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A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization
Po Chen, Rujun Jiang, Peng Wang
https://arxiv.org/abs/2506.20344 https://

A Complete Loss Landscape Analysis of Regularized Deep Matrix Factorization
Despite its wide range of applications across various domains, the optimization foundations of deep matrix factorization (DMF) remain largely open. In this work, we aim to fill this gap by conducting a comprehensive study of the loss landscape of the regularized DMF problem. Toward this goal, we first provide a closed-form expression of all critical points. Building on this, we establish precise conditions under which a critical point is a local minimizer, a global minimizer, a strict saddle po…

SCET sum rules for $\Lambda_b \to \Lambda \ell^ \ell^-$, $\Lambda \gamma$ decays
Long-Shun Lu, Cai-Dian L\"u, Yue-Long Shen, Yan-Bing Wei
https://arxiv.org/abs/2506.21419

SCET sum rules for $Λ_b$ $\rightarrow$ $Λ\ell^+\ell^-$, $Λγ$ decays
We construct light-cone sum rules for various types of effective form factors in the $Λ_b \to Λ\ell^+\ell^-$ and $Λ_b \to Λγ$ decays by analyzing vacuum-to-$Λ_b$ (or $γ^\ast$-to-$Λ_b$) correlation functions with the light $Λ$-baryon interpolating current. These form factors, defined via hadronic matrix elements within soft-collinear effective theory (SCET), enter the next-to-leading-power QCD factorization formulas for large-recoil transitions. Implementing the perturbative matching fr…

Bayesian Non-Negative Matrix Factorization with Correlated Mutation Type Probabilities for Mutational Signatures
Iris Lang, Jenna Landy, Giovanni Parmigiani
https://arxiv.org/abs/2506.15855

Bayesian Non-Negative Matrix Factorization with Correlated Mutation Type Probabilities for Mutational Signatures
Somatic mutations, or alterations in DNA of a somatic cell, are key markers of cancer. In recent years, mutational signature analysis has become a prominent field of study within cancer research, commonly with Nonnegative Matrix Factorization (NMF) and Bayesian NMF. However, current methods assume independence across mutation types in the signatures matrix. This paper expands upon current Bayesian NMF methodologies by proposing novel methods that account for the dependencies between the mutatio…

Sparse Infrared Spectroscopy for Detection of Volatile Organic Compounds
Mira Welner, Andre Hazbun, Thomas Beechem
https://arxiv.org/abs/2506.20678 https:/…

Sparse Infrared Spectroscopy for Detection of Volatile Organic Compounds
To reduce the complexity of infrared spectroscopy hardware while maintaining performance, a data informed, task-specific, spectral collection approach termed Sparse Infrared Spectroscopy (SIRS) is developed. Using a numerically based virtual experiment based on a quantitatively accurate infrared database, non-negative matrix factorization is used to identify the spectral pass bands of a minimal number of filters necessary to identify volatile organic compounds (VOC) within either an inert backg…

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
Dimitrios Mataragkas, Alexandros Vasilopoulos, Nikolaos G. Fytas, Dong-Hee Kim
https://arxiv.org/abs/2506.16483

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension …

Causal Inference for Latent Outcomes Learned with Factor Models
Jenna M. Landy, Dafne Zorzetto, Roberta De Vito, Giovanni Parmigiani
https://arxiv.org/abs/2506.20549

Causal Inference for Latent Outcomes Learned with Factor Models
In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor models or representation learning. In this work, we investigate causal effects on $\textit{latent outcomes}$ derived from high-dimensional observed data using nonnegative matrix factorization. To the best of our knowledge, this is the first study to formally ad…

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Soumyajit Chatterjee, Rahul Utkoor, Uppu Eshwar, Sathya Peri, V. Krishna Nandivada
https://arxiv.org/abs/2506.09463

Efficient Task Graph Scheduling for Parallel QR Factorization in SLSQP
Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming (SLSQP) for solving non-linear programming (NLP) problems. QR factorization decomposes a matrix into an orthogonal matrix Q and an upper triangular matrix R, which are essential for solving systems of linear equations arising from optimization problems. SLSQP uses …

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Boris Martin, Pierre Jolivet, Christophe Geuzaine
https://arxiv.org/abs/2506.16875

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of iterative methods is difficult to obtain. Domain decomposition methods (DDM) constitute one of the most promising strategy so far, by combining direct and iterative approaches: using direct solvers on overlapping or non-overlapping subdomains, as a preconditi…

Khovanov-Rozansky cycle calculus for bipartite links
A. Anokhina, E. Lanina, A. Morozov
https://arxiv.org/abs/2506.08721 https://arxi…

Khovanov-Rozansky cycle calculus for bipartite links
Bipartite calculus is a direct generalization of Kauffman planar expansion from $N=2$ to arbitrary $N$, applicable to the restricted class of knots which are entirely made of antiparallel lock tangles. Whenever applicable, it allows a straightforward generalization of the Khovanov calculus without a need of the technically complicated matrix factorization used for arbitrary $N$ in the Khovanov-Rozansky (KR) approach. The main object here is the $3^{n}$-dimensional hypercube with $n$ being the n…

This https://arxiv.org/abs/2504.20305 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fast LDL factorization for dense and sparse symmetric matrices over an arbitrary field
While existing algorithms may be used to solve a linear system over a general field in matrix-multiplication time, the complexity of constructing a symmetric triangular factorization (LDL) has received relatively little formal study. The LDL factorization is a common tool for factorization of symmetric matrices, and, unlike orthogonal counterparts, generalizes to an arbitrary field. We provide algorithms for dense and sparse LDL nd LU factorization that aim to minimize complexity for factorizat…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- A Second-Order Majorant Algorithm for Nonnegative Matrix Factorization
Mai-Quyen Pham, J\'er\'emy Cohen, Thierry Chonavel

This https://arxiv.org/abs/2505.20730 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

What LLMs Miss in Recommendations: Bridging the Gap with Retrieval-Augmented Collaborative Signals
User-item interactions contain rich collaborative signals that form the backbone of many successful recommender systems. While recent work has explored the use of large language models (LLMs) for recommendation, it remains unclear whether LLMs can effectively reason over this type of collaborative information. In this paper, we conduct a systematic comparison between LLMs and classical matrix factorization (MF) models to assess LLMs' ability to leverage user-item interaction data. We further in…

A new hierarchical distribution on arbitrary sparse precision matrices
Gianluca Mastrantonio, Pierfrancesco Alaimo Di Loro, Marco Mingione
https://arxiv.org/abs/2506.09607

A new hierarchical distribution on arbitrary sparse precision matrices
We introduce a general strategy for defining distributions over the space of sparse symmetric positive definite matrices. Our method utilizes the Cholesky factorization of the precision matrix, imposing sparsity through constraints on its elements while preserving their independence and avoiding the numerical evaluation of normalization constants. In particular, we develop the S-Bartlett as a modified Bartlett decomposition, recovering the standard Wishart as a particular case. By incorporating…

This https://arxiv.org/abs/2410.16826 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery
In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Preconditioned Subgradient Algorithm (OPSA)} and provide, for the first time in the literature, linear convergence rates independent of the rank of the sought asymmetric matrix in the presence of gross corruptions. Our work goes beyond existing results in preconditioned-type approaches addressing their current limitation…

This https://arxiv.org/abs/2412.06551 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deterministic and randomized LU-Householder CholeskyQR
In this work, we develop LU-Householder CholeskyQR (LHC) for QR factorization of tall-skinny matrices. Similar to LU-CholeskyQR \cite{LUChol}, LHC does not require a sufficient condition of $κ_{2}(X)$ for the input tall-skinny matrix $X \in \mathbb{R}^{m\times n}$. This characteristic ensures the algorithm's reliability in the real-world applications, which is different from other CholeskyQR-type algorithms. To address the issue of numerical breakdown in Cholesky factorization of LU-CholeskyQR…

This https://arxiv.org/abs/2410.16826 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery
In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Preconditioned Subgradient Algorithm (OPSA)} and provide, for the first time in the literature, linear convergence rates independent of the rank of the sought asymmetric matrix in the presence of gross corruptions. Our work goes beyond existing results in preconditioned-type approaches addressing their current limitation…

Testing Hypotheses of Covariate Effects on Topics of Discourse
Gabriel Phelan, David A. Campbell
https://arxiv.org/abs/2506.05570 https://

Testing Hypotheses of Covariate Effects on Topics of Discourse
We introduce an approach to topic modelling with document-level covariates that remains tractable in the face of large text corpora. This is achieved by de-emphasizing the role of parameter estimation in an underlying probabilistic model, assuming instead that the data come from a fixed but unknown distribution whose statistical functionals are of interest. We propose combining a convex formulation of non-negative matrix factorization with standard regression techniques as a fast-to-compute and…

Structured Variational $D$-Decomposition for Accurate and Stable Low-Rank Approximation
Ronald Katende
https://arxiv.org/abs/2506.08535 https://

Structured Variational $D$-Decomposition for Accurate and Stable Low-Rank Approximation
We introduce the $D$-decomposition, a non-orthogonal matrix factorization of the form $A \approx P D Q$, where $P \in \mathbb{R}^{n \times k}$, $D \in \mathbb{R}^{k \times k}$, and $Q \in \mathbb{R}^{k \times n}$. The decomposition is defined variationally by minimizing a regularized Frobenius loss, allowing control over rank, sparsity, and conditioning. Unlike algebraic factorizations such as LU or SVD, it is computed by alternating minimization. We establish existence and perturbation stabili…