相关论文: On the Accuracy of Hotelling-Type Tensor Deflation…

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the \textit{Spectral Sensitivity Theorem}, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

We present a variationally consistent wrinkling model based on spectral decomposition of the stress tensor, providing a unified formulation that captures the three distinct membrane states. Compared to the previous strain-based spectral…

For statistical analysis of network data, the $\beta$-model has emerged as a useful tool, thanks to its flexibility in incorporating nodewise heterogeneity and theoretical tractability. To generalize the $\beta$-model, this paper proposes…

Tensor parameters that are amortized or regularized over large tensor powers, often called "asymptotic" tensor parameters, play a central role in several areas including algebraic complexity theory (constructing fast matrix multiplication…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

The tensor rank decomposition problem consists of recovering the unique set of parameters representing a robustly identifiable low-rank tensor when the coordinate representation of the tensor is presented as input. A condition number for…

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition…

We have studied the precession mode, the rotational excitation built on the high-$K$ isomeric state, in comparison with the recently identified wobbling mode. The random-phase-approximation (RPA) formalism, which has been developed for the…

We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…

With the rise of the "big data" phenomenon in recent years, data is coming in many different complex forms. One example of this is multi-way data that come in the form of higher-order tensors such as coloured images and movie clips.…

A symmetric tensor of small rank decomposes into a configuration of only few vectors. We study the variety of tensors for which this configuration is a unit norm tight frame.

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-$1$ update which is the alternating version…

Tensors are often studied by introducing preorders such as restriction and degeneration: the former describes transformations of the tensors by local linear maps on its tensor factors; the latter describes transformations where the local…

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

We study symmetric tensor decompositions, i.e. decompositions of the input symmetric tensor T of order 3 as sum of r 3rd-order tensor powers of u_i where u_i are vectors in \C^n. In order to obtain efficient decomposition algorithms, it is…

We study the generalization capability of nearly-interpolating linear regressors: $\boldsymbol{\beta}$'s whose training error $\tau$ is positive but small, i.e., below the noise floor. Under a random matrix theoretic assumption on the data…

In a recent paper [17], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) model having constant positive spatial curvature and…

The analytic forms of deuteron wave function in coordinate space were applied for theoretical calculations of full set asymmetries of tensor $t_{2j}$ and vector $t_{1i}$ polarizations. Nucleon-nucleon realistic phenomenological potentials…