arXiv subjects
Publications and source records attributed to Hao Xu.
We prove the three balancing inequalities conjectured by the authors about 20 years ago: moving one unit from a larger index to a smaller one cannot decrease a mixed tautological intersection number, whether the two distinguished insertions are psi classes, kappa classes, or Hodge Chern classes.
Malocclusion skeletal grading is a fundamental task in orthodontics, critical for diagnosis and treatment planning. Traditionally, cone-beam computed tomography (CBCT) is used for visual measurement, and the reconstructed lateral cephalograms are handed over to expert dentists for diagnosis. However, manual review is time-consuming, labor-intensive, and subject to inter-operator variability. Therefore, an automatic CBCT-based system is needed for reliable malocclusion skeletal grading. In this case, we develop TeethGNN, a novel graph-based framework designed to combine CBCT image features with morphological information for accurate and efficient malocclusion grading. TeethGNN utilizes a decoupled learnable decoder to directly predict key morphological indicators from CBCT images, eliminating the need for manual measurements. These morphological features are then fused with image features using a graph neural network (GNN), which effectively models the relationships between the modalities. To further enhance robustness and calibration, we introduce a collaborative calibration strategy. This strategy combines multi-scale graph adversarial perturbation for explicit calibration and nonlinear topological graph calibration for implicit confidence adjustment. Extensive experiments and ablation studies on our collected clinical dataset demonstrate that our malocclusion measurement system achieves 77.08\% in accuracy and 89.61\% in AUC, outperforming the compared state-of-the-art methods. These results validate the effectiveness of graph-based multimodal fusion and collaborative calibration in improving malocclusion grading performance. Our system shows strong potential for advancing computer-aided orthodontic diagnosis, providing an accurate and reliable solution for vision-based clinical measurement and diagnosis.
In their celebrated work on the large-genus asymptotic expansion of Weil--Petersson volumes, Mirzakhani and Zograf left open the question of whether the Weil--Petersson constant satisfies $C_{\mathrm{WP}}=π^{-1/2}$. We resolve the conjecture affirmatively. Our strategy is to consider a family of spectral curves interpolating between $y=z-4z^3$ and $y=\sin(2πz)/(2π)$. For each fixed number $n\geq2$ of marked points, we normalize the cusp coefficients using the action integral and the derivative at its first positive zero. We prove that the logarithmic derivatives of these normalized coefficients with respect to the family parameter are $O_n(g^{-1})$, uniformly along the family. The proof combines the descendant recursion, positivity, the dilaton equation, KdV, and coefficient asymptotics for the Painlevé I equation.
Large language model (LLM) agents increasingly use tools to complete tasks in stateful environments. However, many training environments remain largely static apart from changes caused by the agent's own actions, whereas external events introduced by other users, services, or sudden contingencies in real environments can invalidate ongoing plans. To address this gap, we introduce DynaWeave, an automated synthesis framework that transforms existing static tasks into verifiable dynamic scenarios. The framework generates exogenous events relevant to each task, covering changes in task requirements, environment state, and external information. It uses directed acyclic graphs (DAGs) to represent dependencies between events and an execution engine to activate them during agent interaction. A dynamic verifier revises only the evaluation checks affected by events that actually occur and retains all other checks. Using DynaWeave, we collect 2,095 verified interaction trajectories across 36 environments and use them for supervised fine-tuning of Qwen3.5 models. Experiments on Gaia2, CostBench, and ToolMaze show that DynaWeave achieves consistent improvements in overall performance across all three evaluated model sizes, increasing the task completion rate on CostBench by 67.34 percentage points and even exceeding the performance of Gemini-3.1-Pro-Preview on ToolMaze. These results support dynamic scenario synthesis as a practical approach to training agents to adapt to changing environments. Our code is available at https://github.com/Miaow-Lab/DynaWeave.
We investigate the relation between spectral localization and entanglement harvesting in an analytically solvable model of two qubits coupled to a leaky single-mode cavity, which in turn couples to a continuous electromagnetic bath. We derive the no-jump concurrence at a prescribed reference gate time in closed form, $\mathcal C_g(Q)=2e^{-π/(2Q)}(1+e^{-π/(2Q)})/(1+3e^{-π/Q})$, where $Q\equiv|Δ|/κ$ is the ratio of the qubit-cavity detuning $Δ$ to the cavity linewidth $κ$. This reference time is inherited from the first maximally entangling unitary gate. At finite loss, $\mathcal C_g$ is the conditional concurrence at this prescribed readout time. In the high-$Q$ limit, $\mathcal C_g\simeq1-π^2/(16Q^2)$, while in the low-$Q$ limit it decays exponentially. For the Lorentzian spectral family, $Q$ is proportional to a detuning-normalized inverse participation ratio and simultaneously measures the balance between coherent exchange and collective decay. This yields a compact, model-specific description of the crossover from nearly unit conditional entanglement to overdamped suppression. The predicted $\mathcal C_g(Q)$ curve can, in principle, be examined in circuit QED with ideal monitoring and no-jump post-selection.
Humanoid behavior foundation models aim to acquire reusable whole-body control policies from broad human motion priors, enabling a single controller to produce diverse and expressive behaviors. However, existing motion-centric foundation policies largely assume that the reference motion is already physically compatible with the robot's surroundings. This assumption breaks when the demonstrator, operator, and robot inhabit different environments: a human motion may specify the intended behavior, but not the footholds, clearance, body height, or contact timing required by the robot's local terrain. We introduce \emph{Perceptive Behavior Foundation Model} (Perceptive BFM), a terrain-aware humanoid control framework that grounds human motion priors in robot-centric perception. The model preserves raw kinematic motion references as the behavioral interface, while using local terrain observations to adapt contacts, posture, and timing. To provide scalable terrain supervision, we develop \emph{terrain-conformal reference synthesis} (TCRS), which converts locomotion-oriented human motion clips into terrain-consistent references through contact-aware foothold construction, foot-geometry-aware swing optimization, support-aware root reconstruction, collision repair, and multi-point inverse kinematics. We then train a blind adapted-reference teacher and transfer its terrain-conformal behavior to a deployed raw-reference student through target-frame action alignment. The student is an identity-gated Transformer tracker whose terrain features enter through residual pathways initialized to preserve the motion-tracking prior and trained to produce local corrections only when needed.
Spatial memory enables robots to reuse past observations for localization, navigation, and question answering. Designing such memory involves jointly deciding what to retain and how to retrieve it for diverse semantic, metric, and temporal needs. We investigate whether coding agents can automate this design process through iterative implementation and evaluation. Under a fixed development budget, a Designer Agent writes and revises code for memory construction and retrieval using feedback from a fixed Query Agent. The resulting implementations are frozen before building memories from held-out observation histories, without access to downstream questions, and evaluated across five complementary task tracks using the same Query Agent. Across three independent design searches, Codex / GPT-6 Astra averages 44.23 on the equally weighted five-track score, versus 29.32 for ReMEmbR, the strongest evaluated baseline supporting all five tracks, a 50.9% relative improvement. Qualitative analysis relates performance differences to evidence retention and retrieval, while identifying grounding and evidence-use failures. These results demonstrate the potential of coding agents to automate spatial memory design, while revealing task-dependent trade-offs in performance and computational cost. Project page: https://ba-fa-3344.github.io/.
Object retrieval in 3D scenes remains difficult when queries combine hierarchical context, attributes, negation, and chained spatial relations. Existing semantic maps, scene graphs, and agentic memory support open-vocabulary retrieval, but jointly resolving these constraints remains challenging. In this work, we propose INHerit-SG, an incremental hierarchical semantic scene graph with an accompanying retrieval method for complex embodied retrieval. Asynchronous geometric and semantic processing and structural event-driven maintenance organize observations into a hierarchy whose node semantics and spatial relations are recorded as natural language text. The same memory supports direct reading and reasoning by more capable language models or query parsing followed by structured retrieval. Controlled comparisons show that direct reading is more accurate with powerful hosted models, while structured retrieval improves the accuracy of smaller local models and lowers per-query API cost for hosted models. We also construct HM3DSem-SQR, containing 6,084 queries from 36 HM3D-Sem scenes, and evaluate on Main-864, a class-balanced subset spanning all 36 scenes, and in three real-world environments. Experiments show that INHerit-SG outperforms the strongest baselines in both simulator and real-world evaluations. The largest gains come on attribute and compositional queries (7.6 and 6.3 strict Top-1 points on Main-864), with a 9.8-point overall success margin on real robots. Project Page: https://fangyuktung.github.io/INHeritSG.github.io/
Large language models have advanced medical reasoning, but clinically grounded reasoning in traditional Chinese medicine (TCM) remains challenging because prescription decisions require integrating domain knowledge, syndrome differentiation, treatment principles, herbal prescription composition, and dosage determination. We develop a TCM language model family comprising models with 4 billion, 8 billion, and 14 billion parameters. The artificial intelligence contribution is a staged clinical alignment framework integrating large scale continued pretraining on TCM and clinical records, complementary reasoning supervision, and prescription-centered reinforcement learning (RL). We further formulate herbal prescription generation as a structured RL problem with prescription-level feedback, enabling direct optimization of clinical decision outputs beyond knowledge reproduction and generic instruction following. The engineering application is TCM clinical decision support, particularly herbal prescription recommendation. We evaluate the models on a public benchmark containing 25,620 expert-verified items across 13 TCM knowledge and clinical reasoning tasks and on a private retrospective dataset of 4,348 spleen and stomach disease prescription cases. The 14 billion parameter reinforcement aligned model achieves a prescription generation F1 of 37.0 on the public benchmark, compared with 32.3 for DeepSeek-R1 with 671 billion total parameters, and a herb-level F1 of 52.8 on the clinical dataset with improved dosage agreement. Reinforcement post-training consistently improves prescription recommendation across all scales, while physician-source analysis shows that expert heterogeneity affects reward stability. These findings demonstrate a scalable pathway from domain grounding and reasoning supervision to clinically oriented prescription decision support.
Synthesizing believable 4D hand-object grasping sequences is important for character animation, extended reality, and embodied agents. Grasping requires a hand to approach, contact, and lift or manipulate an object coherently. Existing synthesis methods often model only the final static grasp or rely on additional conditions, such as language, target grasps, or object trajectories, to specify the interaction. We instead study the underconstrained problem of generating a complete grasping motion from a single initial hand-object state. Our framework decouples hand-motion generation from object-motion recovery. Given an object point cloud in the initial wrist frame and the initial parameterized hand configuration, conditional flow matching predicts a sequence-level contact map and a hand pose at each normalized sequence time. This time-indexed formulation avoids the error accumulation of autoregressive rollout while representing the complete motion. We then infer an attachment frame and recover rigid-object motion through training-free, contact-guided weighted registration. We evaluate on held-out DexYCB objects and unseen object geometries reconstructed from in-the-wild videos by Open-CHOIR. Compared with LatentHOI, our method produces smoother hand and object motion in every setting, matches or improves on its contact and penetration metrics in the wild under a shared initialization, and is about 30x faster per generated frame. In a 15-participant study, our motions were preferred in roughly two thirds of (forced-choice pairwise) comparisons. Precise contact closure on novel geometry, however, remains a key open challenge.
Accurate channel state information (CSI) acquisition is essential for unleashing the performance gains of extremely large-scale multiple-input multiple-output (XL-MIMO) systems. However, in near-field regions, CSI acquisition is much more challenging than in the far field due to the high-dimensional channel representation and spherical wavefront propagation. To address this, in this paper, we propose an efficient multi-domain near-field channel extrapolation framework for XL-MIMO systems. Leveraging the conditional denoising diffusion implicit model (CDDIM), our approach enables accurate channel extrapolation across the antenna, frequency, and spatial domains. Specifically, we design a physics-aware CDDIM backbone that incorporates position-embedded patch tokenization and a mask-guided multi-head attention mechanism, enabling the model to exploit position-dependent channel correlations induced by near-field spherical-wave propagation. To ensure high-fidelity extrapolation, we incorporate a Wasserstein GAN (WGAN) discriminator that provides adversarial supervision to the CDDIM during both the training and reverse sampling phases. Additionally, a RePaint-style refinement scheme is introduced to optimize the sampling trajectory, further boosting extrapolation accuracy. Extensive experiments demonstrate the superiority of the proposed framework, achieving superior extrapolation accuracy and robust generalization across diverse domains, varied configurations, and severe masking conditions. Codes are available at https://github.com/Lmyxxn/XL-ChannelDiff.
We ask whether everyday open-world monocular videos can be turned into reusable 4D interaction primitives: articulated hand motion, object shape with 6D pose over time, and the when/where of contact. Such a capability would enable scalable mining of real interactions and, beyond reconstruction, support scene-aware synthesis and planning. However, reconstructing hand-object interaction (HOI) from challenging monocular videos remains difficult: methods often assume known objects or curated scenes, and separately estimated hands and objects easily become misaligned under clutter, occlusion, and unseen object geometries. Targeting this setting, we present Open-CHOIR, an Open-world Contact-aware HOI Reconstruction framework for a monocular camera, using contact as an explicit coupling signal between hands and objects. Open-CHOIR first initializes a coarse, contact-agnostic 4D HOI sequence from open-world visual priors. It then introduces a generative HOI spatial rectification module to predict ray-depth corrections and rectify hand-object relative placement, then derive initial per-frame contact correspondences on the rectified geometry. Last, a contact-aware joint optimization with dynamically updated contact constraints enforces geometric, temporal, and contact consistency. Experiments on controlled and challenging videos show that Open-CHOIR improves object reconstruction, physical plausibility, and temporal consistency over state-of-the-art methods. Code, data, and pretrained weights are available at https://github.com/hxwork/CHOIR.
Long-horizon language agents often receive supervision only from terminal task outcomes, leaving little signal for distinguishing productive intermediate behavior from stagnation or even regression. Rather than learning a separate value function or process reward model for every task, we ask whether pretrained models can recognize task progress from their existing world knowledge. We formalize this capability with a World Potential Model (WPM), a goal-conditioned evaluator of task-relative realized progress in agent contexts. In ALFWorld and ScienceWorld, off-the-shelf pretrained models substantially outperform chance at recovering realized-progress structure without task-specific evaluator fine-tuning. We further anchor these progress judgments to task-specific milestones to obtain scalar world potentials, whose temporal differences provide process-sensitive step-level credit for policy optimization. Under matched comparisons, WPM-guided optimization improves success over outcome-only GRPO across all evaluated configurations. Together, these results provide initial evidence that pretrained world knowledge can support reusable realized-progress evaluation and provide useful supervision for long-horizon agents.
Evaluating agents by outcomes alone can obscure the capabilities that produce them. This problem is especially pronounced in evolving environments, where outcomes reflect a closed-loop interaction between agent behavior and changing external conditions. We introduce LiveMACEBench, a process-aware benchmark that uses live financial markets as a naturally evolving testbed for persistent LLM agents. Five frontier LLMs operate along continuous trajectories under matched Tool Use, Persistent Memory, Rule Following, and Multi-Agent Collaboration configurations. We evaluate them through both realized outcomes and mechanism-specific diagnostics derived from complete decision traces. Across 30 days of live evaluation, we find a pronounced outcome-capability gap: realized returns often diverge from capability-specific measurements, and similar outcomes can arise from markedly different patterns of mechanism use. Trace-level diagnostics further expose distinct bottlenecks across capabilities, demonstrating that mechanism access, effective mechanism use, and downstream performance are not interchangeable measures of agent capability. LiveMACEBench makes this distinction measurable, turning live markets from a performance leaderboard into a diagnostic environment for agent capability
We investigate the Cauchy problem of three-dimensional compressible Navier-Stokes equations with far-field vacuum. Based on delicate energy estimates and structures of the systems under consideration, we show the global well-posedness and decay rates of strong solutions provided that some coefficient-coupled scaling invariant initial quantity is suitably small. In particular, our smallness conditions are independent of any initial data and known parameters in the systems. Moreover, there is no need to require the compatibility conditions on the initial data. Our results improve previous works.
Generating full-body co-speech motion for humanoid robots requires coordinating speech prosody, linguistic content, and embodiment-specific motion. To this end, we present ECHO-G, a framework jointly conditioned on speech audio and timed transcripts. Its Speech-Grounded Diffusion Transformer (SGDiT) combines frame-aligned acoustic features with token-level linguistic context, preserving their distinct granularities. Trained with rectified flow matching, it models one-to-many utterance-motion relationships directly in robot space. To support training and evaluation, we introduce a BEAT2-derived audio-text-robot dataset and a benchmark covering co-speech characteristics, robot-motion quality, and runtime efficiency. Comparative evaluation supports direct robot-space generation over the evaluated human-motion generation and retargeting pipelines, while modality ablations highlight the benefits of joint audio-text conditioning. We further demonstrate deployment on a physical humanoid robot. A complementary video-rating study also favors joint conditioning over the alternatives. The dataset and training, inference, and evaluation code are available through our project page.
Reinforcement learning for long-horizon agents typically relies on sparse outcome-based rewards. This leads to a severe cold-start problem, as early-stage policies often fail to solve sampled tasks, leaving little useful reward signal for learning. To mitigate this problem, we use on-policy distillation (OPD) to provide token-level guidance on the student's own rollouts. We find that the benefit of this guidance depends on the performance gap between the teacher and the student. When the teacher substantially outperforms the student, distillation helps guide the student through the early training stage where outcome rewards provide little learning signal. As the gap narrows and eventually reverses, however, continued distillation becomes less beneficial and may hinder further improvement. Motivated by this observation, we propose Gap-Adaptive Teacher Scheduling (GATS), which augments the student's RL objective with an OPD term whose weight adapts to the teacher-student performance gap. Specifically, GATS gradually reduces teacher guidance as the student approaches the teacher's reference performance and withdraws it once that reference is reached. This enables GATS to leverage task-trained teachers smaller than the student, since teacher guidance is primarily needed during early training. Across ALFWorld, WebShop, and ScienceWorld with three Qwen2.5 teacher-student configurations, GATS achieves the highest average success rate among the compared methods in all three configurations, improving over reward-only GRPO by 4.37%-11.87% under matched student rollout budgets. Code is available at https://github.com/Ricardo-H/guide-then-let-go.
Fluid antenna systems (FASs) improve wireless links by repositioning antenna elements to exploit favorable spatial channel variations. Jointly optimizing fluid antenna (FA) positions, beamforming, and transmit power in a multi-cell network is challenging because the problem is non-convex and each base station has only local information during decentralized execution. However, the representative multi-agent reinforcement learning (MARL) algorithms, namely the on-policy multi-agent proximal policy optimization (MAPPO) and the off-policy multi-agent twin delayed deep deterministic policy gradient (MATD3), suffer from excessively long training times. To address this challenge, we formulate the problem as a decentralized partially observable Markov decision process (Dec-POMDP) and propose multi-agent group relative policy optimization (MAGRPO) under centralized training with decentralized execution. MAGRPO constructs relative advantages from groups of joint trajectories, thereby eliminating the centralized critic and generalized advantage estimation used by MAPPO; under parameter sharing, this critic-free design reduces the per-step computational complexity by approximately half. Simulations show that joint FA optimization provides several-fold sum-rate gains over fixed-position configurations. Across the evaluated antenna settings, MAGRPO achieves test sum rates higher than those of MATD3 and comparable to or slightly higher than those of MAPPO. Meanwhile, it reduces the training time by 20%-23% compared with MAPPO and by about 35% compared with MATD3.