Related papers: Overview of Constrained PARAFAC Models
We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format,…
Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…
We seek to impose linear, equality constraints in feedforward neural networks. As top layer predictors are usually nonlinear, this is a difficult task if we seek to deploy standard convex optimization methods and strong duality. To overcome…
Tensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones,…
We present methods for constructing Taylor series surrogate models for covariance preconditioned high dimensional mappings that depend implicitly on the solution of a system of nonlinear equations, e.g., the solution of a partial…
In this paper, uniqueness properties of a coupled tensor model are studied. This new coupled tensor model is used in a new method called Partial Coupled Tensor Factorization of 3D marginals or PCTF3D. This method performs estimation of…
We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…
Over the real numbers, the Kronecker sum is the unique operation on matrices which exponentiates to the Kronecker product. Kronecker quotients provide an algebraic view of decompositions of matrices in terms of Kronecker products. This…
We explore the possibility of improving probabilistic models in structured prediction. Specifically, we combine the models with constrained decoding approaches in the context of token classification for information extraction. The decoding…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…
A recursive deformation of the boson commutation relation is introduced. Each step consists of a minimal deformation of a commutator $[a,\ad]=f_k(\cdots;\no)$ into $[a,\ad]_{q_{k+1}}=f_k(\cdots;\no)$, where $\cdots$ stands for the set of…
Tensor decomposition is one of the fundamental technique for model compression of deep convolution neural networks owing to its ability to reveal the latent relations among complex structures. However, most existing methods compress the…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
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…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
A novel tensor decomposition framework, termed Tensor Star (TS) decomposition, is proposed which represents a new type of tensor network decomposition based on tensor contractions. This is achieved by connecting the core tensors in a ring…
We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…