arXiv Machine Learning
Jul 13
Terminal Dimension Reduction for Time Series with Applications
arXiv:2607. 09490v1 Announce Type: cross Abstract: Terminal embeddings have emerged as a powerful tool for dimension reduction.
Dimension Reduction for Curves: Simplified and Generalized
arXiv:2607. 03112v1 Announce Type: cross Abstract: We revisit random projections for reducing the dimension of high-dimensional polygonal curves.
Related stories
arXiv Machine Learning
Sep 3
Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv Machine Learning
Sep 15
Low-Dimensional Embeddings for Gaussian Kernels on Manifolds
arXiv:2609.15179v1 Announce Type: cross Abstract: The Gaussian kernel is a widely used similarity measure underlying kernel methods such as kernel PCA and spectral clustering, but computing Gaussian...
arXiv Machine Learning
Jun 18
Fisher Width: A Geometric Measure of Complexity on Statistical Manifolds
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
arXiv Machine Learning
Jul 28
Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv Machine Learning
Sep 4
Anisotropic View Distance Metric for High-Dimensional Data: Theory, Geometry, and Fast Computation
The paper introduces View distance, a novel metric that projects high‑dimensional data onto all pairwise two‑dimensional planes and sums the Euclidean distances across these projections. It satisfies metric axioms, couples features, suppresses redundancy, and captures anisotropic geometry. To make it scalable, the authors propose a plane‑selection strategy using iterative Maximum Weight Matching, reducing complexity from ω(n²) to ω(k) and demonstrating competitive performance on twelve datasets.
arXiv Machine Learning
Sep 23
Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention
arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...
arXiv Machine Learning
Aug 28
Hadamard Flattening and Gaussian Pooling Sketch for Least Squares with Coordinate-wise Guarantee
arXiv:2608. 26552v1 Announce Type: cross Abstract: Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem.
arXiv Machine Learning
Jul 9
Fast determinantal sampling on general spaces and diffusion geometry
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
Hugging Face Trending Papers
Aug 27
Hadamard Flattening and Gaussian Pooling Sketch for Least Squares with Coordinate-wise Guarantee
Randomized sketch-and-solve algorithms accelerate overconstrained $\ell_2$ regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the cost of the regress...
arXiv Statistics ML
Sep 4
Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing
The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.
Hugging Face Trending Papers
Sep 24
On the SoS Certifiability of Log-Concave Distributions
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.