Baojian Zhou

Qi He, Huan Chen, Ya Guo et al.

Policy loss estimation remains a fundamental and long-standing challenge in reinforcement learning (RL) for diffusion language models (dLLMs). We introduce Reinforcement Learning from Denoising Feedback (RLDF), a novel training paradigm that leverages feedback obtained from rollout and training processes to facilitate accurate and efficient policy loss estimation. To balance the trade-off between computational efficiency and estimation effectiveness, RLDF optimizes the model toward the clipped clean state $\hat{x}_0$ from intermediate noisy states $x_t$, combined with weighted timestep sampling over $t$. Extensive experiments demonstrate that RLDF achieves consistent and substantial improvements in both performance and generalizability across two representative dLLM architectures, LLaDA and Dream, on multiple reasoning benchmarks. Our work lays a principled foundation for scalable reinforcement learning in diffusion language models. We build Drift, a training framework for dLLMs, available at https://github.com/ant-research/Drift.

Baojian Zhou, Steven Skiena

The Area Under the ROC Curve (AUC) is an important model metric for evaluating binary classifiers, and many algorithms have been proposed to optimize AUC approximately. It raises the question of whether the generally insignificant gains observed by previous studies are due to inherent limitations of the metric or the inadequate quality of optimization. To better understand the value of optimizing for AUC, we present an efficient algorithm, namely AUC-opt, to find the provably optimal AUC linear classifier in $\mathbb{R}^2$, which runs in $\mathcal{O}(n_+ n_- \log (n_+ n_-))$ where $n_+$ and $n_-$ are the number of positive and negative samples respectively. Furthermore, it can be naturally extended to $\mathbb{R}^d$ in $\mathcal{O}((n_+n_-)^{d-1}\log (n_+n_-))$ by calling AUC-opt in lower-dimensional spaces recursively. We prove the problem is NP-complete when $d$ is not fixed, reducing from the \textit{open hemisphere problem}. Experiments show that compared with other methods, AUC-opt achieves statistically significant improvements on between 17 to 40 in $\mathbb{R}^2$ and between 4 to 42 in $\mathbb{R}^3$ of 50 t-SNE training datasets. However, generally the gain proves insignificant on most testing datasets compared to the best standard classifiers. Similar observations are found for nonlinear AUC methods under real-world datasets.

Yuxiang Wang, Yu Xiang, Baojian Zhou et al.

Masked diffusion language models (MDMs) have recently emerged as a promising alternative to standard autoregressive large language models (AR-LLMs), yet their optimization can be substantially less stable. We study blockwise MDMs and compare them with AR-LLMs on three controlled tasks that stress different aspects of structured generation: in-context linear regression, graph path-finding, and Sudoku solving. We find that standard random-masking MDMs fail to reliably learn linear regression, exhibit high variance training dynamics on graph path-finding, while outperforming AR-LLMs on Sudoku. To mitigate these instabilities, we propose two locality aware blockwise models, namely Jigsaw and Scatter, that inject left-to-right inductive bias by enforcing autoregressive locality within blocks while preserving iterative refinement at the block level. Empirically, Jigsaw matches AR-LLM stability on linear regression and remains strong on Sudoku, while Scatter retains diffusion's planning advantage on path-finding. Our results indicate that standard random-masking MDMs, even with blockwise variants, may be a suboptimal instantiation of diffusion LMs for ordered generation, motivating models beyond random masking.

Mingyu Xu, Cheng Fang, Keyue Jiang et al.

We present Logics-STEM, a state-of-the-art reasoning model fine-tuned on Logics-STEM-SFT-Dataset, a high-quality and diverse dataset at 10M scale that represents one of the largest-scale open-source long chain-of-thought corpora. Logics-STEM targets reasoning tasks in the domains of Science, Technology, Engineering, and Mathematics (STEM), and exhibits exceptional performance on STEM-related benchmarks with an average improvement of 4.68% over the next-best model at 8B scale. We attribute the gains to our data-algorithm co-design engine, where they are jointly optimized to fit a gold-standard distribution behind reasoning. Data-wise, the Logics-STEM-SFT-Dataset is constructed from a meticulously designed data curation engine with 5 stages to ensure the quality, diversity, and scalability, including annotation, deduplication, decontamination, distillation, and stratified sampling. Algorithm-wise, our failure-driven post-training framework leverages targeted knowledge retrieval and data synthesis around model failure regions in the Supervised Fine-tuning (SFT) stage to effectively guide the second-stage SFT or the reinforcement learning (RL) for better fitting the target distribution. The superior empirical performance of Logics-STEM reveals the vast potential of combining large-scale open-source data with carefully designed synthetic data, underscoring the critical role of data-algorithm co-design in enhancing reasoning capabilities through post-training. We make both the Logics-STEM models (8B and 32B) and the Logics-STEM-SFT-Dataset (10M and downsampled 2.2M versions) publicly available to support future research in the open-source community.

Jiahe Bai, Baojian Zhou, Deqing Yang et al.

Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative methods require accessing the whole graph per iteration, making them time-consuming for large-scale graphs. While existing local solvers approximate diffusion vectors through heuristic local updates, they often operate sequentially and are typically designed for specific diffusion types, limiting their applicability. Given that diffusion vectors are highly localizable, as measured by the participation ratio, this paper introduces a novel framework for approximately solving GDEs using a local diffusion process. This framework reveals the suboptimality of existing local solvers. Furthermore, our approach effectively localizes standard iterative solvers by designing simple and provably sublinear time algorithms. These new local solvers are highly parallelizable, making them well-suited for implementation on GPUs. We demonstrate the effectiveness of our framework in quickly obtaining approximate diffusion vectors, achieving up to a hundred-fold speed improvement, and its applicability to large-scale dynamic graphs. Our framework could also facilitate more efficient local message-passing mechanisms for GNNs.

Baojian Zhou, Yifan Sun, Reza Babanezhad Harikandeh et al.

Given the damping factor $α$ and precision tolerance $ε$, \citet{andersen2006local} introduced Approximate Personalized PageRank (APPR), the \textit{de facto local method} for approximating the PPR vector, with runtime bounded by $Θ(1/(αε))$ independent of the graph size. Recently, \citet{fountoulakis2022open} asked whether faster local algorithms could be developed using $\tilde{O}(1/(\sqrtαε))$ operations. By noticing that APPR is a local variant of Gauss-Seidel, this paper explores the question of \textit{whether standard iterative solvers can be effectively localized}. We propose to use the \textit{locally evolving set process}, a novel framework to characterize the algorithm locality, and demonstrate that many standard solvers can be effectively localized. Let $\overline{\operatorname{vol}}{ (S_t)}$ and $\overlineγ_{t}$ be the running average of volume and the residual ratio of active nodes $\textstyle S_{t}$ during the process. We show $\overline{\operatorname{vol}}{ (S_t)}/\overlineγ_{t} \leq 1/ε$ and prove APPR admits a new runtime bound $\tilde{O}(\overline{\operatorname{vol}}(S_t)/(α\overlineγ_{t}))$ mirroring the actual performance. Furthermore, when the geometric mean of residual reduction is $Θ(\sqrtα)$, then there exists $c \in (0,2)$ such that the local Chebyshev method has runtime $\tilde{O}(\overline{\operatorname{vol}}(S_{t})/(\sqrtα(2-c)))$ without the monotonicity assumption. Numerical results confirm the efficiency of this novel framework and show up to a hundredfold speedup over corresponding standard solvers on real-world graphs.

Xingzhi Guo, Silong Wang, Baojian Zhou et al.

Real-world graphs grow rapidly with edge and vertex insertions over time, motivating the problem of efficiently maintaining robust node representation over evolving graphs. Recent efficient GNNs are designed to decouple recursive message passing from the learning process, and favor Personalized PageRank (PPR) as the underlying feature propagation mechanism. However, most PPR-based GNNs are designed for static graphs, and efficient PPR maintenance remains as an open problem. Further, there is surprisingly little theoretical justification for the choice of PPR, despite its impressive empirical performance. In this paper, we are inspired by the recent PPR formulation as an explicit $\ell_1$-regularized optimization problem and propose a unified dynamic graph learning framework based on sparse node-wise attention. We also present a set of desired properties to justify the choice of PPR in STOA GNNs, and serves as the guideline for future node attention designs. Meanwhile, we take advantage of the PPR-equivalent optimization formulation and employ the proximal gradient method (ISTA) to improve the efficiency of PPR-based GNNs upto 6 times. Finally, we instantiate a simple-yet-effective model (\textsc{GoPPE}) with robust positional encodings by maximizing PPR previously used as attention. The model performs comparably to or better than the STOA baselines and greatly outperforms when the initial node attributes are noisy during graph evolution, demonstrating the effectiveness and robustness of \textsc{GoPPE}.

Binbin Huang, Luo Luo, Yanghua Xiao et al.

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by $\min\{\tilde{\mathcal{O}}(R^2/ε^2), \tilde{\mathcal{O}}(m)\}$ to obtain an $ε$-approximation of the PPR vector, where $m$ denotes the number of edges in the graph and $R$ is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only $\tilde{\mathcal{O}}(1/\sqrtα)$ such linear systems, where $α$ is the damping factor. When $1/ε^2\ll m$, this implies the existence of an algorithm that computes an $\ epsilon $-approximation of the PPR vector with an overall time complexity of $\tilde{\mathcal{O}}\left(R^2 / (\sqrtαε^2)\right)$, independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Ziyang Ma, Baojian Zhou, Deqing Yang et al.

In-Context Learning (ICL) has emerged as a new paradigm in large language models (LLMs), enabling them to perform novel tasks by conditioning on a few examples embedded in the prompt. Yet, the highly nonlinear behavior of ICL for NLP tasks remains poorly understood. To shed light on its underlying mechanisms, this paper investigates whether LLMs can solve ordinary differential equations (ODEs) under the ICL setting. We formulate standard ODE problems and their solutions as sequential prompts and evaluate GPT-2 models on these tasks. Experiments on two types of ODEs show that GPT-2 can effectively learn a meta-ODE algorithm, with convergence behavior comparable to, or better than, the Euler method, and achieve exponential accuracy gains with increasing numbers of demonstrations. Moreover, the model generalizes to out-of-distribution (OOD) problems, demonstrating robust extrapolation capabilities. These empirical findings provide new insights into the mechanisms of ICL in NLP and its potential for solving nonlinear numerical problems.

Baojian Zhou, Yifan Sun, Reza Babanezhad

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with $\mathcal{O}(n^3)$ runtime and $\mathcal{O}(n^2)$ space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the \textit{online relaxation} technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret $\mathcal{O}(\sqrt{n^{1+γ}})$ when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying $\mathcal{O}(k\sqrt{n^{1+γ}})$ regret based on this relaxation. The key of FastONL is a \textit{generalized local push} method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is $\mathcal{O}(\text{vol}({\mathcal{S}})\log 1/ε)$ locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

Baojian Zhou, Yifan Sun

In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first demonstrate that two popular approximation assumptions (additive and multiplicative gap errors) are not applicable in that no cheap gap-approximate LMO oracle exists. Thus, approximate dual maximization oracles (DMO) are proposed, which approximate the inner product rather than the gap. We prove that the standard FW method using a $δ$-approximate DMO converges as $\mathcal{O}((1-δ) \sqrt{s}/δ)$ in the worst case, and as $\mathcal{O}(L/(δ^2 t))$ over a $δ$-relaxation of the constraint set. Furthermore, when the solution is on the boundary, a variant of FW converges as $\mathcal{O}(1/t^2)$ under the quadratic growth assumption. Our empirical results suggest that even these improved bounds are pessimistic, showing fast convergence in recovering real-world images with graph-structured sparsity.

Zhenhuan Yang, Baojian Zhou, Yunwen Lei et al.

In this paper, we aim to develop stochastic hard thresholding algorithms for the important problem of AUC maximization in imbalanced classification. The main challenge is the pairwise loss involved in AUC maximization. We overcome this obstacle by reformulating the U-statistics objective function as an empirical risk minimization (ERM), from which a stochastic hard thresholding algorithm (\texttt{SHT-AUC}) is developed. To our best knowledge, this is the first attempt to provide stochastic hard thresholding algorithms for AUC maximization with a per-iteration cost $Ø(b d)$ where $d$ and $b$ are the dimension of the data and the minibatch size, respectively. We show that the proposed algorithm enjoys the linear convergence rate up to a tolerance error. In particular, we show, if the data is generated from the Gaussian distribution, then its convergence becomes slower as the data gets more imbalanced. We conduct extensive experiments to show the efficiency and effectiveness of the proposed algorithms.

Baojian Zhou, Yiming Ying, Steven Skiena

The Area Under the ROC Curve (AUC) is a widely used performance measure for imbalanced classification arising from many application domains where high-dimensional sparse data is abundant. In such cases, each $d$ dimensional sample has only $k$ non-zero features with $k \ll d$, and data arrives sequentially in a streaming form. Current online AUC optimization algorithms have high per-iteration cost $\mathcal{O}(d)$ and usually produce non-sparse solutions in general, and hence are not suitable for handling the data challenge mentioned above. In this paper, we aim to directly optimize the AUC score for high-dimensional sparse datasets under online learning setting and propose a new algorithm, \textsc{FTRL-AUC}. Our proposed algorithm can process data in an online fashion with a much cheaper per-iteration cost $\mathcal{O}(k)$, making it amenable for high-dimensional sparse streaming data analysis. Our new algorithmic design critically depends on a novel reformulation of the U-statistics AUC objective function as the empirical saddle point reformulation, and the innovative introduction of the "lazy update" rule so that the per-iteration complexity is dramatically reduced from $\mathcal{O}(d)$ to $\mathcal{O}(k)$. Furthermore, \textsc{FTRL-AUC} can inherently capture sparsity more effectively by applying a generalized Follow-The-Regularized-Leader (FTRL) framework. Experiments on real-world datasets demonstrate that \textsc{FTRL-AUC} significantly improves both run time and model sparsity while achieving competitive AUC scores compared with the state-of-the-art methods. Comparison with the online learning method for logistic loss demonstrates that \textsc{FTRL-AUC} achieves higher AUC scores especially when datasets are imbalanced.

Baojian Zhou, Feng Chen, Yiming Ying

Online learning algorithms update models via one sample per iteration, thus efficient to process large-scale datasets and useful to detect malicious events for social benefits, such as disease outbreak and traffic congestion on the fly. However, existing algorithms for graph-structured models focused on the offline setting and the least square loss, incapable for online setting, while methods designed for online setting cannot be directly applied to the problem of complex (usually non-convex) graph-structured sparsity model. To address these limitations, in this paper we propose a new algorithm for graph-structured sparsity constraint problems under online setting, which we call \textsc{GraphDA}. The key part in \textsc{GraphDA} is to project both averaging gradient (in dual space) and primal variables (in primal space) onto lower dimensional subspaces, thus capturing the graph-structured sparsity effectively. Furthermore, the objective functions assumed here are generally convex so as to handle different losses for online learning settings. To the best of our knowledge, \textsc{GraphDA} is the first online learning algorithm for graph-structure constrained optimization problems. To validate our method, we conduct extensive experiments on both benchmark graph and real-world graph datasets. Our experiment results show that, compared to other baseline methods, \textsc{GraphDA} not only improves classification performance, but also successfully captures graph-structured features more effectively, hence stronger interpretability.

Baojian Zhou, Feng Chen, Yiming Ying

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity information is very specific, e.g., convex sparsity-inducing norms or $\ell^0$-norm. However, these norms cannot be directly applied to the problem of complex (non-convex) graph-structured sparsity models, which have important application in disease outbreak and social networks, etc. In this paper, we propose a stochastic gradient-based method for solving graph-structured sparsity constraint problems, not restricted to the least square loss. We prove that our algorithm enjoys a linear convergence up to a constant error, which is competitive with the counterparts in the batch learning setting. We conduct extensive experiments to show the efficiency and effectiveness of the proposed algorithms.

Feng Chen, Baojian Zhou, Adil Alim et al.

Detection of interesting (e.g., coherent or anomalous) clusters has been studied extensively on plain or univariate networks, with various applications. Recently, algorithms have been extended to networks with multiple attributes for each node in the real-world. In a multi-attributed network, often, a cluster of nodes is only interesting for a subset (subspace) of attributes, and this type of clusters is called subspace clusters. However, in the current literature, few methods are capable of detecting subspace clusters, which involves concurrent feature selection and network cluster detection. These relevant methods are mostly heuristic-driven and customized for specific application scenarios. In this work, we present a generic and theoretical framework for detection of interesting subspace clusters in large multi-attributed networks. Specifically, we propose a subspace graph-structured matching pursuit algorithm, namely, SG-Pursuit, to address a broad class of such problems for different score functions (e.g., coherence or anomalous functions) and topology constraints (e.g., connected subgraphs and dense subgraphs). We prove that our algorithm 1) runs in nearly-linear time on the network size and the total number of attributes and 2) enjoys rigorous guarantees (geometrical convergence rate and tight error bound) analogous to those of the state-of-the-art algorithms for sparse feature selection problems and subgraph detection problems. As a case study, we specialize SG-Pursuit to optimize a number of well-known score functions for two typical tasks, including detection of coherent dense and anomalous connected subspace clusters in real-world networks. Empirical evidence demonstrates that our proposed generic algorithm SG-Pursuit performs superior over state-of-the-art methods that are designed specifically for these two tasks.

Feng Chen, Baojian Zhou

Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost function is a general nonlinear function and, in particular, the sparsity constraint is defined by a graph-structured sparsity model. Existing methods explore this problem in the context of sparse estimation in linear models. To the best of our knowledge, this is the first work to present an efficient approximation algorithm, namely, Graph-structured Matching Pursuit (Graph-Mp), to optimize a general nonlinear function subject to graph-structured constraints. We prove that our algorithm enjoys the strong guarantees analogous to those designed for linear models in terms of convergence rate and approximation accuracy. As a case study, we specialize Graph-Mp to optimize a number of well-known graph scan statistic models for the connected subgraph detection task, and empirical evidence demonstrates that our general algorithm performs superior over state-of-the-art methods that are designed specifically for the task of connected subgraph detection.

Baojian Zhou, Feng Chen

Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured sparsity models have been explored, such as trees, groups, clusters, and paths, connected subgraphs have been rarely explored in the current literature. One of the main technical challenges is that there is no structured sparsity-inducing norm that can directly model the space of connected subgraphs, and there is no exact implementation of a projection oracle for connected subgraphs due to its NP-hardness. In this paper, we explore efficient approximate projection oracles for connected subgraphs, and propose two new efficient algorithms, namely, Graph-IHT and Graph-GHTP, to optimize a generic nonlinear objective function subject to connectivity constraint on the support of the variables. Our proposed algorithms enjoy strong guarantees analogous to several current methods for sparsity-constrained optimization, such as Projected Gradient Descent (PGD), Approximate Model Iterative Hard Thresholding (AM-IHT), and Gradient Hard Thresholding Pursuit (GHTP) with respect to convergence rate and approximation accuracy. We apply our proposed algorithms to optimize several well-known graph scan statistics in several applications of connected subgraph detection as a case study, and the experimental results demonstrate that our proposed algorithms outperform state-of-the-art methods.