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:2605. 00725v2 Announce Type: replace Abstract: Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes.
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:2609.38985v1 Announce Type: new Abstract: Generating compact, artist-style meshes with explicit topology typically relies on autoregressive models which incur prohibitive sequential per-token c...
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv:2505. 15405v3 Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems.
arXiv:2608. 09997v1 Announce Type: new Abstract: Transformers have had a profound impact on the world of language processing and computer vision.
arXiv:2609.37139v1 Announce Type: new Abstract: 3D content generation technology has significantly advanced the work of designers, as well as the 3D printing and gaming industries. However, it remain...
arXiv:2606. 07728v1 Announce Type: new Abstract: It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space.
HoloAegis is a minimally parametric topological inference framework that uses frozen representations to map text onto the unit sphere and makes decisions via Gibbs‑Boltzmann free‑energy differences over pre‑computed anchor centroids. On a frozen three‑benchmark protocol, it matches WildGuard‑7B on toxicity, outperforms it on harmful behaviors, but underperforms on oversafety detection, while ShieldGemma‑2B fails on indirect harms. The study demonstrates that geometric guardrails can substitute for LLM judges in some cases and must defer to them in others, with anchor banks reducing score variance and boundary displacement.
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:2606.07288v2 Announce Type: replace Abstract: Reconstructing surface meshes from multi-view images has remained a core challenge in recent years. Most existing methods, whether implicit or expl...