Related papers: Enhancing the SVD Compression
An increasing bottleneck in decentralized optimization is communication. Bigger models and growing datasets mean that decentralization of computation is important and that the amount of information exchanged is quickly growing. While…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…
In a Jacobi--Davidson (JD) type method for singular value decomposition (SVD) problems, called JDSVD, a large symmetric and generally indefinite correction equation is solved iteratively at each outer iteration, which constitutes the inner…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
This work studies embedding of arbitrary VC classes in well-behaved VC classes, focusing particularly on extremal classes. Our main result expresses an impossibility: such embeddings necessarily require a significant increase in dimension.…
Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…
We propose a new method for compressing physics foundation models (PFMs) which is a new trend in AI for Science. While model compression is essential for reducing memory use and accelerating inference in large foundation models, it remains…
We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…
Filtering based on Singular Value Decomposition (SVD) provides substantial separation of clutter, flow and noise in high frame rate ultrasound flow imaging. The use of SVD as a clutter filter has greatly improved techniques such as vector…
Reconstructing spectral densities from Euclidean lattice correlators requires an inverse Laplace transform, which is inherently ill-conditioned when applied to numerical data with statistical uncertainties. The maximum amount of information…
Images are a substantial portion of the internet, making efficient compression important for reducing storage and bandwidth demands. This study investigates the use of Singular Value Decomposition and low-rank matrix approximations for…
Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…
This work introduces AD-SVFD, a deep learning model for the deformable registration of vascular shapes to a pre-defined reference and for the generation of synthetic anatomies. AD-SVFD operates by representing each geometry as a weighted…
Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated.It is proved that such an m\times n matrix almost surely has a constant…
When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in…
Localizing a cloud of points from noisy measurements of a subset of pairwise distances has applications in various areas, such as sensor network localization and reconstruction of protein conformations from NMR measurements. In [1], Drineas…
Steganography is a method that can improve network security and make communications safer. In this method, a secret message is hidden in content like audio signals that should not be perceptible by listening to the audio or seeing the…