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Related Articles from SNS
Strategyproof Mechanisms for Euclidean Facility Location Problems under $L_p$-norm Social Cost
arXiv:2606.08621v1 Announce Type: new Abstract: We study strategyproof mechanisms for eliciting agents' location preferences truthfully in the Euclidean plane $\mathbb R^2$ and locating a facility so as to minimize the $L_p$-norm social cost, defined as the $L_p$-norm of the vector of distances from the facility to the agents' preferred locations, for any $p \ge 1$. While the cases $p=1$ and $p=\infty$ have been well-studied, open questions remain about the optimal approximation ratios...
The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space
Announce Type: new 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. 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. We introduce $\textbf{Lie...
HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation
arXiv:2602.07739v2 Announce Type: replace Abstract: Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad topics to specific entities that Euclidean embeddings fail to preserve, causing semantically distant documents to appear spuriously similar and increasing hallucination risk. To address these...
Direct Informed Sampling on Riemannian Manifolds via Loewner Order Lower Bounds
arXiv:2606.02879v1 Announce Type: new Abstract: Informed sampling techniques accelerate sampling-based motion planners by focusing the search on promising regions of the state space, yet most existing methods rely on Euclidean heuristics that become inadmissible under configuration-dependent Riemannian metrics. While scalar eigenvalue bounds restore admissibility by uniformly scaling the Euclidean distance, they discard the directional structure of the metric, producing overly conservative...
Gaussian mean width strong converse bound on the classical identification capacity of quantum channels
arXiv:2606.05032v1 Announce Type: cross Abstract: We establish a single-letter and efficiently computable strong converse bound on the classical identification capacity of quantum channels. By equipping the $n$-fold channel output space with a product state-weighted $\sigma$-Euclidean geometry, we allow trace-distance separation constraints for identification codes to be controlled by Euclidean covering estimates. Using Sudakov's inequality, we bound the covering numbers of the $n$-fold...
Geometry-Aware Uncertainty Quantification via Conformal Prediction on Manifolds
arXiv:2602.16015v2 Announce Type: replace Abstract: Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces. When the response lies on a Riemannian manifold, Euclidean residuals and coordinate-based regions can ignore the geometry that defines meaningful error.
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv:2604.20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric...
Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization
Announce Type: replace-cross Abstract: We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation error in a fixed Euclidean norm. This enables the algorithm to exploit problem geometry dynamically.
Exact Optimization-Free Safety Filters for Control Barrier Functions
new Abstract: For control-affine systems, standard and high-order control barrier function conditions are affine in the control input and are commonly enforced through quadratic-program-based safety filters. Although convex, these optimization problems may be undesirable in embedded, high-rate, or resource-limited implementations. This letter studies when the corresponding Euclidean projection can be computed exactly without solving a quadratic program.
Spherical Flows for Sampling Categorical Data
arXiv:2605.05629v3 Announce Type: replace-cross Abstract: We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable.