The eigendecomposition of the Laplace–Beltrami Operator (LBO) is fundamental to geometric analysis, yet computing its low-frequency eigenmodes remains a significant bottleneck due to the high cost of iterative solvers on large-scale data. To amortize this cost, we introduce the Neural Eigenspace Operator (NEO), a feed-forward framework designed to predict the spectrum directly from point clouds. Crucially, NEO circumvents the ill-posed nature of standard eigenvector regression, which suffers from intrinsic sign flips and rotation ambiguities, by learning the stable, invariant low-frequency subspace instead. Specifically, the network predicts a redundant set of basis functions whose span robustly covers the target eigenspace, allowing for the recovery of accurate eigenpairs via a lightweight Rayleigh–Ritz refinement. To handle irregular sampling, we propose a mass-aware neural operator that incorporates per-point area weights into attention-based aggregation, improving robustness to non-uniform densities and enabling zero-shot generalization across resolutions. Our approach achieves near-linear runtime scaling and substantial wall-clock speedups over iterative solvers at comparable accuracy, and exhibits strong zero-shot transfer to high-resolution point clouds. The resulting eigenpairs support standard spectral geometry tasks, while the raw basis functions provide effective point-wise features for downstream learning. Code: https://github.com/Adversarr/NEO.
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Eigenanalysis of partial differential operators is essential in reduced-order modeling for physical simulation, providing eigenmode representations in elasticity, acoustics, and transient heat transport. While recent neural, mesh-free, and geometry-agnostic approaches enable differentiable eigenanalysis over continuously parameterized shape spaces, boundary conditions of eigenfunctions are limited to Neumann-type (natural) conditions, hindering their applicability in scenarios where boundary conditions must be precisely controlled or optimized. In this work, we focus on Laplace-type operators and extend shape space neural eigenanalysis to handle boundary conditions beyond natural Neumann settings. Building on the same variational, energy-based formulation, we show that Dirichlet, Robin, and mixed boundary conditions can be incorporated without altering the underlying eigenvalue optimization principle. In our formulation, boundary configurations—including boundary placement and Robin coefficients modeling boundary exchange processes—are treated as first-class parameters rather than fixed constraints. When combined with shape-parameterized domains, this leads to a joint shape–boundary space formulation, allowing eigenfunctions and spectra to be evaluated consistently across variations in both geometry and boundary configuration. We conduct experiments on representative applications such as boundary-driven spectral optimization for rigid-walled cavity resonance tuning, reduced-order simulation with changing supports, and analysis of transient thermal behavior under varying boundary exchange conditions. By elevating boundary conditions from fixed constraints to operator-wise parameterization, our approach broadens the applicability of Laplace-type neural eigenanalysis to physical systems where boundary constraints serve as critical design and control variables.
Despite recent progress, text-to-image models still struggle to generate semantically diverse and compositionally accurate multi-person interaction scenes, often collapsing to repetitive layouts, stereotypical poses, and poorly grounded interactions. In this work, we bridge this gap by introducing a dual pose–image representation that brings person-centric structural priors into pretrained diffusion transformers. Our model jointly predicts a 2D pose visualization image and its corresponding RGB image, enabling structure and appearance to co-evolve during learning. At its core, a cross-modal alignment scheme binds text, pose, and image representations, ensuring consistent grounding across modalities. Furthermore, we design an iterative scene construction scheme, progressively generating complex multi-human interactions while effectively decomposing the overall generation complexity. Extensive experiments demonstrate that our method substantially improves prompt alignment and scene diversity in multi-person image generation.
Trying different fabrics on existing garments is a widely applicable problem in digital fashion and computer graphics. A comprehensive transformation involves both material reflectance and geometric deformation from fabric drape. In this work, we focus on the visual aspects of this challenge and simplify fabric try-on to a re-texturing task that replaces garment materials while preserving the original geometry and illumination. Prior approaches perform garment re-texturing via 3D or UV-space reconstruction and rendering, making them sensitive to reconstruction accuracy and rendering fidelity. Recent diffusion-based material transfer methods either lack fine-grained geometric and material control or suffer from domain gaps due to training on synthetic rendered data. We propose a fabric try-on framework that leverages the generative priors of modern image editing models. Motivated by the in-context generation capability of Multimodal Diffusion Transformers, we reformulate garment re-texturing as a two-stage process consisting of fabric removal and fabric application via an intermediate material-normalized image. We further introduce a real-image data curation pipeline and a context-aware tile augmentation strategy, enabling coherent and photorealistic fabric try-on from a single image. Extensive experiments show that our method achieves high-quality, controllable fabric transfer while preserving garment geometry and illumination, without requiring costly reconstruction or rendering pipelines. Our project is available at: https://style3d.github.io/fabric_tryon.