A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
T-Basis represents neural network tensors with fewer parameters.
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Laur…
Paper projects GP basis functions using tensor networks to reduce complexity.
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result establishes isomorphisms between these spaces and certain spaces of tensors (at…
New basis for permutation equivariant layers reduces computation costs.
Characterizes a specific type of neural network for alternating group equivariance.
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
New algorithm learns interpretable CP-basis from streaming tensor data under Markovian constraints.
In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view. We give an existence and uniqueness theorem for a remarkab…
Efficiently analyzes multidimensional functional data using separable basis functions.
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may suffer from difficulties when representing higher dimensional surfaces. Motivated by…
The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space . The Ricci identities, together with their corresponding identities of deflection d-tensors, …
Characterizes group-equivariant neural networks for three groups.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
Given a simple algebraic group , a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a bas…
Unified approach to tensor PCA and related problems using tensor cumulants.
New algorithms improve tensor CP decomposition under mild conditions.
MCCA extracts shared structure from multiple tensor datasets.
The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.
The paper defines constraints for commuting endomorphisms in generalized tangent bundles.
GETF efficiently decomposes large-scale Boolean tensors.
-non-degenerate spaces are spacetimes that can be characterized uniquely by their scalar curvature invariants. The ultimate goal of the current work is to construct a basis for the scalar polynomial curvature invariants in three dimensional Lorentzian spacetimes. In particular, we seek a minimal set of alg…
Study shows Calabi-Yau metrics converge to a specific form under certain conditions.
In this paper new general modewise Johnson-Lindenstrauss (JL) subspace embeddings are proposed that are both considerably faster to generate and easier to store than traditional JL embeddings when working with extremely large vectors and/or tensors. Corresponding embedding results are then proven for two different type…
It is studied a 3-dimensional Riemannian manifold equipped with a tensor structure of type (1,1), whose third power is the identity. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant. On such a manifold a fundamental tensor by the metric and by the covariant derivative of…
Unified tensor network formalism for combining neural and symbolic AI.
Neural Chaos uses neural networks instead of polynomials for stochastic modeling.
The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of some of them and onl…
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
Algebraic curvature tensors possess generators which can be formed from symmetric or alternating tensors S, A or tensors θwith an irreducible (2,1)-symmetry. In differential geometry examples of curvature formulas are known which contain generators on the basis of S or A realized by differentiable tensor fields in a na…
Paper improves MVSC using tensor low-rank modeling.
Study on 3D Lie groups finds all generalized Einstein metrics.
New model for network analysis using functional data.
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated using regression techniques. We propose as regression method a tensor decompositi…
Adaptive tensor modeling preserves continuity in multidimensional data.
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra or within a vector manifold framework, here we define geometric calculus directl…
This work is devoted to elaboration on the idea to use block term decomposition for group data analysis and to raise the possibility of modelling group activity with (Lr, 1) and Tucker blocks. A new generalization of block tensor decomposition was considered in application to group data analysis. Suggested approach was…
New method uses tensor decompositions to overcome the curse of dimensionality for large-scale learning.
Study on 3D manifolds with circulant structures and their properties.
The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various non-linear turbulent processes. The pressure-Hessian and the viscous-Laplacian govern the evolution of the velocity-gradients and are known to be non-local in nature. Over the years, several simplified dy…
Tensor logic aims to unify AI types with scalable and transparent features.
Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractography are the only methods to measure the structure of the white matter in the living human brain. The diffusion signal has been modelled as the combined contribution from many individual fascicles of nerve fibers passing through each location in the …
The purpose of this paper is twofold. On one hand, we introduce a modification of the dual canonical basis for invariant tensors of the 3-dimensional irreducible representation of , given in terms of Jacobi diagrams, a central tool in quantum topology. On the other hand, we use this modified basis to study t…
New algorithms for interpreting complex multivariate functions.
Bayesian-TPNN improves ANOVA-TPNN for detecting higher-order components.