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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

Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration

Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.

gr-qc↗
arXiv2026

Observer-robust energy condition verification for warp drive spacetimes

Whether a warp drive metric requires exotic matter is decided by energy conditions quantified over all observers, not only the Eulerian. Each of the null, weak, strong and dominant conditions is equivalent, at a point, to feasibility of a $4\times4$ linear matrix inequality $A_{ab}+σg_{ab}\succeq0$, by the S-lemma, with $A_{ab}$ the stress-energy tensor or its trace reverse and the dominant condition a conjunction of two such tests. It forms no eigendecomposition of $T^a{}_b$, imposes no rapidity cap and assumes no Hawking-Ellis type, so it decides all four alike, Types I and IV not being exhaustive; its multiplier margin is exactly half the null-cone minimum, so the same test returns the severity. Composed with an interval enclosure of the curvature chain it decides a point from the metric itself, not from a floating-point copy of its stress-energy. At Type I each condition reduces instead to an eigenvalue inequality holding for all observers at once. The type label is numerical and tolerance-bound; the reported severities are rapidity-capped diagnostics, not certificates. Everything decided uses only boost-invariant data and stays well posed through $v_s=1$. On a flat slice the Eulerian momentum that opens the Type-IV wall vanishes only for a gradient shift, so among four matched drives the irrotational Rodal geometry is Type I identically, its shift curl-free by an exact profile identity, while Alcubierre and Natário are Type-IV dominated at every sampled speed and Van den Broeck above its transition. A single-frame reading of Rodal misses about 73% of its wall weak-energy violations. All four violate the pointwise null energy condition at every sampled speed, consistent with the Santiago-Schuster-Visser no-go, whose null step is conditional. Both are realized in warpax, a JAX toolkit building $T^a{}_b$ by automatic differentiation.

gr-qc↗
arXiv2026

Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search

In encoder circuits built on the stabilizer formalism, the dominant contribution to circuit complexity comes from the use of controlled (CNOT) gates, making CNOT-count reduction a central circuit-design objective. Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In this paper, we adopt a prior entanglement-assisted QC-LDPC (EAQC) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the baseline EAQC encoder. The optimized circuits also outperform the Patel-Markov-Hayes and greedy cost-minimization baselines, and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

quant-ph↗
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↗
arXiv2026

Standard bases for shift-stable groups and Subgroup Membership in wreath products

We develop a notion of standard bases for subgroups of the restricted direct product $G^{(\mathbb{N}^n)}$ that are stable under translation by $\mathbb{N}^n$, where $G$ is an arbitrary finite group. We construct an algorithm that computes standard bases for such subgroups and use them to solve several algorithmic problems, including membership, saturation, and variable elimination. Our approach is inspired by Buchberger's algorithm and the theory of Gröbner bases for ideals in polynomial rings. Building on the standard bases and our solutions to the algorithmic problems above, we prove that Subgroup Membership is decidable in wreath products $G \wr \mathbb{Z}^n$ for finite $G$ and $n \in \mathbb{N}$.

math.GR↗
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

Grassmann--Plücker Parametrization of Convolutional Filter Subspaces: Regularity and Closed Embeddings

We propose a geometric parametrization of the filters in a single convolutional layer: the parameter is no longer an ordered family of filter vectors, but a fixed-dimensional subspace of the filter space. For one-dimensional finite-stride convolution, the filter-to-convolution-operator correspondence gives an injective linear map $\mathcal{C}:\mathcal{K}\to H$. This map sends filter subspaces in $\mathrm{Gr}(q,\mathcal{K})$ to operator subspaces in $\mathrm{Gr}(q,H)$; composing it with the Plücker embedding yields a projective parametrization $Φ:\mathrm{Gr}(q,\mathcal{K})\to\mathbb{P}(\bigwedge^q H)$. Using $T_U\mathrm{Gr}(q,\mathcal{K})\cong\mathrm{Hom}(U,\mathcal{K}/U)$, we compute the differential of the induced Grassmannian map and show that the differential of $Φ$ is injective at every point. We then use the vanishing equations for Plücker coordinates and standard affine coordinates on a Grassmannian to prove that $\mathrm{Gr}(q,\mathcal{C}(\mathcal{K}))\hookrightarrow\mathrm{Gr}(q,H)$ is a closed embedding, and hence that $Φ$ is a closed embedding. Consequently, the parameter space is isomorphic to its projective image, the parametrization is finite and birational onto its image, every fiber is a singleton, and the resulting projective neural variety is smooth. For $k=4$ and $q=2$, we also use Singular to recover the image ideal and check its dimension, degree, chart rank, and smoothness. This computation illustrates, rather than replaces, the general proof. Finally, we discuss possible connections with filter redundancy and low-rank convolution, while distinguishing the proved geometric results from application proposals requiring numerical validation.

math.AG↗