arXiv Machine Learning
A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance
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arXiv Machine Learning
Jul 27
Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA
arXiv:2607. 21823v1 Announce Type: new Abstract: We show that, up to isotropic scaling, the Gaussian RBF reproducing kernel Hilbert space (RKHS) is asymptotically isometric to Euclidean space in the large bandwidth limit.
arXiv Computer Vision
Sep 1
Orthogonal Polynomial Approximation for Matrix Log Normalization in Global Covariance Pooling
arXiv:2608.19021v2 Announce Type: replace Abstract: Global Covariance Pooling (GCP) improves deep networks by capturing second-order feature statistics, and is especially effective for fine-grained r...
arXiv Machine Learning
Sep 15
Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
arXiv Machine Learning
Sep 21
Optimization Geometry of Equivalent Brownian RKHS Representations
arXiv:2609. 21693v1 Announce Type: new Abstract: Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms.
arXiv Machine Learning
Sep 21
Beyond Gaussian Worlds: Latent Geometry Matters for JEPAs
The paper extends the analysis of Joint-Embedding Predictive Architectures (JEPAs) beyond Euclidean latent spaces to Riemannian manifolds. It shows that when latent variables lie on a sphere and the target distribution matches this spherical geometry, every optimal representation recovers the latent state up to an orthogonal transformation, demonstrating that Gaussian uniqueness is not universal. Experiments confirm that geometrically compatible targets improve linear recovery, especially in high-dimensional toroidal settings.
arXiv Machine Learning
Sep 17
A General Kernel Framework for Non-CND Distance Measures Using |D|-Dimensional Sparse Landmark Embeddings
The paper introduces the Sparse Landmark Embedding (SLE) kernel, a new framework that removes the need for conditionally negative definite (CND) distance measures in kernel methods and Gaussian Processes. By embedding each input into a sparse feature vector using compactly supported bump functions centered at all training points, any standard positive semi-definite (PSD) kernel can be applied in this embedding space, guaranteeing PSD for arbitrary distance measures. The authors provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show through experiments with geodesic and Wasserstein distances that the SLE kernel matches or surpasses domain-specific baselines in predictive accuracy and uncertainty quantification.