arXiv subjects
Publications and source records attributed to Runze Zhang.
We prove that the number of maximal complex totally geodesic submanifolds of a smooth finite-volume non-arithmetic ball quotient is bounded linearly by its volume, with a constant depending only on the complex dimension. This gives a quantitative strengthening of the finiteness theorems of Bader--Fisher--Miller--Stover (Invent. Math., 2023) and Baldi--Ullmo (Ann. of Math., 2023).
Estimating scene illumination from images is challenging as lighting is inherently spatially varying, depending on geometry, occlusion, and light sources. Existing methods incorporate geometric cues by deriving local environment maps or probe-based representations, but largely rely on regression or parametric models, resulting in over-smoothed lighting and limited realism. We revisit spatially-varying illumination estimation from a generative perspective and introduce LUMEN, a geometry-conditioned diffusion framework for synthesizing high-dynamic-range (HDR) environment maps at arbitrary spatial locations from single or multi-view images. Specifically, we reconstruct a coarse 3D scene from input images and render partial environment maps at arbitrary locations to encode visibility and spatial structure. These signals are fused with multi-view image features and fed into a diffusion transformer to generate full HDR environment maps. To train the model, we build a synthetic dataset of 700 indoor scenes with dense spatial supervision, including multi-view RGB images, depth, and HDR illumination at multiple sampled locations. This dataset enables the model to learn spatially consistent lighting distributions across diverse scenes. Extensive experiments demonstrate that LUMEN significantly improves visual fidelity and spatial coherence compared to prior approaches.
We establish uniform multicritical pseudo-Siegel bounds for polynomials of Zakeri type, where all free critical points are on the boundary of an invariant Siegel disk of bounded type. This generalizes the unicritical result~\cite{DL:wZ}. As an application, we show the optimality of the Brjuno condition under the Zakeri restriction: as the rotation number becomes non-Brjuno, the Siegel disk evolves into the Cremer Hedgehog. Combined with~\cite{BCR26}, this implies the optimality of the Brjuno condition for all neutral polynomials, resolving a conjecture by Douady from the 1980s.
Recent advances in large-scale human motion data, motion retargeting, and motion imitation have enabled increasingly capable whole-body control for individual humanoids. Cooperative carrying is more challenging because successful coordination requires not only plausible individual motions, but also consistent cross-agent and agent-object relations, including shared grasp, relative configuration, and whole-body support. We introduce CoCarry, a cooperative-carrying dataset containing 220 synchronized two-person sequences across 21 task schemes, five shared-object geometries, four terrain types, and approximately 61 minutes of motion. We further propose Contact-Support-Structured Retargeting, which starts from nominal individual motions and jointly refines both humanoids around the same prescribed object trajectory. Cooperation-aware object-local hand anchors preserve compatible four-hand grasp relations, while complementary upper object-interaction and lower support structures retain object-relative geometry and coordinated support. Across all 220 CoCarry sequences retargeted to two A3 humanoids, our method achieves 0.9995 contact preservation, reduces penetration duration by 67.0% and 71.0% relative to GMR and OmniRetarget, respectively, and maintains a 100% retargeting success rate. On CORE4D with Unitree G1 humanoids, it achieves 0.9906 contact preservation with zero measured sliding. We further validate the generated references through physics simulation and multiple real-world cooperative carrying experiments on two physical A3 humanoids, demonstrating their usability for downstream dual-humanoid control.
Materials science data collection can be expensive, making dataset reuse and long-term utility important for future discovery. In practice, data collection often prioritizes properties of current interest while other properties are excluded from the acquisition process. This can produce datasets that are well suited for current objectives but lose information needed for properties of future interest. Here, we present how to construct datasets that remain informative for both. We develop and evaluate acquisition frameworks that combine predictive disagreement with diversity in material features, predicted outcomes, or both. We test these approaches across four DFT datasets and an experimental thermoelectric dataset. Diversity inclusion in dataset construction can reduce present and future objectives trade-off by preserving a broader range of materials and property behavior during acquisition. Across all datasets, the Non-dominated Sorting Genetic Algorithm II with disagreements and feature diversity (NSGA-II Dis. + diversity) framework developed in this work provides the most robust balance between current and future objectives. It maintains prediction performance above random sampling for current objectives while mitigating bias on excluded properties and, in many cases, improving their performance beyond random sampling. This diversity-aware acquisition framework provides a practical route to building materials datasets with unbiased quality entries and mitigating cold-start limitations in subsequent modeling and discovery campaigns.
We present Unravel, a training-free framework that turns a single image into an interactive 3D scene, where every object is an independent and movable asset. Existing generators either produce one entangled geometry in which no object can be moved, or predict all objects in one feed-forward pass, where a wrong guess cannot be detected or repaired. Unravel instead takes a different approach: it first takes the scene apart, and then puts it back together. Starting from the input image, an agentic harness that iteratively peels the image layer by layer, and adopts point cloud as major modality for spatial relationship recovery. Specifically, a vision-language model plans which objects are fully visible, an image editor removes them and restores the occluded regions. Every edit is verified before being incorporated into the reconstruction. This process gradually turns occluded parts of the scene into direct observation, allowing objects to be reconstructed when they are best exposed rather than hallucinated from the original image alone. The scene is then rebuilt in reverse removal order, so that the supporting objects are naturally placed before the objects they support. Since a single-view image only reveals part of an object, we treat the observed points as a lower bound on its size: an asset may grow to cover its points, but can not shrink away from them. Finally, we physically settle the reconstructed scene to remove floating objects and interpenetrations, followed by an agentic audit that corrects remaining placement errors. Extensive experiments on diverse indoor scenes show that Unravel recovers more objects, places them more faithfully, and produces scenes that are more physically-plausible than existing methods.
In this paper, we study joint deformations of pairs $(X,E)$, where $X$ is a compact complex manifold and $E\rightarrow X$ is a holomorphic vector bundle. We prove that $(X,E)$ has unobstructed deformations if $X$ is a Fujiki manifold with torsion canonical bundle and $H^2(X,\textrm{End}^0E)=0$, where $\textrm{End}^0 E$ denotes the trace-free endomorphism bundle. When the canonical bundle is trivial, the Fujiki assumption can be replaced by three weak $\partial\bar\partial$-conditions. We construct examples satisfying these conditions whose Frölicher spectral sequences do not degenerate at $E_1$. These results provide non-Kähler extensions of the theorems of Li--Pan and Iacono--Manetti. Without this vanishing assumption, we obtain both unobstructed and obstructed pairs. In Thomas's example, we prove unobstructedness of the pair, although the bundle has obstructed deformations with the manifold fixed. On the other hand, we prove that every strict projective Calabi--Yau manifold of dimension at least three admits a simple bundle with obstructed joint deformations. We also construct obstructed pairs with Hermitian flat bundles on complex tori. These results answer two questions raised by Felten.
Long-horizon camera-controlled video generation requires recovering previously observed content from an ever-growing visual history. Existing approaches either search historical context implicitly or reconstruct it into persistent 3D memory, facing inefficient memory access or accumulated geometric errors. Our key insight is that geometry need not explain the scene--it only needs to determine where visual memory should be read from, while attention decides what should be recovered. Based on this insight, we introduce GEAR, a Geometry-Enabled Attention Routing framework that uses geometry as an explicit token-level address for visual memory. Rather than fusing historical observations into a persistent global 3D representation, GEAR retains them as frame latents and uses per-frame geometry only to establish token-level correspondences with target views, thereby avoiding persistent error accumulation from global fusion. Guided by these correspondences, Geometric Correspondence Attention (GCA) selectively injects geometrically matched historical features into noisy target patches during denoising. We further introduce an Invisible Octree to accumulate visibility evidence and reject geometrically plausible but occluded correspondences. Extensive experiments demonstrate that GEAR achieves state-of-the-art visual quality, precise camera control, and revisit consistency, enabling minute-long video generation along challenging trajectories.
We construct a numerically flat holomorphic vector bundle of rank two on a compact complex threefold satisfying the ordinary $\partial\bar\partial$-lemma and prove that it admits no holomorphic connection. This gives, in particular, a negative answer to a question posed by Cao--Deng--Matsumura. In contrast, for compact simply connected complex manifolds $X$, we prove that the answer is affirmative if $H^1(X,\mathcal O_X)=0$, and hence if the Frölicher spectral sequence of $X$ degenerates at $E_1$.
Synthesizing a structured and editable 3D indoor scene from a few uncalibrated RGB views requires more than generating high-quality individual assets: a system must infer the room structure, associate objects across incomplete observations, and recover a globally consistent spatial configuration. Previous methods mainly focus on 3D scene generation with text input or require continuous visual inputs with additional priors, \ e.g., human-annotated masks or accurate 3D layouts, which makes these methods labor demanding and hard to apply in general cases. We present \textsc{Scenix}, a sparse-view 3D scene reconstruction framework via executable scene programs, a structured representation that can be directly instantiated into editable 3D scenes. Given sparse views, \textsc{Scenix} predicts executable scene programs through perception-grounded asset instantiation and closed-loop spatial refinement. % We present \method, a framework that predicts an executable scene representation from sparse views and realizes it through perception-grounded asset instantiation and closed-loop spatial refinement. To support this task, we construct \dataset, a dataset of approximately 110,000 synthetic and real indoor scenes with multiview imagery, room structures, object-centric descriptions, and metric spatial annotations. We further introduce observation-consistent supervision that aligns each target scene with the visual evidence available in its input views. Experiments on held-out \textsc{XScene} scenes, real indoor images, and out-of-distribution SpatialGen cases evaluate structured scene prediction, object grounding, and spatial refinement.
High-fidelity 3D generative modeling increasingly relies on the latent diffusion paradigm, where the reconstruction quality of the underlying 3D VAE becomes a primary bottleneck. Existing approaches largely follow two paradigms: sparse voxel-based representations achieve strong reconstruction quality but incur significant memory and computational overhead, while set-based representations are compact and continuous yet typically lag in fidelity due to latent sparsity and excessive global smoothness. We propose MSVS-VAE, a hierarchical set-based VAE that closes this fidelity gap without sacrificing compactness. Our key idea is to progressively densify anchored VecSet latents via hierarchical point-shuffle upsampling, increasing spatial capacity for fine-grained geometry modeling. To efficiently decode from the densified hierarchy, we replace global cross-attention with AVS-Conv, a geometry-aware local aggregation operator operating within local neighborhoods rather than the exhaustive latent set. We further introduce multi-scale query decoding to fuse coarse-to-fine latent features, where coarse scales provide stable global context, and fine scales refine localized geometry, reducing artifacts from overly local receptive fields. Extensive experiments on Objaverse, ABO, and in-the-wild benchmarks demonstrate that MSVS-VAE consistently outperforms prior set-based and voxel-based VAEs, delivering approximately 10x faster decoding than prior set-based methods and approximately 10x higher compactness than voxel-based baselines.
Electrochemical impedance spectroscopy (EIS) is a powerful tool for probing kinetic and transport processes in electrochemical systems, but its practical use is often limited by the long acquisition time and noise sensitivity of low-frequency measurements. Here, we present a statistical inference-assisted framework that reduces the reliance on low-frequency sampling by increasing the sampling density in cleaner high-frequency regions. Using AutoEIS and Bayesian inference, the augmented high-frequency data are fitted to selected equivalent circuit models (ECMs) to reconstruct the full impedance spectrum and quantify parameter uncertainty. To evaluate reconstruction performance, we introduce the critical frequency (fc), defined as the highest cutoff frequency at which the full EIS response can still be reliably recovered. The results show that additional high-frequency sampling can not only shift fc to higher values but also reduce the total measurement time. The specific improvement depends on the noise level of the EIS data, the number of added data points, and the ECM structure. Overall, this work provides a practical framework for designing fast and efficient EIS data acquisition and offers guidance for applying partial-frequency EIS reconstruction in real electrochemical characterization.
The intricate motion arising from fluid--boundary interactions is visually compelling, yet notoriously difficult and computationally expensive to simulate in the presence of complex boundaries. Accurately resolving boundary geometry requires body-fitted grids constructed via cut-cell methods, which often leads to poorly conditioned linear systems in the pressure projection stage and, consequently, prohibitive computational cost. We present FastVEM, an efficient boundary-conforming fluid simulation framework that enables high-fidelity flow--boundary interaction at substantially reduced cost. Computational efficiency is achieved through a coordinated, top-down design spanning numerical discretization, grid construction, and linear solvers. FastVEM adopts a Virtual Element Method (VEM) discretization to robustly enforce incompressibility and boundary conditions on irregular body-fitted grids, and employs a VEM polynomial-space Particle-in-Cell scheme for advection. Complementing this discretization, a convexity-preserving cut-cell strategy is introduced to construct simulation-friendly body-fitted grids. To accelerate pressure projection, we develop a Galerkin geometric multigrid solver featuring a diffusion-free prolongation operator that prevents coarse-level matrix densification, along with a nested, boundary-aware grid hierarchy that ensures well-posed placement of coarse-level degrees of freedom. Compared to prior cut-cell--based fluid simulators, FastVEM speeds up the computationally dominant pressure projection stage by up to 100x, while robustly handling even more challenging boundary geometries.
Large language models (LLMs) are increasingly used to simulate human behavior in business, economics, and the social sciences, offering a low-cost complement to laboratory experiments, field studies, and surveys. This paper evaluates how well LLMs replicate human behavior in operations management. Using nine published behavioral-operations experiments, we assess LLM performance along two dimensions: whether LLM-generated data reproduce the original hypothesis-test outcomes, and whether their full response distributions align with human data, measured by Wasserstein distance. We find that LLMs often replicate hypothesis-level effects, suggesting that they can capture salient decision biases and behavioral regularities. However, their response distributions frequently diverge from human data, even for strong proprietary models, with dispersion mismatch playing an important role. We also examine two lightweight mitigation strategies: chain-of-thought prompting and hyperparameter tuning. Both can reduce distributional misalignment, and appropriate tuning can sometimes allow smaller or open-source models to match or outperform larger proprietary systems.
Promptable instance segmentation is widely adopted in embodied and AR systems, yet the performance of foundation models trained on perspective imagery often degrades on 360° panoramas. In this paper, we introduce Segment Any 4K Panorama (SAP), a foundation model for 4K high-resolution panoramic instance-level segmentation. We reformulate panoramic segmentation as fixed-trajectory perspective video segmentation, decomposing a panorama into overlapping perspective patches sampled along a continuous spherical traversal. This memory-aligned reformulation preserves native 4K resolution while restoring the smooth viewpoint transitions required for stable cross-view propagation. To enable large-scale supervision, we synthesize 183,440 4K-resolution panoramic images with instance segmentation labels using the InfiniGen engine. Trained under this trajectory-aligned paradigm, SAP generalizes effectively to real-world 360° images, achieving +17.2 zero-shot mIoU gain over vanilla SAM2 of different sizes on real-world 4K panorama benchmark.
3D learning systems implicitly assume that objects occupy a coherent reference frame. Nonetheless, in practice, every asset arrives with an arbitrary global rotation, and models are left to resolve directional ambiguity on their own. This persistent misalignment suppresses pose-consistent generation, and blocks the emergence of stable directional semantics. To address this issue, we construct \methodName{}, a massive canonical 3D dataset of 320K objects over 1,156 categories -- an order-of-magnitude increase over prior work. At this scale, directional semantics become statistically learnable: Canoverse improves 3D generation stability, enables precise cross-modal 3D shape retrieval, and unlocks zero-shot point-cloud orientation estimation even for out-of-distribution data. This is achieved by a new canonicalization framework that reduces alignment from minutes to seconds per object via compact hypothesis generation and lightweight human discrimination, transforming canonicalization from manual curation into a high-throughput data generation pipeline. The Canoverse dataset will be publicly released upon acceptance. Project page: https://github.com/123321456-gif/Canoverse
Open-world promptable 3D semantic segmentation remains brittle as semantics are inferred in the input sensor coordinates. Yet, humans, in contrast, interpret parts via functional roles in a canonical space -- wings extend laterally, handles protrude to the side, and legs support from below. Psychophysical evidence shows that we mentally rotate objects into canonical frames to reveal these roles. To fill this gap, we propose \methodName{}, which attains canonical space perception by inducing a latent canonical reference frame learned directly from data. By construction, we create a unified canonical dataset through LLM-guided intra- and cross-category alignment, exposing canonical spatial regularities across 200 categories. By induction, we realize canonicality inside the model through a dual-branch architecture with canonical map anchoring and canonical box calibration, collapsing pose variation and symmetry into a stable canonical embedding. This shift from input pose space to canonical embedding yields far more stable and transferable part semantics. Experimental results show that \methodName{} establishes new state of the art in open-world promptable 3D segmentation.
In this paper, we prove a $\partial\bar{\partial}$-type lemma on compact Kähler manifolds for logarithmic differential forms valued in the dual of a certain pseudo-effective line bundle, thereby confirming a conjecture proposed by X. Wan. We then derive several applications, including strengthened results by H. Esnault-E. Viehweg on the degeneracy of the spectral sequence at the $E_1$-stage for projective manifolds associated with the logarithmic de Rham complex, as well as by L. Katzarkov-M. Kontsevich-T. Pantev on the unobstructed locally trivial deformations of a projective generalized log Calabi-Yau pair with some weights, both of which are extended to the broader context of compact Kähler manifolds. Furthermore, we establish the Kähler version of an injectivity theorem originally formulated by F. Ambro in the algebraic setting. Notably, while O. Fujino previously addressed the Kähler case, our proof takes a different approach by avoiding the reliance on mixed Hodge structures for cohomology with compact support.