#geometry

9 curated events

papersTODAY 04:00 UTC

SL(n) Representation Learning in Intrinsic Mixed-Curvature Space

Researchers propose a representation learning framework built on SL(n) that operates in an intrinsic mixed-curvature space rather than relying on manually composed product manifolds. The approach aims to provide higher curvature capacity and deeper order-aware composition for capturing complex geometric structure. It is presented as an alternative to existing product-manifold methods that require hand-specified curvature combinations.

research/representation-learning/geometry/arxiv

papersTODAY 04:00 UTC

CapGeo-Bench separates visual perception from geometric reasoning in multimodal models

A new arXiv paper introduces CapGeo-Bench, a benchmark designed to evaluate geometric understanding in multimodal large language models while distinguishing failures in visual perception from failures in reasoning. The authors note that even strong closed models such as GPT-o3 continue to lag on geometry problems despite success on purely textual math tasks. The benchmark aims to give a clearer picture of where these systems break down.

benchmarks/multimodal/reasoning/geometry

papersTODAY 04:00 UTC

arXiv Paper Diagnoses and Improves Visual Chain-of-Thought for Geometry Solvers

A revised arXiv preprint argues that multimodal models need active visual assistance, such as drawing auxiliary lines, to handle complex geometry problems. The authors examine shortcomings in current evaluation of visual chain-of-thought methods and propose ways to strengthen how models reason with diagrams. The work falls under cs.AI and focuses on diagnosing and improving these visual reasoning pipelines.

multimodal/reasoning/geometry/benchmarks

papersTODAY 04:00 UTC

Paper distinguishes mesh flexibility from topology generalization in neural PDE operators

A new arXiv paper argues that neural operators designed to work on arbitrary meshes are not automatically general across domain topologies, since changing the topology alters the invariant and decaying subspaces of a PDE operator. The authors apply Hodge heat flow as a controlled way to probe this difference. The work points to topology, not just geometry, as a source of failure when such models are applied to unseen domains.

neural-operators/pde/research/geometry

papersTODAY 04:00 UTC

Olympiad geometry theorems proved on a superconducting quantum processor

A new arXiv preprint describes using a superconducting quantum processor to carry out automated proofs of olympiad-style geometry problems. The work sits at the intersection of automated theorem proving and quantum hardware, a pairing that has mostly been explored in theory. It suggests quantum devices could play a role in symbolic mathematical reasoning tasks traditionally handled by classical systems.

quantum-computing/theorem-proving/research/geometry

papersSEP 10 04:00 UTC

New Framework Guides Language Models Through Symbolic Perception and Logical Deduction in Geometry

Researchers have posted an arXiv paper presenting a framework that helps language models solve plane geometry problems by separating visual perception of geometric symbols from logical deduction. The approach aims to reduce reliance on computationally heavy large multimodal models by using symbolic representations to guide text-only reasoning. The work addresses a long-standing AI challenge that requires combining perception with rigorous mathematical reasoning.

reasoning/geometry/research/lmm

papersSEP 10 04:00 UTC

Neural parametric geometry representation proposed for thin-shell shape optimisation

Researchers have introduced a neural-network-based parametric geometry representation designed for thin-shell structures. The method offers a differentiable surface description that can feed gradient-based shape optimisation workflows, where flexible geometric modelling is a key requirement. The paper is available on arXiv in the machine learning category as an updated version.

neural-networks/shape-optimisation/geometry/research

papersSEP 12 04:00 UTC

Canonical Inputs Proposed for Neural Networks on CAD Boundary Representations

A new arXiv paper addresses how the same 3D solid can be described by multiple boundary representations (B-reps) in CAD systems, which creates ambiguity for machine learning models. The authors propose learning canonical inputs so that neural networks operate on the underlying solid rather than the particular file encoding. This aims to make predictions consistent regardless of how a model was originally constructed.

cad/neural-networks/3d-models/geometry

papersSEP 12 04:00 UTC

Paper Proposes Language-Augmented Priors for B-Spline Surface Fitting

A new arXiv preprint describes a technique that uses language-derived semantic information to guide B-spline and NURBS surface fitting, the mathematical basis of modern computer-aided design. The authors argue that traditional CAD geometric kernels remain dependent on predefined assumptions, and that language-augmented priors can improve fitting results. The work sits at the intersection of geometric modeling and language model research.

cad/b-splines/geometry/arxiv