computer graphics developers

Abstract: Strong guidance in text-to-image (T2I) diffusion models concentrates sampling toward high-density modes of the conditional distribution, collapsing independently sampled noise vectors onto nearly identical visual prototypes. This limits utility for tasks that demand distributional breadth, most critically synthetic data augmentation. Diversity, however, is a collective property of the whole batch: a set can preserve every pairwise distance yet still collapse onto a low-dimensional subspace. Existing sum-of-pairwise noise-optimization and repulsion objectives respond only weakly to this higher-order failure. We propose DetNO (Determinant Noise Optimization), which formulates diverse generation as RKHS volume maximization on the initial noise, maximizing the log-determinant of an RBF Gram matrix over one-step Tweedie predictions. This set-level functional equals the squared batch volume; its repulsion is strongest when the batch is most collapsed and self-attenuates as diversity is achieved. An anchor-based fidelity term keeps the optimized noises near plausible regions, and Lagrangian relaxation gives a two-term objective with a single hyperparameter $λ$ governing the diversity-quality trade-off, without training or sampler modification. Across three backbones (SD1.5, SDXL, SD3), DetNO achieves leading intra-batch diversity in VendiScore and Mean Self-Similarity, and a downstream few-shot classification experiment confirms that broader mode coverage brings statistically significant accuracy gains for synthetic data augmentation in the low-shot regime. Fixing the pipeline and varying only the batch objective, both RBF-based aggregators outperform InfoNCE, and the log-determinant attains the best downstream accuracy on both benchmarks. Its diversity advantage over InfoNCE widens as the batch grows. Code is available at https://github.com/mobled37/DetNO.

Abstract: Unit quaternions are widely used in computer graphics making their efficient compression critical for reducing memory consumption and bandwidth requirements. In this paper, we present a novel method for encoding uniformly distributed unit quaternions. Our thorough analysis of several quaternion parameterizations compares their theoretical error properties, quantization behavior, computational cost, and memory efficiency and provides both an analytical and empirical characterization. We show that an infinity-norm parameterization with our optimized warp function consistently offers the smallest maximum error and the best storage efficiency, at a decompression cost equal to or lower than that of parameterization methods found in practice. We demonstrate the practical benefits of the proposed approach in several graphics applications, including tangent-space normal mapping, skeletal animation with blend weights, and Gaussian splatting.

Abstract: We present RoboCloth, a dataset of 500 real cloth materials captured under flexible, calibrated camera and lighting configurations, where both are robotically controlled during acquisition. Each material is imaged in approximately 580 high-dynamic range frames spanning a wide view-light hemisphere; camera poses are refined via structure-from-motion and aligned to the robot frame, yielding per-material sparse surface geometry and structured per-point reflectance observations ready for neural material training. We demonstrate the value of this data through a two-stage neural reconstruction pipeline: Stage 1 trains a shared MLP decoder on our corpus to learn cloth material priors; Stage 2 then freezes the decoder and fits a dense 2048x2048 latent texture to each target material. Evaluating on held-out materials from our own dataset and on the independent UBO2014 benchmark, we show that a decoder trained on our captures outperforms decoders trained on existing measured reflectance datasets and analytic PBR fitting, transferring to unseen acquisition systems without modification. The dataset, calibration files, observation tensors, and train/test splits are released under CC BY 4.0 on the Hugging Face Hub.

Abstract: Compositional structure is pervasive in nature and across scales: atoms combine into molecules, molecules into cells, and cells into organisms, while further compositional hierarchies appear within each level. More broadly, compositionality, the reuse and recombination of parts into novel structures, is a fundamental source of interesting complexity in both natural and artificial systems. Yet despite its importance, and despite our apparent ease in recognizing it, mathematical accounts capturing what we intuitively mean by compositional structure remain limited. Here, we fill this gap by formalizing a simple idea: compositional structure emerges when parts, considered together, reveal shared structure that is not captured when those parts are modeled separately. We express this idea using algorithmic information theory, the mathematics of information and compression, which provides a natural way to identify structure in arbitrary data without specifying in advance what that structure must look like. Applied across scales, our definition informs where and how compositional structure emerges within an object. Using tractable approximations, we then invert the framework to generate compositional objects: we specify the desired form of their compositional structure without prescribing their particular content, and optimize directly over strings and images. The resulting objects exhibit readily recognizable hierarchical reuse and part-whole organization, suggesting that the definition captures compositional structure rather than merely complexity, regularity, or shared information. Finally, we discuss implications for machine learning, including a new perspective on depth in neural architectures and principles for constructing compositional data curricula capable of supporting open-ended learning.

Abstract: We study the problem of testing membership of the origin in the convex hull of $n$ unit vectors in $\mathbb{R}^m$, seeking a convex combination of norm at most $\varepsilon$ or a strict separating hyperplane. The Spherical Triangle Algorithm (STA) uses nearest-point updates on pivot segments. We first establish a conditional $O(1/\varepsilon)$ iteration bound from accumulated geometric progress, allowing deeper pivots to compensate for shallow ones. A three-point example shows that ordinary STA can require $Θ(\varepsilon^{-2})$ iterations. We show that the same conditional bound holds for STA with Wolfe minimum-norm correction (STA--WMC), provided the averaged geometric progress condition holds for the STA steps taken within this corrected method. We then combine STA, WMC, and the Nemirovski weighted-pivot method (NWP) in a hybrid with unconditional bounds of $O(\sqrt{\log n}/\varepsilon)$ matrix--vector products with the input matrix or its transpose and $O(mn\sqrt{\log n}/\varepsilon)$ arithmetic operations, including corrections. We also give a self-contained derivation of the $O(\sqrt{\log n}/\varepsilon)$ membership iteration bound for entropic Nesterov acceleration. Computationally, we compare five methods---ordinary STA, STA--WMC, the hybrid, standalone NWP, and entropic Nesterov acceleration---on convex-hull queries derived from 14 public benchmark datasets and on 204 controlled synthetic inputs. STA--WMC completes all cases in both comparisons, and the hybrid completes all public-data cases. STA performs well on favorable interior and separation instances; Nesterov acceleration is faster than the STA-based methods on the highest-dimensional random membership tests. The experiments show complementary strengths and distinguish practical performance from worst-case guarantees.

Abstract: Monocular world-space human recovery methods excel on current benchmarks, but these rarely include fast camera motion. We introduce the K-Pop stress test, broadcast dance videos that combine fast, large camera motion with dense multi-person choreography. Leading methods produce plausible per-frame meshes on these videos, yet their world-space trajectories drift far from the performers' stage positions. Through a systematic diagnosis, we show that the camera and human estimates each remain self-consistent, and that the drift appears when they are combined at mismatched scales. Each is recovered at its own scale, so a mismatch between the two can turn camera motion into human drift that grows with camera displacement and becomes severe in broadcast dance videos. We derive a closed-form correction that estimates this mismatch and applies one scale to all performers, removing the drift while keeping their relative positions in one shared world frame. It requires no retraining and works with existing backends. Combined with physical constraints, the correction yields stable world-space reconstruction for choreography modeling, scene editing, data generation, and virtual reshooting.

Abstract: Recent video world models have increasingly adopted 3D memory mechanisms to integrate historical observations into a lightweight and persistent scene representation. This naturally raises a complementary question: if 3D representations can serve as an effective mechanism for memorizing observed scenes, can they also be directly used as the latent space for reconstructing and generating scenes? Motivated by this idea, we represent a scene as a compact and unstructured 3D-anchored latent space (\textbf{SceneAE}). Each latent combines an explicit 3D position with an implicit content feature and is spatially grounded to describe its local scene region, forming a sparse latent point cloud. Unlike conventional video-VAE latents that describe how a scene appears from particular viewpoints, our representation directly describes the scene itself, making it naturally applicable to both reconstruction and generation. For reconstruction, once the scene has been generated, our persistent 3D representation can be projected and decoded into RGB-D observations by different target cameras, without the need to regenerate a video for each new camera trajectory. For generation, we leverage the geometry-content separation to first generate camera-controlled 3D geometry and then synthesize content conditioned on it, reducing camera-appearance entanglement and improving camera controllability. Experiments show that this 3D latent achieves superior generation quality, computational cost, and camera controllability.

Abstract: In the classical art gallery problem, a guard sees a target when the segment joining them lies entirely within the polygon. We explore what changes when sight may bend along regular arcs on absolutely irreducible curves, but only those defined by primitive integer polynomials of total degree at most \(d\) and coefficient height at most \(H\). We call such curves admissible sight carriers. Arcs can dramatically improve sight. In a one-sided comb, no straight-line guard sees selected targets in two different teeth, yet a single central guard sees a chosen target in every tooth along parabolic carriers. Sight can also fail in two different ways. Geometrically, the polygon may block every sight arc of the allowed degree between two points. For instance, in an alternating comb, the number of guards needed for a row of targets spanning the comb grows linearly with the number of sides at each fixed degree, even for carriers with arbitrary real coefficients. Arithmetically, no admissible carrier may pass through the points at all. Even in the unit square, at fixed \(d\) and \(H\), the proportion of rational targets that must guard themselves tends to one as the height bound grows. An algebraic target may lie on no rational curve of degree at most \(d\), however large \(H\) is. Both failures can be overcome for finite target sets by allowing the degree and coefficient height to grow. We show that every finite set of algebraic targets in a rational polygon becomes visible from any rational interior guard, with explicit bounds. We also construct, for every \(d\), arbitrarily large Galois orbits in the unit square, all of projective height \(4^{d+1}\), whose points must each guard themselves at degree \(d\) for every \(H\). Yet at degree \(d+1\) and coefficient height one, a single guard sees the whole orbit along \(Z(Y-X^{d+1})\).

Abstract: Contact-rich inverse problems require efficient gradients and reliable enforcement of non-penetration. Existing differentiable methods provide fast simulation and rigid-deformable coupling, but contact treatments based on penalties or velocity-level constraints can permit penetration or positional drift. Incremental Potential Contact (IPC) maintains non-penetration through geometric barriers and {continuous collision detection (CCD)}. However, repeated forward and backward evaluations remain costly in full-space finite-element (FEM) implementations, particularly when nearly rigid components retain many vertex {degrees of freedom (DoFs)}. We present DiffGIPC, a GPU-accelerated differentiable IPC framework for optimizing interacting deformable and nearly rigid bodies. Our affine-body derivatives enable {rest-shape} design, initial-state optimization, and articulated control while retaining only twelve motion DoFs per affine body. These gradients account for how changes in geometry, placement, and actuation affect other objects through collision and friction. We preserve these interactions in one coupled FEM-affine adjoint system per frame, reducing the backward-system size without discarding the dependencies that drive the inverse problem. GPU-optimized backward computation further reduces the cost of repeated gradient evaluations. A reusable PyTorch interface connects supported physical parameters to user-defined parameter maps and losses across design, identification, motion, placement, and articulated control. Experiments demonstrate peak speedups over DiffIPC of approximately 150.0x with full-space FEM and 4133.3x with affine bodies for combined forward simulation and backward differentiation.

Abstract: Projected Walk on Spheres (PWoS) solves surface PDEs through ambient sampling and closest-point projection, but tightly folded embeddings can force short steps or ambiguous projections despite simple intrinsic geometry. We introduce Walk-on-Ambient-Patch (WoAP), which treats the embedding as a solver variable. Edge-isometry constraints and tangent-point repulsion separate intrinsically distant regions, optionally in higher codimension; patch states track residual projection branches without introducing PDE boundaries. We analyze the resulting geometry--sampling tradeoff: additional dimensions provide separation freedom but reduce uniform tangent progress, while strong tangent-biased proposals incur large importance-weight moments. Folded-surface experiments demonstrate reduced projection conflicts, a separate hard-constraint pilot verifies metric preservation, and an internal fixed-RMSE comparison favors higher dimensions at stricter accuracy targets. Together, these results motivate choosing the embedding and projection state jointly with the stochastic solver.

Abstract: We identify explicit closed-form and variational formulae for interpolating the exact values and derivatives through order $s$ of a $C^{s,1}$ function $f:\mathbb{R}^d\to\mathbb{R}$ at $N$ distinct points in $[0,1]^d$. The reconstruction satisfies bounds on its global $C^{s,1}$ seminorm and its Lipschitz constant on $[0,1]^d$ that are independent of the sample size $N$, the latter being the sharp Whitney condition. For $s\ge2$, the reconstruction is real analytic away from the data points and definable in the o-minimal structure $\mathbb{R}_{\exp}$. Our nonlinear extension formula coincides with the formula of McShane (1934) for $s=0$ and with the formulae of Le Gruyer and Phan (2015) and Azagra, Le Gruyer, and Mudarra (2018) for $s=1$, and is new for $s\ge2$. For fixed $d$ and $s\ge2$, our closed-form formula is computable away from the data points by a circuit using only elementary unary and binary real operations, with $\mathcal{O}(N)$ gates and $\mathcal{O}(\log N)$ depth. This yields $\mathcal{O}(N)$ storage and $\mathcal{O}(\log N)$ parallel evaluation time. From the supplied coefficients and weights, the circuit can be compiled with $\mathcal{O}(N)$ one-time work in the exact-real word-RAM model. Thus, in this supplied-data setting, our nonlinear construction improves by a logarithmic factor on the $\mathcal{O}(N\log N)$ initialization bound of Fefferman and Klartag (2009), while retaining linear storage and attaining logarithmic query time through parallel evaluation.

Abstract: Zador's celebrated theorem is a cornerstone of optimal quantisation: it establishes both the weak limit of the empirical distribution of an optimal $n$-point quantiser in $R^d$ and the decay rate of the associated $L_s$-mean quantisation error. In large dimension, however, observing this asymptotic behaviour requires an astronomically large sample size. We prove that, for spherically symmetric target distributions, optimisation over all spherically symmetric distributions is a convex problem and derive an equivalence theorem that both characterises global optimality and yields a constructive algorithm. We show that, for moderate $n$, random quantisers uniformly distributed on a sphere of suitably chosen radius $R$ perform exceptionally well and, over a broad range of values of $n$, are numerically certified to be optimal among all random quantisers. Their expected distortion has an explicit integral representation that can be evaluated to arbitrary precision, and we prove concentration across random quantisers: the distortion variance tends to zero as $n\to\infty$ for fixed $d$. For $s=2$, both the optimal radius and the associated minimum expected distortion admit exact expressions. For general $s$, the optimal radius can be determined efficiently, and extreme-value theory provides useful approximations when $n$ grows with $d$. Depending on this growth rate, $R$ either converges to zero or approaches a positive limit that is independent of $s$.

Abstract: Acquiring realistic microstructure data through Electron Backscatter Diffraction (EBSD) is costly and time consuming, often relying on specialised equipment. As microstructures strongly influence material properties, generating realistic samples is essential for modelling the behaviour of polycrystalline materials. We introduce a generative model for synthesising realistic polycrystalline microstructures using flow matching and graph neural networks. By representing microstructures as anisotropic power diagrams, our model learns a compact geometric parametrisation and can render generated samples at arbitrary pixel resolution. A $C_4$-equivariant architecture incorporates rotational symmetry directly into the model, ensuring that rotations of the input noise produce corresponding rotations of the generated microstructure. We also demonstrate how training-free guidance can be used to generate complex microstructures, based on user defined objective function. In particular, we generate microstructures resembling a copper weld, cast metal slab, 3D-printed stainless steel and heterogeneous lamella titanium.

Abstract: Implicit Neural Representations (INRs) have emerged as a compelling paradigm for modeling multidimensional signals by mapping continuous coordinates to signal values. However, Multi-Layer Perceptrons (MLP)-based INRs inherently suffer from spectral bias, which favors low-frequency components and suppresses the reconstruction of essential high-frequency details. While existing techniques, such as Fourier feature mappings, mitigate this issue, they often rely on sensitive manual tuning and are prone to spectral artifacts. In this paper, we propose a spatial-frequency-aware INR framework that combines an MLP branch with a Kolmogorov-Arnold network (KAN) branch for complementary frequency-oriented modeling. The MLP branch provides a low-frequency-oriented representation of smooth structures, whereas the KAN branch complements localized variations and fine details. To coordinate the two branches, we integrate the discrete wavelet transform (DWT) and inverse discrete wavelet transform (IDWT) into the output fusion stage. The outputs of the two branches are decomposed into wavelet coefficients, and the corresponding coefficients are additively fused before inverse wavelet reconstruction. A wavelet-domain band-separation regularization further penalizes high-frequency responses in the MLP branch and low-frequency responses in the KAN branch, thereby encouraging complementary frequency-oriented behavior. Experiments on 1D signals, 2D images, 3D volumes and signed distance functions, videos, and 4D light-fields demonstrate the applicability of the proposed representation across the evaluated signal modalities. Results demonstrate improved reconstruction fidelity across the evaluated signal modalities.

Abstract: Physics simulation is a cornerstone of many computer graphics applications, ranging from video games and virtual reality to visual effects and computational design. The number of techniques for physically-based modeling and animation has thus skyrocketed over the past few decades, facilitating the simulation of a wide variety of materials and physical phenomena. These course notes provide an in-depth introduction to multiphysics simulation methods for computer graphics, covering the mathematical foundations, key algorithms, and practical considerations behind the most widely used approaches. We focus on methods developed by the computer graphics community for simulating various physical phenomena and materials -- including rigid and deformable bodies, fluids, and granular materials -- as well as the interactions between them. For each method, we present the underlying mathematical framework with detailed derivations and discuss how different materials and coupling strategies fit into the formulation. A selection of software frameworks that offer out-of-the-box multiphysics modeling capabilities is also presented. Finally, we touch on emerging trends in physics-based animation, including machine learning-based methods which have become increasingly popular in recent years.

Abstract: Head avatar modeling requires jointly optimizing multiple objectives with different dominant effects on geometry, appearance, and cross-view consistency. However, their relative effectiveness varies across training states, while existing pipelines typically rely on fixed loss weights or handcrafted stage-wise schedules. A central challenge is therefore to identify which optimization direction is more beneficial at each training state. We propose a counterfactual route optimization framework for Gaussian head avatar modeling, which characterizes state-dependent optimization preference from the realized effects of alternative updates rather than predefined heuristic weighting. Starting from the same training state, we perform short-horizon route-restricted lookahead over geometry, appearance, and joint update routes and evaluate their outcomes under a unified utility. The resulting counterfactual evidence is factorized into a geometry--appearance preference and a residual joint advantage, separately capturing the relative preference between individual update directions and the additional benefit of coordinated optimization. We further amortize this offline evidence into a lightweight controller that directly estimates the current optimization preference and applies bounded modulation to the training objectives during full avatar optimization. Experiments on the NeRSemble dataset validate the effectiveness of the proposed design, consistently outperforming existing methods while preserving clearer local facial structures and finer details.

Abstract: In this paper, we present JAXIGA, an open-source library for isogeometric analysis based on JAX. The library separates the construction of the mesh from the computations which are traced for compilation and differentiation. This allows geometry evaluation, assembly and the supported solvers to be combined in a just-in-time compiled program, for which first-order reverse-mode derivatives can be computed. We consider three numerical methods obtained from a single pointwise energy density. The Galerkin and energy-minimization methods use the same discrete potential and have the same stationary points, while collocation enforces the corresponding strong form. The sensitivities of a converged solution are obtained by solving one adjoint problem, and their accuracy depends on the tolerances of both the primal and adjoint problems. We also describe hierarchical extraction for local refinement of the variational methods and the use of smooth spline spaces for fourth-order problems. The numerical results are compared with analytical solutions and independent FEniCSx and JAX-FEM computations. For the reported GPU benchmark with 36,448 unknowns, assembly is twenty-four times faster than on the host CPU. When the conjugate-gradient solver is also run on the GPU, the total solution time is reduced from 31.8 to 1.38 seconds, and the result agrees with the direct solution to $5\times10^{-11}$. These results show that the choice of solver and the reuse of compilation are important for obtaining an overall reduction in computational cost.

Abstract: I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map $z \mapsto z^α$, $α\in \mathbb{C}$. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse $T^\dagger$ of the non-invertible image transformation $T$, adapted to its recursive constraint. In the idealized formulation, the Penrose identity $TT^\dagger T = T$ makes $TT^\dagger$ an idempotent projection onto geometrically admissible images. Yet denoising only the transformed image remains an out-of-distribution task, even with projection. We therefore braid denoising steps with $T$ and $T^\dagger$: source-space steps develop the untwisted scene, while transformed-space steps refine its appearance and connections in the final geometry. We generate Print Gallery-like compositions and explore further transformations. Rather than distorting a finished image, we let the scene and its distortion develop together.

Abstract: Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this cost, but typically train on expensive, well-converged MC solutions. We propose the Particle Transport Neural Operator (PTNO), a neural operator that learns particle transport surrogates directly from noisy, low-cost MC labels. Such labels pose two challenges: (1) high variance, which destabilizes standard supervised learning, and (2) a high dynamic range (HDR) spanning many orders of magnitude. For the first, we learn the solution operator from noisy labels of many configurations, amortizing MC cost and generalizing to unseen configurations. Because MC labels are unbiased, we show that the squared loss on them shares its minimizer with the loss on converged solutions, and our budget-allocation study over training scenes $M$, MC samples per render $N$, and independent renders per scene $K$ shows that many noisy scenes beat fewer converged ones. For the second, a nonlinear transform such as the logarithm biases noisy supervision. Instead, PTNO keeps labels in physical space and enforces positivity with a softplus output layer that represents small values effectively. We further train with a pointwise relative $L_2$ loss (PRelL2), the stop-gradient relative loss of HDR denoising and neural rendering, which normalizes each residual by the stop-gradient prediction instead of the noisy label. We demonstrate PTNO on neutron transport in fusion reactors and radiative transfer in participating media. On the two neutronics tasks, PTNO is $10^4$-$10^5\times$ faster than converged MC on the same CPU and $10^3$-$10^5\times$ cheaper than MC at matched accuracy; on the two radiative-transfer tasks, MC at matched accuracy costs $0.8$-$11\times$ as much as PTNO.

Abstract: Inference-time alignment of flow and diffusion-based models is critical for achieving flexible generative modeling. Theoretically, Doob's $h$-transform provides an elegant solution to this problem, and most existing methods are based on this principle. However, in practice, estimating the optimal guidance derived from Doob's $h$-transform at inference time is challenging. To deal with this issue, we regard inference-time alignment as a sequential optimization problem in the space of probability measures and propose a novel framework called *Steepest Guidance*, based on the principle of maximizing local improvement in the objective. We provide a theoretical analysis of the proposed method and demonstrate its effectiveness through extensive experiments.

Abstract: Sparse-view 3D Gaussian Splatting is prone to overfitting because limited observations leave many Gaussian primitives weakly constrained, yet their contributions are still accumulated through alpha blending. Without uncertainty estimation, the renderer cannot distinguish unreliable primitives from well-constrained ones, allowing their erroneous contributions to corrupt novel-view synthesis. We introduce UGOD, an uncertainty-guided framework that estimates a view-dependent uncertainty score for each Gaussian and uses it to regulate its rendering contribution. A lightweight uncertainty head conditioned on Gaussian attributes and viewing direction predicts this score, which then drives a differentiable opacity-modulation mechanism that attenuates high-uncertainty primitives before compositing. During training, a detached soft-dropout branch applies an uncertainty-controlled continuous keep mask to discourage the model from relying on poorly constrained Gaussians and thereby reduce overfitting. Crucially, detaching the uncertainty score prevents gradients from this stochastic regulariser from biasing or collapsing the uncertainty prediction. Experiments on Mip-NeRF~360 and LLFF show that UGOD improves sparse-view novel-view synthesis while producing more compact Gaussian representations than the compared methods. These results demonstrate that Gaussian uncertainty provides an effective rendering-time control for sparse-view reconstruction.

Abstract: Reconstructing and animating water scenery from nature produces compelling and immersive visual experiences. Previous work examined this task from the perspective of 2D video textures, with the goal of creating a looping video. In our work, we tackle the problem from a 3D perspective, creating a looping 4D dynamic reconstruction which can be interactively rendered from novel viewpoints from a single non-looping 2D source video. We represent motion as a 3D static \textit{Eulerian} motion field that advects canonical Gaussian splats that are cyclically reborn at fixed time periods, supervised using rendering losses. To model non-periodic and stochastic dynamics present in real-world scenes, we add a non-periodic, time-varying residual term to capture deviations from the static Eulerian motion field. We show quantitatively and qualitatively that our framework enables photorealistic animation of water scenes better than prior art.

Abstract: Instruction-based image editors insert objects, restyle scenes and render new viewpoints, but it is unknown which camera they assume when they paint into a photograph. Asked to cover the floor with a checkerboard, an editor paints projective structure from which classical vanishing-point geometry reads pitch, roll, focal length, yaw and, on renders, the principal point, without any training. Unlike a calibrator such as GeoCalib, which estimates the camera of an image, this isolates the camera under which the editor paints. On 120 rendered cameras with exact ground truth, Qwen-Image-Edit-2511 paints tile edges that meet their vanishing points within 0.26 degrees, and its implicit camera matches the true one to 0.8 degrees in pitch and 6% in focal length, more accurately than GeoCalib except in roll. Asked to draw the horizon or mark a vanishing point instead, the editor fails, so this knowledge is revealed by painting and not by the explicit tasks we tried. The implicit camera has two priors: roll is pulled towards level (slope 0.71), and telephoto perspective towards a default of about 30 mm, which roughly matches the camera the models paint without any scene. For Qwen, the priors do not grow when blur removes four fifths of the line evidence. They are stronger on real photographs, and on NYUv2 a shorter wording of the task removes the difference for roll. On photographs from a 24--240 mm zoom lens the painted perspective grows with only 0.62 of the lens's slope, while GeoCalib and MoGe-2 saturate at about 52 and 42 mm. FLUX.1 Kontext and LongCat-Image-Edit are pulled much harder. Finally, from a level camera a camera-control LoRA executes pose commands at only 50--70% of their strength, and a board painted into its output agrees with the camera it produced.

Abstract: Forward kinetostatics of spatial tendon-driven continuum robots typically requires a nonlinear equilibrium solve for each actuation input. This paper develops a force-to-Cartesian-configuration model with a closed-form solution in quadratures for spatial multi-segment robots under tendon actuation. The Cartesian backbone centerline and accumulated material twist serve as generalized coordinates, from which the strain measures and tendon geometry are derived. Variational equilibrium yields explicit axial and bending relations and establishes zero equilibrium material twist within the proposed model for admissible longitudinal non-helical routing. The solution is propagated segment by segment without an iterative equilibrium solve, while retaining axial deformation, spatially varying axial and bending stiffnesses and tendon-routing diameter, and segment-dependent tendon participation. Numerical comparisons with a full-strain geometric variable-strain model (GVS) yield maximum length-normalized tip-position discrepancies of 8.91 x 10^-6 and 1.01 x 10^-5 for the single- and three-segment robots, respectively. Mean evaluation times of 1.52 μs and 2.94 μs, with corresponding speedups of approximately 1864x and 3348x over the baseline, demonstrate the computational advantage of the explicit force-to-configuration mapping in the reported benchmark.

Abstract: We introduce Neural Harmonic Measure Operator (NHMO), a neural solver for elliptic PDE problems on variable-shape domains. The harmonic measure of a domain is the boundary probability distribution that, integrated against any boundary data, returns the Dirichlet Laplace solution. It depends only on the geometry, not on the boundary data. NHMO parameterizes the density of this measure as a transformer-based boundary kernel supervised by Walk-on-Spheres exit samples, so one trained kernel handles different boundary values on a shape with no retraining. We extend it to Poisson via a classical decomposition, with an auxiliary network amortizing the source-induced correction and avoiding the singular volume quadrature that breaks direct evaluation. At inference, new boundary values and new sources both yield PDE solutions by re-integration against the fitted kernel and lift, with no retraining. NHMO improves over four prior baselines on the MCB-B 3D variable-shape Poisson benchmark across all five categories, and is competitive with major neural-operator baselines on a controlled 2D testbed.

Abstract: Constructing a smooth approximation of an unsigned distance field (UDF) from a raw point cloud is challenging because the input provides neither surface connectivity nor consistently oriented normals. Methods that directly learn a scalar UDF must also handle its non-differentiability on the zero level set and weak supervision away from the samples, which can lead to unstable optimization and spatial artifacts. We introduce Projective Normal Fields (PNFs), an orientation-free representation and convex optimization framework for estimating bidirectional normals from point positions alone. Each normal axis is encoded by a rank-one projector, which is invariant to normal reversal. We relax the non-convex set of hard projectors to its convex hull: the symmetric positive-semidefinite matrices with unit trace. Each soft tensor defines a local quadratic distance model and retains the relative weights of candidate normal axes. We estimate a coherent PNF by combining local tangent-plane fitting, soft-PCA anchoring, and overlap regularization on a fixed neighborhood graph. With positive anchoring weights, the objective is strongly convex and admits a unique global minimizer. Principal eigenvectors provide bidirectional normals, while the corresponding eigengaps provide spectral confidence indicators. We use these indicators to select and weight directional sources for heat diffusion, followed by Poisson integration to construct a regularized UDF approximation. By separating local geometry estimation from scalar-field construction, PNF avoids directly fitting the non-differentiable UDF. Experiments demonstrate reduced sensitivity to neighborhood size, competitive reconstruction under noise and outliers, and improved accuracy near non-manifold junctions. The project page is available at https://anonymous17777367.github.io/PNF-page/

Abstract: Differentiable physics is increasingly used in robotic material manipulation for system identification, trajectory or skill optimization, demonstration generation, and robot or end-effector design. These applications depend on gradients propagated through long, contact-rich simulation rollouts. We study the numerical reliability of those gradients using two Material Point Method (MPM) system-identification benchmarks derived from elastoplastic and granular manipulation. The benchmarks provide controlled cases for three effects that also arise in broader differentiable physics-based optimization. GPU many-to-one sums whose order depends on thread scheduling changed long-horizon gradients and reversed the sign of one parameter gradient relative to a deterministic reference. Finite-difference checks became less reliable for longer rollouts because repeated-run loss variation grew much faster than the loss change produced by the tested parameter perturbations. Observation and loss definitions changed optimization behaviour and the solution preferred by an independent metric. These results motivate reproducible accumulation, finite-difference validation that compares perturbation-induced loss changes with repeated-run variation, and explicit reporting of objective construction when differentiable simulation is used for robotic optimization.

Abstract: Matrix multiplications dominate the inference cost of modern transformer-based vision models, yet existing efficiency techniques such as post-training quantization and mixed-precision inference are largely limited to the small set of fixed-width formats (INT4, INT8, BF16, and FP16) supported by conventional accelerators. We revisit stochastic computing (SC) as a way to lift this constraint: viewed as a dense adaptive quantizer, SC controls precision by bit-stream length L rather than a fixed datapath, while each multiplication reduces to a single AND/XNOR gate. We build a GPU library that emulates SC matrix multiplication at scale, exposes stream lengths as first-class kernel arguments, and evaluates SC end-to-end on image classification, object detection and instance segmentation, class-conditional image generation, and visual world-model planning. On top of this substrate, we develop a dynamic per-row mixed-precision policy that assigns stream length per token or group at matched average budget, requires no retraining, and uses the same SC hardware across schedules. Across tasks, SC remains competitive with fixed-format INT quantization at matched bit budgets, while per-row mixed precision helps maintain accuracy at lower average stream lengths. These results provide software-level feasibility evidence that SC can serve as a dense-precision substrate for fine-grained mixed-precision inference on modern vision transformers.

Abstract: Predicting smooth dynamics and collisions requires modeling continuous evolution and abrupt state changes. We introduce HamiFormer, a dual-expert diffusion field combining whole-window denoising with residual-corrected Hamiltonian propagation. Their mixed-state feedback attenuates the direct contribution of inherited autoregressive error: each mixed state guides subsequent propagation within the jointly refined window. Parallel Local Affine Scan (PLAS) amortizes iterative refinement across rectified-flow steps and evaluates derivatives in parallel across physical time. PLAS's affine symplectic maps achieve lower solver error and runtime than sequential explicit Euler in our evaluation. A Regime Model Tree specializes residuals and routing to balance typical-state accuracy against large tail errors. Our analysis gives conditions for physically consistent refinement and warm-start tracking, and finite-window error bounds under diffusion feedback. In 192-step evaluations, HamiFormer reduces normalized phase-space MSE by 26.3% against PhysiFormer on HamiBalls-1 and 21.4% against DiT on HamiBalls-2, with comparable model capacities. Disjoint-interval comparisons show the lowest late-horizon position and momentum errors among baselines on both datasets. Project page: https://hamiformer.github.io/.

Abstract: We study the problem of approximating the John ellipsoid (JE) of a given (centrally symmetric) polytope of $n$ constraints in a Euclidean space under differential privacy (DP). We give the first differentially private algorithm for this problem under the standard model, where neighboring datasets may differ arbitrarily in one a single constraint. Our work also extends to the complimentary problem of Minimum Enclosing Ellipsoid of $n$ points in the Euclidean space. Our approach is based on the recent non-private multiplicative-weights algorithm of~\cite{pmlr-v99-cohen19a}. First we introduce a non-private generalization of the Cohen et al algorithm, yielding a $(1+γ)$-approximation of the JE problem while violating at most $κn$ constraints in $O(\log(1/κ)/γ)$ iterations. This variant works by projecting the intermediate weights assigned to the constraints onto the set of $κ$-dense distributions, similarly to~\cite{bun2020efficientnoisetolerantprivatelearning}. We then design a $ρ$-zCDP variant of this algorithm by adding Gaussian noise to the weighted covariance matrix aggregated in each step of the algorithm. Under a mild goodness assumption on the data we can assert that the resulting noisy matrix is close to the true matrix, thereby achieving essentially the same guarantee as the non-private algorithm provided sufficiently many input points. Thus our method achieves an efficient DP poly-time algorithm under concrete sample complexity bounds.

Abstract: We present Light Field Primitives (LFP), a formulation for novel view synthesis that replaces the dense ray database with a compact set of differentiable primitives in the classical two-plane parameterization. Each primitive condenses a group of rays into one learned record, and its response to a query is governed by how closely that query belongs to the group. Rendering a camera ray then reduces to compositing all responses it elicits, and a scene can be optimized directly from posed images and rendered in real time with rays. Beyond its competitive performance on standard benchmarks, the main advantage of LFP is structural: its primitives reside directly in the 4D ray space, so optical and appearance effects that are already operations on the light field become behaviors of a single shared renderer. With minimal changes to that renderer, LFP supports multi-scale anti-aliasing, defocus deblurring with refocusing, rendering for fisheye cameras, and even transparent object reconstruction with ray refraction, matching specialized frameworks that devote substantial machinery to these effects.

Abstract: Learned particle simulators based on graph neural networks achieve strong one-step accuracy, but errors compound over long horizons. An underexplored variable is the interaction graph: existing methods fix its topology via k-nearest neighbors or a static radius rule, regardless of local model confidence. We propose making this graph adaptive: a per-particle variance head, trained jointly with the acceleration head under a heteroscedastic Gaussian NLL loss, drives a trajectory in which high-uncertainty particles receive an expanded neighborhood. This is done at little extra inference cost by using the previous step's uncertainty estimate. A key discovery is that the variance head learns a meaningful notion of uncertainty: high-variance particles concentrate near complex regions, such as splash zones or free surfaces. When this signal drives graph topology, the resulting AdaptGNS simulator achieves a strict Pareto improvement on WaterDrop and a modest gain on Sand. Given the model's stronger performance on WaterDrop, we hypothesize that adaptive graphs are most useful when complexity is concentrated in space. Our code can be found at https://github.com/aidenzhou8/AdaptGNS.

Abstract: We investigate the use of neural network solvers for infinity and $p$-Laplace problems, which are fundamental in nonlinear analysis and have practical applications. Our approach employs Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) to address computational challenges associated with large $p$ values, ranging from $2$ to $1000$, on various 2D and 3D domains. Our method offers advantages over traditional physics-based solvers, especially in three dimensions where mesh-based solvers become very costly for these problems. We also establish conditional convergence results for PINN approximations of both problems and a universal approximation result for DeepONet on the parametric $p$-Poisson problem. We demonstrate the effectiveness of these neural network solvers through numerical experiments and compare their performance with conventional methods.

Abstract: We study the \emph{bichromatic line-center problem} for $n$ pairs of points in the plane. A feasible solution assigns one point from each pair to the red set $R$ and the other to the blue set $B$. The goal is to minimize $\max\{w^\circ(R),\,w^\circ(B)\}$, where $w^\circ(X)$ denotes the minimum width of a strip enclosing $X$; the midlines of the corresponding optimal strips define the line-centers of $R$ and $B$. We consider several variants induced by orientational constraints on line-centers and provide efficient algorithms for each. For one line-center, which consists of computing a minimum-width strip that contains at least one point from each pair, we give an $O(n^2)$-time algorithm. For two line-centers, we obtain an $O(n)$-time algorithm when both are horizontal, and $Θ(n\log n)$-time algorithms when the two centers are parallel or when both orientations are prescribed. When exactly one orientation is prescribed, we give an $O(n^2)$-time algorithm. Finally, for the unrestricted case, we present an $O(n^3\log n)$-time algorithm.

Abstract: Hamiltonian normalizing flows are attractive generative models because their phase-space maps are invertible and volume preserving, but most neural constructions are formulated in Euclidean space. We introduce Riemannian Neural Hamiltonian Flows, which combine the fixed kinetic energy of a Riemannian manifold, a learned scalar potential, and an explicit geodesic leapfrog integrator. Our analysis explains how the learned Hamiltonian can be made interpretable. Every normalizable potential defines an implicit profile, and the position marginal initially accelerates along the relative score between that profile and the base. The matched potential is the interpretable specialization for which the implicit profile is the target. In the isotropic Gaussian case, the mechanism corresponds to a phase-space rotation. A local harmonic analysis extends this result around each mode of a general target on a manifold. The gap between the learned and the matched potential is the sum of a residual memory of the base and a bias of the model, and the two potentials agree when the position base has been transferred to the momentum. This can be achieved when the former is broader than the target. Numerical experiments on Euclidean, hyperbolic, and spherical spaces show competitive sample quality and numerical cost against a Riemannian continuous normalizing flow, and confirm the interpretability of the learned potential.

Abstract: Gaussian Splatting has significantly improved the quality of novel view synthesis with explicit Gaussian representation. However, we observed that existing 3D Gaussian Splatting methods (3DGS) often suffer from surface collapse issues on reflective regions, and thus produce inferior geometry and low-quality specular. In this work, we propose a physically-based deferred rendering framework, named Reflection-aware Gaussian Splatting (RGS), that can accurately model specular regions and improve novel view synthesis performance. Specifically, we found that a powerful 3D foundation model can provide a strong 3D geometric prior to foster correct geometric modeling. Based on this, we propose a cross-view shape consistency regularization to regularize the geometry surface with the large model prior and cross-view constraints. In this manner, our RGS can produce smoother geometric surfaces on reflective regions while reducing geometric hollows. To further improve rendering results on reflective regions, we present a reflection-aware densification strategy that is designed to capture specular variations across various views. With this strategy, our RGS is able to render novel views of objects in higher quality. Extensive experiments demonstrate our method consistently renders high-quality reflective objects, achieving state-of-the-art performance.

Abstract: We compute the convex envelope of (nonconvex) bivariate piecewise linear-quadratic (PLQ) functions (bivariate quadratic functions defined on a polyhedral subdivision). Our algorithm is composed of the following steps: (1) compute the convex envelope of each quadratic piece obtaining piecewise rational functions (quadratic divided by linear function) defined over a polyhedral subdivision; (2) compute the (Legendre-Fenchel) conjugate of each resulting piece to obtain piecewise quadratic functions defined over a parabolic subdivision; (3) compute the maximum of all those functions to obtain the conjugate of the original PLQ function as a piecewise quadratic function defined on a parabolic subdivision; (4) compute the conjugate of each resulting piece; and finally (5) compute the maximum over all those functions to obtain the convex envelope (biconjugate) as rational functions (quadratic divided by linear function) defined over a polyhedral subdivision. Our contribution includes a practical algorithm running in linear time, and proving that the convex envelope is a piecewise rational function.

Abstract: Creating deformable assets for robot manipulation requires jointly specifying their geometry, appearance, and physical properties. This is especially challenging for deformable objects, since text and images provide limited evidence about how they deform and respond to contact, yet these responses directly affect their suitability for interaction. Automated generation therefore needs to resolve coupled physical requirements and use interaction evidence to guide construction and refinement. We present DeformSmith, a framework that enables automated generation of interactive, physically credible deformable assets from text or a single image. Through hierarchical agentic construction and a shared physics-grounded harness, it progressively builds, tests, and refines geometry, physical models, material behavior, and robot interaction until the resulting asset is ready for simulation and manipulation. Robot interaction closes the generation loop through manipulation feedback and replayable interaction data. Results show that DeformSmith generates assets with better visual quality and physical plausibility than state-of-the-art baselines, including PhysGen3D, PhysGM, and PhysX-Omni, while supporting the synthesis of data for robotic manipulation of deformable objects. Project page: https://can-lee.github.io/deformsmith-web/

Abstract: We present DiT-Garment to model dynamic 3D clothing over human body models in arbitrary motion. Unlike existing methods, DiT-Garment can animate garments with unseen designs and physical materials, while allowing for direct inference of deformations for any target pose. To achieve this, we leverage a 2D diffusion transformer architecture to learn 3D deformations in a 2D UV-space. As the result is non-deterministic, our generative model learns the distribution of possible outcomes. The template garment is represented as a 3D triangle mesh spatially aligned with a 3D human body model in a standardized pose. To work with different garment designs without the need of a common template or complex graph convolution operations, the diffusion transformer is conditioned on a 3D position map of the template, represented in UV-space, which allows to implicitly learn a deformation of the 3D space around the body in standard pose. Further conditioning on body motion and physical parameters allows to physically ground the model. We quantitatively and qualitatively evaluate DiT-Garment on both synthetic and real data. While only trained on synthetic simulations of automatically generated cloth designs, our method generalizes to captured and artist-made garment designs. Code and data are available for research purposes at https://dumoulina.github.io/dit-garment/.

Abstract: Grasp synthesis aims to generate stable and physically plausible hand--object interactions, and has become a fundamental problem in both human hand modeling and robotic manipulation. However, a unified representation across human and robotic hands is still lacking, mainly due to differences in hand morphology and surface modeling. Prior methods typically rely on either contact maps or dense implicit descriptors to represent interaction, but these representations are often incomplete or computationally expensive and redundant. We propose InterMASH, a unified geometric representation that establishes cross-embodiment correspondence using sphere-fixed anchors. At each anchor, low-degree spherical harmonics compactly encode local hand geometry, object geometry, and contact, forming an explicit and interpretable token sequence. Building on this natively tokenized structure, we introduce a conditional Diffusion Transformer that operates directly in the proposed InterMASH representation space and jointly generates hand geometry and contact, improving consistency and physical plausibility. Our method achieves competitive performance with state-of-the-art methods on key physical feasibility metrics in a large-scale ShadowHand benchmark, supports joint training across multiple hands, and shows that cross-embodiment fine-tuning with human grasp data can improve robotic grasp success and diversity. Project page is available at https://inter-mash.github.io/.

Abstract: Monocular reconstruction of wind-driven vegetation is severely underconstrained: motion along the viewing direction is largely unobservable, a moving canopy offers few reliable correspondences, and nearly the entire scene is dynamic, providing little static reference. Directly-learned deformation fields in 4D Gaussian Splatting therefore optimize photometric consistency rather than recover the motion that produced it. We replace that field with a physically parameterized deformation prior: one damped harmonic oscillator per rigid part, driven by the observed wind and integrated by differentiable RK4, supervised photometrically alone. To test whether such a prior is physically grounded rather than merely well fit, we build a controlled synthetic testbed of three procedurally generated trees spanning an order of magnitude in skeleton complexity, whose per-part natural frequency follows from its own geometry and whose damping ratio is a fixed constant, both held out of training. On it, we measure held-out views, temporal extrapolation, zero-shot transfer to unseen wind speeds, and recovery of the physical parameters themselves. The prior costs appearance fidelity on in-distribution views and extrapolates markedly better outside the training window and the training wind, while parameter recovery is far weaker than it first appears: frequency recovery survives an untrained null control on only the sparsest of the three trees, and damping is not recovered at all.

Abstract: Novel-view synthesis from a single image is a fundamentally ambiguous problem. As the camera moves away from the input viewpoint, previously hidden regions become visible, exposing missing geometry and holes in the reconstructed scene. Existing methods often rely on generative models to complete such regions. However, many of these artifacts are small gaps near depth boundaries and do not require generating new scene content. In order to eliminate expensive process of generating image we introduce ORCA, an occlusion-aware method for reconstructing and completing explorable 3D scenes from a single image. ORCA first introduces 3D structure into a Gaussian-anchor representation using monocular depth while preserving the original camera-ray correspondence. During scene exploration, missing regions are handled based on their size and structure. Small disocclusions are repaired using RGB-D information already available in the reconstruction, while generative inpainting is reserved for larger regions that cannot be reliably recovered from the scene. New Gaussian anchors are added and optimized locally without modifying the existing representation. By reducing unnecessary reliance on generative inpainting, ORCA limits generation-induced hallucinations and better preserves the content and structure of the original scene. On DIV2K, ORCA improves novel-view quality over VistaDream across all reported metrics, increasing MUSIQ from 61.60 to 68.71 and CLIP-IQA from 0.474 to 0.574. These results show that many novel-view artifacts can be repaired effectively by reusing information already present in the reconstructed scene.

Abstract: Text-driven 3D human motion generation models face significant challenges in responding to diverse and unconstrained textual prompts, primarily due to the limited availability of 3D motion training data. To address this, we introduce MoVT, a novel framework that effectively leverages the extensive range of human action videos to enhance text-to-motion generation. At the core of our approach is the cross-modal augmented motion tokenizer, which projects discrete 3D motion tokens into the 2D domain. This projection allows us to enrich the motion codebook with complex, real-world motion patterns derived from videos. The enriched discrete tokens are then mapped back to the 3D domain, resulting in aligned 3D and 2D codebooks with an enhanced capacity to represent intricate motions. These enhanced codebooks are integrated into a generative masked transformer, which predicts masked motion token indices in a modality-agnostic manner. This enables the use of text-index pairs, generated from the 2D codebook and annotated motion videos, to further enhance the generator. Extensive empirical evaluations show that MoVT performs favorably against prior state-of-the-art methods across multiple key metrics.

Abstract: A stencil computation repeatedly updates every cell of a grid from its neighbours' values at the previous timestep. Simulating T steps on N cells directly costs Theta(NT), and a line of work beginning with Ahmad et al. reduces this by composing many timesteps into one linear operator and applying it with a Fast Fourier Transform. That technique needs to know which cells will still obey the same operator when the composed step ends, and in a free-boundary problem they do not: the region governed by a given rule is determined by the solution and moves as it evolves. We study one spatial dimension, a three-point stencil with time-varying coefficients, and a computed region that is a single interval whose two endpoints move by arbitrary amounts at every step, revealed online. Let B be the horizon plus the total variation of the boundary trajectory. We give a schedule whose work is O((B+N) log T log(N+B)) and whose span is O(T log T log(N+B)), and we prove that the values it computes are exact. The best existing bound for a region that moves requires its boundary to travel at most one cell per timestep. We drop that requirement and lose nothing by it: a boundary obeying it has B <= 3T, so our bound stays near-linear on every trajectory the earlier result covers. Elsewhere, B grows only by the distance the boundary actually travels -- one jump of width N costs T + 2N. The reason total variation suffices is that everything the two endpoints touch over a time window of any length lies in two intervals, one per endpoint. This cannot be relaxed: with p regions the bound degrades by a factor p, and at p = sqrt(T) there is an instance on which the work is Theta(T^{3/2}) while B + N = Theta(T). All results are machine-checked in Lean 4, apart from the classical convolution bound, which is imported as an interface.

Abstract: Automatically generating high-quality conforming hexahedral (hex) meshes from general input boundaries remains a challenging problem, despite the numerical advantages hex elements offer in simulation. Grid-based adaptive refinement, followed by hanging-node removal, is the most robust fully automatic choice. Among two-refinement methods, primal templates have better mesh quality than dual templates but depend on a strong balancing condition that over-refines the grid; neither family guarantees planar quadrilateral (quad) faces. This paper generalizes recent primal three-refinement templates to a two-refinement scheme under a moderate balancing condition, a relaxation of the strong one. 32 special and five fundamental patterns resolve all 144 symmetry-reduced configurations, followed by either a fast greedy algorithm or an integer linear programming (ILP) algorithm that trades extra runtime for a further reduction in element count. The scheme is the first two-refinement method in which all hexes have planar faces, and its meshes feed directly into a recent quality-guaranteed hex mesh reconstruction algorithm. At comparable element counts, it attains a similar Hausdorff ratio (HR) and a higher minimum scaled Jacobian (min SJ) than its three-refinement counterpart.

Abstract: Recovering editable 3D parametric curves from 2D images is a fundamental challenge in computer graphics, bridging pixel-based perception and vector-based CAD modeling. Existing NeRF- and 3DGS-based methods often rely on dense calibrated views, precomputed 2D edge maps, and costly per-scene optimization, limiting their applicability to casually captured real-world inputs. We propose CGGT, a Curve-Grounded Geometry Transformer that directly grounds 3D-consistent 2D curve instances in the image space from sparse, unposed multi-view images. CGGT combines a geometry-aware transformer encoder for multi-view feature learning with a curve-aware masked-attention decoder for cross-view instance association. In a single forward pass, it predicts camera parameters, dense depth maps, and instance-level 2D curve masks, which are then lifted into 3D and refined through a fast parametric optimization stage to recover compact, editable 3D curve primitives. To support structured curve learning, we introduce Wireframe-100K, a large-scale dataset comprising 100,000 CAD models with diverse topologies, realistic multi-view renderings, and accurate parametric curve annotations. Extensive experiments show that our framework achieves substantial improvements in both reconstruction accuracy and efficiency, particularly under challenging sparse-view settings and in separating persistent 3D structural edges from view-dependent image edges caused by silhouettes, textures, and appearance variations. Despite being trained solely on synthetic data, CGGT generalizes well to real-world images, demonstrating its potential for practical CAD-style wireframe reconstruction from unconstrained visual inputs.

Abstract: This work presents an algorithm, together with its correctness proof, to determine the minimum perimeter polygon (MPP) for digital objects given as regular complexes in the triangular plane tiling. Such objects are edge-adjacency-connected sets of triangle tiles that have no end tiles, and the point set union of all their tiles forms a simple polygon. Nevertheless, the boundary paths of the objects are not assumed to be simple. Then the MPP is a weakly simple polygon that coincides with the relative convex hull (i.e., geodesic hull) of a set $A$ with respect to a simple polygon $B$, where $A\subset B$, but $A$ is not necessarily a polygon, in fact it is generally not connected. Our MPP algorithm relies on constructing and iteratively constraining cones of visibility through forthcoming boundary tiles, it uses the structure of the canonical boundary path, the MPP frontier is the shortest polygonal curve following this path. We also propose a boundary tracing algorithm to obtain such paths from the objects.

Abstract: Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it enjoys both the strict physical correctness from rigorous numerical physics simulators, and the high efficiency and effectiveness from automatic differentiation and gradient-based optimization. However, currently, this paradigm faces performance issues in optimization. In this work, we target benchmarking the performance of different optimizers to solve various inverse problems. We construct 12 differentiable physics simulators spanning physics domains including discrete mechanics, continuous mechanics, atomistic simulations, rendering, and semi-empirical physics models. Based on these simulators, we design corresponding inverse problems that can be categorized into parameter identification, inverse design, and optimal control. Finally, we conduct extensive experiments to compare the performance of different optimizers, including regular first-order methods, approximate second-order methods, as well as global optimizers, on these inverse problems, and analyze the results to provide insights on how to choose and design optimizers for differentiable programming. We hope such benchmarks can inspire the development of more effective optimizers, and further promote the applications of differentiable programming in various scientific and engineering domains.

Abstract: In rendering, a camera is a sampling operator that maps each finite pixel to a bundle of rays. Different camera models change the geometry of this bundle, thus making a unified and faithful rendering formulation challenging. Consequently, Gaussian ray tracing supports generic cameras (with optical center) through their inverse ray mappings, yet typically reduces every pixel to a single center ray. This ignores the camera-dependent pixel footprint, causing aliasing under minification, while unconstrained Gaussians expose unsupported frequencies under magnification. We present ConeGaussian, a camera-model-agnostic anti-aliasing framework for Gaussian ray-based rendering. Instead of defining the pixel filter on a camera-specific image plane, ConeGaussian constructs an anisotropic footprint directly from neighboring rays produced by the camera's native inverse mapping. We derive a closed-form response under a locally linear, depth-local, moment-matched approximation of the finite pixel footprint, while the same geometry defines a per-Gaussian training-frequency floor. Notably, by construction, our filtering principle can be used unmodified across calibrated central camera models and multiple Gaussian ray-rendering backbones. Additionally, unlike in mip-splatting, our scene-space frequency floor and filtering enable trivial composition at render time, allowing us to remove excess blurring. On pinhole and strongly distorted fisheye captures, ConeGaussian consistently improves two distinct ray-based backbones, by up to 4.3 dB at 1/8 resolution, and reduces fisheye LPIPS by 30% where perspective screen-plane footprint formulations are not directly applicable.

Abstract: Three-dimensional Gaussian Splatting (3DGS) combines explicit primitives with efficient rasterization, yet recent systems increasingly use neural networks to generate or share Gaussian parameters. We characterize this trend along five axes: attribute decoding, spatial sharing, view-conditioned decoding, topology generation, and amortized inference. An analysis of 19 representative methods shows that these choices address different limitations and cannot be reduced to a binary neural label. We also isolate three forms of neural parameterization in a controlled mip-NeRF 360 study. Sharing appearance and opacity improves reconstruction quality, while decoding geometric structure offers no further gain. The evidence favors selective neuralization: shared functions help when they capture reusable correlations without sacrificing the local geometric freedom of explicit splats.

Abstract: Many scientific applications require modeling how diffusive systems evolve over time, not merely their eventual steady states. While conventional steady-state analysis of partial differential equations (PDEs) on complex geometries is already hindered by costly volumetric meshing, transient analysis further requires sequential time stepping and careful step size selection. Grid-free Monte Carlo solvers such as walk on spheres (WoS) and walk on stars (WoSt) avoid this meshing bottleneck but remain largely limited to steady-state problems. We generalize WoS, for pure Dirichlet problems, and WoSt, for mixed Dirichlet--Neumann problems, to heat equations with initial conditions and time-dependent source and boundary data. We equip each random walk with a finite time budget and sample an exit time at every spatial step. If the exit time exceeds the remaining budget, the walk samples an interior point and evaluates the initial condition; otherwise, it continues with a reduced budget, accumulating source and boundary contributions. Our main technical contribution is a suite of kernel sampling and variance reduction techniques, including a low-bias, tabulation-free exit time sampler and efficient rejection samplers. Unlike grid-based transient solvers, our method directly estimates the solution at any requested time without volumetric meshing or sequential time marching. It also retains the parallel, progressive, and output-sensitive evaluation of WoS and WoSt while eliminating time step selection and temporal discretization bias entirely. Finally, we show how sharing walks enables efficient estimates at multiple target times.

Abstract: Qualitative results and an illustration of our core idea. Top left: reconstruction results on benchmark images. Top right: reconstruction results on real-world images. Bottom: illustration of reconstruction-guided noise initialization and modulation. Given multiple input images, we predict a point cloud in canonical space, deterministically inject the predicted geometry into the diffusion process through noise inversion, and modulate the resulting noise to preserve the generative flexibility required to complete unobserved regions and refine visible geometry.

Abstract: Agentic search and automated optimization of GPU kernels are powerful tools for large language model inference. Their effectiveness, however, depends not on the sophistication of the search itself, but on the clarity of the optimization problem being solved. We provide an application-first approach that drives a hierarchical code generation tool from operator specifi cation down to GPU instructions, and show that a clearly defined computational model makes the optimization problem tractable.

Abstract: Geodesic polar coordinates (GPCs) provide an intrinsic parameterization over curved surfaces, but their accurate estimation remains challenging, particularly in the presence of anisotropic metrics, high curvature and complex topology. We introduce iLogMap, a method for computing GPCs in curved domains that recasts the angular component of the logarithmic map to a ground-state magnetic eigenproblem over the circumferential direction field of geodesic distance. Our method effortlessly extends to anisotropic metric tensors and solid volumes, enabling cylindrical and spherical parameterizations in tetrahedral meshes. Experiments on diverse shapes with varying genus confirm competitive angular accuracy and reduced metric distortion relative to heat-based methods, with improved performance on surfaces with boundary and domains with anisotropy. We demonstrate the utility of iLogMap in computational cardiology applications, where we use it to initialize spiral phases on atrial surfaces and estimate local activation patterns in ventricular models.

Abstract: We propose Semi-Implicit Pairwise Descent (SIPD), a unified nonlocal pairwise framework for simulating large-scale hyperelastic materials involving complex contact and friction. By reformulating the Finite Element Method (FEM) equations of motion into a pairwise force representation from a nonlocal perspective, our approach avoids costly Hessian computations, leading to a reduction in per-iteration computational overhead. Furthermore, we propose an analytical projection strategy for projecting our Hessian-free coefficient matrices to positive semi-definiteness. And we treat contact and friction as a unified anisotropic elastic energy, allowing for a seamless integration into the elastic solver framework. We mathematically prove that our method is unconditionally stable and numerically convergent.Experimental results demonstrate that SIPD achieves real-time performance for million-scale simulations even under intricate contact and friction conditions.

Abstract: Three properties determine whether a differentiable simulator can drive gradient-based optimization through contact: simulation accuracy, gradient reliability, and per-iteration cost. Tape-based engines such as MJX and Newton Semi-Implicit require timesteps small enough to keep contacts numerically tractable, and their backpropagation memory grows linearly with the number of timesteps T. Surrogate models bound memory by approximating contact away, but the resulting gradients lose the geometry the optimization depends on. We present Ostrich, a GPU-accelerated rigid-body simulator that resolves hard contacts and friction with non-smooth Newton iteration at large timesteps (h ~ 0.1 s), and differentiates the converged residual via the implicit function theorem, reusing the forward Schur complement to compute the adjoint at O(1) memory per timestep. On real-robot trajectories over a pallet obstacle, Ostrich holds MuJoCo's sim-to-real accuracy up to a 50x larger timestep. Its gradients converge from random initializations where MJX descends slowly and Newton Semi-Implicit stalls; a warm iteration runs 211x faster than MJX's and 4.7x faster than Semi-Implicit's. On the same scene Ostrich differentiates 8,192 parallel worlds on a single 24 GB GPU, sustaining 29x checkpointed MJX's optimization throughput; without checkpointing both baselines exhaust memory at far fewer worlds. We close with a gradient-based trajectory optimization demonstration over triangle-mesh terrain across a 10 s horizon, a setting where prior engines either restrict to primitive geometry or face the convergence and memory limits shown above.

Abstract: Pigment deposition in paper marbling displaces the pattern already present, coupling the appearance of each gesture to later actions. We recover executable programs for a deposition-based digital marbling model: given a target image, we optimise an ordered program of capsule insertions whose replay approximates it. The capsule primitive continuously joins circular drops to elongated deposits. Its transport is exactly area-preserving and has a closed-form inverse on the exterior of the deposited region. A replay adjoint reconstructs intermediate states, retaining coordinates lost inside deposits and periodic position checkpoints. At 2000 gestures and 1024^2 pixels, the PyTorch replay implementation uses 8.7x less memory than the tested checkpointed-autograd configuration at comparable step time; the fused implementation fits a program in about four minutes on one workstation GPU. We evaluate image reconstruction on five marbled sheets, compare against transport-disabled fitting, one-pass geometric compensation and a published stroke-based fitter at matched stroke count, and measure sensitivity to an alternative ordered-drop transport. Recovered programs replay across a 4x range of linear resolution. Edits specified in program order or in palette space -- inserting a gesture, recolouring a stage, translating a stage -- replay correctly under the same model; edits specified by image content, such as moving a motif, do not. On synthetic targets with known generating programs, the recovered programs match the images but not the generating gestures under a positional matching statistic. The output is an editable program in the specified digital medium.

Abstract: Learning physically plausible dynamics from visual observations is essential for interactive world models and embodied agents. However, modeling real-world deformable objects remains challenging because their dynamics often arise from complex, spatially heterogeneous material responses. To address this challenge, we propose PhysReal, a video-driven framework for learning and simulating the underlying physics of real deformable objects. PhysReal integrates a spatially varying hybrid expert-neural constitutive model with a differentiable MPM simulator and 3DGS renderer. Analytical expert models provide interpretable physical priors, while neural constitutive residuals capture material responses beyond predefined formulations. Spatially distributed patches parameterize the constitutive field, enabling a continuous representation of local material variations. To organize the identification of this model from sparse visual observations, we adopt a progressive curriculum that sequentially optimizes global material properties, spatially varying local parameters, and neural constitutive residuals, together with complementary motion and mask supervision. Extensive experiments on diverse deformable-object interactions demonstrate that PhysReal achieves superior performance in dynamic reconstruction and future-state prediction, while showing strong potential for downstream robotic applications.

Abstract: In a weighted graph $G = (V, E)$, the maximum weight matching problem (MWM) asks for a matching (i.e. pairing) of its vertices, such that each vertex is paired with at most one other vertex and the total sum of weights of all edges connecting paired vertices is maximised. If the vertices of the graph correspond to points in the Euclidean plane and the weights to their pairwise Euclidean distances, we get the Euclidean maximum weight matching problem (Euclidean MWM). The best optimum-solution algorithm for this problem runs in $O(n^{2.5})$. Furthermore, there exists an FPTAS guaranteeing a $(1 - ε)$-approximation ratio, which runs in $O(m ε^{-1} \log ε^{-1})$ time. Heuristics with a subquadratic running time (with respect to the number of vertices $|V|$) are known, but often yield solutions of a modest quality. In this paper, we present a novel algorithm for solving the Euclidean MWM running in $O(n \log n)$ time and providing excellent solution quality, especially for larger instances. In particular, in our computational tests, the algorithm yielded optimum or near-optimum solutions for all test instances; the worst observed optimality gap was less than $1.38\%$. This makes the algorithm highly attractive for practical applications, especially when exact methods become computationally prohibitive due to the size of the instance.

Abstract: Flow matching, together with classifier-free guidance (CFG), is widely used in generative modeling, yet much of the theoretical understanding remains distribution-wise. Since practical sampling follows individual trajectories, distribution-level guarantees alone do not fully capture how trajectories interact with the data geometry or how guidance reshapes it. To overcome this limitation, we establish a unified stagewise geometric theory of attraction and absorption for both continuous dynamics and explicit Euler discretization. Specifically, with $t\in[0,1]$ running from noise to data, we show that unconditional flow trajectories are successively attracted toward a neighborhood of the global mean, the data convex hull, and a neighborhood of a possibly nonconvex local cluster. Across these stages, the corresponding distance satisfies a common contraction estimate, yielding an ${O}(1-t)$ decay of the distance in the final stage. For CFG, the same structure persists with an extrapolated mean, an inflated conditional convex hull, and, near the target cluster, the restored local geometry of conditional flow matching. We further show that a general time schedule $a(t)$ replaces the $O(1-t)$ decay by $O(1-a(t))$. Together, these results provide a unified particle-level geometric account of flow matching and CFG across continuous and discrete sampling.