arXiv subjects

Xiaoming Wu

Publications and source records attributed to Xiaoming Wu.

15 recordsLinked to original sources

arXiv2026

Uniform-in-Time Weak and Ergodic Error Estimates of a Nonlinearity-Explicit Full Discretization for Superlinear SPDEs Driven by Multiplicative Noise

For a class of superlinear SPDEs driven by multiplicative noise, we prove an (essentially) sharp uniform-in-time (UIT) weak convergence rate for the nonlinearity-explicit Galerkin tamed Euler method (GTEM). Under standard monotonicity assumptions, the proof combines Malliavin calculus with regularity theory for the associated backward Kolmogorov equation (BKE), leading to UIT moment, Hölder, and Malliavin estimates, along with regularity estimates for the BKE solution. These estimates, together with a weak error decomposition and Malliavin integration by parts (IBP) formula, then yield a UIT weak convergence rate $τ^ρ+λ_N^{-(ρ+γ/2)}$ for any $ρ\in (0,1)$, where $γ\in[0,1)$ quantifies the assumed spatial Sobolev regularity. Consequently, we obtain a sharp ergodic error estimate between the exact and numerical invariant measures. Numerical experiments support the theory.

math.NA↗

arXiv2026

Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs

We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise.These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results.

math.NA↗

arXiv2026

Kairos: A Regret-Aware Native World-Action Model Stack for Physical AI

We introduce \textbf{Kairos}, a regret-aware native world-action model stack for Physical AI. Kairos is motivated by the view that a physical world model should not aim to fully simulate all future pixels, but should learn and maintain the information most relevant to embodiment control: object state, spatial relations, contact conditions, task progress, action consequences, failure boundaries, and deployment uncertainty. Kairos establishes three model-side prerequisites toward this goal. First, it \textbf{learns} control-relevant information through a \textbf{Cross-Embodiment Data Curriculum}, which organizes open-world videos, human behavioral data, and robot interactions into an intervention-strength progression from passive physical observation to intentional behavior and embodied action grounding. Second, it \textbf{maintains} control-sufficient states through a unified \textbf{understanding, generation, and prediction architecture} equipped with \textbf{Hybrid Linear Temporal Attention}, where local, mid-range, and global temporal pathways support multi-timescale state maintenance under efficient inference. Third, it \textbf{deploys} these states through a \textbf{Deployment-Aware System Co-Design}, treating latency, memory footprint, and hardware compatibility as first-order constraints for future observation, action, and feedback loops. Experiments on embodied world-model benchmarks, world-action benchmarks, long-horizon generation, and inference-efficiency evaluation show that Kairos achieves superior performance while offering a favorable efficiency to capability trade-off.

cs.AI↗

arXiv2026

Graph is a Substrate Across Data Modalities

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are constructed within individual task contexts and discarded thereafter. As a result, structural regularities across modalities and tasks are repeatedly reconstructed rather than accumulated at the level of intermediate graph representations. This motivates a representation-learning question: how should graph structure be organized so that it can persist and accumulate across heterogeneous modalities and tasks? We adopt a representation-centric perspective in which graph structure is treated as a structural substrate that persists across learning contexts. To instantiate this perspective, we propose G-Substrate, a graph substrate framework that organizes learning around shared graph structures. G-Substrate comprises two complementary mechanisms: a unified structural schema that ensures compatibility among graph representations across heterogeneous modalities and tasks, and an interleaved role-based training strategy that exposes the same graph structure to multiple functional roles during learning. Experiments across multiple domains, modalities, and tasks show that G-Substrate outperforms task-isolated and naive multi-task learning methods. The codebase, model, and datasets are available at https://github.com/zmli6/G-Substrate.

cs.LG↗

arXiv2026

Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs

We first derive the exponential ergodicity of the stochastic theta method (STM) with $θ\in (1/2,1]$ for monotone jump-diffusion stochastic ordinary differential equations (SODEs) under a dissipative condition. Then we establish the weak error estimates of the backward Euler method (BEM), corresponding to the STM with $θ=1$. In particular, the time-independent estimate for the BEM in the jump-free case yields a one-order convergence rate between the exact and numerical invariant measures, answering a question left in {\it Z. Liu and Z. Liu, J. Sci. Comput. (2025) 103:87}.

math.NA↗

arXiv2026

MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

cs.LG↗

arXiv2025

FedeCouple: Fine-Grained Balancing of Global-Generalization and Local-Adaptability in Federated Learning

In privacy-preserving mobile network transmission scenarios with heterogeneous client data, personalized federated learning methods that decouple feature extractors and classifiers have demonstrated notable advantages in enhancing learning capability. However, many existing approaches primarily focus on feature space consistency and classification personalization during local training, often neglecting the local adaptability of the extractor and the global generalization of the classifier. This oversight results in insufficient coordination and weak coupling between the components, ultimately degrading the overall model performance. To address this challenge, we propose FedeCouple, a federated learning method that balances global generalization and local adaptability at a fine-grained level. Our approach jointly learns global and local feature representations while employing dynamic knowledge distillation to enhance the generalization of personalized classifiers. We further introduce anchors to refine the feature space; their strict locality and non-transmission inherently preserve privacy and reduce communication overhead. Furthermore, we provide a theoretical analysis proving that FedeCouple converges for nonconvex objectives, with iterates approaching a stationary point as the number of communication rounds increases. Extensive experiments conducted on five image-classification datasets demonstrate that FedeCouple consistently outperforms nine baseline methods in effectiveness, stability, scalability, and security. Notably, in experiments evaluating effectiveness, FedeCouple surpasses the best baseline by a significant margin of 4.3%.

cs.CV↗

arXiv2025

ADP-VRSGP: Decentralized Learning with Adaptive Differential Privacy via Variance-Reduced Stochastic Gradient Push

Differential privacy is widely employed in decentralized learning to safeguard sensitive data by introducing noise into model updates. However, existing approaches that use fixed-variance noise often degrade model performance and reduce training efficiency. To address these limitations, we propose a novel approach called decentralized learning with adaptive differential privacy via variance-reduced stochastic gradient push (ADP-VRSGP). This method dynamically adjusts both the noise variance and the learning rate using a stepwise-decaying schedule, which accelerates training and enhances final model performance while providing node-level personalized privacy guarantees. To counteract the slowed convergence caused by large-variance noise in early iterations, we introduce a progressive gradient fusion strategy that leverages historical gradients. Furthermore, ADP-VRSGP incorporates decentralized push-sum and aggregation techniques, making it particularly suitable for time-varying communication topologies. Through rigorous theoretical analysis, we demonstrate that ADP-VRSGP achieves robust convergence with an appropriate learning rate, significantly improving training stability and speed. Experimental results validate that our method outperforms existing baselines across multiple scenarios, highlighting its efficacy in addressing the challenges of privacy-preserving decentralized learning.

cs.LG↗

arXiv2025

BianCang: A Traditional Chinese Medicine Large Language Model

The surge of large language models (LLMs) has driven significant progress in medical applications, including traditional Chinese medicine (TCM). However, current medical LLMs struggle with TCM diagnosis and syndrome differentiation due to substantial differences between TCM and modern medical theory, and the scarcity of specialized, high-quality corpora. To this end, in this paper we propose BianCang, a TCM-specific LLM, using a two-stage training process that first injects domain-specific knowledge and then aligns it through targeted stimulation to enhance diagnostic and differentiation capabilities. Specifically, we constructed pre-training corpora, instruction-aligned datasets based on real hospital records, and the ChP-TCM dataset derived from the Pharmacopoeia of the People's Republic of China. We compiled extensive TCM and medical corpora for continual pre-training and supervised fine-tuning, building a comprehensive dataset to refine the model's understanding of TCM. Evaluations across 11 test sets involving 31 models and 4 tasks demonstrate the effectiveness of BianCang, offering valuable insights for future research. Code, datasets, and models are available on https://github.com/QLU-NLP/BianCang.

cs.CL↗

arXiv2025

Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs

A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems. Under a non-contractive condition, we establish a non-asymptotic error bound between the law of the numerical approximation and the target distribution in Wasserstein-1 ($\mathcal{W}_1$) distance through a time-independent weak convergence rate for the proposed schemes. As a by-product of this weak error estimate, we obtain an $\mathcal{O}(τ|\ln τ|)$ convergence rate between the exact and numerical invariant measures.

math.NA↗

arXiv2025

Choice Outweighs Effort: Facilitating Complementary Knowledge Fusion in Federated Learning via Re-calibration and Merit-discrimination

Cross-client data heterogeneity in federated learning induces biases that impede unbiased consensus condensation and the complementary fusion of generalization- and personalization-oriented knowledge. While existing approaches mitigate heterogeneity through model decoupling and representation center loss, they often rely on static and restricted metrics to evaluate local knowledge and adopt global alignment too rigidly, leading to consensus distortion and diminished model adaptability. To address these limitations, we propose FedMate, a method that implements bilateral optimization: On the server side, we construct a dynamic global prototype, with aggregation weights calibrated by holistic integration of sample size, current parameters, and future prediction; a category-wise classifier is then fine-tuned using this prototype to preserve global consistency. On the client side, we introduce complementary classification fusion to enable merit-based discrimination training and incorporate cost-aware feature transmission to balance model performance and communication efficiency. Experiments on five datasets of varying complexity demonstrate that FedMate outperforms state-of-the-art methods in harmonizing generalization and adaptation. Additionally, semantic segmentation experiments on autonomous driving datasets validate the method's real-world scalability.

cs.LG↗

arXiv2025

FedSaaS: Class-Consistency Federated Semantic Segmentation via Global Prototype Supervision and Local Adversarial Harmonization

Federated semantic segmentation enables pixel-level classification in images through collaborative learning while maintaining data privacy. However, existing research commonly overlooks the fine-grained class relationships within the semantic space when addressing heterogeneous problems, particularly domain shift. This oversight results in ambiguities between class representation. To overcome this challenge, we propose a novel federated segmentation framework that strikes class consistency, termed FedSaaS. Specifically, we introduce class exemplars as a criterion for both local- and global-level class representations. On the server side, the uploaded class exemplars are leveraged to model class prototypes, which supervise global branch of clients, ensuring alignment with global-level representation. On the client side, we incorporate an adversarial mechanism to harmonize contributions of global and local branches, leading to consistent output. Moreover, multilevel contrastive losses are employed on both sides to enforce consistency between two-level representations in the same semantic space. Extensive experiments on several driving scene segmentation datasets demonstrate that our framework outperforms state-of-the-art methods, significantly improving average segmentation accuracy and effectively addressing the class-consistency representation problem.

cs.CV↗

arXiv2024

Strong convergence rates for long-time approximations of SDEs with non-globally Lipschitz continuous coefficients

This paper is concerned with long-time strong approximations of SDEs with non-globally Lipschitz coefficients.Under certain non-globally Lipschitz conditions, a long-time version of fundamental strong convergence theorem is established for general one-step time discretization schemes. With the aid of the fundamental strong convergence theorem, we prove the expected strong convergence rate over infinite time for two types of schemes such as the backward Euler method and the projected Euler method in non-globally Lipschitz settings. Numerical examples are finally reported to confirm our findings.

math.NA↗

arXiv2022

FedSiam-DA: Dual-aggregated Federated Learning via Siamese Network under Non-IID Data

Federated learning is a distributed learning that allows each client to keep the original data locally and only upload the parameters of the local model to the server. Despite federated learning can address data island, it remains challenging to train with data heterogeneous in a real application. In this paper, we propose FedSiam-DA, a novel dual-aggregated contrastive federated learning approach, to personalize both local and global models, under various settings of data heterogeneity. Firstly, based on the idea of contrastive learning in the siamese network, FedSiam-DA regards the local and global model as different branches of the siamese network during the local training and controls the update direction of the model by constantly changing model similarity to personalize the local model. Secondly, FedSiam-DA introduces dynamic weights based on model similarity for each local model and exercises the dual-aggregated mechanism to further improve the generalization of the global model. Moreover, we provide extensive experiments on benchmark datasets, the results demonstrate that FedSiam-DA achieves outperforming several previous FL approaches on heterogeneous datasets.

cs.LG↗

arXiv2022

A Framework Based on Generational and Environmental Response Strategies for Dynamic Multi-objective Optimization

Due to the dynamics and uncertainty of the dynamic multi-objective optimization problems (DMOPs), it is difficult for algorithms to find a satisfactory solution set before the next environmental change, especially for some complex environments. One reason may be that the information in the environmental static stage can not be used well in the traditional framework. In this paper, a novel framework based on generational and environmental response strategies (FGERS) is proposed, in which response strategies are run both in the environmental change stage and the environmental static stage to obtain population evolution information of those both stages. Unlike in the traditional framework, response strategies are only run in the environmental change stage. For simplicity, the feed-forward center point strategy was chosen to be the response strategy in the novel dynamic framework (FGERS-CPS). FGERS-CPS is not only to predict change trend of the optimum solution set in the environmental change stage, but to predict the evolution trend of the population after several generations in the environmental static stage. Together with the feed-forward center point strategy, a simple memory strategy and adaptive diversity maintenance strategy were used to form the complete FGERS-CPS. On 13 DMOPs with various characteristics, FGERS-CPS was compared with four classical response strategies in the traditional framework. Experimental results show that FGERS-CPS is effective for DMOPs.

cs.NE↗