arXiv:2606. 00248v1 Announce Type: new Abstract: Vector Symbolic Algebras (VSAs) enable robust neurosymbolic reasoning by encoding symbolic information into high-dimensional distributed representations.
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.
Multimodal large language models (MLLMs) have advanced image geolocalization mainly by improving how they reason about geographic cues. How that reasoning isdecoded into coordinates, however, has lagged behind.
arXiv:2602. 10099v2 Announce Type: replace Abstract: Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis.
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:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent 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.
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:2510. 09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective.
arXiv:2606. 09859v1 Announce Type: cross Abstract: MLLMs frequently hallucinate objects inconsistent with visual inputs.
arXiv:2607. 06620v1 Announce Type: cross Abstract: Recent Multimodal Large Language Models (MLLMs) struggle to bridge the representational gap between 2D semantic understanding and 3D spatial geometry.
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
Geometry is invariant to viewpoint, which makes any collection of images a redundant encoding of a single 3D state. Existing feed-forward reconstruction models fail to exploit this: per-view methods emit overlapping, unaligned pointmaps that grow linearly with input count, while global-latent methods commit to a fixed, low-resolution output.