The paper introduces PRISM, a novel representation learning framework that learns isometric embeddings by explicitly modeling the intrinsic geodesic metric of 3D surfaces, achieving superior performan…

The paper proposes GASP, a framework that injects fundamental geometric priors directly into Vision-Language Models (VLMs) using ground-truth video geometry, significantly enhancing 3D spatial reasoni…

The paper introduces Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes deep learning training in non-smooth loss landscapes by dynamically damping updates based on local geometric ins…

This paper proposes Wat3R, a cross-domain semi-supervised learning framework for adapting 3D reconstruction models from air to underwater scenes using unlabeled real underwater video footage and a tea…

MViewRouter proposes a multi-view framework that internalizes geometric equivariance using a Multi-view Alternating Attention mechanism to improve generalization and stabilize training for combinatori…

This paper introduces CuBAS, an adaptive data selection method for supervised classification based on curvature estimation from a labeled dataset using the Potts MRF model.

The paper proposes Latent Geometric Chords (LGC) and LGC-H, a novel method that navigates decision boundaries using curvature-aware geometric search within a semantic manifold to generate high-fidelit…

Proposed G$^3$VLA, a camera-aware geometric module for pretrained vision-language-action models, injecting calibrated structure into visual tokens using intrinsic-conditioned ray embeddings, projectiv…

This paper introduces Curvature-Weighted Gradient Diversity (CWGD), a geometry-aware measure for optimization noise that reduces the asymptotic optimization error floor by up to a factor of two compar…

This paper systematically explores the convex polygon reconstruction problem with specified sets of features, contributing new testing algorithms and hardness results.

The paper introduces Geometric Latent Reasoning (GLR), a method that models reasoning as continuous paths in the embedding space, showing that this continuous approach allows LLMs to solve problems us…

This paper demonstrates that large language models spontaneously develop geometric structures corresponding to human perceptual domains (like color or pitch) within their internal layers, suggesting t…

The paper introduces MeRa, a metric-space bias module, demonstrating that latent reasoning only improves spatial prediction when it is explicitly grounded in the underlying metric space.

This paper shows that finite unions of intersecting affine modules in one dimension are efficiently exactly learnable using equivalence and subset queries.

The paper proposes a novel geometric embedding hashing method to recover object correspondences (vector links) between two embedding clouds generated by different black-box encoders using only a small…

The paper investigates applying Riemannian optimization techniques to low-rank matrix parameters for deep learning, but finds that the proposed methods do not conclusively outperform the AdamW baselin…