Chen Cheng

Yang Liu, Cheng Yu, Lei Shang et al.

Recent advancement in personalized image generation have unveiled the intriguing capability of pre-trained text-to-image models on learning identity information from a collection of portrait images. However, existing solutions are vulnerable in producing truthful details, and usually suffer from several defects such as (i) The generated face exhibit its own unique characteristics, \ie facial shape and facial feature positioning may not resemble key characteristics of the input, and (ii) The synthesized face may contain warped, blurred or corrupted regions. In this paper, we present FaceChain, a personalized portrait generation framework that combines a series of customized image-generation model and a rich set of face-related perceptual understanding models (\eg, face detection, deep face embedding extraction, and facial attribute recognition), to tackle aforementioned challenges and to generate truthful personalized portraits, with only a handful of portrait images as input. Concretely, we inject several SOTA face models into the generation procedure, achieving a more efficient label-tagging, data-processing, and model post-processing compared to previous solutions, such as DreamBooth ~\cite{ruiz2023dreambooth} , InstantBooth ~\cite{shi2023instantbooth} , or other LoRA-only approaches ~\cite{hu2021lora} . Besides, based on FaceChain, we further develop several applications to build a broader playground for better showing its value, including virtual try on and 2D talking head. We hope it can grow to serve the burgeoning needs from the communities. Note that this is an ongoing work that will be consistently refined and improved upon. FaceChain is open-sourced under Apache-2.0 license at \url{https://github.com/modelscope/facechain}.

Shriram Chennakesavalu, Kirill Shmilovich, Hayley Weir et al. · mit

Large Language Models (LLMs) have the potential to accelerate small molecule drug design due to their ability to reason about information from diverse sources and formats. However, their practical utility remains unclear due to the lack of benchmarks that reflect real-world scenarios. In this work, we introduce a suite of chemically-grounded tasks spanning molecular property prediction, molecular representation transformations, and molecular design. Importantly, we formulate these tasks as reinforcement learning (RL) environments, enabling a unified approach for evaluation and post-training. Across three model families, we find that frontier models are increasingly proficient at chemical tasks, but that there is significant room for improvement, especially in experimental settings with low data. Critically, we show that RL-based post-training can substantially improve performance. A smaller model post-trained on our environments becomes competitive with state-of-the-art frontier models, despite a significantly weaker base model. This suggests a practical route toward employing LLMs in drug discovery; by combining carefully-designed evaluation tasks with targeted post-training, we can both elucidate and close critical capability gaps.

Chen Cheng, Hilal Asi, John Duchi

The construction of most supervised learning datasets revolves around collecting multiple labels for each instance, then aggregating the labels to form a type of "gold-standard". We question the wisdom of this pipeline by developing a (stylized) theoretical model of this process and analyzing its statistical consequences, showing how access to non-aggregated label information can make training well-calibrated models more feasible than it is with gold-standard labels. The entire story, however, is subtle, and the contrasts between aggregated and fuller label information depend on the particulars of the problem, where estimators that use aggregated information exhibit robust but slower rates of convergence, while estimators that can effectively leverage all labels converge more quickly if they have fidelity to (or can learn) the true labeling process. The theory makes several predictions for real-world datasets, including when non-aggregate labels should improve learning performance, which we test to corroborate the validity of our predictions.

Chen Cheng, Gary Cheng, John Duchi

We study the problem of collaboratively learning least squares estimates for $m$ agents. Each agent observes a different subset of the features$\unicode{x2013}$e.g., containing data collected from sensors of varying resolution. Our goal is to determine how to coordinate the agents in order to produce the best estimator for each agent. We propose a distributed, semi-supervised algorithm Collab, consisting of three steps: local training, aggregation, and distribution. Our procedure does not require communicating the labeled data, making it communication efficient and useful in settings where the labeled data is inaccessible. Despite this handicap, our procedure is nearly asymptotically local minimax optimal$\unicode{x2013}$even among estimators allowed to communicate the labeled data such as imputation methods. We test our method on real and synthetic data.

Chen Cheng, Jingkuan Song, Xiaosu Zhu et al.

The focus of this study is on Unsupervised Continual Learning (UCL), as it presents an alternative to Supervised Continual Learning which needs high-quality manual labeled data. The experiments under the UCL paradigm indicate a phenomenon where the results on the first few tasks are suboptimal. This phenomenon can render the model inappropriate for practical applications. To address this issue, after analyzing the phenomenon and identifying the lack of diversity as a vital factor, we propose a method named Codebook for Unsupervised Continual Learning (CUCL) which promotes the model to learn discriminative features to complete the class boundary. Specifically, we first introduce a Product Quantization to inject diversity into the representation and apply a cross quantized contrastive loss between the original representation and the quantized one to capture discriminative information. Then, based on the quantizer, we propose an effective Codebook Rehearsal to address catastrophic forgetting. This study involves conducting extensive experiments on CIFAR100, TinyImageNet, and MiniImageNet benchmark datasets. Our method significantly boosts the performances of supervised and unsupervised methods. For instance, on TinyImageNet, our method led to a relative improvement of 12.76% and 7% when compared with Simsiam and BYOL, respectively.

Chen Cheng, Sheng Zhang, Gia-Wei Chern

We present a machine learning (ML) framework for large-scale dynamical simulations of charge density wave (CDW) states. The charge modulation in a CDW state is often accompanied by a concomitant structural distortion, and the adiabatic evolution of a CDW order is governed by the dynamics of the lattice distortion. Calculation of the electronic contribution to the driving forces, however, is computationally very expensive for large systems. Assuming the principle of locality for electron systems, a neural-network model is developed to accurately and efficiently predict local electronic forces with input from neighborhood configurations. Importantly, the ML model makes possible a linear complexity algorithm for dynamical simulations of CDWs. As a demonstration, we apply our approach to investigate the phase ordering dynamics of the Holstein model, a canonical system of CDW order. Our large-scale simulations uncover an intriguing growth of the CDW domains that deviates significantly from the expected Allen-Cahn law for phase ordering of Ising-type order parameter field. This anomalous domain-growth could be attributed to the complex structure of domain-walls in this system. Our work highlights the promising potential of ML-based force-field models for dynamical simulations of functional electronic materials.

Meirui Jiang, Hongzheng Yang, Chen Cheng et al.

Federated learning (FL) allows multiple medical institutions to collaboratively learn a global model without centralizing client data. It is difficult, if possible at all, for such a global model to commonly achieve optimal performance for each individual client, due to the heterogeneity of medical images from various scanners and patient demographics. This problem becomes even more significant when deploying the global model to unseen clients outside the FL with unseen distributions not presented during federated training. To optimize the prediction accuracy of each individual client for medical imaging tasks, we propose a novel unified framework for both \textit{Inside and Outside model Personalization in FL} (IOP-FL). Our inside personalization uses a lightweight gradient-based approach that exploits the local adapted model for each client, by accumulating both the global gradients for common knowledge and the local gradients for client-specific optimization. Moreover, and importantly, the obtained local personalized models and the global model can form a diverse and informative routing space to personalize an adapted model for outside FL clients. Hence, we design a new test-time routing scheme using the consistency loss with a shape constraint to dynamically incorporate the models, given the distribution information conveyed by the test data. Our extensive experimental results on two medical image segmentation tasks present significant improvements over SOTA methods on both inside and outside personalization, demonstrating the potential of our IOP-FL scheme for clinical practice.

Dawei Gao, Zitao Li, Xuchen Pan et al.

With the rapid advancement of Large Language Models (LLMs), significant progress has been made in multi-agent applications. However, the complexities in coordinating agents' cooperation and LLMs' erratic performance pose notable challenges in developing robust and efficient multi-agent applications. To tackle these challenges, we propose AgentScope, a developer-centric multi-agent platform with message exchange as its core communication mechanism. The abundant syntactic tools, built-in agents and service functions, user-friendly interfaces for application demonstration and utility monitor, zero-code programming workstation, and automatic prompt tuning mechanism significantly lower the barriers to both development and deployment. Towards robust and flexible multi-agent application, AgentScope provides both built-in and customizable fault tolerance mechanisms. At the same time, it is also armed with system-level support for managing and utilizing multi-modal data, tools, and external knowledge. Additionally, we design an actor-based distribution framework, enabling easy conversion between local and distributed deployments and automatic parallel optimization without extra effort. With these features, AgentScope empowers developers to build applications that fully realize the potential of intelligent agents. We have released AgentScope at https://github.com/modelscope/agentscope, and hope AgentScope invites wider participation and innovation in this fast-moving field.

Yangming Shi, Shixiang Zhu, Tao Shen et al.

We present Mamoda2.5, a unified AR-Diffusion framework that seamlessly integrates multimodal understanding and generation within a single architecture. To efficiently enhance the model's generation capability, we equip the Diffusion Transformer backbone with a fine-grained Mixture-of-Experts (MoE) design (128 experts, Top-8 routing), yielding a 25B-parameter model that activates only 3B parameters, significantly reducing training costs while scaling up the model capacity. Mamoda2.5 achieves top-tier generation performance on VBench 2.0 and sets a new record in video editing quality, surpassing evaluated open-source models and matching the performance of current top-tier proprietary models, including the Kling O1 on OpenVE-Bench. Furthermore, we introduce a joint few-step distillation and reinforcement learning framework that compresses the 30-step editing model into a 4-step model and greatly accelerates model inference. Compared to open-source baselines, Mamoda2.5 achieves up to $95.9\times$ faster video editing inference. In real-world applications, Mamoda2.5 has been successfully deployed for content moderation and creative restoration tasks in advertising scenarios, achieving a 98% success rate in internal advertising video editing scenario.

Chen Cheng, Jinglai Li

Predicting the behaviors of pedestrian crowds is of critical importance for a variety of real-world problems. Data driven modeling, which aims to learn the mathematical models from observed data, is a promising tool to construct models that can make accurate predictions of such systems. In this work, we present a data-driven modeling approach based on the ODE-Net framework, for constructing continuous-time models of crowd dynamics. We discuss some challenging issues in applying the ODE-Net method to such problems, which are primarily associated with the dimensionality of the underlying crowd system, and we propose to address these issues by incorporating the social-force concept in the ODE-Net framework. Finally application examples are provided to demonstrate the performance of the proposed method.

Chen Cheng

After the outbreak of COVID-19, mask detection, as the most convenient and effective means of prevention, plays a crucial role in epidemic prevention and control. An excellent automatic real-time mask detection system can reduce a lot of work pressure for relevant staff. However, by analyzing the existing mask detection approaches, we find that they are mostly resource-intensive and do not achieve a good balance between speed and accuracy. And there is no perfect face mask dataset at present. In this paper, we propose a new architecture for mask detection. Our system uses SSD as the mask locator and classifier, and further replaces VGG-16 with MobileNetV2 to extract the features of the image and reduce a lot of parameters. Therefore, our system can be deployed on embedded devices. Transfer learning methods are used to transfer pre-trained models from other domains to our model. Data enhancement methods in our system such as MixUp effectively prevent overfitting. It also effectively reduces the dependence on large-scale datasets. By doing experiments in practical scenarios, the results demonstrate that our system performed well in real-time mask detection.

Chen Cheng, Xinzhi Yu, Haodong Wen et al. · pku

Recently, the mysterious In-Context Learning (ICL) ability exhibited by Transformer architectures, especially in large language models (LLMs), has sparked significant research interest. However, the resilience of Transformers' in-context learning capabilities in the presence of noisy samples, prevalent in both training corpora and prompt demonstrations, remains underexplored. In this paper, inspired by prior research that studies ICL ability using simple function classes, we take a closer look at this problem by investigating the robustness of Transformers against noisy labels. Specifically, we first conduct a thorough evaluation and analysis of the robustness of Transformers against noisy labels during in-context learning and show that they exhibit notable resilience against diverse types of noise in demonstration labels. Furthermore, we delve deeper into this problem by exploring whether introducing noise into the training set, akin to a form of data augmentation, enhances such robustness during inference, and find that such noise can indeed improve the robustness of ICL. Overall, our fruitful analysis and findings provide a comprehensive understanding of the resilience of Transformer models against label noises during ICL and provide valuable insights into the research on Transformers in natural language processing. Our code is available at https://github.com/InezYu0928/in-context-learning.

Chen Cheng, Qingping Zhou

This paper investigates the application of unsupervised learning methods for computed tomography (CT) reconstruction. To motivate our work, we review several existing priors, namely the truncated Gaussian prior, the $l_1$ prior, the total variation prior, and the deep image prior (DIP). We find that DIP outperforms the other three priors in terms of representational capability and visual performance. However, the performance of DIP deteriorates when the number of iterations exceeds a certain threshold due to overfitting. To address this issue, we propose a novel method (MCDIP-ADMM) based on Multi-Code Deep Image Prior and plug-and-play Alternative Direction Method of Multipliers. Specifically, MCDIP utilizes multiple latent codes to generate a series of feature maps at an intermediate layer within a generator model. These maps are then composed with trainable weights, representing the complete image prior. Experimental results demonstrate the superior performance of the proposed MCDIP-ADMM compared to three existing competitors. In the case of parallel beam projection with Gaussian noise, MCDIP-ADMM achieves an average improvement of 4.3 dB over DIP, 1.7 dB over ADMM DIP-WTV, and 1.2 dB over PnP-DIP in terms of PSNR. Similarly, for fan-beam projection with Poisson noise, MCDIP-ADMM achieves an average improvement of 3.09 dB over DIP, 1.86 dB over ADMM DIP-WTV, and 0.84 dB over PnP-DIP in terms of PSNR.

Bing Zhao, Chenfei Wu, Deqing Li et al.

We present Qwen-Image-2.0, an omni-capable image generation foundation model that unifies high-fidelity generation and precise image editing within a single framework. Despite recent progress, existing models still struggle with ultra-long text rendering, multilingual typography, high-resolution photorealism, robust instruction following, and efficient deployment, especially in text-rich and compositionally complex scenarios. Qwen-Image-2.0 addresses these challenges by coupling Qwen3-VL as the condition encoder with a Multimodal Diffusion Transformer for joint condition-target modeling, supported by large-scale data curation and a customized multi-stage training pipeline. This enables strong multimodal understanding while preserving flexible generation and editing capabilities. The model supports instructions of up to 1K tokens for generating text-rich content such as slides, posters, infographics, and comics, while significantly improving multilingual text fidelity and typography. It also enhances photorealistic generation with richer details, more realistic textures, and coherent lighting, and follows complex prompts more reliably across diverse styles. Extensive human evaluations show that Qwen-Image-2.0 substantially outperforms previous Qwen-Image models in both generation and editing, marking a step toward more general, reliable, and practical image generation foundation models.

Chenliang Li, Hehong Chen, Ming Yan et al.

Large language models (LLMs) have recently demonstrated remarkable capabilities to comprehend human intentions, engage in reasoning, and design planning-like behavior. To further unleash the power of LLMs to accomplish complex tasks, there is a growing trend to build agent framework that equips LLMs, such as ChatGPT, with tool-use abilities to connect with massive external APIs. In this work, we introduce ModelScope-Agent, a general and customizable agent framework for real-world applications, based on open-source LLMs as controllers. It provides a user-friendly system library, with customizable engine design to support model training on multiple open-source LLMs, while also enabling seamless integration with both model APIs and common APIs in a unified way. To equip the LLMs with tool-use abilities, a comprehensive framework has been proposed spanning over tool-use data collection, tool retrieval, tool registration, memory control, customized model training, and evaluation for practical real-world applications. Finally, we showcase ModelScopeGPT, a real-world intelligent assistant of ModelScope Community based on the ModelScope-Agent framework, which is able to connect open-source LLMs with more than 1000 public AI models and localized community knowledge in ModelScope. The ModelScope-Agent library\footnote{https://github.com/modelscope/modelscope-agent} and online demo\footnote{https://modelscope.cn/studios/damo/ModelScopeGPT/summary} are now publicly available.

Chenfei Wu, Jiahao Li, Jingren Zhou et al.

We present Qwen-Image, an image generation foundation model in the Qwen series that achieves significant advances in complex text rendering and precise image editing. To address the challenges of complex text rendering, we design a comprehensive data pipeline that includes large-scale data collection, filtering, annotation, synthesis, and balancing. Moreover, we adopt a progressive training strategy that starts with non-text-to-text rendering, evolves from simple to complex textual inputs, and gradually scales up to paragraph-level descriptions. This curriculum learning approach substantially enhances the model's native text rendering capabilities. As a result, Qwen-Image not only performs exceptionally well in alphabetic languages such as English, but also achieves remarkable progress on more challenging logographic languages like Chinese. To enhance image editing consistency, we introduce an improved multi-task training paradigm that incorporates not only traditional text-to-image (T2I) and text-image-to-image (TI2I) tasks but also image-to-image (I2I) reconstruction, effectively aligning the latent representations between Qwen2.5-VL and MMDiT. Furthermore, we separately feed the original image into Qwen2.5-VL and the VAE encoder to obtain semantic and reconstructive representations, respectively. This dual-encoding mechanism enables the editing module to strike a balance between preserving semantic consistency and maintaining visual fidelity. Qwen-Image achieves state-of-the-art performance, demonstrating its strong capabilities in both image generation and editing across multiple benchmarks.

Chen Cheng, Rina Foygel Barber

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to the prior distribution $π$, giving explicit conditions under which optimal generalization necessitates that the training error be (i) near interpolating relative to the noise size (i.e., memorization is necessary), or (ii) close to the noise level (i.e., overfitting is harmful). Remarkably, these phenomena occur when the noise reaches thresholds determined by the Fisher information and the variance parameters of the prior $π$.

Macheng Shen, Chen Cheng

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets time-series data as \textit{discrete samples from an underlying continuous dynamical system}, and models its time evolution using Neural Stochastic Differential Equation (Neural SDE), where both the flow (drift) and diffusion terms are parameterized by neural networks. We derive a principled maximum likelihood objective and a \textit{simulation-free} scheme for efficient training of our Neural SDE model. We demonstrate the versatility of our approach through experiments on sequence modeling tasks across both embodied and generative AI. Notably, to the best of our knowledge, this is the first work to show that SDE-based continuous-time modeling also excels in such complex scenarios, and we hope that our work opens up new avenues for research of SDE models in high-dimensional and temporally intricate domains.

Supriyo Ghosh, Sheng Zhang, Chen Cheng et al.

We present a scalable machine learning (ML) force-field model for the adiabatic dynamics of cooperative Jahn-Teller (JT) systems. Large scale dynamical simulations of the JT model also shed light on the orbital ordering dynamics in colossal magnetoresistance manganites. The JT effect in these materials describes the distortion of local oxygen octahedra driven by a coupling to the orbital degrees of freedom of $e_g$ electrons. An effective electron-mediated interaction between the local JT modes leads to a structural transition and the emergence of long-range orbital order at low temperatures. Assuming the principle of locality, a deep-learning neural-network model is developed to accurately and efficiently predict the electron-induced forces that drive the dynamical evolution of JT phonons. A group-theoretical method is utilized to develop a descriptor that incorporates the combined orbital and lattice symmetry into the ML model. Large-scale Langevin dynamics simulations, enabled by the ML force-field models, are performed to investigate the coarsening dynamics of the composite JT distortion and orbital order after a thermal quench. The late-stage coarsening of orbital domains exhibits pronounced freezing behaviors which are likely related to the unusual morphology of the domain structures. Our work highlights a promising avenue for multi-scale dynamical modeling of correlated electron systems.

Haiquan Zhao, Chenhan Yuan, Fei Huang et al.

As large language models (LLMs) become more capable and widely used, ensuring the safety of their outputs is increasingly critical. Existing guardrail models, though useful in static evaluation settings, face two major limitations in real-world applications: (1) they typically output only binary "safe/unsafe" labels, which can be interpreted inconsistently across diverse safety policies, rendering them incapable of accommodating varying safety tolerances across domains; and (2) they require complete model outputs before performing safety checks, making them fundamentally incompatible with streaming LLM inference, thereby preventing timely intervention during generation and increasing exposure to harmful partial outputs. To address these challenges, we present Qwen3Guard, a series of multilingual safety guardrail models with two specialized variants: Generative Qwen3Guard, which casts safety classification as an instruction-following task to enable fine-grained tri-class judgments (safe, controversial, unsafe); and Stream Qwen3Guard, which introduces a token-level classification head for real-time safety monitoring during incremental text generation. Both variants are available in three sizes (0.6B, 4B, and 8B parameters) and support up to 119 languages and dialects, providing comprehensive, scalable, and low-latency safety moderation for global LLM deployments. Evaluated across English, Chinese, and multilingual benchmarks, Qwen3Guard achieves state-of-the-art performance in both prompt and response safety classification. All models are released under the Apache 2.0 license for public use.

Yang Yang, Chen Cheng, Yunhao Fan et al.

The phase ordering kinetics of emergent orders in correlated electron systems is a fundamental topic in non-equilibrium physics, yet it remains largely unexplored. The intricate interplay between quasiparticles and emergent order-parameter fields could lead to unusual coarsening dynamics that is beyond the standard theories. However, accurate treatment of both quasiparticles and collective degrees of freedom is a multi-scale challenge in dynamical simulations of correlated electrons. Here we leverage modern machine learning (ML) methods to achieve a linear-scaling algorithm for simulating the coarsening of charge density waves (CDWs), one of the fundamental symmetry breaking phases in functional electron materials. We demonstrate our approach on the square-lattice Hubbard-Holstein model and uncover an intriguing enhancement of CDW coarsening which is related to the screening of on-site potential by electron-electron interactions. Our study provides fresh insights into the role of electron correlations in non-equilibrium dynamics and underscores the promise of ML force-field approaches for advancing multi-scale dynamical modeling of correlated electron systems.

Chen Cheng, Ang Li

Out-of-distribution (OOD) generalization remains a fundamental challenge in real-world classification, where test distributions often differ substantially from training data. Most existing approaches pursue domain-invariant representations, implicitly assuming that invariance implies reliability. However, features that are invariant across domains are not necessarily causally effective for prediction. In this work, we revisit OOD classification from a causal perspective and propose to evaluate learned representations based on their necessity and sufficiency under distribution shift. We introduce an explicit segment-level framework that directly measures causal effectiveness across domains, providing a more faithful criterion than invariance alone. Experiments on multi-domain benchmarks demonstrate consistent improvements in OOD performance, particularly under challenging domain shifts, highlighting the value of causal evaluation for robust generalization.

Tao Shen, Xin Wan, Taicai Chen et al.

Unified multimodal models aim to integrate understanding and generation within a single framework, yet bridging the gap between discrete semantic reasoning and high-fidelity visual synthesis remains challenging. We present MammothModa2 (Mammoth2), a unified autoregressive-diffusion (AR-Diffusion) framework designed to effectively couple autoregressive semantic planning with diffusion-based generation. Mammoth2 adopts a serial design: an AR path equipped with generation experts performs global semantic modeling over discrete tokens, while a single-stream Diffusion Transformer (DiT) decoder handles high-fidelity image synthesis. A carefully designed AR-Diffusion feature alignment module combines multi-layer feature aggregation, unified condition encoding, and in-context conditioning to stably align AR's representations with the diffusion decoder's continuous latents. Mammoth2 is trained end-to-end with joint Next-Token Prediction and Flow Matching objectives, followed by supervised fine-tuning and reinforcement learning over both generation and editing. With roughly 60M supervised generation samples and no reliance on pre-trained generators, Mammoth2 delivers strong text-to-image and instruction-based editing performance on public benchmarks, achieving 0.87 on GenEval, 87.2 on DPGBench, and 4.06 on ImgEdit, while remaining competitive with understanding-only backbones (e.g., Qwen3-VL-8B) on multimodal understanding tasks. These results suggest that a carefully coupled AR-Diffusion architecture can provide high-fidelity generation and editing while maintaining strong multimodal comprehension within a single, parameter- and data-efficient model.

Chen Cheng, John Duchi

We demonstrate that learning procedures that rely on aggregated labels, e.g., label information distilled from noisy responses, enjoy robustness properties impossible without data cleaning. This robustness appears in several ways. In the context of risk consistency -- when one takes the standard approach in machine learning of minimizing a surrogate (typically convex) loss in place of a desired task loss (such as the zero-one mis-classification error) -- procedures using label aggregation obtain stronger consistency guarantees than those even possible using raw labels. And while classical statistical scenarios of fitting perfectly-specified models suggest that incorporating all possible information -- modeling uncertainty in labels -- is statistically efficient, consistency fails for ``standard'' approaches as soon as a loss to be minimized is even slightly mis-specified. Yet procedures leveraging aggregated information still converge to optimal classifiers, highlighting how incorporating a fuller view of the data analysis pipeline, from collection to model-fitting to prediction time, can yield a more robust methodology by refining noisy signals.

Michael Celentano, Chen Cheng, Ashwin Pananjady et al.

We develop a toolbox for exact analysis of iterative algorithms on a class of high-dimensional nonconvex optimization problems with random data. While prior work has shown that low-dimensional statistics of (generalized) first-order methods can be predicted by a deterministic recursion known as state evolution, our focus is on developing such a prediction for a more general class of algorithms. We provide a state evolution for any method whose iterations are given by (possibly interleaved) first-order and saddle point updates, showing two main results. First, we establish a rigorous state evolution prediction that holds even when the updates are not coordinate-wise separable. Second, we establish finite-sample guarantees bounding the deviation of the empirical updates from the established state evolution. In the process, we develop a technical toolkit that may prove useful in related problems. One component of this toolkit is a general Hilbert space lifting technique to prove existence and uniqueness of a convenient parameterization of the state evolution. Another component of the toolkit combines a generic application of Bolthausen's conditioning method with a sequential variant of Gordon's Gaussian comparison inequality, and provides additional ingredients that enable a general finite-sample analysis.

Chen Cheng, John Duchi, Rohith Kuditipudi

We examine the necessity of interpolation in overparameterized models, that is, when achieving optimal predictive risk in machine learning problems requires (nearly) interpolating the training data. In particular, we consider simple overparameterized linear regression $y = X θ+ w$ with random design $X \in \mathbb{R}^{n \times d}$ under the proportional asymptotics $d/n \to γ\in (1, \infty)$. We precisely characterize how prediction (test) error necessarily scales with training error in this setting. An implication of this characterization is that as the label noise variance $σ^2 \to 0$, any estimator that incurs at least $\mathsf{c}σ^4$ training error for some constant $\mathsf{c}$ is necessarily suboptimal and will suffer growth in excess prediction error at least linear in the training error. Thus, optimal performance requires fitting training data to substantially higher accuracy than the inherent noise floor of the problem.

Shicong Cen, Chen Cheng, Yuxin Chen et al.

Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops $\textit{non-asymptotic}$ convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on discounted Markov decision processes (MDPs). Assuming access to exact policy evaluation, we demonstrate that the algorithm converges linearly -- or even quadratically once it enters a local region around the optimal policy -- when computing optimal value functions of the regularized MDP. Moreover, the algorithm is provably stable vis-à-vis inexactness of policy evaluation. Our convergence results accommodate a wide range of learning rates, and shed light upon the role of entropy regularization in enabling fast convergence.

Chen Cheng, Yuting Wei, Yuxin Chen

This paper aims to address two fundamental challenges arising in eigenvector estimation and inference for a low-rank matrix from noisy observations: (1) how to estimate an unknown eigenvector when the eigen-gap (i.e. the spacing between the associated eigenvalue and the rest of the spectrum) is particularly small; (2) how to perform estimation and inference on linear functionals of an eigenvector -- a sort of "fine-grained" statistical reasoning that goes far beyond the usual $\ell_2$ analysis. We investigate how to address these challenges in a setting where the unknown $n\times n$ matrix is symmetric and the additive noise matrix contains independent (and non-symmetric) entries. Based on eigen-decomposition of the asymmetric data matrix, we propose estimation and uncertainty quantification procedures for an unknown eigenvector, which further allow us to reason about linear functionals of an unknown eigenvector. The proposed procedures and the accompanying theory enjoy several important features: (1) distribution-free (i.e. prior knowledge about the noise distributions is not needed); (2) adaptive to heteroscedastic noise; (3) minimax optimal under Gaussian noise. Along the way, we establish optimal procedures to construct confidence intervals for the unknown eigenvalues. All this is guaranteed even in the presence of a small eigen-gap (up to $O(\sqrt{n/\mathrm{poly}\log (n)})$ times smaller than the requirement in prior theory), which goes significantly beyond what generic matrix perturbation theory has to offer.

Chen Cheng, Daniel Levy, John C. Duchi

We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- such as those mirror descent employs -- are necessary for optimal convergence. When the constraint set is quadratically convex, diagonally pre-conditioned stochastic gradient methods are minimax optimal. We provide quantitative converses showing that the ``distance'' of the underlying constraints from quadratic convexity determines the sub-optimality of subgradient methods. These results apply, for example, to any $\ell_p$-ball for $p < 2$, and the computation/accuracy tradeoffs they demonstrate exhibit a striking analogy to those in Gaussian sequence models.

Yuxin Chen, Chen Cheng, Jianqing Fan

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\mathbf{M}$ is observed. The noise matrix $\mathbf{M}-\mathbf{M}^{\star}$ is composed of zero-mean independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise, for example, when we have two independent samples for each entry of $\mathbf{M}^{\star}$ and arrange them into an {\em asymmetric} data matrix $\mathbf{M}$. The aim is to estimate the leading eigenvalue and eigenvector of $\mathbf{M}^{\star}$. We demonstrate that the leading eigenvalue of the data matrix $\mathbf{M}$ can be $O(\sqrt{n})$ times more accurate --- up to some log factor --- than its (unadjusted) leading singular value in eigenvalue estimation. Further, the perturbation of any linear form of the leading eigenvector of $\mathbf{M}$ --- say, entrywise eigenvector perturbation --- is provably well-controlled. This eigen-decomposition approach is fully adaptive to heteroscedasticity of noise without the need of careful bias correction or any prior knowledge about the noise variance. We also provide partial theory for the more general rank-$r$ case. The takeaway message is this: arranging the data samples in an asymmetric manner and performing eigen-decomposition could sometimes be beneficial.