Related papers: The Multi-Orientable Random Tensor Model, a Review
Invariance has recently proven to be a powerful inductive bias in machine learning models. One such class of predictive or generative models are tensor networks. We introduce a new numerical algorithm to construct a basis of tensors that…
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\nu$, $0<\nu<1$. The stability and…
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the number of rows (columns) to grow polynomially in the number…
Attention matrices are fundamental to transformer research, supporting a broad range of applications including interpretability, visualization, manipulation, and distillation. Yet, most existing analyses focus on individual attention heads…
This article introduces a novel approach to the mathematical development of Ordinary Least Squares and Neural Network regression models, diverging from traditional methods in current Machine Learning literature. By leveraging Tensor…
We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…
Researchers are increasingly incorporating numeric high-order data, i.e., numeric tensors, within their practice. Just like the matrix/vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and…
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…
Human perception of the empirical world involves recognizing the diverse appearances, or 'modalities', of underlying objects. Despite the longstanding consideration of this perspective in philosophy and cognitive science, the study of…
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a…
Markov Chain Monte Carlo (MCMC), and Tensor Networks (TN) are two powerful frameworks for numerically investigating many-body systems, each offering distinct advantages. MCMC, with its flexibility and theoretical consistency, is well-suited…
The multilinear normal distribution is a widely used tool in tensor analysis of magnetic resonance imaging (MRI). Diffusion tensor MRI provides a statistical estimate of a symmetric 2nd-order diffusion tensor, for each voxel within an…
Various tensor models have been recently shown to have the same properties as the celebrated Sachdev-Ye-Kitaev (SYK) model. In this paper we study in detail the diagrammatics of two such SYK-like tensor models: the multi-orientable (MO)…
Multi-objective optimization (MOO) is a well-studied problem for several important recommendation problems. While multiple approaches have been proposed, in this work, we focus on using constrained optimization formulations (e.g., quadratic…
This paper extends the univariate Theory of Connections, introduced in (Mortari,2017), to the multivariate case on rectangular domains with detailed attention to the bivariate case. In particular, it generalizes the bivariate Coons surface,…
Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to…
Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…
We study the $O(N)^3$ supersymmetric quantum field theory of a scalar superfield $\Phi_{abc}$ with a tetrahedral interaction. In the large $N$ limit the theory is dominated by the melonic diagrams. We solve the corresponding Dyson-Schwinger…
As a fundamental piece of multi-object Bayesian inference, multi-object density has the ability to describe the uncertainty of the number and values of objects, as well as the statistical correlation between objects, thus perfectly matches…
In this paper we study the Rotor Model of Martins and Nienhuis. After introducing spectral parameters, a combined use of integrability, polynomiality of the ground state wave function and a mapping into the fully-packed O(1)-model allows us…