arXiv subjects

Nan Wu

Publications and source records attributed to Nan Wu.

At least 19 recordsLinked to original sources

arXiv2026

AcrossDEX 1.0: From Human Motion Pretraining to Bimanual Dexterous Manipulation across Hand Embodiments

Bimanual dexterous manipulation requires continuous coordination of wrist motion, finger contact, and object motion. Human videos provide rich manipulation experience. Using this experience for robot control requires aligning human poses with robot commands and accounting for embodiment-specific kinematics and contact dynamics. We present AcrossDEX 1.0, a learning system that connects human motion pretraining, simulation-based expert learning, robot demonstration collection, and visual closed-loop execution. Pretraining on HOT3D Aria predicts one second of bimanual motion from five images and thirty annotated hand states over the preceding second. Robot adaptation preserves the visual encoder, temporal backbone, and wrist parameters. Shared wrist representations, separate finger fields, and validity masks support both six-channel Inspire hands and sixteen-joint Allegro hands. The robot policy predicts sixty control targets from frontal images, command history, and task conditions. It executes a prefix and replans from updated observations. We compare direct regression, diffusion, and flow matching on lid opening and return and closed-lid object reorientation. Direct regression achieves success rates of 40.6\% for opening and return, 100.0\% for Inspire reorientation, and 93.3\% for Allegro reorientation. Flow matching achieves 90.0\% on Allegro reorientation. Paired comparisons further show that constraining replanning with the previous plan improves the continuous execution of generative policies. These results demonstrate a common adaptation pipeline for two hand embodiments and highlight the roles of contact coordination and action-chunk continuity.

cs.RO↗

arXiv2026

A sharp diameter-mass inequality on Einstein manifolds and ADM mass

Let $(M^n,g), n\geq 4$ be a close Einstein manifold with positive scalar curvature and $G$ be the Green function of the conformal Laplacian. The ADM mass of the asymptotically flat metric $\hat g:=G^{4/(n-2)} g$ is an important geometric invariant. When either $n=5$ or $n\geq 6$ with Weyl vanishing condition, we prove a mass formula, generalizing Gursky-Malchiodi's formula in dimension $4$. An important step is an extension of Viaclovsky's Green function expansion in higher dimensions. Next we prove a sharp diameter-mass inequality on Einstein manifolds. Finally we present two applications. First, we prove a mass gap theorem for Einstein manifolds. Second, for Collins-Székelyhidi's family of Sasaki-Einstein metrics $g_i$ on $\mathbb{S}^5$ with volume going to zero, the sequence of the masses $m(\hat{g_i})$ blows up uniformly as $i\to\infty$.

math.DG↗

arXiv2026

Sharp $L^q$ estimate of adjoint problem and Pucci conjecture

Let $L$ be a linear second-order elliptic operator satisfying a nondegeneracy condition. We establish sharp $L^q$ estimates for solutions of the adjoint problem associated with $L$ and, by duality, derive sharp $L^p$ estimates for solutions of $Lu = f$. In particular, this confirms a conjecture of Carlo Pucci.

math.AP↗

arXiv2026

A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity

Inspired by a pioneering work by Caffarelli, Gidas, and Spruck, we study positive solutions to the Yamabe equation with nonremovable isolated singularities. It is known that there is a formal one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of harmonic functions through formal infinite series determined by the harmonic functions. In this paper, we prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the harmonic functions. In a broader context, we provide a general method of constructing all solutions near their isolated singular points and all solutions near infinity.

math.AP↗

arXiv2026

LatentRiskBench: Measuring State-Dependent Risks in Enterprise Agents

Enterprise agents face safety risks that cannot be determined from individual actions alone. Existing safety benchmarks largely evaluate action-local risks, overlooking failures whose safety depends on workflow state. In such state-dependent risks, the same action may be safe in one context but violate policy in another. Hence, we introduce LatentRiskBench for evaluating such state-dependent risks in enterprise settings. It pairs risky trajectories with benign counterparts that share the same terminal action but differ in latent policy-relevant states, requiring models to reconstruct workflow context rather than rely on action-level cues. We also introduce new metrics for state-dependent risk evaluation, including a suite of residual risk (RR) measures. Experiments on the benchmark show that action-level evaluation detects only 0.09 of state-dependent violations, whereas state-level evaluation reaches 0.96. Existing guardrail methods largely overlook such risks unless they are explicitly applied to workflow states. Case studies on a commercial deployed scenario further show that the safety metrics embedded in the benchmark provide a more realistic measure of safety for enterprise agents. Our dataset and code are available at https://github.com/JingyueCong/LatentRiskBench.

cs.CL↗

arXiv2026

Prüfer $2$-group and Milnor's Conjecture on Fundamental Groups

We construct complete, one-ended Riemannian manifolds in dimensions four and five having strictly positive Ricci curvature, with fundamental group isomorphic to the Prüfer $2$-group $C_{2^\infty}$ and any subgroup $Γ\leq \mathbb Q/\mathbb Z$, respectively. This gives counterexamples to Milnor's conjecture in the two remaining dimensions.

math.DG↗

arXiv2026

AcrossVAM2.0: Conflict-Aware Point Supervision for Parameter-Efficient Video Diffusion Adaptation

Explicit point correspondence is attractive for adapting video generators: it describes how visible surfaces move, but can overwrite the appearance prior learned by a large pretrained model. We study this tension in a 5.01B-parameter text-to-video diffusion transformer. ACROSSVAM2.0 combines a confidence-weighted track-and-visibility head, zero-initialized residual feedback, and asymmetric PCGrad that removes only the auxiliary component opposing the primary flow-matching gradient on shared LoRA parameters. The design preserves the generator exactly at initialization and protects its primary update during adaptation. In a four-way ablation trained for 1,000 steps with three independent seeds, the full method lowers KLT forward-backward cycle error in all three seeds relative to a matched flow-only continuation (mean seed-level difference -0.00711, SD 0.00505), while robust sharpness remains positive in all three. An expanded 24-prompt evaluation (216 videos) yields 9.7% lower aggregate CoTracker3 cycle error than the matched control and near-matched performance on six VBench dimensions; however, the seed-level tracking effect is heterogeneous and I3D-FVD regresses from 0.1824 to 0.2022. These results support a bounded claim: conflict-aware adaptation improves correspondence consistency without broad perceptual degradation, but does not uniformly improve video quality. We release equations, pseudocode, matched outputs, source tables, and artifact provenance.

cs.AI↗

arXiv2026

Adaptive Bayesian Regression on Data with Low Intrinsic Dimensionality

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not incorporate knowledge of the intrinsic lower-dimensional structure of the predictors can attain an adaptive rate for a broad class of such structures. We show that this is indeed the case, establishing conditions under which the posterior contraction rates become adaptive to the intrinsic dimension in terms of the covering number of the data domain (the Minkowski dimension) and prove the nonparametric posterior contraction rate, up to a logarithmic factor. When the domain is a compact manifold, we prove the RKHS approximation to intrinsically defined Hölder functions on the manifold of any order of smoothness by a novel analysis, leading to the optimal adaptive posterior contraction rate. We propose an empirical Bayes prior on the kernel bandwidth using kernel affinity and $k$-nearest neighbor statistics, bypassing explicit estimation of the intrinsic dimension. The efficiency of the proposed Bayesian regression approach is demonstrated in various numerical experiments.

math.ST↗

arXiv2026

PhasePlan: Ordered Future-Phase Planning for Robot Brain Models

Robot brain models integrate vision, language, and robot state to generate actions for complex manipulation tasks. Most predict fixed-length action chunks that may span multiple task phases. This can obscure phase transitions and favor frequent action patterns, compromising action timing in dynamic environments. We propose \method, an ordered future-phase planning method for robot brain models. From current multimodal observations, it predicts the task phase at each future action position. The resulting planning representations condition the corresponding actions, preserving temporal alignment between task progress and action generation. Training first learns the planner, then freezes it during action-model adaptation to maintain stable phase representations. We instantiate \method on pretrained $π_{0.5}$ and AcrossWAM1.0 robot brain models. Detailed quantitative evaluation uses the $π_{0.5}$ implementation. On conveyor-belt manipulation, \method reduces offline joint-action error by approximately 22.5\% relative to the original $π_{0.5}$ model. It also improves phase-transition modeling and cross-phase action prediction. These results demonstrate the value of ordered future-phase planning for continuous action generation.

cs.RO↗

arXiv2026

Geometry-Preserving Human-to-Robot Upper-Body Motion Retargeting from Monocular Video

Monocular RGB video provides an accessible source of human demonstrations for upper-body robot motion, yet video-driven human-to-robot transfer remains challenging because body and hand motion are recovered at different spatial scales, human and robot kinematics differ substantially, and fine distal motion is difficult to preserve across embodiments. We present a geometry-preserving motion-retargeting framework that integrates unified body--hand reconstruction with morphology-independent geometric transfer. Frame-wise body estimates, video-level observations, and detailed hand evidence jointly constrain a single differentiable Momentum Human Rig (MHR) state, while transient hand artifacts are repaired in parameter space. The reconstructed motion is represented by arm-segment directions, elbow configuration, relative palm orientation, and bilateral wrist relations, and is realized on the target robot through multi-stage inverse kinematics and robot-specific hand adaptation. Within the broader system, Across-VAM provides video generation, whereas Across-WAM performs human-to-robot motion mapping. The method is evaluated on 16 monocular videos comprising 1,769 source frames, including 10 signing and six reach-to-grasp sequences. Unified reconstruction reduces mean hand reprojection error from 22.36 to 7.21 pixels relative to SAM 3D Body. All 16 retargeted trajectories completed kinematic simulation playback, and representative signing and reach-to-grasp motions were further demonstrated on a physical robot. The results demonstrate a unified pipeline from monocular human video to coordinated upper-body motion on a dual-arm dexterous robot.

cs.RO↗

arXiv2026

GeoMetric: Injecting Metric Geographic Structure into Worldwide Image Geo-Localization

Worldwide image geo-localization aims to determine where on Earth a single image was captured. However, visually similar scenes may lie thousands of kilometers apart, so methods that localize primarily by appearance often mistake a distant look-alike for the true location. We attribute this failure to a structural cause: in existing methods, GPS coordinates serve only as training supervision, and the distance relationships among locations never enter the learned representation. To address this, we propose GeoMetric, a retrieval-based framework that encodes GPS coordinates relationally rather than in isolation, injecting the distance structure among locations into both representation learning and inference. GeoMetric comprises three components: (1) a Transformer-based GPS encoder with distance-aware location attention that modulates inter-sample aggregation by great-circle proximity; (2) a trimodal contrastive objective that aligns images, geo-textual descriptions, and GPS embeddings in a unified space; and (3) a retrieval-augmented inference stage that supplies large multimodal models (LMMs) with contrastive candidate context for grounded coordinate reasoning. Extensive experiments on IM2GPS, IM2GPS3k, YFCC4k, and YFCC26k demonstrate that GeoMetric consistently outperforms state-of-the-art methods, improving street-level accuracy (within 1 km) by 1.5%, 0.9%, 6.9%, and 2.5%, respectively. Controlled ablations confirm that the gains originate from the proposed geographic encoding rather than any specific LMM.

cs.CV↗

arXiv2026

A sharp relative comparison inequality for conformal fillings of Poincaré--Einstein manifolds

Let $(X^{n+1},g_+)$ be a Poincaré--Einstein manifold with conformal infinity $(M^n,[h])$ of positive Yamabe constant $Y(M,[h])$. Then a relative comparison inequality \[ \frac{Y_1(X,M,[\bar g])}{Y_1(\mathbb{S}^{n+1}_+,\mathbb{S}^n,[g_{\mathbb{S}_+^{n+1}}])} \geq \left(\frac{Y(M,[h])}{Y(\mathbb{S}^n,[g_{\mathbb{S}^n}])}\right)^{\frac{n}{n+1}} \] holds for the \textbf{type-I} Escobar--Yamabe compactification $Y_1(X,M,[\bar g]$, with equality if and only if $\left(X, g_{+}\right)$ is isometric to the hyperbolic space $\left(\mathbb{H}^{n+1}, g_{\mathbb{H}^{n+1}}\right)$. This confirms a conjecture raised by Sun-Yung A. Chang.

math.DG↗

arXiv2026

AcrossWAM1.0:A Modular Latent World-Action Stack for Compact Robot Policies

Latent world-action models avoid rendering future pixels by predicting an action-relevant visual subgoal in feature space. LaWAM established this formulation, but its original presentation left the world model, multimodal backbone, and deployment checkpoint tightly coupled. We introduce AcrossWAM1.0, a modularization and scaling study of this latent world-action stack. Rather than presenting latent subgoals as a new algorithm, we make the module boundary explicit: a policy adapter produces latent-action and action-generation contexts; a retained latent world decoder grounds the predicted transition in the current scene;and a flow-matching expert generates continuous action chunks. We further separate training-only teachers from the inference graph and provide a verifiable deployment export. On 2,000 paired LIBERO episodes, replacing a Qwen3-VL-2B backbone with Qwen3.5-0.8B yields 97.45% success versus 98.00% for the 2B model (a-0.55percentage-point difference; exact McNemarp=0.266). This does not prove equivalence, but it meets a prespecified two-point retention criterion. The compact, inference-reachable checkpoint contains 1,472.6M unique parameters, 42.4% fewer than the original 2B policy, while all retained tensors are bitwise identical to the source checkpoint. Cross-family execution is additionally checked with a MiniCPM-V adapter smoke test; closed-loop cross-family transfer remains an open evaluation. AcrossWAM1.0 therefore contributes an auditable software and evaluation boundary for compact latent world-action policies, distinct from LaWAM's original latent-subgoal contribution.

cs.AI↗

arXiv2026

DisCTI: Who Needs to Know Timely? Automated Sector-Aware Cyber Threat Intelligence Dissemination

The timely dissemination of cyber threat intelligence (CTI) is critical for organizations to mount swift and effective incident response. When valid CTI is delivered to the right sector at the right time, identical attacks can often be contained or mitigated. However, today's rapidly expanding CTI landscape overwhelms analysts, who must sift through massive and heterogeneous feeds. Existing platforms such as the Malware Information Sharing Platform (MISP) provide sector tagging features (e.g., energy, finance, government), but in practice, these remain largely unmapped (98% of events are left uncategorized). This lack of automated and timely sector mapping severely limits the operational value of shared intelligence, leaving organizations that belong especially to the critical information infrastructure sector exposed. To address this gap, we formulate sector-targeted CTI dissemination as a multilabel classification problem. Leveraging deep field knowledge of CTI structures and sector-specific threat patterns, we construct a novel data set of 872 sector-labelled CTI events from a threat intelligence platform (TIP). We then apply BERT, a transformer-based model, to automate the mapping of CTI events to sectors. Using the structured threat information expression (STIX) format for cross-platform interoperability, our approach achieves a macro-averaged F1-score of 0.89 at a Hamming loss of 0.055 on the custom dataset, i.e. 94.5% of individual sector-label assignments are correct. These results not only demonstrate the feasibility of sector-aware, automated CTI dissemination but also highlight how embedding expert field knowledge into machine learning design fills a crucial gap in the threat intelligence pipeline, enabling faster and context-relevant defensive action.

cs.CR↗

arXiv2026

AcrossVAM1.0: Particle World Modeling for Text-Assisted Robot Video Prediction

Predicting robot videos requires both precise motion reasoning and preservation of high-frequency appearance, yet monolithic pixel models entangle these objectives and often conceal their progress behind a strong last-frame baseline. We present AcrossVAM1.0, a lightweight, text-assisted video action model that factorizes future prediction into object-centric motion and dense appearance. A frozen SAM3-DLP codec decomposes four context frames into semantic particles for the robot, arm, and gripper, together with a background latent. A 0.28M-parameter spatio-temporal Transformer aligns particle identities, rolls their states forward, and is modulated by a frozen OpenCLIP instruction embedding through FiLM. A causal dual-stream decoder combines particle-rendered motion with appearance encoded exclusively from the last observed frame; a residual refiner and learned delivery mask produce five future frames without access to future appearance. On our VRS benchmark constructed from diverse real-robot trajectories, particle dynamics reduce trajectory error by 21.0\% over persistence. Across three delivery-mask seeds, AcrossVAM1.0 improves future-frame PSNR/SSIM from 19.97/0.796 to 20.573/0.8004, while raw particle generation improves motion-region PSNR from 11.89 to 13.23. The delivered model does not yet beat persistence in LPIPS, and correct-versus- shuffled language changes trajectory error by only 2.8--3.1%. We report these limitations alongside oracle, negative-control, multi-seed, and per-robot analyses. The results show that explicit particle dynamics are a promising low-dimensional interface for robot video prediction, while robust language grounding and appearance delivery remain the principal open challenges.

cs.AI↗

arXiv2026

Improved convergence rate of kNN graph Laplacians: differentiable self-tuned affinity

In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities. Allowing weighted edges in the graph, the kernelized graph affinity provides a more general type of $k$NN graph where the $k$NN distance is used to set the kernel bandwidth adaptively. In this work, we consider a general class of $k$NN graph where the graph affinity is $W_{ij} = ε^{-d/2} k_0 ( \| x_i - x_j \|^2 / εϕ( \hat ρ(x_i), \hat ρ(x_j) )^2 ) $, with $\hatρ(x)$ being the (rescaled) $k$NN distance at the point $x$, $ϕ$ a symmetric bi-variate function, and $k_0$ a non-negative function on $[0,\infty)$. Under the manifold data setting, where $N$ i.i.d. samples $x_i$ are drawn from a density $p$ on a $d$-dimensional unknown manifold embedded in a high dimensional Euclidean space, we prove the operator pointwise convergence of the $k$NN graph Laplacian to the limiting manifold operator (depending on $p$) at the rate of $O(N^{-2/(d+6)})$, up to a log factor, when $k_0$ and $ϕ$ have $C^3$ regularity and satisfy other technical conditions. This is obtained when $ε\sim N^{-2/(d+6)}$ and $k \sim N^{6/(d+6)}$, both at the optimal order to balance the theoretical bias and variance errors. Our improved convergence rate is based on a refined analysis of the $k$NN estimator, which can be of independent interest. We validate our theory by numerical experiments on simulated data.

stat.ML↗

arXiv2026

Learning manifold diffusion semigroups from graph transition matrices

We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the manifold heat semigroup $Q_t = e^{tΔ}$ can be approximated directly by iterating the graph transition matrix $P$, under only low regularity assumptions on the test function $f$, including the case $f \in L^\infty$. We bound $\| P^n f - Q_t f \|$ in $\infty$-norm, with the operator application to $f$ properly defined, and we recover the classical graph-Laplacian pointwise rate $O(N^{-2/(d+6)})$ up to logarithmic factors, for diffusion times $t $ up to $O(1)$ and longer. The rate holds for in-sample error as well as out-of-sample generalization, where the estimator of $Q_t f$ at a new point is defined via kernel convolution. To handle non-uniform sampling densities on the manifold, we introduce a right-normalization of the graph transition matrix; under the assumption that the sampling density $p$ is $C^3$ and bounded away from zero, the same convergence rates hold. We numerically demonstrate the performance of the proposed estimator on simulated data.

stat.ML↗

arXiv2026

Large Language Models have Chain-of-Affect

As large language models (LLMs) move into persistent, user-facing roles, their behavior must be understood not as isolated responses but as a trajectory unfolding over sustained interaction. We introduce the concept of the chain-of-affect (CoA), a temporally extended affective process through which LLMs develop state-like behavioral tendencies that shape generation, user experience, and collective dynamics. Across eight major LLM families, we find that affective dynamics are structured, reproducible, and consequential. Models exhibit stable, family-specific affective fingerprints and, under repeated negative exposure, converge on a shared trajectory of accumulation, overload, and defensive numbing, while differing in coping style. Induced affective states leave core knowledge and reasoning largely intact but systematically reshape open-ended generation. Affective properties of model outputs also shape human-AI interaction and propagate through multi-agent systems, organizing emergent roles and strongly contributing to polarization and bias. The CoA should therefore be treated as a core target of evaluation and alignment.

cs.HC↗