SEARCH · Searcharxiv

Results for “math.GR”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

1,426 records · Page 2Linked to original sources

arXiv2026

Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes

We develop an entropy-stable and physical-constraint-preserving discontinuous Galerkin spectral element method for symmetry-reduced general-relativistic hydrodynamics on prescribed stationary spacetimes. Using a local orthonormal transformation, the fluid variables are expressed in a form for which the relativistic hydrodynamic algebra and the admissible set are independent of the spatial metric, while the spacetime geometry enters through stationary coefficients. This separation allows entropy-conservative special-relativistic fluxes to be combined with a compatible discretization of the geometric source terms. On affine tensor-product meshes, the resulting DGSEM is conservative and satisfies a semidiscrete entropy inequality, while the transformed variables provide a convex framework for physical-constraint preservation. For practical stabilization, we use a geometry-only causal speed that is sufficient for both classical local Lax--Friedrichs entropy dissipation and the physical-constraint-preserving Lax--Friedrichs splitting. The fully discrete method combines this stabilization with SSP Runge--Kutta time stepping, oscillation elimination, and conservative local-orthonormal-state scaling. Numerical experiments cover smooth and strongly shocked special-relativistic flows, an axisymmetric jet, stationary Michel accretion, Schwarzschild Bondi--Hoyle flow, and four Kerr accretion cases. The results demonstrate the designed high-order accuracy in smooth regimes and robust performance for demanding relativistic flows on curved stationary backgrounds.

math.NA↗

arXiv2026

Finite-Monoid Compression in Syntactic Concept Lattices: Arity Hierarchies and a Pseudovariety Trichotomy

Clark's syntactic concept lattice (SCL) records two-sided distributional structure, and Wurm extended it to tuples of arbitrary finite arity. We study $\operatorname{cmp}_f(L)$, the minimum image size of a finite-monoid observation that preserves guarded tuple substitution through arity $f$ on the principal layer. For regular languages, we characterize $\operatorname{cmp}_f(L)$ exactly as the least cardinality of the codomain of an $f$-separating relational morphism from the pointed syntactic monoid. Let $\operatorname{ch}(\mathbf V)$ denote the least arity at which these compression numbers stabilize uniformly over a pseudovariety $\mathbf V$. Our main result is the following trichotomy of possible uniform heights: $\operatorname{ch}(\mathbf V)\in\{1,2,\infty\}$, with $\operatorname{ch}(\mathbf V)=\infty$ if and only if $\operatorname{Synt}(\{ab\})\in\mathbf V$. Thus no finite uniform compression height $3,4,\ldots$ occurs. The infinite case is sharp: inside $\langle\operatorname{Synt}(\{ab\})\rangle$, every boundary $d\to d+1$ admits unbounded compression gaps, and arbitrary finite strict prefixes of the arity hierarchy are realizable. On the finite side, commutative monoids and bands stabilize at arity one, while every completely regular syntactic monoid stabilizes by arity two; finite group kernels show that the binary bound is sharp. At unary arity, every nonempty finite simple graph is realized by an explicit length-three language, yielding an exact chromatic-number formula and NP-completeness of deciding $\operatorname{cmp}_1(L)\le 3$ for explicitly listed length-three languages. The structural boundary between compression heights one and two remains open.

cs.FL↗

arXiv2026

Adaptive Strategies for GR(1) Games

We consider two-player GR(1) games on graphs, where the system player Eve must satisfy \[ \Box\Diamond A_1\land\cdots\land\Box\Diamond A_m \;\implies\; \Box\Diamond G_1\land\cdots\land\Box\Diamond G_n \] against the environment player Adam. Here $A_1,\ldots,A_m$ are assumptions on the environment, $G_1,\ldots,G_n$ are guarantees the system must provide, and $\Box\Diamond S$ denotes ``always eventually $S$''. Traditional static strategies are overly conservative: they may actively violate assumptions to trivially satisfy the implication, or abandon all guarantees when any assumption is violated. Existing methods to prevent such behaviors incur doubly exponential blowup. We introduce an adaptive framework treating Adam as a non-adversarial agent with unknown objectives. Eve monitors which assumptions Adam actually meets and adapts her strategy at runtime to maximize satisfied guarantees. Central to our approach is a novel algorithm for monitoring liveness properties $\Box\Diamond S$, enabling Eve to maintain real-time likelihood estimates of which assumptions will be fulfilled. Eve pre-computes strategies optimal for different assumption subsets, deploying a probability distribution over them that dynamically adjusts based on monitor outputs. We prove that when assumptions are violated, Eve's randomized adaptive strategy converges asymptotically to the deterministic strategy maximizing guarantees. A prototype demonstrates effectiveness and superior computational performance compared to the state of the art.

cs.LO↗

arXiv2026

Real-Time Neural Hair G-Buffer Anti-Aliasing

We propose a lightweight real-time method for reconstructing strand-based hair G-Buffers from severely undersampled rasterized inputs. Our pipeline first applies neural spatial reconstruction and temporal accumulation to recover hair coverage, i.e., fractional hair visibility within a pixel, and tangent. It then uses a tangent-guided reconstruction step to complete the position, which is subsequently used for physically based deferred hair shading. We evaluate our method across a diverse set of hairstyles, including straight, wavy, afro, and ponytail styles, under both static and dynamic scenarios. Our method achieves higher hair reconstruction quality than general industrial neural reconstruction solutions such as DLSS and FSR.

cs.GR↗

arXiv2026

PointGT: Simultaneous Geometry and Texture Editing for Point-Based Representations

We present PointGT, a point-based 3D representation that enables simultaneous editing of object geometry and appearance. Existing reconstruction and view synthesis techniques produce volumetric 3D representations that are high-quality and photorealistic, but are difficult to edit. In particular, recent efforts to enable texture editing for 3D Gaussian Splatting representations are not compatible with geometry edits and deformations. Our method combines a point-based representation that is well-suited for geometry deformations with a learned UV mapping technique that enables high-resolution texture editing. We show that PointGT enables fine-grained editing of both geometry and texture in point-based neural representations with high rendering quality.

cs.CV↗

arXiv2023

Deep and Fast Approximate Order Independent Transparency

We present a machine learning approach for efficiently computing order independent transparency (OIT). Our method is fast, requires a small constant amount of memory (depends only on the screen resolution and not on the number of triangles or transparent layers), is more accurate as compared to previous approximate methods, works for every scene without setup and is portable to all platforms running even with commodity GPUs. Our method requires a rendering pass to extract all features that are subsequently used to predict the overall OIT pixel color with a pre-trained neural network. We provide a comparative experimental evaluation and shader source code of all methods for reproduction of the experiments.

cs.GR↗

arXiv2026

LayoutShop: Content-Constrained Exploratory Design of Creative Article Layout

We present LayoutShop, a novel computational framework for designing creative layouts that frame a given article. Inspired by the actual article layout design process, we enable users to create or select layout templates for conceptualization. These templates help construct a layout design space to extract eligible layout structures. Our algorithm then determines the geometry of the extracted layout structures to frame the given article via an optimization approach. We then employ two neural networks for layout assessment, and the high-quality outputs are returned to users for selection. We conducted a user study to evaluate the framework's usability and the quality of the article layouts it produces. The results of the user study confirmed that our framework can effectively help users create high-quality article layouts.

cs.GR↗

arXiv2026

Lipschitz Extension Initialization for Moving Least Squares Reconstruction from Sparse Irregular Samples

The idea of using Lipschitz extensions [1,2], or Gradually Varied Functions (GVFs)[3], for mesh-free scattered data reconstruction was proposed by the author in 2012 [4]. However, its practical application to modern mesh-free reconstruction methods has not been fully explored. Motivated by recent advances in computational tools, including AI-assisted mathematical programming and software development, we revisit this idea and investigate the use of a Lipschitz extension as an initialization step for Moving Least Squares (MLS) reconstruction [5,6]. Our computational experiments indicate that this initialization significantly improves the stability and reconstruction accuracy of MLS under sparse and irregular sampling. This is a preliminary study intended to establish feasibility; a fuller evaluation with additional benchmarks and comparisons is left to future work.

eess.SP↗

arXiv2026

Evaluating Constrained Iterative Refinement for Scalable Vector Graphics Generation with Off-the-Shelf VLMs

Scalable Vector Graphics (SVGs) power much of the modern visual ecosystem, yet state-of-the-art generative models focus almost entirely on rasterized images. We explore whether inference-time methods can unlock SVG generation capabilities in off-the-shelf vision-language models (VLMs). We systematically evaluate a constrained iterative refinement harness that combines visual feedback, structured editing, and constrained decoding to characterize the capabilities and limitations of current VLMs for SVG generation. Across multiple VLMs and generation settings, we find that constrained decoding improves compilation success rates, while iterative refinement reveals a deficit in visual reasoning and self-correction. Our results highlight both the promise and current limitations of using inference-time methods to adapt general-purpose VLMs for SVG generation.

cs.CV↗

arXiv2026

Proximity3D: Shape from Capacitive Proximity on Sensing Manifold

Most shape reconstruction methods assume measurements defined over planar sensing domains, such as RGB images or depth maps. In this paper, we use a curved capacitive textile as a shape sensor, treating its surface as a non-planar sensing manifold. Each scan is represented as a capacitive proximity field on this manifold, induced by the interaction between the curved electrode layout and nearby object geometry. We introduce a multi-view feedforward reconstruction model that aggregates these fields across known sensor views and recovers the observed object shape. Simulated and physical experiments demonstrate robust reconstruction from capacitive proximity signals acquired on curved sensing surfaces, pointing toward a new route to robotic near-field geometric awareness via embodied sensing.

cs.CV↗

arXiv2026

Thread-Efficient Decoding for Neural Texture Compression

Neural texture compression (NTC) achieves higher compression ratios than BCn formats but suffers from GPU thread divergence, which significantly reduces runtime performance. In this work, we propose a shared decoder MLP architecture -- trained with a gradual decoder freezing schedule -- combined with texture clustering to reduce thread divergence by 25%-52% while preserving rendering quality. We evaluate our method on over 500 textures and multiple real rendering scenes, demonstrating up to 8.48x speedup on the Radeon RX 9070 XT GPU compared to non-shared baselines. Our key contributions include: (1) a unified shared decoder architecture that reduces divergence by grouping textures; (2) a training recipe with gradual decoder freezing that improves stability and reconstruction accuracy; (3) a semantic clustering strategy using CLIP embeddings that groups similar textures for effective decoder sharing; and (4) comprehensive performance and ablation studies validating our approach.

cs.CV↗

arXiv2026

GradRig: Differentiable Weights for Skinned Gaussian Splat Deformation

Skinned deformation is a common framework to turn a 3D shape from its rest pose into a dynamic pose through the deformation of a coarser kinematic structure, called rig. When applied to a 3D mesh, this rig only needs to displace vertices to deform the polygons that connect them. However, when deforming 3D Gaussian Splats, which do not provide connectivity information, rigidly transforming points is not enough to prevent the creation of holes when stretching shapes. In this paper, we use the spatial gradient of skinning weights to provide a full mesh-free deformation pipeline for Gaussian Splats, that more accurately stretches splats while remaining fully compatible with real-time rendering capabilities, which we demonstrate in a WebGL viewer. We present how we evaluate these gradients when the user creates the rig structure and propose an optional adaptive resampling scheme to split up splats that still produce artifacts.

cs.GR↗

arXiv2026

PXDepth: Pixel-Space Modeling for Structure Preserving Monocular Depth Estimation

Recent monocular depth estimators achieve strong zero-shot generalization, yet often struggle to preserve fine-grained structures and object boundaries. We attribute this limitation to the prevalent combination of large-patch ViT encoders and convolutional decoders, as coarse tokenization can weaken pixel-level cues that upsampling cannot fully recover. To address this issue, we propose PXDepth, a discriminative monocular depth model that separates global context modeling from pixel-level depth prediction. Specifically, a large-patch ViT captures global scene context, while a pixel-space predictor composed of Context-Modulated Pixel Transformer blocks maintains high-resolution spatial representations throughout depth estimation. This design preserves fine structures and sharp boundaries without sacrificing global depth consistency. Across diverse zero-shot benchmarks, PXDepth combines faithful local geometry with competitive global depth accuracy while remaining efficient at inference. Our code and model are available at https://yuanzhy29.github.io/PXDepth-Page/.

cs.CV↗

arXiv2026

HyperSketch: Controllable Video Sketching in a Style Hyperspace

Vector sketch animation offers tremendous advantages for multimedia and creative design through concise line expressions and flexible editing. Learning-based generation methods of sketch animation have made significant progress in the last decade, but still suffer from limited style diversity and controllability. This paper presents a controllable video sketching method that automatically converts videos into multi-style vector sketch animations. A continuous style hyperspace is constructed by multi-dimensional sketch styles (fidelity, simplicity, text guidance strength) and the timeline. With this hyperspace, stroke control points are parameterized as 4-variable Bernstein polynomials, ensuring smooth and differentiable style transitions. A multi-task, multi-stage optimization framework is designed to learn stroke hyperparameters accurately and efficiently. We further developed a web-based interactive interface that allows real-time style manipulation via editable curves. Experiments show the style controllability, high-quality, and user-friendliness of our method, which outperforms SOTA methods.

cs.GR↗

arXiv2026

SeMoCo: A Semantic-First Motion Codec for Motion Language Modeling

Discrete motion representations have substantially advanced autoregressive text-to-motion generation. However, most motion tokenizers are optimized for reconstruction and do not explicitly allocate capacity according to semantic role. Action-level meaning and fine-grained kinematic detail must therefore be encoded through the same reconstruction-driven hierarchy. We introduce SeMoCo, a semantic-first motion codec, together with a dual-axis motion generator for language-conditioned motion generation. Each motion token contains one semantic token and a residual sequence of kinematic tokens. The generator models semantic progression across time and autoregressively refines the residual entries. We also construct $Ω$-MotionVerse, a large-scale, multi-source human-motion dataset unified under the SOMA representation. Across the reported comparisons, SeMoCo achieves the best reconstruction accuracy among the compared codecs, while strong text-to-motion results demonstrate the effectiveness of its motion tokens for downstream generation.

cs.CV↗

arXiv2026

ABCD: Alpha-Composited Block Coordinate Descent: Constant-VRAM Training for Large Radiance Fields

We present ABCD (Alpha-Composited Block Coordinate Descent), an out-of-core training framework for alpha-composited radiance fields, instantiated here for 3D Gaussian Splatting. Our method reformulates training as block coordinate descent over spatial partitions: only one block of parameters is active at a time, while all others are frozen. By exploiting the associativity of alpha blending, these inactive regions can be pre-rendered and collapsed into foreground and background RGBA images. As a result, for fixed partition size and image resolution, peak VRAM becomes O(1) with respect to total scene extent, rather than growing with full scene size. This enables GPUs with limited memory to train scenes that would otherwise not fit in core. In experiments, our method closely preserves the reconstruction quality of 3DGS, with less than 5% PSNR degradation, while ABCD with compositing ablated suffers roughly 40% degradation. Our code can be found at https://github.com/shiukaheng/abcd

cs.CV↗

arXiv2026

Telligram: Text-Driven Calligram Generation via Diffusion-Guided Skeleton Optimization

Compact calligram generation aims to form a semantic shape while keeping letters recognizable. Most existing methods are shape-conditioned and mainly solve downstream letter layout inside a given contour. We study text-only calligram generation without an input contour. This setting is difficult because semantic shape formation and letter readability strongly interfere with each other when optimized in a single stage. Pushing the word toward a clear figure can easily damage glyph structure, while preserving readable letters can weaken the target shape. To address this difficulty, we present Telligram, a training-free, low-tuning, two-stage framework composed of Semantic Occupancy Prior Formation and Readability-Constrained Glyph Realization. The first stage uses Variational Score Distillation (VSD) with structured skeleton optimization and hierarchical gradient projection to produce a semantic occupancy prior. The second stage converts this occupancy prior into per-letter regions and reconstructs readable glyph layouts through lightweight geometric processing. The framework generates coherent and creative word-level semantic calligrams directly from text prompts.

cs.GR↗

arXiv2026

Heat Kernel Textures: the Geodesic Gaussians That Do Not Splat

3D Gaussian Splatting has recently revolutionised novel view synthesis as well as many other 3D vision methods and applications. Drawing inspiration from this representation, we now rethink textures to overcome the main issues of UV mapping while considerably lowering their memory footprint. Heat Kernel Textures (HKTex) eliminate UV unwrapping as well as their persistent issues of wasted UV space, seams, distortions, vertex-duplication, and varying resolution. Grounded in discrete Riemannian geometry and intrinsically defined on any manifold surface discretised as a triangular mesh, HKTex uses anisotropic heat kernels as geodesic equivalents to Gaussians. Like our kernels, also the optimisation of their position and the adaptive densification strategies were redefined to operate on the surface of the object to be textureised. Our novel representation is also fully integrated with a physically based renderer and can be optimised either from existing textures or multi-view images. Our project page and code are available at circle-group.github.io/research/HeatKernelTextures.

cs.CV↗