Singular Value Decomposition
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Sparse Functional Singular Value Decomposition for Biclustering and Triclustering Longitudinal Data
arXiv:2606.05488v1 Announce Type: cross Abstract: Identifying subtypes of complex conditions, such as Inflammatory Bowel Disease (IBD), often requires capturing latent patterns in longitudinal omics data. However, these data are typically high-dimensional, sparsely sampled, and irregularly observed over time, posing substantial challenges for conventional (bi)clustering and functional data analysis methods. We propose Tri-SfSVD, a unified sparse functional Singular Value Decomposition...
TwinQuant: Learnable Subspace Decomposition for 4-Bit LLM Quantization
arXiv:2606.01556v1 Announce Type: new Abstract: 4-bit quantization reduces the memory footprint and latency of large language model inference, but its aggressive precision reduction can severely degrade accuracy. Prior methods address this by decomposing each weight matrix into two components (e.g., via singular value decomposition) and quantizing them separately, assigning the bulk of values to a low-precision residual component while handling outliers with a high-precision low-rank...
Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection
arXiv:2510.20116v2 Announce Type: replace Abstract: This work investigates the reduction of phasor measurement unit (PMU) data through low-rank matrix approximations. To reconstruct a PMU data matrix from fewer measurements, we propose the framework of interpolatory matrix decompositions (IDs). In contrast to methods relying on principal component analysis or singular value decomposition, IDs recover the complete data matrix using only a few of its rows (PMU datastreams) and/or a few of its...
A Parareal Algorithm with Low-Rank Coarse Solvers
arXiv:2508.08873v2 Announce Type: replace Abstract: We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from truncated SVD approximations of the transfer operators mapping initial values for a given time interval to the solution at the end of the interval. By leveraging randomized singular value decompositions, these low-rank approximations are obtained embarrassingly parallel by computing local fine solutions...
Quaternion Maximum-Volume Submatrix Selection with Applications to Multichannel Imaging and Visual Data
arXiv:2606.08175v1 Announce Type: new Abstract: Low-rank approximation based on selected rows and columns is a useful alternative to singular value decompositions when the goal is an interpretable and compact matrix representation. A standard way to choose these rows and columns is the maximum-volume principle: it selects submatrices with large volume, which usually leads to stable interpolation coefficients and accurate CUR-type approximations. In this paper, we study this idea for...
SigmaScale: LLM Compression with SVD-based Low-Rank Decomposition and Learned Scaling Matrices
Announce Type: new Abstract: We present SigmaScale, a method for learning auxiliary scaling matrices $S$ to aid truncated Singular Value Decomposition (SVD) based Large Language Model (LLM) compression. Instead of deriving scaling matrices analytically, SigmaScale optimizes two sets of vectors that define diagonal row and column scaling transformations under an activation-aware compression loss. We show that learned scaling lowers the effective intrinsic rank of weight matrices, as reflected...
Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures
arXiv:2411.12438v2 Announce Type: replace Abstract: We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the...
Factorizing binary tensors into quantics tensor trains
new Abstract: The conversion of functions to quantics tensor trains is a well-established procedure and can either be done analytically or numerically. Numerical conversion schemes are based on singular value decompositions, where access to the full tensor is necessary, or on cross interpolations, which only depend on sampling a function. When dealing with large binary tensors, the first approach becomes prohibitively expensive while the second approach might fail to converge due to the...
TailLoR: Protecting Principal Components in Parameter-Efficient Continual Learning
Announce Type: new Abstract: Parameter-efficient finetuning methods based on spectral decomposition have enabled progress in Continual Learning. In this paper we introduce TailLoR, which utilizes the singular bases U and V of the pre-trained weights as a fixed reference frame to learn a low-rank update applied to the singular value matrix. A soft spectral penalty discourages updates aligned with dominant singular directions, reducing interference while routing fine-grained adaptation into...
Spectral Asymptotics of Neural Network Loss Landscapes: An Exact Decomposition of the Curvature Exponent
arXiv:2606.02596v1 Announce Type: new Abstract: The curvature exponent $\alpha$ in $h_k \propto \sigma_k^\alpha$ -- governing how Hessian eigenvalues scale with gradient singular values -- varies systematically across layer types ($\alpha \approx 2$ for convolutions, $\approx 1$ for transformer attention, $< 1$ for MLP up-projections). We prove the Spectral Alignment Decomposition: $\alpha = 2 + d\log\Phi_k / d\log\sigma_k$, where $\Phi_k$ measures alignment between Kronecker factor...