MoR) to synergize the RL training on more than 1000 tasks simultaneously. Through integrated innovations in algorithms, data, and training systems, Intern-S1 achieved top-tier performance in online RL training. On comprehensive evaluation benchmarks, Intern-S1 demonstrates competitive performance on general reasoning tasks among open-source models and significantly outperforms open-source models in scientific domains, surpassing closed-source state-of-the-art models in professional tasks, such as molecular synthesis planning, reaction condition prediction, predicting thermodynamic stabilities for crystals. Our models are available at https://huggingface.co/internlm/Intern-S1.

Yuchen Wu, Kangjie Zhou, Weijie Su

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

Xuehui Wang, Zhenyu Wu, JingJing Xie et al. · pku

We introduce MMBench-GUI, a hierarchical benchmark for evaluating GUI automation agents across Windows, macOS, Linux, iOS, Android, and Web platforms. It comprises four levels: GUI Content Understanding, Element Grounding, Task Automation, and Task Collaboration, covering essential skills for GUI agents. In addition, we propose a novel Efficiency-Quality Area (EQA) metric to assess GUI agent execution efficiency in online automation scenarios. Through MMBench-GUI, we identify accurate visual grounding as a critical determinant of overall task success, emphasizing the substantial benefits of modular frameworks that integrate specialized grounding modules. Furthermore, to achieve reliable GUI automation, an agent requires strong task planning and cross-platform generalization abilities, with long-context memory, a broad action space, and long-term reasoning playing a critical role. More important, task efficiency remains a critically underexplored dimension, and all models suffer from substantial inefficiencies, with excessive redundant steps even when tasks are ultimately completed. The integration of precise localization, effective planning, and early stopping strategies is indispensable to enable truly efficient and scalable GUI automation. Our benchmark code, evaluation data, and running environment will be publicly available at https://github.com/open-compass/MMBench-GUI.

Chenyu Yang, Shiqian Su, Shi Liu et al.

The rapid advancement of large Vision-Language Models (VLMs) has propelled the development of pure-vision-based GUI Agents, capable of perceiving and operating Graphical User Interfaces (GUI) to autonomously fulfill user instructions. However, existing approaches usually adopt an offline learning framework, which faces two core limitations: (1) heavy reliance on high-quality manual annotations for element grounding and action supervision, and (2) limited adaptability to dynamic and interactive environments. To address these limitations, we propose ZeroGUI, a scalable, online learning framework for automating GUI Agent training at Zero human cost. Specifically, ZeroGUI integrates (i) VLM-based automatic task generation to produce diverse training goals from the current environment state, (ii) VLM-based automatic reward estimation to assess task success without hand-crafted evaluation functions, and (iii) two-stage online reinforcement learning to continuously interact with and learn from GUI environments. Experiments on two advanced GUI Agents (UI-TARS and Aguvis) demonstrate that ZeroGUI significantly boosts performance across OSWorld and AndroidLab environments. The code is available at https://github.com/OpenGVLab/ZeroGUI.

Tim Tsz-Kit Lau, Weijie Su

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible updates consistently improve final validation loss, and in several cases training stability, over corresponding AdamW updates.

Handong Zheng, Yumeng Li, Kaile Zhang et al.

We present Multimodal OCR (MOCR), a document parsing paradigm that jointly parses text and graphics into unified textual representations. Unlike conventional OCR systems that focus on text recognition and leave graphical regions as cropped pixels, our method, termed dots.mocr, treats visual elements such as charts, diagrams, tables, and icons as first-class parsing targets, enabling systems to parse documents while preserving semantic relationships across elements. It offers several advantages: (1) it reconstructs both text and graphics as structured outputs, enabling more faithful document reconstruction; (2) it supports end-to-end training over heterogeneous document elements, allowing models to exploit semantic relations between textual and visual components; and (3) it converts previously discarded graphics into reusable code-level supervision, unlocking multimodal supervision embedded in existing documents. To make this paradigm practical at scale, we build a comprehensive data engine from PDFs, rendered webpages, and native SVG assets, and train a compact 3B-parameter model through staged pretraining and supervised fine-tuning. We evaluate dots.mocr from two perspectives: document parsing and structured graphics parsing. On document parsing benchmarks, it ranks second only to Gemini 3 Pro on our OCR Arena Elo leaderboard, surpasses existing open-source document parsing systems, and sets a new state of the art of 83.9 on olmOCR Bench. On structured graphics parsing, dots.mocr achieves higher reconstruction quality than Gemini 3 Pro across image-to-SVG benchmarks, demonstrating strong performance on charts, UI layouts, scientific figures, and chemical diagrams. These results show a scalable path toward building large-scale image-to-code corpora for multimodal pretraining. Code and models are publicly available at https://github.com/rednote-hilab/dots.mocr.

Zhehang Du, Weijie Su

The Muon optimizer has received considerable attention for its strong performance in training large language models, yet the design principle behind its matrix-gradient orthogonalization remains largely elusive. In this paper, we introduce a surrogate model that not only sheds new light on the design of Muon, but more importantly leads to a new optimizer. In the same spirit as the derivation of Newton's method, the surrogate approximates the loss as a quadratic function of the perturbation to a weight matrix $W$ using only three matrices: the gradient $G$, an output-space curvature matrix $H$, and the data matrix $Z$ that stacks the layer inputs. By minimizing this surrogate in one step and adopting a certain isotropic assumption on the weights, we obtain the closed-form update rule (up to momentum and weight decay) $W \leftarrow W - η\cdot \mathrm{msgn}(G(ZZ^\top)^{-1})$, where $η$ is the learning rate and $\mathrm{msgn}(X)=UV^\top$ if $X=USV^\top$ is a compact singular value decomposition. This new optimization method, which we refer to as Newton-Muon, shows that standard Muon can be interpreted as an implicit Newton-type method that neglects the right preconditioning induced by the input second moment. Empirically, on a reproduction of the earliest publicly released Modded-NanoGPT speedrun configuration using Muon for GPT-2 pretraining, Newton-Muon reaches the target validation loss in 6\% fewer iteration steps and reduces wall-clock training time by about 4\%.

Zhaoyang Liu, Jingjing Xie, Zichen Ding et al.

Vision-Language Models (VLMs) have enabled computer use agents (CUAs) that operate GUIs autonomously, showing great potential, yet progress is limited by the lack of large-scale, open-source computer use data and foundation models. In this work, we introduce ScaleCUA, a step toward scaling open-source CUAs. It offers a large-scale dataset spanning 6 operating systems and 3 task domains, built via a closed-loop pipeline uniting automated agents with human experts. Trained on this scaled-up data, ScaleCUA can operate seamlessly across platforms. Specifically, it delivers strong gains over baselines (+26.6 on WebArena-Lite-v2, +10.7 on ScreenSpot-Pro) and sets new state-of-the-art results (94.4% on MMBench-GUI L1-Hard, 60.6% on OSWorld-G, 47.4% on WebArena-Lite-v2). These findings underscore the power of data-driven scaling for general-purpose computer use agents. We will release data, models, and code to advance future research: https://github.com/OpenGVLab/ScaleCUA.

Yichi Zhang, Grant Schoenebeck, Weijie Su

In the setting of conference peer review, the conference aims to accept high-quality papers and reject low-quality papers based on noisy review scores. A recent work proposes the isotonic mechanism, which can elicit the ranking of paper qualities from an author with multiple submissions to help improve the conference's decisions. However, the isotonic mechanism relies on the assumption that the author's utility is both an increasing and a convex function with respect to the review score, which is often violated in peer review settings (e.g.~when authors aim to maximize the number of accepted papers). In this paper, we propose a sequential review mechanism that can truthfully elicit the ranking information from authors while only assuming the agent's utility is increasing with respect to the true quality of her accepted papers. The key idea is to review the papers of an author in a sequence based on the provided ranking and conditioning the review of the next paper on the review scores of the previous papers. Advantages of the sequential review mechanism include 1) eliciting truthful ranking information in a more realistic setting than prior work; 2) improving the quality of accepted papers, reducing the reviewing workload and increasing the average quality of papers being reviewed; 3) incentivizing authors to write fewer papers of higher quality.

Garrett G. Wen, Buxin Su, Natalie Collina et al.

Machine learning and artificial intelligence conferences such as NeurIPS and ICML now regularly receive tens of thousands of submissions, posing significant challenges to maintaining the quality and consistency of the peer review process. This challenge is particularly acute for best paper awards, which are an important part of the peer review process, yet whose selection has increasingly become a subject of debate in recent years. In this paper, we introduce an author-assisted mechanism to facilitate the selection of best paper awards. Our method employs the Isotonic Mechanism for eliciting authors' assessments of their own submissions in the form of a ranking, which is subsequently utilized to adjust the raw review scores for optimal estimation of the submissions' ground-truth quality. We demonstrate that authors are incentivized to report truthfully when their utility is a convex additive function of the adjusted scores, and we validate this convexity assumption for best paper awards using publicly accessible review data of ICLR from 2019 to 2023 and NeurIPS from 2021 to 2023. Crucially, in the special case where an author has a single quota -- that is, may nominate only one paper -- we prove that truthfulness holds even when the utility function is merely nondecreasing and additive. This finding represents a substantial relaxation of the assumptions required in prior work. For practical implementation, we extend our mechanism to accommodate the common scenario of overlapping authorship. Finally, simulation results demonstrate that our mechanism significantly improves the quality of papers selected for awards.

Yizhou Zhao, Xiang Li, Peter Song et al.

The rise of generative AI has enabled the production of high-fidelity synthetic tabular data across fields such as healthcare, finance, and public policy, raising growing concerns about data provenance and misuse. Watermarking offers a promising solution to address these concerns by ensuring the traceability of synthetic data, but existing methods face many limitations: they are computationally expensive due to reliance on large diffusion models, struggle with mixed discrete-continuous data, or lack robustness to post-modifications. To address them, we propose TAB-DRW, an efficient and robust post-editing watermarking scheme for generative tabular data. TAB-DRW embeds watermark signals in the frequency domain: it normalizes heterogeneous features via the Yeo-Johnson transformation and standardization, applies the discrete Fourier transform (DFT), and adjusts the imaginary parts of adaptively selected entries according to precomputed pseudorandom bits. To further enhance robustness and efficiency, we introduce a novel rank-based pseudorandom bit generation method that enables row-wise retrieval without incurring storage overhead. Experiments on five benchmark tabular datasets show that TAB-DRW achieves strong detectability and robustness against common post-processing attacks, while preserving high data fidelity and fully supporting mixed-type features.

Weiqing He, Xiang Li, Tianqi Shang et al.

Large language models (LLMs) raise concerns about content authenticity and integrity because they can generate human-like text at scale. Text watermarks, which embed detectable statistical signals into generated text, offer a provable way to verify content origin. Many detection methods rely on pivotal statistics that are i.i.d. under human-written text, making goodness-of-fit (GoF) tests a natural tool for watermark detection. However, GoF tests remain largely underexplored in this setting. In this paper, we systematically evaluate eight GoF tests across three popular watermarking schemes, using three open-source LLMs, two datasets, various generation temperatures, and multiple post-editing methods. We find that general GoF tests can improve both the detection power and robustness of watermark detectors. Notably, we observe that text repetition, common in low-temperature settings, gives GoF tests a unique advantage not exploited by existing methods. Our results highlight that classic GoF tests are a simple yet powerful and underused tool for watermark detection in LLMs.

Chenyu Yang, Xizhou Zhu, Jinguo Zhu et al.

Recently, vision model pre-training has evolved from relying on manually annotated datasets to leveraging large-scale, web-crawled image-text data. Despite these advances, there is no pre-training method that effectively exploits the interleaved image-text data, which is very prevalent on the Internet. Inspired by the recent success of compression learning in natural language processing, we propose a novel vision model pre-training method called Latent Compression Learning (LCL) for interleaved image-text data. This method performs latent compression learning by maximizing the mutual information between the inputs and outputs of a causal attention model. The training objective can be decomposed into two basic tasks: 1) contrastive learning between visual representation and preceding context, and 2) generating subsequent text based on visual representation. Our experiments demonstrate that our method not only matches the performance of CLIP on paired pre-training datasets (e.g., LAION), but can also leverage interleaved pre-training data (e.g., MMC4) to learn robust visual representation from scratch, showcasing the potential of vision model pre-training with interleaved image-text data. Code is released at https://github.com/OpenGVLab/LCL.

Xizhou Zhu, Yuntao Chen, Hao Tian et al.

The captivating realm of Minecraft has attracted substantial research interest in recent years, serving as a rich platform for developing intelligent agents capable of functioning in open-world environments. However, the current research landscape predominantly focuses on specific objectives, such as the popular "ObtainDiamond" task, and has not yet shown effective generalization to a broader spectrum of tasks. Furthermore, the current leading success rate for the "ObtainDiamond" task stands at around 20%, highlighting the limitations of Reinforcement Learning (RL) based controllers used in existing methods. To tackle these challenges, we introduce Ghost in the Minecraft (GITM), a novel framework integrates Large Language Models (LLMs) with text-based knowledge and memory, aiming to create Generally Capable Agents (GCAs) in Minecraft. These agents, equipped with the logic and common sense capabilities of LLMs, can skillfully navigate complex, sparse-reward environments with text-based interactions. We develop a set of structured actions and leverage LLMs to generate action plans for the agents to execute. The resulting LLM-based agent markedly surpasses previous methods, achieving a remarkable improvement of +47.5% in success rate on the "ObtainDiamond" task, demonstrating superior robustness compared to traditional RL-based controllers. Notably, our agent is the first to procure all items in the Minecraft Overworld technology tree, demonstrating its extensive capabilities. GITM does not need any GPU for training, but a single CPU node with 32 CPU cores is enough. This research shows the potential of LLMs in developing capable agents for handling long-horizon, complex tasks and adapting to uncertainties in open-world environments. See the project website at https://github.com/OpenGVLab/GITM.

Xizhou Zhu, Weijie Su, Lewei Lu et al.

DETR has been recently proposed to eliminate the need for many hand-designed components in object detection while demonstrating good performance. However, it suffers from slow convergence and limited feature spatial resolution, due to the limitation of Transformer attention modules in processing image feature maps. To mitigate these issues, we proposed Deformable DETR, whose attention modules only attend to a small set of key sampling points around a reference. Deformable DETR can achieve better performance than DETR (especially on small objects) with 10 times less training epochs. Extensive experiments on the COCO benchmark demonstrate the effectiveness of our approach. Code is released at https://github.com/fundamentalvision/Deformable-DETR.

Weijie Su, Xizhou Zhu, Yue Cao et al.

We introduce a new pre-trainable generic representation for visual-linguistic tasks, called Visual-Linguistic BERT (VL-BERT for short). VL-BERT adopts the simple yet powerful Transformer model as the backbone, and extends it to take both visual and linguistic embedded features as input. In it, each element of the input is either of a word from the input sentence, or a region-of-interest (RoI) from the input image. It is designed to fit for most of the visual-linguistic downstream tasks. To better exploit the generic representation, we pre-train VL-BERT on the massive-scale Conceptual Captions dataset, together with text-only corpus. Extensive empirical analysis demonstrates that the pre-training procedure can better align the visual-linguistic clues and benefit the downstream tasks, such as visual commonsense reasoning, visual question answering and referring expression comprehension. It is worth noting that VL-BERT achieved the first place of single model on the leaderboard of the VCR benchmark. Code is released at \url{https://github.com/jackroos/VL-BERT}.

Yue Zhao, Jiatao Gu, Paloma Jeretič et al.

Understanding the distance between human languages is central to linguistics, anthropology, and tracing human evolutionary history. Yet, while linguistics has long provided rich qualitative accounts of cross-linguistic variation, a unified and scalable quantitative approach to measuring language distance remains lacking. In this paper, we introduce a method that leverages pretrained multilingual language models as systematic instruments for linguistic measurement. Specifically, we show that the spontaneously emerged attention mechanisms of these models provide a robust, tokenization-agnostic measure of cross-linguistic distance, termed Attention Transport Distance (ATD). By treating attention matrices as probability distributions and measuring their geometric divergence via optimal transport, we quantify the representational distance between languages during translation. Applying ATD to a large and diverse set of languages, we demonstrate that the resulting distances recover established linguistic groupings with high fidelity and reveal patterns aligned with geographic and contact-induced relationships. Furthermore, incorporating ATD as a regularizer improves transfer performance in low-resource machine translation. Our results establish a principled foundation for testing linguistic hypotheses using artificial neural networks. This framework transforms multilingual models into powerful tools for quantitative linguistic discovery, facilitating more equitable multilingual AI.

Yangxinyu Xie, Bowen Jiang, Tanwi Mallick et al.

Recent advancement of large language models (LLMs) represents a transformational capability at the frontier of artificial intelligence. However, LLMs are generalized models, trained on extensive text corpus, and often struggle to provide context-specific information, particularly in areas requiring specialized knowledge, such as wildfire details within the broader context of climate change. For decision-makers focused on wildfire resilience and adaptation, it is crucial to obtain responses that are not only precise but also domain-specific. To that end, we developed WildfireGPT, a prototype LLM agent designed to transform user queries into actionable insights on wildfire risks. We enrich WildfireGPT by providing additional context, such as climate projections and scientific literature, to ensure its information is current, relevant, and scientifically accurate. This enables WildfireGPT to be an effective tool for delivering detailed, user-specific insights on wildfire risks to support a diverse set of end users, including but not limited to researchers and engineers, for making positive impact and decision making.

Weijie Su

Machine learning (ML) and artificial intelligence (AI) conferences including NeurIPS and ICML have experienced a significant decline in peer review quality in recent years. To address this growing challenge, we introduce the Isotonic Mechanism, a computationally efficient approach to enhancing the accuracy of noisy review scores by incorporating authors' private assessments of their submissions. Under this mechanism, authors with multiple submissions are required to rank their papers in descending order of perceived quality. Subsequently, the raw review scores are calibrated based on this ranking to produce adjusted scores. We prove that authors are incentivized to truthfully report their rankings because doing so maximizes their expected utility, modeled as an additive convex function over the adjusted scores. Moreover, the adjusted scores are shown to be more accurate than the raw scores, with improvements being particularly significant when the noise level is high and the author has many submissions -- a scenario increasingly prevalent at large-scale ML/AI conferences. We further investigate whether submission quality information beyond a simple ranking can be truthfully elicited from authors. We establish that a necessary condition for truthful elicitation is that the mechanism be based on pairwise comparisons of the author's submissions. This result underscores the optimality of the Isotonic Mechanism, as it elicits the most fine-grained truthful information among all mechanisms we consider. We then present several extensions, including a demonstration that the mechanism maintains truthfulness even when authors have only partial rather than complete information about their submission quality. Finally, we discuss future research directions, focusing on the practical implementation of the mechanism and the further development of a theoretical framework inspired by our mechanism.

Tim Tsz-Kit Lau, Qi Long, Weijie Su

The ever-growing scale of deep learning models and datasets underscores the critical importance of efficient optimization methods. While preconditioned gradient methods such as Adam and AdamW are the de facto optimizers for training neural networks and large language models, structure-aware preconditioned optimizers like Shampoo and Muon, which utilize the matrix structure of gradients, have demonstrated promising evidence of faster convergence. In this paper, we introduce a unifying framework for analyzing "matrix-aware" preconditioned methods, which not only sheds light on the effectiveness of Muon and related optimizers but also leads to a class of new structure-aware preconditioned methods. A key contribution of this framework is its precise distinction between preconditioning strategies that treat neural network weights as vectors (addressing curvature anisotropy) versus those that consider their matrix structure (addressing gradient anisotropy). This perspective provides new insights into several empirical phenomena in language model pre-training, including Adam's training instabilities, Muon's accelerated convergence, and the necessity of learning rate warmup for Adam. Building upon this framework, we introduce PolarGrad, a new class of preconditioned optimization methods based on the polar decomposition of matrix-valued gradients. As a special instance, PolarGrad includes Muon with updates scaled by the nuclear norm of the gradients. We provide numerical implementations of these methods, leveraging efficient numerical polar decomposition algorithms for enhanced convergence. Our extensive evaluations across diverse matrix optimization problems and language model pre-training tasks demonstrate that PolarGrad outperforms both Adam and Muon.

Jinho Bok, Weijie Su, Jason M. Altschuler

Noisy gradient descent and its variants are the predominant algorithms for differentially private machine learning. It is a fundamental question to quantify their privacy leakage, yet tight characterizations remain open even in the foundational setting of convex losses. This paper improves over previous analyses by establishing (and refining) the "privacy amplification by iteration" phenomenon in the unifying framework of $f$-differential privacy--which tightly captures all aspects of the privacy loss and immediately implies tighter privacy accounting in other notions of differential privacy, e.g., $(\varepsilon,δ)$-DP and Rényi DP. Our key technical insight is the construction of shifted interpolated processes that unravel the popular shifted-divergences argument, enabling generalizations beyond divergence-based relaxations of DP. Notably, this leads to the first exact privacy analysis in the foundational setting of strongly convex optimization. Our techniques extend to many settings: convex/strongly convex, constrained/unconstrained, full/cyclic/stochastic batches, and all combinations thereof. As an immediate corollary, we recover the $f$-DP characterization of the exponential mechanism for strongly convex optimization in Gopi et al. (2022), and moreover extend this result to more general settings.

Chenyu Yang, Xuan Dong, Xizhou Zhu et al.

Large Vision-Language Models (VLMs) have been extended to understand both images and videos. Visual token compression is leveraged to reduce the considerable token length of visual inputs. To meet the needs of different tasks, existing high-performance models usually process images and videos separately with different token compression strategies, limiting the capabilities of combining images and videos. To this end, we extend each image into a "static" video and introduce a unified token compression strategy called Progressive Visual Token Compression (PVC), where the tokens of each frame are progressively encoded and adaptively compressed to supplement the information not extracted from previous frames. Video tokens are efficiently compressed with exploiting the inherent temporal redundancy. Images are repeated as static videos, and the spatial details can be gradually supplemented in multiple frames. PVC unifies the token compressing of images and videos. With a limited number of tokens per frame (64 tokens by default), spatial details and temporal changes can still be preserved. Experiments show that our model achieves state-of-the-art performance across various video understanding benchmarks, including long video tasks and fine-grained short video tasks. Meanwhile, our unified token compression strategy incurs no performance loss on image benchmarks, particularly in detail-sensitive tasks.

Yangxinyu Xie, Bowen Jiang, Tanwi Mallick et al.

Large language models (LLMs) are a transformational capability at the frontier of artificial intelligence and machine learning that can support decision-makers in addressing pressing societal challenges such as extreme natural hazard events. As generalized models, LLMs often struggle to provide context-specific information, particularly in areas requiring specialized knowledge. In this work we propose a retrieval-augmented generation (RAG)-based multi-agent LLM system to support analysis and decision-making in the context of natural hazards and extreme weather events. As a proof of concept, we present WildfireGPT, a specialized system focused on wildfire hazards. The architecture employs a user-centered, multi-agent design to deliver tailored risk insights across diverse stakeholder groups. By integrating natural hazard and extreme weather projection data, observational datasets, and scientific literature through an RAG framework, the system ensures both the accuracy and contextual relevance of the information it provides. Evaluation across ten expert-led case studies demonstrates that WildfireGPT significantly outperforms existing LLM-based solutions for decision support.

Weijie Su

In this paper, we introduce a model for analyzing deep learning optimization over a single iteration by leveraging the matrix structure of the weights. We derive the model by assuming isotropy of curvature, including the second-order Hessian and higher-order terms, of the loss function across all perturbation directions; hence, we call it the isotropic curvature model. This model is a convex optimization program amenable to analysis, which allows us to understand how an update on the weights in the form of a matrix relates to the change in the total loss function. As an application, we use the isotropic curvature model to analyze the recently introduced Muon optimizer and other matrix-gradient methods for training language models. First, we show that under a general growth condition on the curvature, the optimal update matrix is obtained by making the spectrum of the original gradient matrix more homogeneous -- that is, making its singular values closer in ratio -- which in particular improves the conditioning of the update matrix. Next, we show that the orthogonalized gradient becomes optimal for the isotropic curvature model when the curvature exhibits a phase transition in growth. Taken together, these results suggest that the gradient orthogonalization employed in Muon and other related methods is directionally correct but may not be strictly optimal. Finally, we discuss future research on how to leverage the isotropic curvature model for designing new optimization methods for training deep learning and language models.

Weijie Su

Large language models (LLMs) represent a new paradigm for processing unstructured data, with applications across an unprecedented range of domains. In this paper, we address, through two arguments, whether the development and application of LLMs would genuinely benefit from foundational contributions from the statistics discipline. First, we argue affirmatively, beginning with the observation that LLMs are inherently statistical models due to their profound data dependency and stochastic generation processes, where statistical insights are naturally essential for handling variability and uncertainty. Second, we argue that the persistent black-box nature of LLMs -- stemming from their immense scale, architectural complexity, and development practices often prioritizing empirical performance over theoretical interpretability -- renders closed-form or purely mechanistic analyses generally intractable, thereby necessitating statistical approaches due to their flexibility and often demonstrated effectiveness. To substantiate these arguments, the paper outlines several research areas -- including alignment, watermarking, uncertainty quantification, evaluation, and data mixture optimization -- where statistical methodologies are critically needed and are already beginning to make valuable contributions. We conclude with a discussion suggesting that statistical research concerning LLMs will likely form a diverse ``mosaic'' of specialized topics rather than deriving from a single unifying theory, and highlighting the importance of timely engagement by our statistics community in LLM research.

Weiqing He, Xiang Li, Li Shen et al.

Watermarking is a principled approach for tracing the provenance of large language model (LLM) outputs, but its deployment in practice is hindered by inference inefficiency. Speculative sampling accelerates inference, with efficiency improving as the acceptance rate between draft and target models increases. Yet recent work reveals a fundamental trade-off: higher watermark strength reduces acceptance, preventing their simultaneous achievement. We revisit this trade-off and show it is not absolute. We introduce a quantitative measure of watermark strength that governs statistical detectability and is maximized when tokens are deterministic functions of pseudorandom numbers. Using this measure, we fully characterize the trade-off as a constrained optimization problem and derive explicit Pareto curves for two existing watermarking schemes. Finally, we introduce a principled mechanism that injects pseudorandomness into draft-token acceptance, ensuring maximal watermark strength while maintaining speculative sampling efficiency. Experiments further show that this approach improves detectability without sacrificing efficiency. Our findings uncover a principle that unites speculative sampling and watermarking, paving the way for their efficient and practical deployment.

Dong Dong, Weijie Su

We introduce a new tokenizer for language models that minimizes the average tokens per character, thereby reducing the number of tokens needed to represent text during training and to generate text during inference. Our method, which we refer to as the Length-MAX tokenizer, obtains its vocabulary by casting a length-weighted objective maximization as a graph partitioning problem and developing a greedy approximation algorithm. On FineWeb and diverse domains, it yields 14--18\% fewer tokens than Byte Pair Encoding (BPE) across vocabulary sizes from 10K to 50K, and the reduction is 13.0\% when the size is 64K. Training GPT-2 models at 124M, 355M, and 1.3B parameters from scratch with five runs each shows 18.5\%, 17.2\%, and 18.5\% fewer steps, respectively, to reach a fixed validation loss, and 13.7\%, 12.7\%, and 13.7\% lower inference latency, together with a 16\% throughput gain at 124M, while consistently improving on downstream tasks including reducing LAMBADA perplexity by 11.7\% and enhancing HellaSwag accuracy by 4.3\%. Moreover, the Length-MAX tokenizer achieves 99.62\% vocabulary coverage and the out-of-vocabulary rate remains low at 0.12\% on test sets. These results demonstrate that optimizing for average token length, rather than frequency alone, offers an effective approach to more efficient language modeling without sacrificing -- and often improving -- downstream performance. The tokenizer is compatible with production systems and reduces embedding and KV-cache memory by 18\% at inference.

Ganlin Yang, Tianyi Zhang, Haoran Hao et al.

While significant research has focused on developing embodied reasoning capabilities using Vision-Language Models (VLMs) or integrating advanced VLMs into Vision-Language-Action (VLA) models for end-to-end robot control, few studies directly address the critical gap between upstream VLM-based reasoning and downstream VLA policy learning. In this work, we take an initial step toward bridging embodied reasoning with VLA policy learning by introducing Vlaser - a Vision-Language-Action Model with synergistic embodied reasoning capability, which is a foundational vision-language model designed to integrate high-level reasoning with low-level control for embodied agents. Built upon the high-quality Vlaser-6M dataset, Vlaser achieves state-of-the-art performance across a range of embodied reasoning benchmarks - including spatial reasoning, embodied grounding, embodied QA, and task planning. Furthermore, we systematically examine how different VLM initializations affect supervised VLA fine-tuning, offering novel insights into mitigating the domain shift between internet-scale pre-training data and embodied-specific policy learning data. Based on these insights, our approach achieves state-of-the-art results on the WidowX benchmark and competitive performance on the Google Robot benchmark.

Changyao Tian, Hao Li, Gen Luo et al.

Compositional training has been the de-facto paradigm in existing Multimodal Large Language Models (MLLMs), where pre-trained vision encoders are connected with pre-trained LLMs through continuous multimodal pre-training. However, the multimodal scaling property of this paradigm remains difficult to explore due to the separated training. In this paper, we focus on the native training of MLLMs in an end-to-end manner and systematically study its design space and scaling property under a practical setting, i.e., data constraint. Through careful study of various choices in MLLM, we obtain the optimal meta-architecture that best balances performance and training cost. After that, we further explore the scaling properties of the native MLLM and indicate the positively correlated scaling relationship between visual encoders and LLMs. Based on these findings, we propose a native MLLM called NaViL, combined with a simple and cost-effective recipe. Experimental results on 14 multimodal benchmarks confirm the competitive performance of NaViL against existing MLLMs. Besides that, our findings and results provide in-depth insights for the future study of native MLLMs.

Buxin Su, Natalie Collina, Garrett Wen et al.

Peer review in academic research aims not only to ensure factual correctness but also to identify work of high scientific potential that can shape future research directions. This task is especially critical in fast-moving fields such as artificial intelligence (AI), yet it has become increasingly difficult given the rapid growth of submissions. In this paper, we investigate an underexplored measure for identifying high-impact research: authors' own rankings of their multiple submissions to the same AI conference. Grounded in game-theoretic reasoning, we hypothesize that self-rankings are informative because authors possess unique understanding of their work's conceptual depth and long-term promise. To test this hypothesis, we conducted a large-scale experiment at a leading AI conference, where 1,342 researchers self-ranked their 2,592 submissions by perceived quality. Tracking outcomes over more than a year, we found that papers ranked highest by their authors received twice as many citations as their lowest-ranked counterparts; self-rankings were especially effective at identifying highly cited papers (those with over 150 citations). Moreover, we showed that self-rankings outperformed peer review scores in predicting future citation counts. Our results remained robust after accounting for confounders such as preprint posting time and self-citations. Together, these findings demonstrate that authors' self-rankings provide a reliable and valuable complement to peer review for identifying and elevating high-impact research in AI.

Zhu Li, Weijie Su, Dino Sejdinovic

Modern machine learning often operates in the regime where the number of parameters is much higher than the number of data points, with zero training loss and yet good generalization, thereby contradicting the classical bias-variance trade-off. This \textit{benign overfitting} phenomenon has recently been characterized using so called \textit{double descent} curves where the risk undergoes another descent (in addition to the classical U-shaped learning curve when the number of parameters is small) as we increase the number of parameters beyond a certain threshold. In this paper, we examine the conditions under which \textit{Benign Overfitting} occurs in the random feature (RF) models, i.e. in a two-layer neural network with fixed first layer weights. We adopt a new view of random feature and show that \textit{benign overfitting} arises due to the noise which resides in such features (the noise may already be present in the data and propagate to the features or it may be added by the user to the features directly) and plays an important implicit regularization role in the phenomenon.

Matteo Sordello, Niccolò Dalmasso, Hangfeng He et al.

This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, that is, the iterates are likely to bounce at around a vicinity of a local minimum. The detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. Owing to this simple yet provably valid stationarity detection, SplitSGD is easy-to-implement and essentially does not incur additional computational cost than standard SGD. Through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. Importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, can yield better generalization performance than other adaptive gradient methods such as Adam.

Zhiqi Bu, Jason Klusowski, Cynthia Rush et al.

SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many existing techniques invalid or inconclusive in analyzing the SLOPE solution. In this paper, we develop an asymptotically exact characterization of the SLOPE solution under Gaussian random designs through solving the SLOPE problem using approximate message passing (AMP). This algorithmic approach allows us to approximate the SLOPE solution via the much more amenable AMP iterates. Explicitly, we characterize the asymptotic dynamics of the AMP iterates relying on a recently developed state evolution analysis for non-separable penalties, thereby overcoming the difficulty caused by the sorted l1 penalty. Moreover, we prove that the AMP iterates converge to the SLOPE solution in an asymptotic sense, and numerical simulations show that the convergence is surprisingly fast. Our proof rests on a novel technique that specifically leverages the SLOPE problem. In contrast to prior literature, our work not only yields an asymptotically sharp analysis but also offers an algorithmic, flexible, and constructive approach to understanding the SLOPE problem.

Tengyuan Liang, Weijie Su

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the sampling nature of the data. In contrast, recognizing the randomness in the data, statisticians are keen to provide uncertainty quantification, or confidence, for the solution obtained using iterative optimization methods. This paper makes progress along this direction by introducing the moment-adjusted stochastic gradient descents, a new stochastic optimization method for statistical inference. We establish non-asymptotic theory that characterizes the statistical distribution for certain iterative methods with optimization guarantees. On the statistical front, the theory allows for model mis-specification, with very mild conditions on the data. For optimization, the theory is flexible for both convex and non-convex cases. Remarkably, the moment-adjusting idea motivated from "error standardization" in statistics achieves a similar effect as acceleration in first-order optimization methods used to fit generalized linear models. We also demonstrate this acceleration effect in the non-convex setting through numerical experiments.

Cynthia Dwork, Weijie Su, Li Zhang

We provide the first differentially private algorithms for controlling the false discovery rate (FDR) in multiple hypothesis testing, with essentially no loss in power under certain conditions. Our general approach is to adapt a well-known variant of the Benjamini-Hochberg procedure (BHq), making each step differentially private. This destroys the classical proof of FDR control. To prove FDR control of our method, (a) we develop a new proof of the original (non-private) BHq algorithm and its robust variants -- a proof requiring only the assumption that the true null test statistics are independent, allowing for arbitrary correlations between the true nulls and false nulls. This assumption is fairly weak compared to those previously shown in the vast literature on this topic, and explains in part the empirical robustness of BHq. Then (b) we relate the FDR control properties of the differentially private version to the control properties of the non-private version. \end{enumerate} We also present a low-distortion "one-shot" differentially private primitive for "top $k$" problems, e.g., "Which are the $k$ most popular hobbies?" (which we apply to: "Which hypotheses have the $k$ most significant $p$-values?"), and use it to get a faster privacy-preserving instantiation of our general approach at little cost in accuracy. The proof of privacy for the one-shot top~$k$ algorithm introduces a new technique of independent interest.

Weijie Su, Malgorzata Bogdan, Emmanuel Candes

In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that in a regime of linear sparsity---meaning that the fraction of variables with a non-vanishing effect tends to a constant, however small---this cannot really be the case, even when the design variables are stochastically independent. We demonstrate that true features and null features are always interspersed on the Lasso path, and that this phenomenon occurs no matter how strong the effect sizes are. We derive a sharp asymptotic trade-off between false and true positive rates or, equivalently, between measures of type I and type II errors along the Lasso path. This trade-off states that if we ever want to achieve a type II error (false negative rate) under a critical value, then anywhere on the Lasso path the type I error (false positive rate) will need to exceed a given threshold so that we can never have both errors at a low level at the same time. Our analysis uses tools from approximate message passing (AMP) theory as well as novel elements to deal with a possibly adaptive selection of the Lasso regularizing parameter.

Weijie Su, Junyang Qian, Linxi Liu

The false discovery rate (FDR)---the expected fraction of spurious discoveries among all the discoveries---provides a popular statistical assessment of the reproducibility of scientific studies in various disciplines. In this work, we introduce a new method for controlling the FDR in meta-analysis of many decentralized linear models. Our method targets the scenario where many research groups---possibly the number of which is random---are independently testing a common set of hypotheses and then sending summary statistics to a coordinating center in an online manner. Built on the knockoffs framework introduced by Barber and Candes (2015), our procedure starts by applying the knockoff filter to each linear model and then aggregates the summary statistics via one-shot communication in a novel way. This method gives exact FDR control non-asymptotically without any knowledge of the noise variances or making any assumption about sparsity of the signal. In certain settings, it has a communication complexity that is optimal up to a logarithmic factor.

Weijie Su, Stephen Boyd, Emmanuel J. Candes

We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.