arXiv:2608. 07566v1 Announce Type: new Abstract: We introduce a continuous metric field framework trained by a single causal contrastive loss.
arXiv:2606. 18828v1 Announce Type: cross Abstract: Traditional approaches place intelligence in the agent, whether as a learned policy or a search procedure.
arXiv:2607. 05489v1 Announce Type: cross Abstract: The AInstein architecture introduced an unsupervised neural method for solving the Riemannian Einstein equations on arbitrary manifolds.
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
arXiv:2606. 01847v1 Announce Type: cross Abstract: Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\mathbb{R}^{12}$ vectors.
The paper introduces SE(3) neural potential fields that learn collision‑free 6‑DoF trajectory planning directly from posed RGB images, eliminating the need for explicit 3D reconstruction. By supervising the field with a navigation function based on geodesic distances to the grasp, the method avoids the classic pitfalls of artificial potential fields, achieving near‑goal convergence within 3 cm from any start and producing collision‑free paths on a UR10 robot. Experiments on two tabletop scenes show significant improvements in clearance, reduced arm‑link contacts, and a 90 % grasp success rate, while planning time drops from over a minute to about 2 seconds compared to RRT* on a reconstructed scene.
We present FoundationGeo, a two-stage framework that explicitly bridges relative and metric prediction via spatial calibration and principled data design. Stage 1 learns a high-fidelity, affine-invariant geometry model by initializing with DINOv3 and training on a curated 10.
Reaching a 6-DoF grasp pose in clutter requires a collision-free trajectory, conventionally obtained by reconstructing the scene in 3D and planning inside that reconstruction, at the cost of its accur...
Geometric foundation models, such as the Visual Geometry Grounded Transformer (VGGT), provide strong 3D priors from unposed images. However, such models operate purely in a feed-forward, deterministic regime, \ie~they cannot generate plausible geometry beyond what the input views directly support.
arXiv:2609.35436v2 Announce Type: replace Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....
Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost.
arXiv:2607. 14228v1 Announce Type: cross Abstract: In this paper, we ask whether vision foundation models construct representations that reflect the intrinsic properties of 3D Euclidean space.
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.