Xiaoyuan Cheng

Xiaoyuan Cheng, Haoyu Wang, Wenxuan Yuan et al. · cmu

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the $L_2$ regularization as an upper bound of the 2-Wasserstein distance ($W_2$), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the $L_2$ (or upper bound of $W_2$) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

Xiaoyuan Cheng, Wenxuan Yuan, Zhancun Mu et al.

Model-based reinforcement learning (RL) can be effectively supported at scale through the use of world models. However, in practice, scaling such approaches remains fundamentally limited. A commonly recognized challenge is model bias and error compounding, which degrade long-horizon predictions. Beyond these issues, we identify a more critical yet underexplored bottleneck: a structural misalignment between search and value learning in existing world model approaches. In particular, policy improvement often relies on value functions induced by a separate, non-search policy, resulting in training inconsistency and ultimately suboptimal learning. To address this limitation, we propose Model-Based Diffusion Policy Optimization (MBDPO) in world models, a framework that unifies search and policy optimization through diffusion policy representations, thereby unlocking the potential of world models for scalable policy learning. Instead of constructing an explicit planner over a learned world model, we reformulate policy optimization as a diffusion process over searched trajectories in latent world models. In this view, we extract an implicit energy function from the collected dataset that anchors the policy, enabling MBDPO to refine the score field for policy optimization while mitigating misalignment. We evaluate MBDPO across a wide range of settings, including multi-task offline pretraining, online learning, and offline-to-online fine-tuning. In the offline regime, we further investigate its scaling behavior by pretraining on large-scale datasets, observing consistent and monotonic performance gains with increasing model capacity.

Yanlong Zhao, Xiaoyuan Cheng, Huihang Liu et al.

Post-training quantization (PTQ) is an effective approach for deploying large language models (LLMs) under memory and latency constraints. Most existing PTQ methods determine quantization parameters by minimizing a layer-wise reconstruction error on a predetermined calibration dataset, usually optimized via either scale search or Gram-based methods. However, from the perspective of generalization risk, existing calibration objectives of PTQ based only on empirical reconstruction error on limited or unrepresentative calibration data could move the quantized weights away from the original weights. This may cause the generalization risk to diverge, potentially degrading downstream performance. To address this issue, we propose \emph{Saliency-Aware Regularized Quantization Calibration} (SARQC) a unified framework that augments the standard PTQ objective with a saliency-aware regularization term. This term encourages quantized weights to stay close to the original weights during calibration, leading to improved generalization during inference. SARQC integrates seamlessly into existing PTQ pipelines, enhancing both scale search and Gram-based methods under a unified formulation. Extensive experiments on dense and Mixture-of-Experts LLMs demonstrate consistent improvements in perplexity and zero-shot accuracy, without additional computational overhead during inference.

Kewei Zhu, Yanze Xin, Jinwei Hu et al.

Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational techniques, reducing prediction accuracy. To address these limitations, we propose a novel method: a Physics-Spatiotemporal Masked Autoencoder. This method integrates convolutional autoencoders for spatial feature extraction with masked autoencoders optimised for irregular time series, leveraging attention mechanisms to reconstruct the entire physical sequence in a single prediction pass. The model avoids the need for data imputation while preserving physical integrity of the system. Here, 'physics' refers to high-dimensional fields generated by underlying dynamical systems, rather than the enforcement of explicit physical constraints or PDE residuals. We evaluate this approach on multiple simulated datasets and real-world ocean temperature data. The results demonstrate that our method achieves significant improvements in prediction accuracy, robustness to nonlinearities, and computational efficiency over traditional convolutional and recurrent network methods. The model shows potential for capturing complex spatiotemporal patterns without requiring domain-specific knowledge, with applications in climate modelling, fluid dynamics, ocean forecasting, environmental monitoring, and scientific computing.

Xiaoyuan Cheng, Wenxuan Yuan, Yiming Yang et al.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Binjie Guo, Hanyu Zheng, Guowei Su et al.

Recent years have witnessed significant progress in reinforcement learning, especially with Zero-like paradigms, which have greatly boosted the generalization and reasoning abilities of large-scale language models. Nevertheless, existing frameworks are often plagued by high implementation complexity and poor reproducibility. To tackle these challenges, we present AlphaZero-Edu, a lightweight, education-focused implementation built upon the mathematical framework of AlphaZero. It boasts a modular architecture that disentangles key components, enabling transparent visualization of the algorithmic processes. Additionally, it is optimized for resource-efficient training on a single NVIDIA RTX 3090 GPU and features highly parallelized self-play data generation, achieving a 3.2-fold speedup with 8 processes. In Gomoku matches, the framework has demonstrated exceptional performance, achieving a consistently high win rate against human opponents. AlphaZero-Edu has been open-sourced at https://github.com/StarLight1212/AlphaZero_Edu, providing an accessible and practical benchmark for both academic research and industrial applications.

Xiaoyuan Cheng, Yiming Yang, Xiaohang Tang et al.

An efficient way to control systems with unknown nonlinear dynamics is to find an appropriate embedding or representation for simplified approximation (e.g. linearization), which facilitates system identification and control synthesis. Nevertheless, there has been a lack of embedding methods that can guarantee (i) embedding the dynamical system comprehensively, including the vector fields (ODE form) of the dynamics, and (ii) preserving the consistency of control effect between the original and latent space. To address these challenges, we propose Koopman Embedded Equivariant Control (KEEC) to learn an embedding of the states and vector fields such that a Koopman operator is approximated as the latent dynamics. Due to the Koopman operator's linearity, learning the latent vector fields of the dynamics becomes simply solving linear equations. Thus in KEEC, the analytical form of the greedy control policy, which is dependent on the learned differential information of the dynamics and value function, is also simplified. Meanwhile, KEEC preserves the effectiveness of the control policy in the latent space by preserving the metric in two spaces. Our algorithm achieves superior performances in the experiments conducted on various control domains, including the image-based Pendulum, Lorenz-63 and the wave equation. The code is available at https://github.com/yyimingucl/Koopman-Embedded-Equivariant-Control.

Chenyang Yuan, Xiaoyuan Cheng

Intelligent access point (AP) deployment remains challenging in next-generation wireless networks due to complex indoor geometries and signal propagation. We firstly benchmark general-purpose large language models (LLMs) as agentic optimizers for AP planning and find that, despite strong wireless domain knowledge, their dependence on external verifiers results in high computational costs and limited scalability. Motivated by these limitations, we study generative inference models guided by a unified reward function capturing core AP deployment objectives across diverse floorplans. We show that diffusion samplers consistently outperform alternative generative approaches. The diffusion process progressively improves sampling by smoothing and sharpening the reward landscape, rather than relying on iterative refinement, which is effective for non-convex and fragmented objectives. Finally, we introduce a large-scale real-world dataset for indoor AP deployment, requiring over $50k$ CPU hours to train general reward functions, and evaluate in- and out-of-distribution generalization and robustness. Our results suggest that diffusion-based generative inference with a unified reward function provides a scalable and domain-agnostic foundation for indoor AP deployment planning.

Yiming Yang, Xiaoyuan Cheng, Yi He et al.

Diffusion models have recently emerged as powerful learned priors for Bayesian inverse problems (BIPs). Diffusion-based solvers rely on a presumed likelihood for the observations in BIPs to guide the generation process. However, the link between likelihood and recovery quality for BIPs is unclear in previous works. We bridge this gap by characterizing the posterior approximation error and proving the \emph{stability} of the diffusion-based solvers. Meanwhile, an immediate result of our findings on stability demonstrates the lack of robustness in diffusion-based solvers, which remains unexplored. This can degrade performance when the presumed likelihood mismatches the unknown true data generation processes. To address this issue, we propose a simple yet effective solution, \emph{robust diffusion posterior sampling}, which is provably \emph{robust} and compatible with existing gradient-based posterior samplers. Empirical results on scientific inverse problems and natural image tasks validate the effectiveness and robustness of our method, showing consistent performance improvements under challenging likelihood misspecifications.

Yiming Yang, Xiaoyuan Cheng, Daniel Giles et al.

Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings. Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results. In this paper, we propose Tensor-Var, a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space. Moreover, our method provides a new perspective for solving 4D-Var in a linear way, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To handle large-scale problems, we propose a method to learn deep features using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving a 10- to 20-fold speed improvement.

Xiaoyuan Cheng, Wenxuan Yuan, Boyang Li et al.

Diffusion policy sampling enables reinforcement learning (RL) to represent multimodal action distributions beyond suboptimal unimodal Gaussian policies. However, existing diffusion-based RL methods primarily focus on offline settings for reward maximization, with limited consideration of safety in online settings. To address this gap, we propose Augmented Lagrangian-Guided Diffusion (ALGD), a novel algorithm for off-policy safe RL. By revisiting optimization theory and energy-based model, we show that the instability of primal-dual methods arises from the non-convex Lagrangian landscape. In diffusion-based safe RL, the Lagrangian can be interpreted as an energy function guiding the denoising dynamics. Counterintuitively, direct usage destabilizes both policy generation and training. ALGD resolves this issue by introducing an augmented Lagrangian that locally convexifies the energy landscape, yielding a stabilized policy generation and training process without altering the distribution of the optimal policy. Theoretical analysis and extensive experiments demonstrate that ALGD is both theoretically grounded and empirically effective, achieving strong and stable performance across diverse environments.

Xiao Xue, Marco F. P. ten Eikelder, Mingyang Gao et al.

The lattice Boltzmann equation (LBE), rooted in kinetic theory, provides a powerful framework for capturing complex flow behaviour by describing the evolution of single-particle distribution functions (PDFs). Despite its success, solving the LBE numerically remains computationally intensive due to strict time-step restrictions imposed by collision kernels. Here, we introduce a physics-informed neural operator framework for the LBE that enables prediction over large time horizons without step-by-step integration, effectively bypassing the need to explicitly solve the collision kernel. We incorporate intrinsic moment-matching constraints of the LBE, along with global equivariance of the full distribution field, enabling the model to capture the complex dynamics of the underlying kinetic system. Our framework is discretization-invariant, enabling models trained on coarse lattices to generalise to finer ones (kinetic super-resolution). In addition, it is agnostic to the specific form of the underlying collision model, which makes it naturally applicable across different kinetic datasets regardless of the governing dynamics. Our results demonstrate robustness across complex flow scenarios, including von Karman vortex shedding, ligament breakup, and bubble adhesion. This establishes a new data-driven pathway for modelling kinetic systems.

Yuqing Hu, Xiaoyuan Cheng, Suhang Wang et al.

The world is increasingly urbanizing and the building industry accounts for more than 40% of energy consumption in the United States. To improve urban sustainability, many cities adopt ambitious energy-saving strategies through retrofitting existing buildings and constructing new communities. In this situation, an accurate urban building energy model (UBEM) is the foundation to support the design of energy-efficient communities. However, current UBEM are limited in their abilities to capture the inter-building interdependency due to their dynamic and non-linear characteristics. Those models either ignored or oversimplified these building interdependencies, which can substantially affect the accuracy of urban energy modeling. To fill the research gap, this study proposes a novel data-driven UBEM synthesizing the solar-based building interdependency and spatial-temporal graph convolutional network (ST-GCN) algorithm. Especially, we took a university campus located in downtown Atlanta as an example to predict the hourly energy consumption. Furthermore, we tested the feasibility of the proposed model by comparing the performance of the ST-GCN model with other common time-series machine learning models. The results indicate that the ST-GCN model overall outperforms all others. In addition, the physical knowledge embedded in the model is well interpreted. After discussion, it is found that data-driven models integrated engineering or physical knowledge can significantly improve the urban building energy simulation.