Related papers: Permutation invariant Gaussian 2-matrix models
Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…
In this paper we consider the mixed tensor space of a $\mathbb Z_2$-graded vector space. We obtain a spanning set of invariants of the associated symmetric algebra under the action of the general linear supergroup as well as the queer…
For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…
Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism.…
Some conceptual issues concerning general invariant theories, with special emphasis on general relativity, are analyzed. The common assertion that observables must be required to be gauge invariant is examined in the light of the role…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
Graphical Transformation Models (GTMs) are introduced as a novel approach to effectively model multivariate data with intricate marginals and complex dependency structures semiparametrically, while maintaining interpretability through the…
Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the…
The two-matrix model is defined on pairs of Hermitian matrices $(M_1,M_2)$ of size $n\times n$ by the probability measure $$\frac{1}{Z_n} \exp\left(\textrm{Tr} (-V(M_1)-W(M_2)+\tau M_1M_2)\right)\ dM_1\ dM_2, $$ where $V$ and $W$ are given…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)$\ast\ast 6$\ invariants are obtained. These…
We show the explicit expression for the covariance matrix of general Gaussian states in terms of the symplectic group matrices. We discuss how the criteria to characterize squeezing and entanglement using the covariance matrix give rise to…
Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in…
This paper propose a novel decomposable graphical model to accommodate skew Gaussian graphical models. We encode conditional independence structure among the components of the multivariate closed skew normal random vector by means of a…
This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…
Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…
Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under $S_N$, the symmetric group of all permutations of $N$ objects. In this paper, the permutation invariant…
Gaussian graphical models are nowadays commonly applied to the comparison of groups sharing the same variables, by jointy learning their independence structures. We consider the case where there are exactly two dependent groups and the…