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.
Proves minimality of tensor varieties, generalizing previous results.
Introduces tensor product for quiver representations and applies to stable bundles and character varieties.
Integrable Killing tensors are used to classify orthogonal coordinates in which the classical Hamilton-Jacobi equation can be solved by a separation of variables. We completely solve the Nijenhuis integrability conditions for Killing tensors on the sphere and give a set of isometry invariants for the integrabilit…
Estimates the probability of a random symmetric tensor being close to rank-one.
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer…
Equivalence proven between uniformizing varieties and tensors, generalizing uniformization results.
Complex projective varieties are quotients of polydiscs under specific group actions.
We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism \s of the tensor product T\otimes T' of the tangent bundle T with the cotangent bundle T'. To such a curvature type tensor \s one associates the fir…
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software a…
The paper proposes a noncommutative deformation of toric varieties.
New stability and isolation results for Einstein manifolds.
Work consists of introduction, two chapters, conclusion and four applications. In this work is examined the condition, with which the wave space metrics of Riemann- Cartan is the solution of Einstein equation in the void. Geometric structures were for this purpose studied on the differentiated variety: connectedness, c…
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is a recently proposed version of tensor decomposition that allows for a variety of…
Study on tensor nuclear norm's decomposability and subdifferential.
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably rec…
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent simplicial complexes and polytopes. In this paper, we formalize incidence tensors,…
In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases where the columns are points on a low-dimensional nonlinear algebraic variety, a pr…
OGRe simplifies tensor calculations in general relativity.
The study connects conic connections and torsion-free principal connections on G-structures.
Explicit formula for Bergman kernel of abelian varieties proved.
Tensor decompositions are used in various data mining applications from social network to medical applications and are extremely useful in discovering latent structures or concepts in the data. Many real-world applications are dynamic in nature and so are their data. To deal with this dynamic nature of data, there exis…
Holomorphic tensors on algebraic cones are invariant under certain group actions.
Tensor networks improve sequence modeling with efficient sampling and parallelism.
We propose a restricted class of tensor network state, built from number-state preserving tensors, for supervised learning tasks. This class of tensor network is argued to be a natural choice for classifiers as (i) they map classical data to classical data, and thus preserve the interpretability of data under tensor tr…
Study of hyperkähler reduction on abelian varieties and toric manifolds.
Low-bit training framework reduces energy consumption in CNNs.
Spatio-temporal data compression method reduces memory usage.
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…
We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been dedicated to this problem, prior algorithms either are computationally too expensive f…
We propose a new framework for the analysis of low-rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank SVD for matrices and multi-linear SVD for tensors. Then, building …
We investigate the holonomy group of singular Kähler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a connection between irreducibility of holonomy representations and stability of the tange…
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motiv…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…
New algorithm detects tensor dependence structure alterations efficiently.
Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information retrieval using deep-learning classifiers, such encodings are learnt on the flattened la…
Sparse symmetric tensor regression reduces brain connectivity complexity.
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure featu…
A popular tool for unsupervised modelling and mining multi-aspect data is tensor decomposition. In an exploratory setting, where and no labels or ground truth are available how can we automatically decide how many components to extract? How can we assess the quality of our results, so that a domain expert can factor th…
EM optimizes tensor density estimation by relaxing -divergence to KL-divergence.
We combine Recurrent Neural Networks with Tensor Product Representations to learn combinatorial representations of sequential data. This improves symbolic interpretation and systematic generalisation. Our architecture is trained end-to-end through gradient descent on a variety of simple natural language reasoning tasks…
Develops SymGCP for tensor decompositions with general symmetry.
Researchers reconstruct stiffness tensors from limited data in anisotropic elasticity.
SPIDER uses deep neural networks for streaming tensor factorization.
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embedd…
TEC combines multiple RPSTMs to classify big tensors efficiently.
Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.
The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In add…
In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor representation, such as support tensor machine (STM) need to solve iteratively which occu…