arXiv:2606. 26660v1 Announce Type: cross Abstract: Triangulations, i.
arXiv:2605. 27770v2 Announce Type: cross Abstract: We introduce `dualGNN', an autoregressive message-passing GNN for sampling fine, regular triangulations (FRTs) of convex polytopes.
arXiv:2512. 23192v4 Announce Type: replace Abstract: While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge.
The paper introduces the Geometric Simplicial Weisfeiler–Lehman (GSWL) test, which extends the classic WL and SWL tests by incorporating vertex coordinates into color refinement for geometric simplicial complexes. It demonstrates that geometry‑aware simplicial message passing schemes are bounded by GSWL in expressivity and can match GSWL’s discriminating power on any fixed finite family of complexes. By combining GSWL with the Euler Characteristic Transform, the authors provide a complete invariant and an approximation framework, validated through experiments that reveal a clear hierarchy from combinatorial to geometry‑aware models.
arXiv:2305. 06315v3 Announce Type: replace-cross Abstract: For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting.
arXiv:2605. 01171v2 Announce Type: replace-cross Abstract: Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets.
arXiv:2606.23489v2 Announce Type: replace-cross Abstract: Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains...
TriFlow introduces a generative method for creating compact 3D meshes with artist‑like triangle topology directly from input geometry such as signed distance fields. It represents mesh topology as a nearest‑vertex vector field (NVF) over the surface, trains a latent flow‑matching model to synthesize this field, and then clusters surface regions to guide a constrained quadric error metric simplification. The resulting meshes closely match the input geometry while exhibiting structured, artist‑like connectivity, achieving 90% lower Chamfer Distance and an 8× speedup over state‑of‑the‑art learning‑based approaches.
arXiv:2608. 09997v1 Announce Type: new Abstract: Transformers have had a profound impact on the world of language processing and computer vision.
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv:2608. 18570v1 Announce Type: cross Abstract: Machine learning and data analysis techniques have recently emerged as powerful tools for identifying patterns and formulating conjectures in mathematical research, most notably in the field of low-dimensional topology.
The paper introduces Solver Agent, an AI framework that uses large language models to perform calculations and proofs in mathematics and theoretical physics, tracking the solution process via a persistent ledger. It applies this framework to study global F‑theory uplifts of Type IIB orientifolds and S‑folds, establishing conditions for Weierstrass models over projective threefolds with terminal ζ_k quotient singularities to yield Ε-factorial elliptically fibered Calabi‑Yau fourfolds. The authors derive fixed‑point contributions to Hodge data and Euler characteristics, demonstrate how these corrections determine localized D3‑brane charges for tadpole cancellation, and illustrate the results with toric hypersurface constructions and methods for four‑form flux analysis in Δ=1 compactifications.
arXiv:2604. 14727v2 Announce Type: replace Abstract: To quantify the geometric capacity of transformers, we develop a tropical-geometric framework for analyzing the spatial partitions induced by conditioned self-attention.