arXiv:2606. 01734v1 Announce Type: cross Abstract: This paper proposes ``FlatVPR,'' a novel geometric rectification paradigm that effectively bridges the trade-off between map lightweightness and localization accuracy in visual place recognition (VPR) by enforcing a feature manifold structure where any descriptor between two adjacent anchors $\mathbf{z}_A$ and $\mathbf{z}_B$ can be accurately reconstructed via linear interpolation $\hat{\mathbf{z}}_{pseudo} = (1-t)\mathbf{z}_A + t\mathbf{z}_B$, where $t \in [0,1]$ denotes the relative position.
By Rai Hisada, Kanji Tanaka
This paper proposes ``FlatVPR,'' a novel geometric rectification paradigm that effectively bridges the trade-off between map lightweightness and localization accuracy in visual place recognition (VPR) by enforcing a feature manifold structure where any descriptor between two adjacent anchors $\mathbf{z}_A$ and $\mathbf{z}_B$ can be accurately reconstructed via linear interpolation $\hat{\mathbf{z}}_{pseudo} = (1-t)\mathbf{z}_A + t\mathbf{z}_B$, where $t \in [0,1]$ denotes the relative position. While state-of-the-art foundation models such as DINOv2-ViT-S/14 provide robust semantic features, their latent manifolds exhibit prominent curvature, projecting uniform linear motion in physical space onto highly non-linear trajectories in the feature space, which hinders reliable reconstruction under sparse anchor conditions.
arXiv:2607. 07034v1 Announce Type: cross Abstract: We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data.
By Alexandre Quemy
arXiv:2607. 25299v1 Announce Type: cross Abstract: Optimization over the Stiefel manifold plays a significant role in various machine learning tasks.
By Yuan Zhang, Jiang Hu, Zhijian Lai, Lin Lin, Zaiwen Wen
arXiv:2606. 17513v1 Announce Type: cross Abstract: Neural operators provide fast surrogates for PDEs but their deterministic predictions limit their use in tasks requiring uncertainty quantification (UQ), especially under geometric variability.
By Oriol Vendrell-Gallart, Nima Negarandeh, Ramin Bostanabad
arXiv:2607. 02386v1 Announce Type: cross Abstract: While Vision Transformers have achieved remarkable success across computer vision and language applications, the geometric evolution of their internal representations throughout training remains insufficiently understood.
By Kaustubh Kapil, Kishor P. Upla
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
By Marios Koulakis, Constantin Seibold
arXiv:2509. 03758v5 Announce Type: replace Abstract: We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations.
By Alvaro Almeida Gomez
arXiv:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
By Eduardo Fernandes Montesuma, Yassir Bendou, Mike Gartrell
arXiv:2607. 03145v1 Announce Type: cross Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution.
By Alexandre L. M. Levada
arXiv:2606. 25347v1 Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space.
By Hongye Xu, Bartosz Krawczyk
arXiv:2608. 10016v1 Announce Type: cross Abstract: Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, sensing modalities, model architectures, latent dimensionalities, and local learning objectives.
By Gabriele D'Acunto, Enrico Grimaldi, Valeria Avino, Mario Edoardo Pandolfo, Leonardo Di Nino, Sergio Barbarossa, Paolo Di Lorenzo