Related papers: A higher-order LQ decomposition for separable cova…
We consider the problem of decomposing a higher-order tensor with binary entries. Such data problems arise frequently in applications such as neuroimaging, recommendation system, topic modeling, and sensor network localization. We propose a…
The development of over-parameterized pre-trained language models has made a significant contribution toward the success of natural language processing. While over-parameterization of these models is the key to their generalization power,…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
While there has been some progress on the decomposition of Kronecker products of characters of the symmetric groups in recent times, results on the symmetric and alternating part of Kronecker squares are still scarce. Here, new results (and…
This paper derives the CUR-type factorization for tensors in the Tucker format based on a new variant of the discrete empirical interpolation method known as L-DEIM. This novel sampling technique allows us to construct an efficient…
We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dirichlet, Neumann, Robin, and mixed boundary conditions are…
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the…
We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…
Large Language Models (LMs) have achieved state-of-the-art performance on many Natural Language Processing (NLP) benchmarks. With the growing number of new benchmarks, we build bigger and more complex LMs. However, building new LMs may not…
When studying deformations of an $A$-module $M$, Laudal and Yau showed that one can consider 1-cocycles in the Hochschild cohomology of $A$ with coefficients in the bi-module $End_k(M).$ With this in mind, the use of higher order Hochschild…
It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…
Leveraging the large body of work devoted in recent years to describe redundancy and synergy in multivariate interactions among random variables, we propose a novel approach to quantify cooperative effects in feature importance, one of the…
We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that…
We generalize the theory of Lorentz-covariant distributions to broader classes of functionals including ultradistributions, hyperfunctions, and analytic functionals with a tempered growth. We prove that Lorentz-covariant functionals with…
We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
This study clarifies the proper criteria to assess the modeling capacity of a general tensor model. The work analyze the problem based on the study of tensor ranks, which is not a well-defined quantity for higher order tensors. To process,…
In the linear mixed model (LMM), the simultaneous assessment and comparison of dispersion relevance of explanatory variables associated with fixed and random effects remains an important open practical problem. Based on the restricted…