Liang Yan

Liang Yan, Tao Zhou

The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may severely distort the estimate of the posterior distribution. This error can be corrected by increasing the order of the PC expansion, but the cost for building the surrogate may increase dramatically. In this work, we seek to address this challenge by proposing an adaptive procedure to construct a multi-fidelity PC surrogate. This new strategy combines (a large number of) low-fidelity surrogate model evaluations and (a small number of) high-fidelity model evaluations, yielding an adaptive multi-fidelity approach. Here the low-fidelity surrogate is chosen as the prior-based PC surrogate, while the high-fidelity model refers to the true forward model. The key idea is to construct and refine the multi-fidelity approach over a sequence of samples adaptively determined form data, so that the approximation can eventually concentrate to the posterior distribution. We illustrate the performance of the proposed strategy through two nonlinear inverse problems. It is shown that the proposed adaptive multi-fidelity approach can improve significantly the accuracy, yet without a dramatic increase in the computational complexity. The numerical results also indicate that our new algorithm can enhance the efficiency by several orders of magnitude compared to a standard MCMC approach using only the true forward model.

Liang Yan, Gengchen Wei, Chen Yang et al.

This paper introduces a new approach to address the issue of class imbalance in graph neural networks (GNNs) for learning on graph-structured data. Our approach integrates imbalanced node classification and Bias-Variance Decomposition, establishing a theoretical framework that closely relates data imbalance to model variance. We also leverage graph augmentation technique to estimate the variance, and design a regularization term to alleviate the impact of imbalance. Exhaustive tests are conducted on multiple benchmarks, including naturally imbalanced datasets and public-split class-imbalanced datasets, demonstrating that our approach outperforms state-of-the-art methods in various imbalanced scenarios. This work provides a novel theoretical perspective for addressing the problem of imbalanced node classification in GNNs.

Fenglian Yang, Liang Yan

In this study, we consider an ensemble Kalman inversion (EKI) for the numerical solution of time-fractional diffusion inverse problems (TFDIPs). Computational challenges in the EKI arise from the need for repeated evaluations of the forward model. We address this challenge by introducing a non-intrusive reduced basis (RB) method for constructing surrogate models to reduce computational cost. In this method, a reduced basis is extracted from a set of full-order snapshots by the proper orthogonal decomposition (POD), and a doubly stochastic radial basis function (DSRBF) is used to learn the projection coefficients. The DSRBF is carried out in the offline stage with a stochastic leave-one-out cross-validation algorithm to select the shape parameter, and the outputs for new parameter values can be obtained rapidly during the online stage. Due to the complete decoupling of the offline and online stages, the proposed non-intrusive RB method -- referred to as POD-DSRBF -- provides a powerful tool to accelerate the EKI approach for TFDIPs. We demonstrate the practical performance of the proposed strategies through two nonlinear time-fractional diffusion inverse problems. The numerical results indicate that the new algorithm can achieve significant computational gains without sacrificing accuracy.

Liang Yan, Shengzhong Zhang, Bisheng Li et al.

Class imbalance in graph data presents a significant challenge for effective node classification, particularly in semi-supervised scenarios. In this work, we formally introduce the concept of geometric imbalance, which captures how message passing on class-imbalanced graphs leads to geometric ambiguity among minority-class nodes in the riemannian manifold embedding space. We provide a rigorous theoretical analysis of geometric imbalance on the riemannian manifold and propose a unified framework that explicitly mitigates it through pseudo-label alignment, node reordering, and ambiguity filtering. Extensive experiments on diverse benchmarks show that our approach consistently outperforms existing methods, especially under severe class imbalance. Our findings offer new theoretical insights and practical tools for robust semi-supervised node classification.

Liang Yan

Modern generative modeling has grown into a broad collection of related but often separately implemented paradigms, including denoising diffusion models, score-based stochastic differential equations, flow matching, variational autoencoders, normalizing flows, adversarial models, and energy-based models. For newcomers, this fragmentation makes it difficult to compare training objectives, inference procedures, sampling algorithms, and conditioning mechanisms within a single coherent codebase. We introduce V ENOM, an educational PyTorch toolkit that implements representative generative modeling families under a unified, MNIST-first interface. V ENOM emphasizes breadth, readability, reproducible entry points, and consistent training and sampling APIs rather than large-scale performance engineering. The package currently includes diffusion and score-based models, flow matching and one-step generators, variational autoencoders, normalizing flows, generative adversarial networks, and energy-based models. It provides separate training and sampling scripts, classifier and classifier-free guidance examples, bilingual tutorial notebooks, and a model-family organization that supports teaching, prototyping, and lightweight benchmarking.

Xin T. Tong, Yanyan Wang, Liang Yan

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the underlying system behavior. In this work, we propose a latent autoencoder ensemble Kalman filter (LAE-EnKF) that addresses this limitation by reformulating the assimilation problem in a learned latent space with linear and stable dynamics. The proposed method learns a nonlinear encoder--decoder together with a stable linear latent evolution operator and a consistent latent observation mapping, yielding a closed linear state-space model in the latent coordinates. This construction restores compatibility with the Kalman filtering framework and allows both forecast and analysis steps to be carried out entirely in the latent space. Compared with existing autoencoder-based and latent assimilation approaches that rely on unconstrained nonlinear latent dynamics, the proposed formulation emphasizes structural consistency, stability, and interpretability. We provide a theoretical analysis of learning linear dynamics on low-dimensional manifolds and establish generalization error bounds for the proposed latent model. Numerical experiments on representative nonlinear and chaotic systems demonstrate that the LAE-EnKF yields more accurate and stable assimilation than the standard EnKF and related latent-space methods, while maintaining comparable computational cost and data-driven.

Ancheng Xu, Zhihao Yang, Jingpeng Li et al.

E-commerce platforms increasingly rely on Large Language Models (LLMs) and Vision-Language Models (VLMs) to detect illicit or misleading product content. However, these models remain vulnerable to evasive content: inputs (text or images) that superficially comply with platform policies while covertly conveying prohibited claims. Unlike traditional adversarial attacks that induce overt failures, evasive content exploits ambiguity and context, making it far harder to detect. Existing robustness benchmarks provide little guidance for this demanding, real-world challenge. We introduce EVADE, the first expert-curated, Chinese, multimodal benchmark specifically designed to evaluate foundation models on evasive content detection in e-commerce. The dataset contains 2,833 annotated text samples and 13,961 images spanning six demanding product categories, including body shaping, height growth, and health supplements. Two complementary tasks assess distinct capabilities: Single-Violation, which probes fine-grained reasoning under short prompts, and All-in-One, which tests long-context reasoning by merging overlapping policy rules into unified instructions. Notably, the All-in-One setting significantly narrows the performance gap between partial and full-match accuracy, suggesting that clearer rule definitions improve alignment between human and model judgment. We benchmark 26 mainstream LLMs and VLMs and observe substantial performance gaps: even state-of-the-art models frequently misclassify evasive samples. By releasing EVADE and strong baselines, we provide the first rigorous standard for evaluating evasive-content detection, expose fundamental limitations in current multimodal reasoning, and lay the groundwork for safer and more transparent content moderation systems in e-commerce. The dataset is publicly available at https://huggingface.co/datasets/koenshen/EVADE-Bench.

Shaoming Duan, Zirui Wang, Chuanyi Liu et al.

Recent advances in large language models (LLMs) have significantly improved the accuracy of Text-to-SQL systems. However, a critical challenge remains: the semantic mismatch between natural language questions (NLQs) and their corresponding SQL queries. This issue is exacerbated in large-scale databases, where semantically similar attributes hinder schema linking and semantic drift during SQL generation, ultimately reducing model accuracy. To address these challenges, we introduce CRED-SQL, a framework designed for large-scale databases that integrates Cluster Retrieval and Execution Description. CRED-SQL first performs cluster-based large-scale schema retrieval to pinpoint the tables and columns most relevant to a given NLQ, alleviating schema mismatch. It then introduces an intermediate natural language representation-Execution Description Language (EDL)-to bridge the gap between NLQs and SQL. This reformulation decomposes the task into two stages: Text-to-EDL and EDL-to-SQL, leveraging LLMs' strong general reasoning capabilities while reducing semantic deviation. Extensive experiments on two large-scale, cross-domain benchmarks-SpiderUnion and BirdUnion-demonstrate that CRED-SQL achieves new state-of-the-art (SOTA) performance, validating its effectiveness and scalability. Our code is available at https://github.com/smduan/CRED-SQL.git

Rong Sha, Binglin Wang, Jun Yang et al.

Large language models (LLM) exhibit broad utility but face limitations in quantum sensor development, stemming from interdisciplinary knowledge barriers and involving complex optimization processes. Here we present QCopilot, an LLM-based multi-agent framework integrating external knowledge access, active learning, and uncertainty quantification for quantum sensor design and diagnosis. Comprising commercial LLMs with few-shot prompt engineering and vector knowledge base, QCopilot employs specialized agents to adaptively select optimization methods, automate modeling analysis, and independently perform problem diagnosis. Applying QCopilot to atom cooling experiments, we generated 10${}^{\rm{8}}$ sub-$\rmμ$K atoms without any human intervention within a few hours, representing $\sim$100$\times$ speedup over manual experimentation. Notably, by continuously accumulating prior knowledge and enabling dynamic modeling, QCopilot can autonomously identify anomalous parameters in multi-parameter experimental settings. Our work reduces barriers to large-scale quantum sensor deployment and readily extends to other quantum information systems.

Yunwen Yin, Liang Yan

In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem when only indirect observation data and a physical model are available. A fundamental question arises in light of these limitations: is it possible to enable deep learning to work on inverse problems without labeled data and to be aware of what it is learning? This work proposes a deep decomposition method (DDM) for such purposes, which does not require ground truth labels. It accomplishes this by providing physical operators associated with the scattering model to the neural network architecture. Additionally, a deep learning based data completion scheme is implemented in DDM to prevent distorting the solution of the inverse problem for limited aperture data. Furthermore, apart from addressing the ill-posedness imposed by the inverse problem itself, DDM is the first physics-aware machine learning technique that can have interpretability property for the obstacle detection. The convergence result of DDM is theoretically investigated. We also prove that adding small noise to the input limited aperture data can introduce additional regularization terms and effectively improve the smoothness of the learned inverse operator. Numerical experiments are presented to demonstrate the validity of the proposed DDM even when the incident and observation apertures are extremely limited.

Zhihao Yang, Ancheng Xu, Jingpeng Li et al.

Large language models (LLMs) face significant challenges when processing complex rule systems, as they typically treat interdependent rules as unstructured textual data rather than as logically organized frameworks. This limitation results in reasoning divergence, where models often overlook critical rule dependencies essential for accurate interpretation. Although existing approaches such as Chain-of-Thought (CoT) reasoning have shown promise, they lack systematic methodologies for structured rule processing and are particularly susceptible to error propagation through sequential reasoning chains. To address these limitations, we propose the Dynamic Adjudication Template (DAT), a novel framework inspired by expert human reasoning processes. DAT structures the inference mechanism into three methodical stages: qualitative analysis, evidence gathering, and adjudication. During the qualitative analysis phase, the model comprehensively evaluates the contextual landscape. The subsequent evidence gathering phase involves the targeted extraction of pertinent information based on predefined template elements ([placeholder]), followed by systematic verification against applicable rules. Finally, in the adjudication phase, the model synthesizes these validated components to formulate a comprehensive judgment. Empirical results demonstrate that DAT consistently outperforms conventional CoT approaches in complex rule-based tasks. Notably, DAT enables smaller language models to match, and in some cases exceed, the performance of significantly larger LLMs, highlighting its efficiency and effectiveness in managing intricate rule systems.

Liang Yan, Tao Zhou

The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional nonlinear PDEs, as EKI requires a relatively large ensemble size to guarantee its performance. In this paper, we propose an adaptive multi-fidelity polynomial chaos (PC) based EKI technique to address this challenge. Our new strategy combines a large number of low-order PC surrogate model evaluations and a small number of high-fidelity forward model evaluations, yielding a multi-fidelity approach. Especially, we present a new approach that adaptively constructs and refines a multi-fidelity PC surrogate during the EKI simulation. Since the forward model evaluations are only required for updating the low-order multi-fidelity PC model, whose number can be much smaller than the total ensemble size of the classic EKI, the entire computational costs are thus significantly reduced. The new algorithm was tested through the two-dimensional time fractional inverse diffusion problems and demonstrated great effectiveness in comparison with PC based EKI and classic EKI.

Ling Guo, Akil Narayan, Liang Yan et al.

We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations on $L^2$ spaces weighted by a probability density function. Our procedure is a particular weighted version of the approximate Fekete points method, with the weight function chosen as the (inverse) Christoffel function. Our procedure has theoretical advantages: when linear systems with optimal condition number exist, the procedure finds them. In the one-dimensional setting with any density function, our greedy procedure almost always generates optimally-conditioned linear systems. Our method also has practical advantages: our procedure is impartial to compactness of the domain of approximation, and uses only pivoted linear algebraic routines. We show through numerous examples that our sampling design outperforms competing randomized and deterministic designs when the domain is both low and high dimensional.