arXiv subjects

Chenghan Xie

Publications and source records attributed to Chenghan Xie.

4 recordsLinked to original sources

arXiv2026

Sobolev Regularized Score Difference Estimation in Diffusion Models

Estimating the difference of two Stein's score functions is a fundamental problem in generative modeling. In particular, score differences arise naturally in transfer learning, where the score difference provides the mechanism for adapting a pre-trained model to a new target distribution, and in diffusion model-based post-training methods such as discriminator guidance. Existing estimators for score differences in these settings either lack of statistical consistency or are difficult to scale up in high-dimensions. We propose a statistically consistent and scalable estimator for score differences based on Sobolev regularization, which plays a crucial role in ensuring consistency and stablizing the training in the small-sample regime. Mathematically, we establish a convergence rate of $O(n^{-\frac{s-1}{d+2s-2}})$ where $d$ is the dimension and $s$ denotes the smoothness of the underlying densities, and provide a minimax lower bound of $\tildeΩ(n^{-\frac{2(s-1)}{d+2s}})$ (in mean-squared error). Empirically, our estimator exhibits significantly improved stability in small-sample regimes compared to existing methods. We demonstrate its effectiveness on real-world tasks, including transfer learning for ECG signal generation, where it substantially outperforms non-regularized score difference estimators in downstream classification performance.

stat.ML↗

arXiv2026

ChartWalker: Benchmarking the Cross-Chart RAG Task with Hierarchical Knowledge Graphs

Cross-Chart Retrieval-Augmented Generation (RAG) is critical for complex multi-modal analytical tasks in scientific, business, and political domains. However, existing benchmarks either focus on tables, which are well-structured and textualized, or generate cross-chart questions by simply extracting key points, which often induces lexical overlap between queries and evidence and yields logically inconsistent reasoning chains. To address this, we introduce ChartWalker, a novel framework for constructing challenging cross-chart RAG tasks. ChartWalker features a hierarchical knowledge graph construction method tailored to charts, which organizes entities and relations by granularity to preserve analytical structure. We then propose a structure-aware sampling algorithm that synthesizes semantically coherent, multi-hop reasoning paths, enabling explicit control over query difficulty and granularity for QA generation. Built with this framework, we release ChartWalker-Bench, a comprehensive benchmark spanning diverse domains and cross-chart query types. Extensive evaluations across major RAG paradigms reveal significant performance gaps, underscoring the benchmark's difficulty and utility. Furthermore, we provide ChartWalker-Agent, an agentic baseline to facilitate analysis and inspire future system design.

cs.IR↗

arXiv2025

Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO). We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption. We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions. Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of $\mathcal{O}(ε^{-3.5})$ for convergence to second-order stationary points. By incorporating variance reduction, the second-order trust region method obtains an even better complexity of $\mathcal{O}(ε^{-3})$, matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization. Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods.

math.OC↗

arXiv2023

Stochastic Dimension-reduced Second-order Methods for Policy Optimization

In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy gradient methods. Specifically, we propose a dimension-reduced second-order method (DR-SOPO) which repeatedly solves a projected two-dimensional trust region subproblem. We show that DR-SOPO obtains an $\mathcal{O}(ε^{-3.5})$ complexity for reaching approximate first-order stationary condition and certain subspace second-order stationary condition. In addition, we present an enhanced algorithm (DVR-SOPO) which further improves the complexity to $\mathcal{O}(ε^{-3})$ based on the variance reduction technique. Preliminary experiments show that our proposed algorithms perform favorably compared with stochastic and variance-reduced policy gradient methods.

math.OC↗