arXiv research

Study higher rank inner products and their tilings to describe tori degenerations.

Researchers prove inner product recovery is impossible in latent space models.

New metrics measure knots' shapes without changing their orientation.

Convex learning for diverse invariances in semi-inner-product space.

We describe a construction of fibrewise inner products on the cotangent bundle of the smooth free loop space of a Riemannian manifold. Using this inner product, we construct an operator over the loop space of a string manifold which is directly analogous to the Dirac operator of a spin manifold.

This study approximates neural network features for modeling relations and attention mechanisms.

Paper proposes a new method to optimize feature coordinates for better image classification.

We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …

Being E a vector space with inner product and S the sphere of E, will be given a demonstration that every application of the sphere S itself it such that preserve inner product is the restriction of a linear isometry in E.

The paper studies geometric properties of Grassman manifolds within Euclidean spaces.

The paper explores linear representations in language models using counterfactuals.

Geometrically, tensors of fixed rank form a minimal submanifold.

In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product is preserved by the full symmetry group of Euclidean space (translations, rotations, and reflections). In equiaffine ge…

GPU-accelerates multiuser detection for 5G URLLC systems.

Paper proposes efficient inner product approximation for hybrid sparse and dense vectors.

The Bergman kernels of holomorphic vector bundles are studied to extend the Fubini-Study map.

Improved ITL descriptors using explicit inner product spaces for scalable systems.

We formulate a quantization commutes with reduction principle in the setting where the Lie group $G$, the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and a…

The curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.

A new method uses Gram matrix for efficient multivariate functional principal components.

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of arbitrary extrinsic symmetric spaces in pseudo-Euclidean spaces by corresponding …

WIPS optimizes inner product weights to approximate various similarities.

Quantum connections replace metrics with operator inner products.

Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.

Study on kernel regression risk in high dimensions using Pinsker bound.

We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively n…

Paper proves smoothness for variational inference, giving convergence guarantees.

In this paper we study isometry-invariant Finsler metrics on inner product spaces over $\mathbb{R}$ or $\mathbb{C}$, i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most g…

The paper introduces polarizations in symplectic and orthogonal settings.

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However, these techniques require tensor decomposition which could lead to the loss of infor…

There are considered 4-dimensional pseudo-Riemannian spaces with inner products of signature (3,1) and (2,2). The objects of investigation are space-like and time-like hyperspheres in the respective cases. These hypersurfaces are equipped with almost contact B-metric structures. The constructed manifolds are characteri…

New vector quantization method reduces relevance of parallel components in database points.

New algorithm for linear bandits tackles Optimal Transport problems.

Enhances CLIP's similarity computation using PMI's linear structure.

Estimates latent inner products from an anisotropic Gaussian graph with improved spectral method.

PieClam autoencodes graphs into communities, improving graph anomaly detection.

A Lie algebra is called nonsoliton if it does not admit a soliton inner product. We demonstrate that the subset of nonsoliton Lie algebras in the moduli space of indecomposable n-dimensional N-graded nilpotent Lie algebras is discrete if and only if n <= 7.

New attacks break robust aggregation methods for SGD in Byzantine-tolerant systems.

Classifies metrics on specific Lie groups.

We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical $\mathcal{L}^2$ and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for whic…

We propose a robust elastic net (REN) model for high-dimensional sparse regression and give its performance guarantees (both the statistical error bound and the optimization bound). A simple idea of trimming the inner product is applied to the elastic net model. Specifically, we robustify the covariance matrix by trimm…

We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements. On the other hand, we give an example of a solvable unimodular Lie algebra of dimension 5 that has no orthonormal geodesic basis, for any inner product.

Signature Isolation Forest removes constraints from FIF by using rough path theory's signature transform.

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric {\bf g} on the moduli spaces $\M…

Equivalent tests for SGD batch size selection found.

A new method improves maximum inner product search by locally decomposing residual vectors.

Gaussian sketching preserves kernel inner products in low dimensions.