arXiv:2607. 17377v1 Announce Type: new Abstract: The paper presents a new parameter-efficient adaptation method called ChebyMA (Chebyshev Manifold Adaptation).
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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.
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.
RecKAN introduces a learnable recursive polynomial basis for Kolmogorov–Arnold Networks, replacing fixed bases like B-splines or Chebyshev polynomials. The basis is defined by a second‑order polynomial recurrence whose five coefficients are jointly learned with the network, enabling it to encompass classical families such as Chebyshev, Fibonacci, Pell, and Jacobsthal. Experiments across image, text, biomedical time‑series classification, and forecasting tasks show RecKAN outperforming parameter‑matched KAN baselines and achieving state‑of‑the‑art results on several benchmarks.
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.
arXiv:2609.31458v1 Announce Type: new Abstract: Transformers have become a central architecture for in-context learning (ICL), particularly through their state-of-the-art performance in large languag...
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.