arXiv research

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Core-Halo solves large-scale fixed-point problems by decentralizing updates.

NA$_0$CT$^2$ improves tensor regression predictions with $\ell_0$ regularization.

KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.

A new algorithm reduces graph complexity for better dense subgraph analysis.

The main result is that an s-cobordism (topological or smooth) of 4-manifolds has a product structure outside a ``core'' sub s-cobordism. These cores are arranged to have quite a bit of structure, for example they are smooth and abstractly (forgetting boundary structure) diffeomorphic to a standard neighborhood of a 1-…

Estimates covariance matrices for matrix-variate data via core covariance geometry.

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove that any $n$-fold vector bundle admits a non-canonical isomorphism to a decomposed …

We construct a geometric decomposition for the convex core of a thick hyperbolic 3-manifold M with bounded rank. Corollaries include upper bounds in terms of rank and injectivity radius on the Heegaard genus of M and on the radius of any embedded ball in the convex core of M.

Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.

FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.

We implement a Tensor Train layer in the TensorFlow Neural Machine Translation (NMT) model using the t3f library. We perform training runs on the IWSLT English-Vietnamese '15 and WMT German-English '16 datasets with learning rates $\in \{0.0004,0.0008,0.0012\}$, maximum ranks $\in \{2,4,8,16\}$ and a range of core dime…

We show that the interior of the convex core of a quasifuchsian punctured-torus group admits an ideal decomposition (usually an infinite triangulation) which is canonical in two different senses: in a combinatorial sense via the pleating invariants, and in a geometric sense via an Epstein-Penner convex hull constructio…

MARS automatically selects tensor decomposition ranks, improving performance in neural network tasks.

A new method for traffic data imputation considering spatiotemporal correlations.

Unified model for tensor completion using low-rank and sparse Tucker decomposition.

Tensor decomposition on big data has attracted significant attention recently. Among the most popular methods is a class of algorithms that leverages compression in order to reduce the size of the tensor and potentially parallelize computations. A fundamental requirement for such methods to work properly is that the lo…

The abstract proves spherical surface decompositions with conical singularities.

A new kernel improves tensor classification accuracy and reduces computation time.

The paper tackles scalability issues in Graph Representation Learning.

Bayesian tensor train method recovers streaming data with high accuracy.

We investigate the representation theory of the polynomial core of the quantum Teichmuller space of a punctured surface S. This is a purely algebraic object, closely related to the combinatorics of the simplicial complex of ideal cell decompositions of S. Our main result is that irreducible finite-dimensional represent…

Galerkin method outperforms graph-based methods in spectral decompositions.

Word embedding is a powerful tool in natural language processing. In this paper we consider the problem of word embedding composition \--- given vector representations of two words, compute a vector for the entire phrase. We give a generative model that can capture specific syntactic relations between words. Under our …

Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.

This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same…

ProbFM provides principled uncertainty quantification for financial forecasting.

We introduce Fenchel-Nielsen coordinates on Teicmüller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geom…

The paper bounds distances and transformations between pants decompositions and triangulations on surfaces.

Paper introduces a new method for efficient portfolio risk quantification.

The PARAFAC tensor decomposition has enjoyed an increasing success in exploratory multi-aspect data mining scenarios. A major challenge remains the estimation of the number of latent factors (i.e., the rank) of the decomposition, which yields high-quality, interpretable results. Previously, we have proposed an automate…

New method decomposes sensory information from neurons into specific stimuli and features.

Paper introduces a PDE-free method for decomposing forces in any dimension.

We consider the problem of maximum a posteriori (MAP) inference in discrete graphical models. We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction method of multipliers (ADMM). However, unlike the standard ADMM, we use an inexa…

Dual-Channel Tensor Neural Network (DC-TNN) decomposes tensor data into low-rank and sparse components for better estimation and inference.

New method approximates high-dimensional probability densities efficiently.

A new tensor ring mixture model improves density estimation efficiency.

We introduce a general tensor model suitable for data analytic tasks for {\em heterogeneous} datasets, wherein there are joint low-rank structures within groups of observations, but also discriminative structures across different groups. To capture such complex structures, a double core tensor (DCOT) factorization mode…

Derives a primal-dual MLSVD formulation for multilinear data.

A fair PCA method using JEVD ensures balanced data representation.

Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition m…

There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both the geometry and combinatorics of the triangulation. We prove that detecting ta…

Paper proposes TBSD for efficient anomaly detection in textured images.

By recent results of Baker--Etnyre--Van Horn-Morris, a rational open book decomposition defines a compatible contact structure. We show that the Heegaard Floer contact invariant of such a contact structure can be computed in terms of the knot Floer homology of its (rationally null-homologous) binding. We then use this …

New method deforms function algebras on manifolds using spectral decomposition.

Proposes a method for tensor completion with sparse factors and missing data.

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: ag…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le i \le r}$ and output $y\in \mathbb R$, i.e., $y=\sum_{i=1}^r σ( \boldsymbol w_i…