computer graphics developers

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.