arXiv subjects

Liang Yan

Publications and source records attributed to Liang Yan.

At least 19 recordsLinked to original sources

arXiv2026

Venom: A PyTorch Generative Modeling Toolkit

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.

cs.LG↗

arXiv2026

Latent Autoencoder Ensemble Kalman Filter for Nonlinear Data assimilation

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.

cs.LG↗

arXiv2025

Structuring Reasoning for Complex Rules Beyond Flat Representations

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.

cs.AI↗

arXiv2025

CRED-SQL: Enhancing Real-world Large Scale Database Text-to-SQL Parsing through Cluster Retrieval and Execution Description

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

cs.CL↗

arXiv2025

LLM-based Multi-Agent Copilot for Quantum Sensor

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-$\rm{\mu}$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.

quant-ph↗

arXiv2025

A Novel Two-Dimensional Smoothing Algorithm

Smoothing and filtering two-dimensional sequences are fundamental tasks in fields such as computer vision. Conventional filtering algorithms often rely on the selection of the filtering window, limiting their applicability in certain scenarios. To this end, we propose a novel Two-Dimensional Smoothing (TDS) algorithm for the smoothing and filtering problem of two-dimensional sequences. Typically, the TDS algorithm does not require assumptions about the type of noise distribution. It is simple and easy to implement compared to conventional filtering methods, such as 2D adaptive Wiener filtering and Gaussian filtering. The TDS algorithm can effectively extract the trend contained in the two-dimensional sequence and reduce the influence of noise on the data by adjusting only a single parameter. In this work, unlike existing algorithms that depend on the filtering window, we introduce a loss function, where the trend sequence is identified as the solution when this loss function takes a minimum value. Therefore, within the framework of the TDS algorithm, a general two-dimensional sequence can be innovatively decomposed into a trend sequence and a fluctuation sequence, in which the trend sequence contains the main features of the sequence and the fluctuation sequence contains the detailed features or noise interference of the sequence. To ensure the reliability of the TDS algorithm, a crucial lemma is first established, indicating that the trend sequence and fluctuation sequence obtained by the TDS algorithm are existent and unique when the global smoothing parameter is determined. Three modified algorithms are then proposed based on the TDS algorithm, with corresponding lemmas and corollaries demonstrating their reliability. Finally, the accuracy and effectiveness of the TDS algorithm are further verified through numerical simulations and image processing cases.

cs.IT↗

arXiv2025

EVADE-Bench: Multimodal Benchmark for Evaluating and Enhancing Evasive Content Detection

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, which refers to inputs that have been deliberately modified through techniques such as word splitting, euphemistic language, or image cropping to conceal policy violations while still conveying prohibited claims. Crucially, detecting such content requires a model to simultaneously master two capabilities: accurately comprehending complex rules, and correctly inferring the true intent behind deliberately obfuscated multimodal inputs. While prior work has separately explored LLM reasoning over complex rules and LLM-based detection of evasive content, no existing benchmark combines both within a unified evaluation framework. This gap is particularly consequential in e-commerce, where accurate moderation demands that both capabilities operate in concert. To address this gap, we introduce EVADE-Bench, the first expert-curated Chinese multimodal benchmark specifically designed to evaluate LLMs and VLMs on evasive content detection in real-world e-commerce scenarios. Our comprehensive evaluation of 26 open- and closed-source LLMs and VLMs reveals that even state-of-the-art models frequently misclassify evasive samples. We further demonstrate that clearer rule categorization significantly improves model prediction consistency and reduces false predictions, highlighting the critical role of benchmark design in enabling reliable evaluation. To explore paths for performance improvement, we investigate the feasibility of multi-agent decomposition for multimodal reasoning, wherein visual description and logical inference are decoupled into separate agents, and find that this strategy yields notable accuracy gains.

cs.CL↗

arXiv2024

TCSR-SQL: Towards Table Content-aware Text-to-SQL with Self-retrieval

Large Language Model-based (LLM-based) Text-to-SQL methods have achieved important progress in generating SQL queries for real-world applications. When confronted with table content-aware questions in real-world scenarios, ambiguous data content keywords and nonexistent database schema column names within the question lead to the poor performance of existing methods. To solve this problem, we propose a novel approach towards Table Content-aware Text-to-SQL with Self-Retrieval (TCSR-SQL). It leverages LLM's in-context learning capability to extract data content keywords within the question and infer possible related database schema, which is used to generate Seed SQL to fuzz search databases. The search results are further used to confirm the encoding knowledge with the designed encoding knowledge table, including column names and exact stored content values used in the SQL. The encoding knowledge is sent to obtain the final Precise SQL following multi-rounds of generation-execution-revision process. To validate our approach, we introduce a table-content-aware, question-related benchmark dataset, containing 2115 question-SQL pairs. Comprehensive experiments conducted on this benchmark demonstrate the remarkable performance of TCSR-SQL, achieving an improvement of at least 27.8% in execution accuracy compared to other state-of-the-art methods.

cs.DB↗

arXiv2024

A novel direct imaging method for passive inverse obstacle scattering problem

This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges, leading to the failure of classical direct sampling methods that rely on scattered field measurements. To address this issue, we introduce the Doubly Cross-Correlating Method (DCM), a novel direct imaging scheme that consists of two major steps. Initially, DCM creates a cross-correlation between two passive measurements. This specially designed cross-correlation effectively handles the uncontrollability of incident sources and connects to the active scattering model via the Helmholtz-Kirchhoff identity. Subsequently, this cross-correlation is used to create a correlation-based imaging function that can qualitatively identify the obstacle. The stability and resolution of DCM are theoretically analyzed. Extensive numerical examples, including scenarios with two closely positioned obstacles and multiscale obstacles, demonstrate that DCM is computationally efficient, stable, and fast.

math.NA↗

arXiv2024

Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem

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.

math.NA↗

arXiv2023

Rethinking Semi-Supervised Imbalanced Node Classification from Bias-Variance Decomposition

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.

cs.LG↗

arXiv2023

Adaptive operator learning for infinite-dimensional Bayesian inverse problems

The fundamental computational issues in Bayesian inverse problems (BIP) governed by partial differential equations (PDEs) stem from the requirement of repeated forward model evaluations. A popular strategy to reduce such costs is to replace expensive model simulations with computationally efficient approximations using operator learning, motivated by recent progress in deep learning. However, using the approximated model directly may introduce a modeling error, exacerbating the already ill-posedness of inverse problems. Thus, balancing between accuracy and efficiency is essential for the effective implementation of such approaches. To this end, we develop an adaptive operator learning framework that can reduce modeling error gradually by forcing the surrogate to be accurate in local areas. This is accomplished by adaptively fine-tuning the pre-trained approximate model with training points chosen by a greedy algorithm during the posterior evaluation process. To validate our approach, we use DeepOnet to construct the surrogate and unscented Kalman inversion (UKI) to approximate the BIP solution, respectively. Furthermore, we present a rigorous convergence guarantee in the linear case using the UKI framework. The approach is tested on a number of benchmarks, including the Darcy flow, the heat source inversion problem, and the reaction-diffusion problem. The numerical results show that our method can significantly reduce computational costs while maintaining inversion accuracy.

math.NA↗

arXiv2023

Geometric Imbalance in Semi-Supervised Node Classification

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.

cs.LG↗

arXiv2023

Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation

This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (FI-PINNs). In our previous work \cite{gao2022failure}, we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator, where the truncated Gaussian model has been adopted for estimating the indicator. In this work, we present two novel extensions to FI-PINNs. The first extension consist in combining with a re-sampling technique, so that the new algorithm can maintain a constant training size. This is achieved through a cosine-annealing, which gradually transforms the sampling of collocation points from uniform to adaptive via training progress. The second extension is to present the subset simulation algorithm as the posterior model (instead of the truncated Gaussian model) for estimating the error indicator, which can more effectively estimate the failure probability and generate new effective training points in the failure region. We investigate the performance of the new approach using several challenging problems, and numerical experiments demonstrate a significant improvement over the original algorithm.

math.NA↗

arXiv2022

Failure-informed adaptive sampling for PINNs

Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can vary dramatically with different sampling procedures. For instance, a fixed set of (prior chosen) training points may fail to capture the effective solution region (especially for problems with singularities). To overcome this issue, we present in this work an adaptive strategy, termed the failure-informed PINNs (FI-PINNs), which is inspired by the viewpoint of reliability analysis. The key idea is to define an effective failure probability based on the residual, and then, with the aim of placing more samples in the failure region, the FI-PINNs employs a failure-informed enrichment technique to adaptively add new collocation points to the training set, such that the numerical accuracy is dramatically improved. In short, similar as adaptive finite element methods, the proposed FI-PINNs adopts the failure probability as the posterior error indicator to generate new training points. We prove rigorous error bounds of FI-PINNs and illustrate its performance through several problems.

math.NA↗

arXiv2022

Hyperon physics at BESIII

Using the largest $J/\psi$ and $\psi(3686)$ data samples collected at the BESIII experiment, the hyperon anti-hyperon pairs are generated in their quantum entangle system. The polarization of hyperon has been observed, which makes it possible to measure the decay parameters of hyperon and anti-hyperon precisely. The CP conservation observables have been estimated which is important to test the Standard Model. In the meanwhile, the branching fractions and angular distributions related to hyperon pair production have been measured.

hep-ex↗

arXiv2022

A Less Uncertain Sampling-Based Method of Batch Bayesian Optimization

This paper presents a method called sampling-computation-optimization (SCO) to design batch Bayesian optimization. SCO does not construct new high-dimensional acquisition functions but samples from the existing one-site acquisition function to obtain several candidate samples. To reduce the uncertainty of the sampling, the general discrepancy is computed to compare these samples. Finally, the genetic algorithm and switch algorithm are used to optimize the design. Several strategies are used to reduce the computational burden in the SCO. From the numerical results, the SCO designs were less uncertain than those of other sampling-based methods. As for application in batch Bayesian optimization, SCO can find a better solution when compared with other batch methods in the same dimension and batch size. In addition, it is also flexible and can be adapted to different one-site methods. Finally, a complex experimental case is given to illustrate the application value and scenario of SCO method.

math.OC↗

arXiv2021

An acceleration strategy for randomize-then-optimize sampling via deep neural networks

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO may be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel strategy to substantially reduce the computation burden of RTO by using a goal-oriented deep neural networks (DNN) surrogate approach. In particular, the training points for the DNN-surrogate are drawn from a local approximated posterior distribution, and it is shown that the resulting algorithm can provide a flexible and efficient sampling algorithm, which converges to the direct RTO approach. We present a Bayesian inverse problem governed by a benchmark elliptic PDE to demonstrate the computational accuracy and efficiency of our new algorithm (i.e., DNN-RTO). It is shown that with our algorithm, one can significantly outperform the traditional RTO.

math.NA↗