geometry

This paper introduces a normal-fan geometry for finite-horizon adversarial MDPs with fixed transitions, developing a face-crossing price that separates consequential from harmless non-stationarity. It shows that dynamic regret decomposes into intrinsic priced face motion plus within-face selection error.

This paper introduces SD-GPS, a solver-driven framework for geometry problem solving that uses autoformalization guided by solver feedback and verified theorem proposing to overcome bottlenecks in neuro-symbolic systems.

This paper investigates the geometric relationship between directions in language model activations that detect a behavior versus those that control it, finding that for hallucination detection they are nearly orthogonal (cosine ~0.12), while for output format they align perfectly, challenging a common assumption in mechanistic interpretability.

The tweet highlights a research finding that signals of physical plausibility can be extracted from the geometry of frozen image encoders without video training or physics supervision.

This paper provides a theoretical explanation for why diffusion models can generate clean samples without explicit noise-level conditioning, attributing it to high-dimensional geometry and analyzing why some model parameterizations succeed while others collapse.

Introduces FllumaOne, a multimodal CAD dataset of 100,000 samples generated by executable Python programs in the Flluma CAD system, providing feature trees, STEP geometry, point clouds, and language descriptions to support editable CAD research.

VeriGeo introduces a controllable geometry question generation framework that uses verification-guided reflection to ensure numerical and analytical consistency. The method produces high-quality synthetic data, achieving state-of-the-art results on GeoQA and strong performance on PGPS9K and MathVista-GPS.

This paper introduces SGR-BIM, a graph-driven semantic reasoning framework that dynamically aligns regulatory intent with BIM geometry to automate geometry-intensive compliance checks, achieving 84.3% accuracy on fire safety code queries.

This paper from the Axiom team investigates the rarity of lattice triangles, presenting a mathematical result on the distribution of convex lattice polygons.

This paper analyzes on-policy distillation (OPD), finding that OPD updates are sparse, distributed across layers and FFN-heavy, and retain geometric properties distinct from dense parameter rewriting. The sparse structure is operationally useful, but sparsity-inducing SGD underperforms AdamW due to heterogeneous gradient scales.

This paper introduces Topological Neural Operators, which lift neural operators from point-only domains to cell complexes, embedding geometry and topology to reduce the learning burden. It demonstrates that operator learning improves when geometry is not an afterthought, though the topology remains prescribed.

This paper investigates whether spatial geometry improves language-agent memory recall, demonstrating that geometry must lead recall over recency and importance, and that a ray-tracing visibility predicate is crucial for occlusion handling in 3D voxel worlds.

This paper compares the geometric structures induced by deep learning vector embeddings (CamemBERT) and lexical co-occurrence graph models on the French 'Great National Debate' corpus, finding similar local topology but distinct global organization, highlighting complementarity between the two approaches.

The paper provides a geometric interpretation of last-layer model stealing attacks on transformers using exterior differential systems, showing that recovery of the projection matrix is governed by the polar space of a quadric. It also characterizes an identifiability wall below the last layer, revealing what can and cannot be extracted.

This paper introduces a probabilistic polygonal representation for plane curves using Gaussian Mixture Models, preserving local tangent, normal, and arc length while encoding uncertainty in the normal direction. The framework applies to various plane curves and supports uncertainty-aware geometric modeling for CAD, robotics, and trajectory planning.

edulab adds analytic geometry problem type, supports random problem generation, dynamic geometry board (2D Canvas drawing curves, moving lines, moving points, vectors, etc.) and KaTeX step-by-step parsing. It is an update to the open-source education skill tool.

A critique of the AI tutor Koji, highlighting flaws in its math teaching approach, such as allowing students to fumble without guidance and missing key conceptual explanations.

A pictorial introduction to differential geometry, showing how Maxwell's equations emerge from geometric concepts, based on a 2017 arXiv paper.

This paper investigates why LLMs fail at basic multi-operand addition by probing residual-stream activations, revealing geometric structures called Iso-Raw-Sum Trajectories (IRSTs) and explaining off-by-one errors as geometric slippages due to noisy latent carry representations.

Geomatic is a command-driven geometry studio that leverages automatic differentiation for interactive geometric operations.