arXiv:2510. 15141v5 Announce Type: replace-cross Abstract: Most existing manifold dimension estimators rely on the assumption that the underlying manifold is locally flat within the neighborhoods under consideration.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.
arXiv:2604. 13230v2 Announce Type: replace Abstract: Exploratory Landscape Analysis (ELA) provides numerical features for characterizing black-box optimization problems.
arXiv:2608.29867v1 Announce Type: new Abstract: Autoencoders are widely used for nonlinear dimensionality reduction and manifold learning. While most common implementations rely on both nonlinear enc...
The paper investigates whether the performance of anomaly detection systems can be predicted without labeled anomalies. For kNN-based detectors, it derives a lower bound on AUC that links detection performance to the separation and variance of inlier and outlier scores, and uses this to analyze how density variation, intrinsic dimensionality, and domain mismatch affect score variability. The authors introduce pseudo‑anomaly probes that provide a reference for estimating relative score separation, and demonstrate through experiments on DCASE benchmarks that these probes enable anomaly‑free model selection to outperform conventional development‑set selection, especially under domain shift.
arXiv:2606. 15280v1 Announce Type: new Abstract: Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space.
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.
arXiv:2605. 29987v2 Announce Type: replace Abstract: Although multi-scales representation learning enables elastic-dimension embeddings, nested subspaces often suffer from dimensional redundancy and spectral collapse.
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.
arXiv:2610. 22592v1 Announce Type: cross Abstract: Empirical averages are fundamental statistical primitives.
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:2606. 25347v1 Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space.