arXiv subjects
Publications and source records attributed to Na Li.
Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms. For any fixed prime divisor $p$ of $|G|$, we prove that if every non-nilpotent maximal $A$-invariant subgroup of $G$ of order divisible by $p$ is normal then $G$ has a Sylow tower and $G$ is $q$-nilpotent or $q$-closed for each prime divisor $q$ of $|G|$.
Buildings cause nearly 40\% of carbon emissions in the US. Of total building emissions, HVAC systems are responsible for approximately 40-60\% and account for 15\% of global energy consumption. Despite advances in artificial intelligence, most buildings still operate as inefficiently as they did decades ago. Building optimization, perhaps more so than any other optimization problem, has enormous potential for Machine Learning (ML) driven impact on climate change, in both the short and long term. One of the biggest obstacles for building optimization is the lack of policy transfer. Most building control systems, whether simulation or learning based, don't generalize: they only work well for the building they were developed for, but not for other buildings. To solve this problem, we propose a challenge for the development of building foundation models that easily adapt to new buildings with minimal configuration and thereby enable building optimization to scale across the globe. Participants will build control policies on a set of simulated buildings, and have their policies evaluated on an unseen set of buildings. The buildings vary in size, layout, weather, material properties, and HVAC system. Successful outcomes from this initiative promise a massive leap forward in global sustainability efforts and demonstrate the great potential of ML to combat climate change.
Online decision-making faces a tension between efficient inference and long-horizon reasoning. Value-based methods rely on short-horizon bootstrapping that limits the propagation of long-term information, while trajectory optimization methods plan explicitly but must solve a high-dimensional optimization problem at every decision step. We propose Generative Trajectory Planning (GTP), a model-based framework that addresses this tension by learning a generative model as a proposal distribution over action sequences. Instead of optimizing sequences from scratch, GTP samples candidate sequences from a diffusion prior and refines them using learned dynamics, reward, and value models, enabling efficient trajectory-level reasoning. Across continuous control and long-horizon manipulation tasks, GTP matches or exceeds state-of-the-art model-free, diffusion-policy, and model-based baselines, and remains stable in regimes where strong baselines degrade. Our results suggest that generative models are best understood not as policies, but as structured proposal distributions for planning, offering a new perspective on how to integrate generative modeling with model-based decision-making.
Generating a game is not the same as making one playable. Existing code-generation approaches often translate a prompt directly into an artifact, leaving interaction-level failures undetected. We argue that game generation requires a player and study two roles for graphical user interface (GUI) agents. First, we introduce \textbf{PlaytestArena}, an evaluation environment containing 200 browser-based game-generation tasks across eight genres, each paired with rubrics of expected in-play behaviors. An independent GUI judge loads and plays each build to adjudicate these rubrics. Second, we propose \textbf{Play2Code}, in which a game agent and a rubric-blind GUI playtester iteratively generate, play, and refine games through shared memory. The playtester provides gameplay traces and actionable feedback, while a separate GPT-5.5 judge assigns final benchmark scores. Across three frontier backbones, Play2Code achieves a 66.8\% rubric pass rate, outperforming single-pass and agentic-coding baselines by 37.1 and 14.6 points, respectively. Its scores also improve monotonically across refinement rounds. Further analysis shows that GUI-agent feedback is fully logged and traceable, while its priorities vary substantially across model backbones. These results establish GUI playtesting as an evaluation and refinement signal for interactive code generation. Our project website is available at https://continual-game-generation.vercel.app/
Coding agents are beginning to move beyond purely digital tasks to tackle physical-world challenges, particularly in robotics. Existing robotics benchmarks, however, primarily focus on the performance of individual artifacts, such as policies or controllers, offering limited coverage of coding agents' broader engineering capabilities. Real-world robotics extends beyond control: agents must build, integrate, diagnose, and improve heterogeneous artifacts under resource constraints and reason from multimodal feedback. To evaluate these broader capabilities, we introduce RLE-Bench, a benchmark of robot-learning tasks spanning four representative robotics development workflows: interactive control, policy learning, perception and estimation, and mechanical design. We use diverse task-specific metrics to evaluate the artifacts submitted by the coding agents, from the success rate the agents achieved to the policy agents trained, the harness agent built, and the mechanical structures the agent designed. We aggregate these metrics into an overall RLE Index and report workflow-specific capability profiles, enabling systematic comparison of coding agents' capabilities across multiple capability dimensions. Beyond performance ranks, we also conduct in-depth case studies examining agent behavior on representative tasks, highlighting both current capabilities and limitations, and pointing to the opportunities robotics tasks have to offer for future agent training.
Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples. In this paper, we leverage such capability to design an efficient universal diffusion-based solver for parameterized black-box optimizations (BBO), where the optimizer has only black-box access to queries of the objective function at the learning stage, yet is able to reduce the additional computational cost at the inference stage for each BBO instance while also capturing the potential multi-modal landscape of non-convex objectives. To cast our formulation as a compatible generative modeling task, we introduce the notion of minimization policy as a new solution concept, which defines a sampling distribution over the solutions that should concentrate around the minimizer set for each BBO instance. We then propose Diffusion-based Iterative Minimization Policy Learning (D-IMPL), a practical generative-model-based solver for solving parameterized BBOs that employs diffusion models to learn a minimization policy, whose density is proportional to the exponential of the negated objective values, thereby amortizing the computational costs across different BBO instances. Furthermore, we demonstrate the performance of our D-IMPL algorithm by establishing a sample complexity guarantee showing that a $δ$-approximate minimization policy can be effectively learned within $O(\log(1/δ))$ iterations, and by extensive empirical evaluations over a range of constrained and unconstrained BBO tasks.
Quantum entanglement is a fundamental resource for quantum information processing and serves as a critical benchmark for quantum hardware performance. Cluster states are a special class of entangled states that serve as universal resources for measurement-based quantum computation and possess an intrinsic symmetry-protected topological order, which confers robustness against symmetry-respecting noise. Here we report the scalable preparation and verification of genuine multipartite cluster states on the 105-qubit Zuchongzhi 3.1 superconducting processor. We achieve one-dimensional cluster states of up to 95 qubits and two-dimensional cluster states of up to 72 qubits. The symmetry-protected topological cluster states exhibit input-state-dependent robustness under symmetry-breaking perturbations due to an operational parity structure that enhances the performance of measurement-based quantum computation. Furthermore, we use our two-dimensional cluster states to implement the Deutsch-Jozsa algorithm within the measurement-based quantum computation framework, achieving higher output-state fidelity compared with traditional circuit-based models and a query efficiency advantage over classical approaches. Our work establishes a scalable platform that combines large-scale entanglement generation, symmetry-protected topological order and practical quantum algorithms to enable robust, fault-tolerant measurement-based quantum computation.
Oxygen vacancies are central to the functionality of oxides, yet they typically exist as randomly distributed point defects, limiting the ability to precisely manipulate their collective behavior. Here, we report the room-temperature formation of a long-range-ordered oxygen-vacancy superstructure in single-crystalline Aurivillius-phase Bi2WO6 thin films via a mild nitrogen-plasma treatment. This structural transformation unlocks a colossal, reversible modulation of electrical conductivity by more than nine orders of magnitude, accompanied by a striking optical transition from transparent to black. Atomic-resolution imaging and spectroscopy reveal that the vacancies selectively order within the perovskite-like tungsten oxide layers, forming a coherent defect lattice that is absent in the pristine film. Oxygen-plasma treatment removes the vacancy superstructure and restores the initial state, whereas subsequent nitrogen-plasma treatment reconstructs it, enabling repeatable room-temperature switching between distinct structural, electronic and optical states. The phenomenon is also observed in another Aurivillius member, Bi2MoO6, suggesting its generality across the Aurivillius family. These findings establish a new paradigm for atomic-scale defect engineering - using gentle plasma chemistry to construct ordered defect lattices, opening avenues for reversible property modulation in complex oxides.
Motivated by a green finance problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the state system and the cost functional incorporate a conditional mean-field term. Applying continuation method and induction method, we first establish the existence and uniqueness of the conditional mean-field forward-backward stochastic differential equations with Markovian switching. Based on it, we prove the unique solvability of Hamiltonian systems associated with the two followers and the leader. Moreover, utilizing stochastic maximum principle, decoupling approach and optimal filtering technique, we obtain the optimal feedback strategies for the two followers and the leader. Employing the theoretical results, we solve the green finance problem with some numerical simulations.
The matrix-aware optimizer Muon improves large model training by balancing updates across singular directions, yet its scaling behavior and end-to-end efficiency on large Diffusion Transformers (DiTs) remain unclear. We first establish Muon's scaling behavior on DiTs from 1.3B to 15B parameters, showing that its optimization and generative quality advantages over AdamW persist across model scales. However, at scale, the 5-step Newton--Schulz iteration (NS5) performed at every optimization step, together with full-momentum materialization, introduces substantial computation and communication overhead that can offset Muon's step-efficiency advantage. We introduce \emph{Periodic Row-wise Muon}, which performs a full NS5 spectral update once every \(K\) steps and applies a low compute and communication cost row-wise constrained update based on the current momentum at the remaining steps. We further co-design a distributed implementation that operates directly on sharded momentum during non-refresh steps and accelerates spectral refreshes through bucketed all-gather and communication--computation overlap. Across all scales, Muon improves the best observed generative quality over AdamW by 12.9--19.1\%. Compared with vanilla Muon, Periodic Row-wise Muon remains within 0.5\% in best generative quality on the 1.3B--4B models and improves it by 4.5\% at 9B. It reduces optimizer time by 46.9--54.3\%, end-to-end step time by 15.7--24.3\%, and logical communication volume by 66.7\%, while reaching its respective best generative quality with 33.7--64.8\% less active training time. These results show that Periodic Row-wise Muon preserves Muon's generative quality advantage while translating it into end-to-end training efficiency for large DiTs.
Recent advances in continuous diffusion and flow-based language models (LMs) have achieved performance competitive with discrete LMs. However, existing continuous frameworks still rely on decoders supervised with cross entropy (CE) because the flow trajectories are not guaranteed to terminate at valid token embeddings. Motivated by this limitation, we introduce \textbf{ConvergeFlow}, an embedding-space flow-based LM, which constrains the data predictor to the convex hull of token embeddings and trains it solely with the mean squared error objective induced by flow matching. Under suitable regularity conditions, we prove that the resulting flow converges to valid token embeddings despite errors in the data predictor, enabling direct token prediction without a CE-supervised decoder. We further develop three sampling mechanisms for controlling the trade-off between the generative perplexity and entropy. Experiments on OpenWebText demonstrate that ConvergeFlow achieves performance competitive with existing continuous and discrete diffusion LMs. These findings demonstrate the potential of the flow-based paradigm for language modeling. Our code is available at https://github.com/Na-Li66/ConvergeFlow.
Superconducting circuits exhibit remarkable potential for constructing large-scale quantum simulation and computation systems, featuring numerous qubits, extended coherence time, and precise control. Nevertheless, the growing number of signal cables poses a challenge in dilution refrigerators due to space and heat load constraints. To overcome this issue, we experimentally implemented an optically-assisted transmission line as an alternative to coaxial cables. By modulating microwave signals on laser intensities at room temperature and regenerating the signals at a cryogenic plate within the dilution refrigerator, we demonstrated full control of superconducting qubits using photocurrent. We demonstrate and benchmark both single-qubit and two-qubit gates on frequency tunable transmon qubits, achieving fidelities of 99.915% $\pm$ 0.005% and 99.676% $\pm$ 0.041%, respectively, which have reached the requirement of the surface code.
With the rapid development of e-commerce, auto-bidding has become a key asset in optimizing advertising performance under diverse advertiser environments. The current approaches focus on reinforcement learning (RL) and generative models. These efforts imitate offline historical behaviors by utilizing a complex structure with expensive hyperparameter tuning. The suboptimal trajectories further exacerbate the difficulty of policy learning. To address these challenges, we proposes QGA, a novel Q-value regularized Generative Auto-bidding method. In QGA, we propose to plug a Q-value regularization with double Q-learning strategy into the Decision Transformer backbone. This design enables joint optimization of policy imitation and action-value maximization, allowing the learned bidding policy to both leverage experience from the dataset and alleviate the adverse impact of the suboptimal trajectories. Furthermore, to safely explore the policy space beyond the data distribution, we propose a Q-value guided dual-exploration mechanism, in which the DT model is conditioned on multiple return-to-go targets and locally perturbed actions. This entire exploration process is dynamically guided by the aforementioned Q-value module, which provides principled evaluation for each candidate action. Experiments on public benchmarks and simulation environments demonstrate that QGA consistently achieves superior or highly competitive results compared to existing alternatives. Notably, in large-scale real-world A/B testing, QGA achieves a 3.27% increase in Ad GMV and a 2.49% improvement in Ad ROI.
This paper investigates an indefinite stochastic linear-quadratic (SLQ) control problem with parameters subject to Markov regime-switching. Based on the well-posedness of the SLQ problem, we introduce a relaxed compensator that extends SLQ control problems from the positive definite case to the indefinite case. We analyze the corresponding stochastic Hamiltonian system for both unconstrained and constrained control cases under the indefinite framework and derive the corresponding optimal open-loop controls. We further investigate the associated Riccati equations for both unconstrained and constrained control cases and derive the closed-loop feedback forms of optimal controls. We illustrate the theoretical results with an equity-bond asset allocation problem under un-constrained and non-negative control constraints. Numerical simulations validate the effectiveness of the theoretical framework and demonstrate its practical value in solving complex stochastic control problems with Markov regime-switching.
Sepsis is a leading cause of mortality, yet optimal treatment policies remain contested. Existing reinforcement learning (RL) approaches learn fixed strategies for sepsis treatment, limiting adaptability to changing clinical objectives during inference. We propose EHRMPC, a framework that decouples learning patient dynamics from optimizing treatment by training a patient digital twin in the form of a generative electronic health record (EHR) model. The digital twin predicts clinical trajectories under interventions and enables model predictive control (MPC) to optimize treatments via inference-time planning over simulations. We evaluate EHR-MPC on a multicenter ICU sepsis cohort spanning 8 hospitals in the Mass General Brigham health system using both off-policy importance sampling and on-policy simulation-based evaluation. Relative to RL baselines, EHR-MPC achieves comparable off-policy performance and improved simulation performance. Unlike RL, this work frames sepsis treatment optimization as inference-time control over learned patient dynamics, establishing a general framework for decision making with generative clinical models.
Physically grounded robot intelligence requires robots to perceive, reason about, and regulate their interactions with the physical world. This capability is particularly critical in contact-sensitive manipulation, where successful task execution depends not only on visual perception and motion generation, but also on force regulation and adaptive control. In this context, recent robot learning methods have made substantial progress by integrating force, tactile, vision, language, and proprioceptive sensing into learned manipulation policies. In parallel, many systems adopt multi-phase architectures that combine high-level policies, action-refinement modules, and low-level controllers to bridge semantic task understanding with reactive physical execution. Despite these advances, existing surveys have not explicitly reviewed force- and tactile-aware robot learning from a unified perspective that jointly captures multimodal sensing and multi-phase system design. This survey addresses this gap by proposing TF-ART, a Tactile/Force-Aware Robot learning Taxonomy for multimodal and multi-phase frameworks, which maps individual methods into a unified hierarchical structure. The framework characterizes how recent works organize observation modalities, encode and fuse heterogeneous sensory inputs, generate and refine actions across multiple phases, and connect learned policies to reactive robot-end control. Building on this methodological view, we further examine the task settings and infrastructure requirements of physical interaction, thereby integrating both algorithmic and practical perspectives on force- and tactile-aware robot learning.
This paper addresses infinite-horizon continuous-time stochastic linear quadratic optimal control problems with regime switching. We propose a paradigm shift from model-based design by adopting an adaptive dynamic programming approach, specifically developing on-policy and off-policy Q-learning algorithms that learn the optimal controller solely from online state trajectory data. The theoretical core of our work consists of a complete proof of the equivalence between the on- and off-policy architectures, alongside a rigorous analysis establishing the stability of the closed-loop system and the convergence of the algorithms to the optimal solution. For computational tractability, we implement these algorithms using vectorization and Kronecker product algebra. The theoretical results are corroborated by numerical case studies that clearly demonstrate the operational effectiveness and practical feasibility of the proposed model-free control strategy.
Diffusion-based methods have achieved remarkable empirical success in solving inverse problems. However, many existing posterior samplers either lack rigorous theoretical guarantees or incur substantial computational overhead. We propose a simple and efficient algorithm, called \pddim, for solving linear inverse problems with diffusion priors via a DDIM-type sampler. Our method requires only lightweight, coordinate-wise modifications to the standard DDIM update, while explicitly incorporating the measurement model. The key idea is to perform posterior sampling separately along each singular direction of the measurement operator: for each direction, the sampler follows the learned diffusion prior when the observation signal-to-noise ratio (SNR) is below the corresponding diffusion SNR, and switches to a calibrated measurement-based predictor otherwise. We prove that the proposed sampler converges to the Bayesian posterior conditioned on the measurements. Empirical results show that the proposed sampler performs favorably against existing diffusion-based posterior samplers across a range of image restoration tasks, achieving the best performance on the majority of evaluation metrics considered. Overall, our results convert posterior sampling for noisy linear inverse problems to simple coordinate-wise DDIM updates, yielding an efficient, easy-to-implement algorithm with provable posterior consistency.