Zhihua Zhang

Yanjin Xiang, Zhihua Zhang

We isolate a layerwise refinement of the terminal testing-discrepancy step in Chen's perturbed reverse-heat approach~\cite{Chen2026} to Talagrand's convolution conjecture on the Boolean cube. Built on the joint-filtration martingale formulation of Chen's coupling, and on Chen's approximate monotonicity and conditional squared-score estimates being available in the joint-filtration form stated below, we prove the localized testing estimate \[ D_E\le C_τ\bigl(\cS_E+\sqrt{\cS_E\,\Pp(E)}\bigr), \qquad E\in\mathcal F_θ, \] where \(D_E\) is the localized terminal testing discrepancy and \(\cS_E\) is the stopped perturbative score energy. Applying this estimate to the layers \(G_r(θ)=\{r\le R_θ<r+1\}\) replaces the global Cauchy--Schwarz discrepancy cost by the layerwise cost \[ O_τ\left(\fracα{\sqrt r}+\frac{α^2}{r}\right) \Pp(G_r(θ)), \qquad α\simeq\log\logη. \] Under these imported joint-filtration inputs, combining the localized estimate with the time-smoothed anti-concentration profile yields the black-box consequence \[ μ\{P_τf>η\|f\|_1\} \le C_τ\frac{\log\logη}{η\sqrt{\logη}}, \qquad η>e^3, \] for the Boolean heat semigroup. This makes a $(\log\logη)^{1/2}$ improvement over Chen's result.

Yanjin Xiang, Zhihua Zhang

We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted point. The deterministic finite-sample conditions are stated explicitly, but under a coarse fixed-order multilinear noise event they reduce to a conservative high-signal regime for fixed or slowly expanding local radii. We then separate the warm-start mechanism from any specific spectral construction. A generic one-sweep principle shows that, if a sign-compatible initializer has correlation \(γ_N\), first-sweep noise level \(a_N\), and \(a_N/(γ_N^{d-1}ω_{N,d})\to0\), then one can choose an expanding radius \(r_N=o(ω_{N,d})\) for which the first sweep enters the local basin. After entry, the local affine contraction yields convergence to the unique informative local fixed point in that basin. For centered-Gram initialization, we verify the required correlation and same-sample first-sweep noise bound under i.i.d. finite-fourth-moment noise by a signal-preserving noise-only leave-one comparison and an averaged leave-one slice-contraction estimate, which we call a pressed-back estimate. The leave-one comparison keeps the spike fixed and averages over the deleted coordinate, so planted coordinates enter through \(\ell_2\)-weighted sums rather than worst-case incoherence bounds.

Shusen Wang, Zhihua Zhang

The CUR matrix decomposition and the Nyström approximation are two important low-rank matrix approximation techniques. The Nyström method approximates a symmetric positive semidefinite matrix in terms of a small number of its columns, while CUR approximates an arbitrary data matrix by a small number of its columns and rows. Thus, CUR decomposition can be regarded as an extension of the Nyström approximation. In this paper we establish a more general error bound for the adaptive column/row sampling algorithm, based on which we propose more accurate CUR and Nyström algorithms with expected relative-error bounds. The proposed CUR and Nyström algorithms also have low time complexity and can avoid maintaining the whole data matrix in RAM. In addition, we give theoretical analysis for the lower error bounds of the standard Nyström method and the ensemble Nyström method. The main theoretical results established in this paper are novel, and our analysis makes no special assumption on the data matrices.

Weijian Luo, Hao Jiang, Tianyang Hu et al.

Energy-Based Models (EBMs) have been widely used for generative modeling. Contrastive Divergence (CD), a prevailing training objective for EBMs, requires sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which leads to an irreconcilable trade-off between the computational burden and the validity of the CD. Running MCMCs till convergence is computationally intensive. On the other hand, short-run MCMC brings in an extra non-negligible parameter gradient term that is difficult to handle. In this paper, we provide a general interpretation of CD, viewing it as a special instance of our proposed Diffusion Contrastive Divergence (DCD) family. By replacing the Langevin dynamic used in CD with other EBM-parameter-free diffusion processes, we propose a more efficient divergence. We show that the proposed DCDs are both more computationally efficient than the CD and are not limited to a non-negligible gradient term. We conduct intensive experiments, including both synthesis data modeling and high-dimensional image denoising and generation, to show the advantages of the proposed DCDs. On the synthetic data learning and image denoising experiments, our proposed DCD outperforms CD by a large margin. In image generation experiments, the proposed DCD is capable of training an energy-based model for generating the Celab-A $32\times 32$ dataset, which is comparable to existing EBMs.

Hao Jin, Yang Peng, Wenhao Yang et al.

We study a Federated Reinforcement Learning (FedRL) problem in which $n$ agents collaboratively learn a single policy without sharing the trajectories they collected during agent-environment interaction. We stress the constraint of environment heterogeneity, which means $n$ environments corresponding to these $n$ agents have different state transitions. To obtain a value function or a policy function which optimizes the overall performance in all environments, we propose two federated RL algorithms, \texttt{QAvg} and \texttt{PAvg}. We theoretically prove that these algorithms converge to suboptimal solutions, while such suboptimality depends on how heterogeneous these $n$ environments are. Moreover, we propose a heuristic that achieves personalization by embedding the $n$ environments into $n$ vectors. The personalization heuristic not only improves the training but also allows for better generalization to new environments.

Shusen Wang, Zhihua Zhang, Tong Zhang

The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear algebra, the power method is widely applied to improve the quality of randomized sketching, and relative-error bounds have been well established. Recently, Musco & Musco (2015) proposed a block Krylov subspace method that fully exploits the intermediate results of the power iteration to accelerate convergence. They showed spectral gap-independent bounds which are stronger than the power method by order-of-magnitude. This paper offers novel error analysis techniques and significantly improves the bounds of both the randomized power method and the block Lanczos method. This paper also establishes the first gap-independent bound for the warm-start block Lanczos method.

Dachao Lin, Yuze Han, Haishan Ye et al.

We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $δ$-similarity and $μ$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of $\tilde{\mathcal{O}}(n {+} \sqrt{n}δ/μ)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{δ/μ})$ communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.

Haishan Ye, Luo Luo, Zhihua Zhang

Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention due to their efficiency at each iteration, rectified a weakness in the ordinary Newton method of suffering a high cost in each iteration while commanding a high convergence rate. Other efficient stochastic second order methods are also proposed. However, the convergence properties of these methods are still not well understood. There are also several important gaps between the current convergence theory and the performance in real applications. In this paper, we aim to fill these gaps. We propose a unifying framework to analyze both local and global convergence properties of second order methods. Based on this framework, we present our theoretical results which match the performance in real applications well.

Haishan Ye, Yujun Li, Zhihua Zhang

Prior optimal CUR decomposition and near optimal column reconstruction methods have been established by combining BSS sampling and adaptive sampling. In this paper, we propose a new approach to the optimal CUR decomposition and near optimal column reconstruction by just using leverage score sampling. In our approach, both the BSS sampling and adaptive sampling are not needed. Moreover, our approach is the first $O(\mathrm{nnz}(\A))$ optimal CUR algorithm where $\A$ is a data matrix in question. We also extend our approach to the Nystr{ö}m method, obtaining a fast algorithm which runs $\tilde{O}(n^{2})$ or $O(\mathrm{\nnz}(\A))$

Miao Lu, Wenhao Yang, Liangyu Zhang et al.

In an Markov decision process (MDP), unobservable confounders may exist and have impacts on the data generating process, so that the classic off-policy evaluation (OPE) estimators may fail to identify the true value function of the target policy. In this paper, we study the statistical properties of OPE in confounded MDPs with observable instrumental variables. Specifically, we propose a two-stage estimator based on the instrumental variables and establish its statistical properties in the confounded MDPs with a linear structure. For non-asymptotic analysis, we prove a $\mathcal{O}(n^{-1/2})$-error bound where $n$ is the number of samples. For asymptotic analysis, we prove that the two-stage estimator is asymptotically normal with a typical rate of $n^{1/2}$. To the best of our knowledge, we are the first to show such statistical results of the two-stage estimator for confounded linear MDPs via instrumental variables.

Boya Zhang, Weijian Luo, Zhihua Zhang

Adversarial attacks have the potential to mislead deep neural network classifiers by introducing slight perturbations. Developing algorithms that can mitigate the effects of these attacks is crucial for ensuring the safe use of artificial intelligence. Recent studies have suggested that score-based diffusion models are effective in adversarial defenses. However, existing diffusion-based defenses rely on the sequential simulation of the reversed stochastic differential equations of diffusion models, which are computationally inefficient and yield suboptimal results. In this paper, we introduce a novel adversarial defense scheme named ScoreOpt, which optimizes adversarial samples at test-time, towards original clean data in the direction guided by score-based priors. We conduct comprehensive experiments on multiple datasets, including CIFAR10, CIFAR100 and ImageNet. Our experimental results demonstrate that our approach outperforms existing adversarial defenses in terms of both robustness performance and inference speed.

Wenhao Yang, Han Wang, Tadashi Kozuno et al.

Robust Markov Decision Processes (MDPs) are receiving much attention in learning a robust policy which is less sensitive to environment changes. There are an increasing number of works analyzing sample-efficiency of robust MDPs. However, there are two major barriers to applying robust MDPs in practice. First, most works study robust MDPs in a model-based regime, where the transition probability needs to be estimated and requires a large amount of memories $\mathcal{O}(|\mathcal{S}|^2|\mathcal{A}|)$. Second, prior work typically assumes a strong oracle to obtain the optimal solution as an intermediate step to solve robust MDPs. However, in practice, such an oracle does not exist usually. To remove the oracle, we transform the original robust MDPs into an alternative form, which allows us to use stochastic gradient methods to solve the robust MDPs. Moreover, we prove the alternative form still plays a similar role as the original form. With this new formulation, we devise a sample-efficient algorithm to solve the robust MDPs in a model-free regime, which does not require an oracle and trades off a lower storage requirement $\mathcal{O}(|\mathcal{S}||\mathcal{A}|)$ with being able to generate samples from a generative model or Markovian chain. Finally, we validate our theoretical findings via numerical experiments, showing the efficiency with the alternative form of robust MDPs.

Dachao Lin, Zhihua Zhang

In this short note, we give the convergence analysis of the policy in the recent famous policy mirror descent (PMD). We mainly consider the unregularized setting following [11] with generalized Bregman divergence. The difference is that we directly give the convergence rates of policy under generalized Bregman divergence. Our results are inspired by the convergence of value function in previous works and are an extension study of policy mirror descent. Though some results have already appeared in previous work, we further discover a large body of Bregman divergences could give finite-step convergence to an optimal policy, such as the classical Euclidean distance.

Haishan Ye, Zhihua Zhang

First, we extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Second, We develop a class of fast approximate generalized linear regression algorithms with respect to the spectral norm. Finally, We give a fast approximate SVD.

Boya Zhang, Weijian Luo, Zhihua Zhang

Adversarial attacks can mislead neural network classifiers. The defense against adversarial attacks is important for AI safety. Adversarial purification is a family of approaches that defend adversarial attacks with suitable pre-processing. Diffusion models have been shown to be effective for adversarial purification. Despite their success, many aspects of diffusion purification still remain unexplored. In this paper, we investigate and improve upon three limiting designs of diffusion purification: the use of an improved diffusion model, advanced numerical simulation techniques, and optimal control of randomness. Based on our findings, we propose Purify++, a new diffusion purification algorithm that is now the state-of-the-art purification method against several adversarial attacks. Our work presents a systematic exploration of the limits of diffusion purification methods.

Weijian Luo, Boya Zhang, Zhihua Zhang

Efficiently sampling from un-normalized target distributions is a fundamental problem in scientific computing and machine learning. Traditional approaches such as Markov Chain Monte Carlo (MCMC) guarantee asymptotically unbiased samples from such distributions but suffer from computational inefficiency, particularly when dealing with high-dimensional targets, as they require numerous iterations to generate a batch of samples. In this paper, we introduce an efficient and scalable neural implicit sampler that overcomes these limitations. The implicit sampler can generate large batches of samples with low computational costs by leveraging a neural transformation that directly maps easily sampled latent vectors to target samples without the need for iterative procedures. To train the neural implicit samplers, we introduce two novel methods: the KL training method and the Fisher training method. The former method minimizes the Kullback-Leibler divergence, while the latter minimizes the Fisher divergence between the sampler and the target distributions. By employing the two training methods, we effectively optimize the neural implicit samplers to learn and generate from the desired target distribution. To demonstrate the effectiveness, efficiency, and scalability of our proposed samplers, we evaluate them on three sampling benchmarks with different scales.

Liangyu Zhang, Yang Peng, Jiadong Liang et al.

In this paper, we study distributional reinforcement learning from the perspective of statistical efficiency. We investigate distributional policy evaluation, aiming to estimate the complete return distribution (denoted $η^π$) attained by a given policy $π$. We use the certainty-equivalence method to construct our estimator $\hatη^π$, given a generative model is available. In this circumstance we need a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\varepsilon^{2p}(1-γ)^{2p+2}}\right)$ to guarantee the $p$-Wasserstein metric between $\hatη^π$ and $η^π$ less than $\varepsilon$ with high probability. This implies the distributional policy evaluation problem can be solved with sample efficiency. Also, we show that under different mild assumptions a dataset of size $\widetilde O\left(\frac{|\mathcal{S}||\mathcal{A}|}{\varepsilon^{2}(1-γ)^{4}}\right)$ suffices to ensure the Kolmogorov metric and total variation metric between $\hatη^π$ and $η^π$ is below $\varepsilon$ with high probability. Furthermore, we investigate the asymptotic behavior of $\hatη^π$. We demonstrate that the ``empirical process'' $\sqrt{n}(\hatη^π-η^π)$ converges weakly to a Gaussian process in the space of bounded functionals on Lipschitz function class $\ell^\infty(\mathcal{F}_{\text{W}})$, also in the space of bounded functionals on indicator function class $\ell^\infty(\mathcal{F}_{\text{KS}})$ and bounded measurable function class $\ell^\infty(\mathcal{F}_{\text{TV}})$ when some mild conditions hold. Our findings give rise to a unified approach to statistical inference of a wide class of statistical functionals of $η^π$.

Yizheng Hu, Zhihua Zhang

Cooperative multi-agent reinforcement learning (cMARL) has many real applications, but the policy trained by existing cMARL algorithms is not robust enough when deployed. There exist also many methods about adversarial attacks on the RL system, which implies that the RL system can suffer from adversarial attacks, but most of them focused on single agent RL. In this paper, we propose a \textit{sparse adversarial attack} on cMARL systems. We use (MA)RL with regularization to train the attack policy. Our experiments show that the policy trained by the current cMARL algorithm can obtain poor performance when only one or a few agents in the team (e.g., 1 of 8 or 5 of 25) were attacked at a few timesteps (e.g., attack 3 of total 40 timesteps).

Liangyu Zhang, Yang Peng, Wenhao Yang et al.

We propose a novel generalization of constrained Markov decision processes (CMDPs) that we call the \emph{semi-infinitely constrained Markov decision process} (SICMDP). Particularly, we consider a continuum of constraints instead of a finite number of constraints as in the case of ordinary CMDPs. We also devise two reinforcement learning algorithms for SICMDPs that we call SI-CRL and SI-CPO. SI-CRL is a model-based reinforcement learning algorithm. Given an estimate of the transition model, we first transform the reinforcement learning problem into a linear semi-infinitely programming (LSIP) problem and then use the dual exchange method in the LSIP literature to solve it. SI-CPO is a policy optimization algorithm. Borrowing the ideas from the cooperative stochastic approximation approach, we make alternative updates to the policy parameters to maximize the reward or minimize the cost. To the best of our knowledge, we are the first to apply tools from semi-infinitely programming (SIP) to solve constrained reinforcement learning problems. We present theoretical analysis for SI-CRL and SI-CPO, identifying their iteration complexity and sample complexity. We also conduct extensive numerical examples to illustrate the SICMDP model and demonstrate that our proposed algorithms are able to solve complex sequential decision-making tasks leveraging modern deep reinforcement learning techniques.

Yuanchi Ma, Kaize Shi, Hui He et al.

Large Language Models (LLMs) have demonstrated remarkable capabilities in narrative generation. However, they often produce structurally homogenized stories, frequently following repetitive arrangements and combinations of plot events along with stereotypical resolutions. In this paper, we propose a novel theoretical framework for analysis by incorporating Proppian narratology and narrative functions. This framework is used to analyze the composition of narrative texts generated by LLMs to uncover their underlying narrative logic. Taking Chinese web literature as our research focus, we extend Propp's narrative theory, defining 34 narrative functions suited to modern web narrative structures. We further construct a human-annotated corpus to support the analysis of narrative structures within LLM-generated text. Experiments reveal that the primary reasons for the singular narrative logic and severe homogenization in generated texts are that current LLMs are unable to correctly comprehend the meanings of narrative functions and instead adhere to rigid narrative generation paradigms.

Pu Wang, Shuning Sun, Jialang Lu et al.

Purple flare, a diffuse chromatic aberration artifact commonly found around highlight areas, severely degrades the tone transition and color of the image. Existing traditional methods are based on hand-crafted features, which lack flexibility and rely entirely on fixed priors, while the scarcity of paired training data critically hampers deep learning. To address this issue, we propose a novel network built upon decoupled HSV Look-Up Tables (LUTs). The method aims to simplify color correction by adjusting the Hue (H), Saturation (S), and Value (V) components independently. This approach resolves the inherent color coupling problems in traditional methods. Our model adopts a two-stage architecture: First, a Chroma-Aware Spectral Tokenizer (CAST) converts the input image from RGB space to HSV space and independently encodes the Hue (H) and Value (V) channels into a set of semantic tokens describing the Purple flare status; second, the HSV-LUT module takes these tokens as input and dynamically generates independent correction curves (1D-LUTs) for the three channels H, S, and V. To effectively train and validate our model, we built the first large-scale purple flare dataset with diverse scenes. We also proposed new metrics and a loss function specifically designed for this task. Extensive experiments demonstrate that our model not only significantly outperforms existing methods in visual effects but also achieves state-of-the-art performance on all quantitative metrics.

Yuhang Zhang, Yue Liu, Zhihua Zhang

The purpose of this work is to transport the information from multiple randomized controlled trials to the target population where we only have the control group data. Previous works rely critically on the mean exchangeability assumption. However, as pointed out by many current studies, the mean exchangeability assumption might be violated. Motivated by the synthetic control method, we construct a synthetic treatment group for the target population by a weighted mixture of treatment groups of source populations. We estimate the weights by minimizing the conditional maximum mean discrepancy between the weighted control groups of source populations and the target population. We establish the asymptotic normality of the synthetic treatment group estimator based on the sieve semiparametric theory. Our method can serve as a novel complementary approach when the mean exchangeability assumption is violated. Experiments are conducted on synthetic and real-world datasets to demonstrate the effectiveness of our methods.

Yang Peng, Kaicheng Jin, Liangyu Zhang et al.

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The aim of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy π. Previous works on statistical analysis of distributional TD learning mainly focus on the tabular case. In contrast, we first consider the linear function approximation setting and derive sharp finite-sample rates. Our theoretical results demonstrate that the sample complexity of linear distributional TD learning matches that of classic linear TD learning. This implies that, with linear function approximation, learning the full distribution of the return from streaming data is no more difficult than learning its expectation (value function). To derive tight sample complexity bounds, we conduct a fine-grained analysis of the linear-categorical Bellman equation and employ the exponential stability arguments for products of random matrices. Our results provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.

Chuhan Xie, Kaicheng Jin, Jiadong Liang et al.

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the averaged iterates to a scaled sum of Gaussians in both linear and nonlinear SA problems. We then construct three types of asymptotic confidence sequences that are valid uniformly across all times with coverage guarantees, in an asymptotic sense that the starting time is sufficiently large. These coverage guarantees remain valid if the unknown covariance matrix is replaced by its plug-in estimator, and we conduct experiments to validate our methodology.

Yang Peng, Liangyu Zhang, Zhihua Zhang

Distributional reinforcement learning (DRL) has achieved empirical success in various domains. One core task in DRL is distributional policy evaluation, which involves estimating the return distribution $η^π$ for a given policy $π$. Distributional temporal difference learning has been accordingly proposed, which extends the classic temporal difference learning (TD) in RL. In this paper, we focus on the non-asymptotic statistical rates of distributional TD. To facilitate theoretical analysis, we propose non-parametric distributional TD (NTD). For a $γ$-discounted infinite-horizon tabular Markov decision process, we show that for NTD with a generative model, we need $\tilde{O}(\varepsilon^{-2}μ_{\min}^{-1}(1-γ)^{-3})$ interactions with the environment to achieve an $\varepsilon$-optimal estimator with high probability, when the estimation error is measured by the $1$-Wasserstein. This sample complexity bound is minimax optimal up to logarithmic factors. In addition, we revisit categorical distributional TD (CTD), showing that the same non-asymptotic convergence bounds hold for CTD in the case of the $1$-Wasserstein distance. We also extend our analysis to the more general setting where the data generating process is Markovian. In the Markovian setting, we propose variance-reduced variants of NTD and CTD, and show that both can achieve a $\tilde{O}(\varepsilon^{-2} μ_{π,\min}^{-1}(1-γ)^{-3}+t_{mix}μ_{π,\min}^{-1}(1-γ)^{-1})$ sample complexity bounds in the case of the $1$-Wasserstein distance, which matches the state-of-the-art statistical results for classic policy evaluation. To achieve the sharp statistical rates, we establish a novel Freedman's inequality in Hilbert spaces. This new Freedman's inequality would be of independent interest for statistical analysis of various infinite-dimensional online learning problems.

Jingxin Zhan, Yuchen Xin, Chenjie Sun et al.

We consider a common case of the combinatorial semi-bandit problem, the $m$-set semi-bandit, where the learner exactly selects $m$ arms from the total $d$ arms. In the adversarial setting, the best regret bound, known to be $\mathcal{O}(\sqrt{nmd})$ for time horizon $n$, is achieved by the well-known Follow-the-Regularized-Leader (FTRL) policy. However, this requires to explicitly compute the arm-selection probabilities via optimizing problems at each time step and sample according to them. This problem can be avoided by the Follow-the-Perturbed-Leader (FTPL) policy, which simply pulls the $m$ arms that rank among the $m$ smallest (estimated) loss with random perturbation. In this paper, we show that FTPL with a Fréchet perturbation also enjoys the near optimal regret bound $\mathcal{O}(\sqrt{nm}(\sqrt{d\log(d)}+m^{5/6}))$ in the adversarial setting and approaches best-of-both-world regret bounds, i.e., achieves a logarithmic regret for the stochastic setting. Moreover, our lower bounds show that the extra factors are unavoidable with our approach; any improvement would require a fundamentally different and more challenging method.

Xian-Xian Liu, Mingkun Xu, Yuanyuan Wei et al.

Timely and precise classification and segmentation of gastric bleeding in endoscopic imagery are pivotal for the rapid diagnosis and intervention of gastric complications, which is critical in life-saving medical procedures. Traditional methods grapple with the challenge posed by the indistinguishable intensity values of bleeding tissues adjacent to other gastric structures. Our study seeks to revolutionize this domain by introducing a novel deep learning model, the Dual Spatial Kernelized Constrained Fuzzy C-Means (Deep DuS-KFCM) clustering algorithm. This Hybrid Neuro-Fuzzy system synergizes Neural Networks with Fuzzy Logic to offer a highly precise and efficient identification of bleeding regions. Implementing a two-fold coarse-to-fine strategy for segmentation, this model initially employs the Spatial Kernelized Fuzzy C-Means (SKFCM) algorithm enhanced with spatial intensity profiles and subsequently harnesses the state-of-the-art DeepLabv3+ with ResNet50 architecture to refine the segmentation output. Through extensive experiments across mainstream gastric bleeding and red spots datasets, our Deep DuS-KFCM model demonstrated unprecedented accuracy rates of 87.95%, coupled with a specificity of 96.33%, outperforming contemporary segmentation methods. The findings underscore the model's robustness against noise and its outstanding segmentation capabilities, particularly for identifying subtle bleeding symptoms, thereby presenting a significant leap forward in medical image processing.

Yanjin Xiang, Zhihua Zhang

We study the rank-one spiked tensor model in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance, and finite fourth moment.This setting extends the classical Gaussian framework to a substantially broader class of noise distributions.Focusing on asymmetric tensors of order $d$ ($\ge 3$), we analyze the maximum likelihood estimator of the best rank-one approximation.Under a mild assumption isolating informative critical points of the associated optimization landscape, we show that the empirical spectral distribution of a suitably defined block-wise tensor contraction converges almost surely to a deterministic limit that coincides with the Gaussian case.As a consequence, the asymptotic singular value and the alignments between the estimated and true spike directions admit explicit characterizations identical to those obtained under Gaussian noise. These results establish a universality principle for spiked tensor models, demonstrating that their high-dimensional spectral behavior and statistical limits are robust to non-Gaussian noise. Our analysis relies on resolvent methods from random matrix theory, cumulant expansions valid under finite moment assumptions, and variance bounds based on Efron-Stein-type arguments. A key challenge in the proof is how to handle the statistical dependence between the signal term and the noise term.

Kaicheng Jin, Yang Peng, Jiansheng Yang et al.

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The purpose of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy. Previous works on statistical analysis of distributional TD learning focus mainly on the tabular case. We first consider the linear function approximation setting and conduct a fine-grained analysis of the linear-categorical Bellman equation. Building on this analysis, we further incorporate variance reduction techniques in our new algorithms to establish tight sample complexity bounds independent of the support size $K$ when $K$ is large. Our theoretical results imply that, when employing distributional TD learning with linear function approximation, learning the full distribution of the return function from streaming data is no more difficult than learning its expectation. This work provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.

Jingxin Zhan, Yuze Han, Zhihua Zhang

The convergence analysis of online learning algorithms is central to machine learning theory, where last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time. However, in multi-armed bandits, most existing algorithmic analyses mainly focus on the order of regret, while the last-iterate (simple regret) convergence rate remains less explored -- especially for the widely studied Follow-the-Regularized-Leader (FTRL) algorithms. Recently, a growing line of work has established the Best-of-Both-Worlds (BOBW) property of FTRL algorithms in bandit problems, showing in particular that they achieve logarithmic regret in stochastic bandits. Nevertheless, their last-iterate convergence rate has not yet been studied. Intuitively, logarithmic regret should correspond to a $t^{-1}$ last-iterate convergence rate. This paper partially confirms this intuition through theoretical analysis, showing that the Bregman divergence, defined by the regular function $Ψ(p)=-4\sum_{i=1}^{d}\sqrt{p_i}$ associated with the BOBW FTRL algorithm $1/2$-Tsallis-INF (arXiv:1807.07623), between the point mass on the optimal arm and the probability distribution over the arm set obtained at iteration $t$, decays at a rate of $t^{-1/2}$.

Pu Wang, Zhihua Zhang, Dianjie Lu et al.

Since human and environmental factors interfere, captured polyp images usually suffer from issues such as dim lighting, blur, and overexposure, which pose challenges for downstream polyp segmentation tasks. To address the challenges of noise-induced degradation in polyp images, we present AgentPolyp, a novel framework integrating CLIP-based semantic guidance and dynamic image enhancement with a lightweight neural network for segmentation. The agent first evaluates image quality using CLIP-driven semantic analysis (e.g., identifying ``low-contrast polyps with vascular textures") and adapts reinforcement learning strategies to dynamically apply multi-modal enhancement operations (e.g., denoising, contrast adjustment). A quality assessment feedback loop optimizes pixel-level enhancement and segmentation focus in a collaborative manner, ensuring robust preprocessing before neural network segmentation. This modular architecture supports plug-and-play extensions for various enhancement algorithms and segmentation networks, meeting deployment requirements for endoscopic devices.

Pu Wang, Huaizhi Ma, Zhihua Zhang et al.

Accurate polyp segmentation remains challenging due to irregular lesion morphologies, ambiguous boundaries, and heterogeneous imaging conditions. While U-Net variants excel at local feature fusion, they often lack explicit mechanisms to model the dynamic evolution of segmentation confidence under uncertainty. Inspired by the interpretable nature of flow-based models, we present \textbf{PolypFLow}, a flow-matching enhanced architecture that injects physics-inspired optimization dynamics into segmentation refinement. Unlike conventional cascaded networks, our framework solves an ordinary differential equation (ODE) to progressively align coarse initial predictions with ground truth masks through learned velocity fields. This trajectory-based refinement offers two key advantages: 1) Interpretable Optimization: Intermediate flow steps visualize how the model corrects under-segmented regions and sharpens boundaries at each ODE-solver iteration, demystifying the ``black-box" refinement process; 2) Boundary-Aware Robustness: The flow dynamics explicitly model gradient directions along polyp edges, enhancing resilience to low-contrast regions and motion artifacts. Numerous experimental results show that PolypFLow achieves a state-of-the-art while maintaining consistent performance in different lighting scenarios.

Jingxin Zhan, Yuchen Xin, Kaicheng Jin et al.

We study a stochastic convex bandit problem where the subgaussian noise parameter is assumed to decrease linearly as the learner selects actions closer and closer to the minimizer of the convex loss function. Accordingly, we propose a Regularized Online Newton Method (RONM) for solving the problem, based on the Online Newton Method (ONM) of arXiv:2406.06506. Our RONM reaches a polylogarithmic regret in the time horizon $n$ when the loss function grows quadratically in the constraint set, which recovers the results of arXiv:2402.12042 in linear bandits. Our analyses rely on the growth rate of the precision matrix $Σ_t^{-1}$ in ONM and we find that linear growth solves the question exactly. These analyses also help us obtain better convergence rates when the loss function grows faster. We also study and analyze two new bandit models: stochastic convex bandits with noise scaled to a subgaussian parameter function and convex bandits with stochastic multiplicative noise.

Hao Jin, Yang Peng, Liangyu Zhang et al.

We study problems of federated control in Markov Decision Processes. To solve an MDP with large state space, multiple learning agents are introduced to collaboratively learn its optimal policy without communication of locally collected experience. In our settings, these agents have limited capabilities, which means they are restricted within different regions of the overall state space during the training process. In face of the difference among restricted regions, we firstly introduce concepts of leakage probabilities to understand how such heterogeneity affects the learning process, and then propose a novel communication protocol that we call Federated-Q protocol (FedQ), which periodically aggregates agents' knowledge of their restricted regions and accordingly modifies their learning problems for further training. In terms of theoretical analysis, we justify the correctness of FedQ as a communication protocol, then give a general result on sample complexity of derived algorithms FedQ-X with the RL oracle , and finally conduct a thorough study on the sample complexity of FedQ-SynQ. Specifically, FedQ-X has been shown to enjoy linear speedup in terms of sample complexity when workload is uniformly distributed among agents. Moreover, we carry out experiments in various environments to justify the efficiency of our methods.

Hao Jin, Liangyu Zhang, Zhihua Zhang

We study a Federated Reinforcement Learning (FedRL) problem with constraint heterogeneity. In our setting, we aim to solve a reinforcement learning problem with multiple constraints while $N$ training agents are located in $N$ different environments with limited access to the constraint signals and they are expected to collaboratively learn a policy satisfying all constraint signals. Such learning problems are prevalent in scenarios of Large Language Model (LLM) fine-tuning and healthcare applications. To solve the problem, we propose federated primal-dual policy optimization methods based on traditional policy gradient methods. Specifically, we introduce $N$ local Lagrange functions for agents to perform local policy updates, and these agents are then scheduled to periodically communicate on their local policies. Taking natural policy gradient (NPG) and proximal policy optimization (PPO) as policy optimization methods, we mainly focus on two instances of our algorithms, ie, {FedNPG} and {FedPPO}. We show that FedNPG achieves global convergence with an $\tilde{O}(1/\sqrt{T})$ rate, and FedPPO efficiently solves complicated learning tasks with the use of deep neural networks.

Weijian Luo, Tianyang Hu, Shifeng Zhang et al.

Due to the ease of training, ability to scale, and high sample quality, diffusion models (DMs) have become the preferred option for generative modeling, with numerous pre-trained models available for a wide variety of datasets. Containing intricate information about data distributions, pre-trained DMs are valuable assets for downstream applications. In this work, we consider learning from pre-trained DMs and transferring their knowledge to other generative models in a data-free fashion. Specifically, we propose a general framework called Diff-Instruct to instruct the training of arbitrary generative models as long as the generated samples are differentiable with respect to the model parameters. Our proposed Diff-Instruct is built on a rigorous mathematical foundation where the instruction process directly corresponds to minimizing a novel divergence we call Integral Kullback-Leibler (IKL) divergence. IKL is tailored for DMs by calculating the integral of the KL divergence along a diffusion process, which we show to be more robust in comparing distributions with misaligned supports. We also reveal non-trivial connections of our method to existing works such as DreamFusion, and generative adversarial training. To demonstrate the effectiveness and universality of Diff-Instruct, we consider two scenarios: distilling pre-trained diffusion models and refining existing GAN models. The experiments on distilling pre-trained diffusion models show that Diff-Instruct results in state-of-the-art single-step diffusion-based models. The experiments on refining GAN models show that the Diff-Instruct can consistently improve the pre-trained generators of GAN models across various settings.

Hao Cheng, Meng Zhang, Weixuan Wang et al.

Length-controllable machine translation is a type of constrained translation. It aims to contain the original meaning as much as possible while controlling the length of the translation. We can use automatic summarization or machine translation evaluation metrics for length-controllable machine translation, but this is not necessarily suitable and accurate. This work is the first attempt to evaluate the automatic metrics for length-controllable machine translation tasks systematically. We conduct a rigorous human evaluation on two translation directions and evaluate 18 summarization or translation evaluation metrics. We find that BLEURT and COMET have the highest correlation with human evaluation and are most suitable as evaluation metrics for length-controllable machine translation.

Hao Cheng, Meng Zhang, Liangyou Li et al.

Utilizing pivot language effectively can significantly improve low-resource machine translation. Usually, the two translation models, source-pivot and pivot-target, are trained individually and do not utilize the limited (source, target) parallel data. This work proposes an end-to-end training method for the cascaded translation model and configures an improved decoding algorithm. The input of the pivot-target model is modified to weighted pivot embedding based on the probability distribution output by the source-pivot model. This allows the model to be trained end-to-end. In addition, we mitigate the inconsistency between tokens and probability distributions while using beam search in pivot decoding. Experiments demonstrate that our method enhances the quality of translation.

Kun Chen, Dachao Lin, Zhihua Zhang

In this paper, we follow Eftekhari's work to give a non-local convergence analysis of deep linear networks. Specifically, we consider optimizing deep linear networks which have a layer with one neuron under quadratic loss. We describe the convergent point of trajectories with arbitrary starting point under gradient flow, including the paths which converge to one of the saddle points or the original point. We also show specific convergence rates of trajectories that converge to the global minimizer by stages. To achieve these results, this paper mainly extends the machinery in Eftekhari's work to provably identify the rank-stable set and the global minimizer convergent set. We also give specific examples to show the necessity of our definitions. Crucially, as far as we know, our results appear to be the first to give a non-local global analysis of linear neural networks from arbitrary initialized points, rather than the lazy training regime which has dominated the literature of neural networks, and restricted benign initialization in Eftekhari's work. We also note that extending our results to general linear networks without one hidden neuron assumption remains a challenging open problem.

Xiang Li, Wenhao Yang, Jiadong Liang et al.

We study Q-learning with Polyak-Ruppert averaging in a discounted Markov decision process in synchronous and tabular settings. Under a Lipschitz condition, we establish a functional central limit theorem for the averaged iteration $\bar{\boldsymbol{Q}}_T$ and show that its standardized partial-sum process converges weakly to a rescaled Brownian motion. The functional central limit theorem implies a fully online inference method for reinforcement learning. Furthermore, we show that $\bar{\boldsymbol{Q}}_T$ is the regular asymptotically linear (RAL) estimator for the optimal Q-value function $\boldsymbol{Q}^*$ that has the most efficient influence function. We present a nonasymptotic analysis for the $\ell_{\infty}$ error, $\mathbb{E}\|\bar{\boldsymbol{Q}}_T-\boldsymbol{Q}^*\|_{\infty}$, showing that it matches the instance-dependent lower bound for polynomial step sizes. Similar results are provided for entropy-regularized Q-learning without the Lipschitz condition.

Xiang Li, Jiadong Liang, Xiangyu Chang et al.

Federated Learning (FL) makes a large amount of edge computing devices (e.g., mobile phones) jointly learn a global model without data sharing. In FL, data are generated in a decentralized manner with high heterogeneity. This paper studies how to perform statistical estimation and inference in the federated setting. We analyze the so-called Local SGD, a multi-round estimation procedure that uses intermittent communication to improve communication efficiency. We first establish a {\it functional central limit theorem} that shows the averaged iterates of Local SGD weakly converge to a rescaled Brownian motion. We next provide two iterative inference methods: the {\it plug-in} and the {\it random scaling}. Random scaling constructs an asymptotically pivotal statistic for inference by using the information along the whole Local SGD path. Both the methods are communication efficient and applicable to online data. Our theoretical and empirical results show that Local SGD simultaneously achieves both statistical efficiency and communication efficiency.

Luo Luo, Guangzeng Xie, Tong Zhang et al.

This paper considers stochastic first-order algorithms for convex-concave minimax problems of the form $\min_{\bf x}\max_{\bf y}f(\bf x, \bf y)$, where $f$ can be presented by the average of $n$ individual components which are $L$-average smooth. For $μ_x$-strongly-convex-$μ_y$-strongly-concave setting, we propose a new method which could find a $\varepsilon$-saddle point of the problem in $\tilde{\mathcal O} \big(\sqrt{n(\sqrt{n}+κ_x)(\sqrt{n}+κ_y)}\log(1/\varepsilon)\big)$ stochastic first-order complexity, where $κ_x\triangleq L/μ_x$ and $κ_y\triangleq L/μ_y$. This upper bound is near optimal with respect to $\varepsilon$, $n$, $κ_x$ and $κ_y$ simultaneously. In addition, the algorithm is easily implemented and works well in practical. Our methods can be extended to solve more general unbalanced convex-concave minimax problems and the corresponding upper complexity bounds are also near optimal.

Yuekai Zhao, Li Dong, Yelong Shen et al.

Differentiable architecture search (DARTS) is successfully applied in many vision tasks. However, directly using DARTS for Transformers is memory-intensive, which renders the search process infeasible. To this end, we propose a multi-split reversible network and combine it with DARTS. Specifically, we devise a backpropagation-with-reconstruction algorithm so that we only need to store the last layer's outputs. By relieving the memory burden for DARTS, it allows us to search with larger hidden size and more candidate operations. We evaluate the searched architecture on three sequence-to-sequence datasets, i.e., WMT'14 English-German, WMT'14 English-French, and WMT'14 English-Czech. Experimental results show that our network consistently outperforms standard Transformers across the tasks. Moreover, our method compares favorably with big-size Evolved Transformers, reducing search computation by an order of magnitude.

Dachao Lin, Zhihua Zhang

We consider the fundamental problem of learning linear predictors (i.e., separable datasets with zero margin) using neural networks with gradient flow or gradient descent. Under the assumption of spherically symmetric data distribution, we show directional convergence guarantees with exact convergence rate for two-layer non-linear networks with only two hidden nodes, and (deep) linear networks. Moreover, our discovery is built on dynamic from the initialization without both initial loss and perfect classification constraint in contrast to previous works. We also point out and study the challenges in further strengthening and generalizing our results.

Wenhao Yang, Liangyu Zhang, Zhihua Zhang

In this paper, we study the non-asymptotic and asymptotic performances of the optimal robust policy and value function of robust Markov Decision Processes(MDPs), where the optimal robust policy and value function are solved only from a generative model. While prior work focusing on non-asymptotic performances of robust MDPs is restricted in the setting of the KL uncertainty set and $(s,a)$-rectangular assumption, we improve their results and also consider other uncertainty sets, including $L_1$ and $χ^2$ balls. Our results show that when we assume $(s,a)$-rectangular on uncertainty sets, the sample complexity is about $\widetilde{O}\left(\frac{|\mathcal{S}|^2|\mathcal{A}|}{\varepsilon^2ρ^2(1-γ)^4}\right)$. In addition, we extend our results from $(s,a)$-rectangular assumption to $s$-rectangular assumption. In this scenario, the sample complexity varies with the choice of uncertainty sets and is generally larger than the case under $(s,a)$-rectangular assumption. Moreover, we also show that the optimal robust value function is asymptotic normal with a typical rate $\sqrt{n}$ under $(s,a)$ and $s$-rectangular assumptions from both theoretical and empirical perspectives.

Guangzeng Xie, Hao Jin, Dachao Lin et al.

We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning rate, and casts the joint updating process of parameters and learning rates into a maxmin problem. Given any regularization term, our approach facilitates the generation of practical algorithms. When \textit{Meta-Regularization} takes the $\varphi$-divergence as a regularizer, the resulting algorithms exhibit comparable theoretical convergence performance with other first-order gradient-based algorithms. Furthermore, we theoretically prove that some well-designed regularizers can improve the convergence performance under the strong-convexity condition of the objective function. Numerical experiments on benchmark problems demonstrate the effectiveness of algorithms derived from some common $\varphi$-divergence in full batch as well as online learning settings.

Yuze Han, Guangzeng Xie, Zhihua Zhang

In this paper, we study the lower complexity bounds for finite-sum optimization problems, where the objective is the average of $n$ individual component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have access to the gradient and proximal oracles for each component function. To incorporate loopless methods, we also allow PIFO algorithms to obtain the full gradient infrequently. We develop a novel approach to constructing the hard instances, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of PIFO algorithms. Based on this construction, we establish the lower complexity bounds for finite-sum minimax optimization problems when the objective is convex-concave or nonconvex-strongly-concave and the class of component functions is $L$-average smooth. Most of these bounds are nearly matched by existing upper bounds up to log factors. We can also derive similar lower bounds for finite-sum minimization problems as previous work under both smoothness and average smoothness assumptions. Our lower bounds imply that proximal oracles for smooth functions are not much more powerful than gradient oracles.

Guangzeng Xie, Yuze Han, Zhihua Zhang

This paper studies bilinear saddle point problems $\min_{\bf{x}} \max_{\bf{y}} g(\bf{x}) + \bf{x}^{\top} \bf{A} \bf{y} - h(\bf{y})$, where the functions $g, h$ are smooth and strongly-convex. When the gradient and proximal oracle related to $g$ and $h$ are accessible, optimal algorithms have already been developed in the literature \cite{chambolle2011first, palaniappan2016stochastic}. However, the proximal operator is not always easy to compute, especially in constraint zero-sum matrix games \cite{zhang2020sparsified}. This work proposes a new algorithm which only requires the access to the gradients of $g, h$. Our algorithm achieves a complexity upper bound $\tilde{\mathcal{O}}\left( \frac{\|\bf{A}\|_2}{\sqrt{μ_x μ_y}} + \sqrt[4]{κ_x κ_y (κ_x + κ_y)} \right)$ which has optimal dependency on the coupling condition number $\frac{\|\bf{A}\|_2}{\sqrt{μ_x μ_y}}$ up to logarithmic factors.

Xiao Guo, Xiang Li, Xiangyu Chang et al.

Eigenspace estimation is fundamental in machine learning and statistics, which has found applications in PCA, dimension reduction, and clustering, among others. The modern machine learning community usually assumes that data come from and belong to different organizations. The low communication power and the possible privacy breaches of data make the computation of eigenspace challenging. To address these challenges, we propose a class of algorithms called \textsf{FedPower} within the federated learning (FL) framework. \textsf{FedPower} leverages the well-known power method by alternating multiple local power iterations and a global aggregation step, thus improving communication efficiency. In the aggregation, we propose to weight each local eigenvector matrix with {\it Orthogonal Procrustes Transformation} (OPT) for better alignment. To ensure strong privacy protection, we add Gaussian noise in each iteration by adopting the notion of \emph{differential privacy} (DP). We provide convergence bounds for \textsf{FedPower} that are composed of different interpretable terms corresponding to the effects of Gaussian noise, parallelization, and random sampling of local machines. Additionally, we conduct experiments to demonstrate the effectiveness of our proposed algorithms.

Xiang Li, Zhihua Zhang

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for LCPs call a projection after each (stochastic) gradient descent, resulting in that the required number of projections equals that of gradient descents (or total iterations). Motivated by the recent progress in distributed optimization, we propose the delayed projection technique that calls a projection once for a while, lowering the projection frequency and improving the projection efficiency. Accordingly, we devise a series of stochastic methods for LCPs using the technique, including a variance reduced method and an accelerated one. We theoretically show that it is feasible to improve projection efficiency in both strongly convex and generally convex cases. Our analysis is simple and unified and can be easily extended to other methods using delayed projections. When applying our new algorithms to federated optimization, a newfangled and privacy-preserving subfield in distributed optimization, we obtain not only a variance reduced federated algorithm with convergence rates better than previous works, but also the first accelerated method able to handle data heterogeneity inherent in federated optimization.