A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New technique stabilizes singular values in concatenated matrices.
Quantum SVT reduces credit risk analysis costs.
This work analyzes self-attention matrices using random matrix theory.
Optimal rank-adaptive matrix estimation from linear measurements.
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
We regard pre-trained residual networks (ResNets) as nonlinear systems and use linearization, a common method used in the qualitative analysis of nonlinear systems, to understand the behavior of the networks under small perturbations of the input images. We work with ResNet-56 and ResNet-110 trained on the CIFAR-10 dat…
Study analyzes perturbations in singular subspaces under random noise.
We compared the regular Singular Value Decomposition (SVD), truncated SVD, Krylov method and Randomized PCA, in terms of time and space complexity. It is well-known that Krylov method and Randomized PCA only performs well when k << n, i.e. the number of eigenpair needed is far less than that of matrix size. We compared…
In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis, the blow-up analysis usually strongly utilizes conformal invariance, which yields …
Study shows XRP price correlates with transaction network metrics.
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with c…
Randomized SVD shows phase transitions in noisy data.
Paper analyzes singular subspace estimation in noisy matrix models.
New framework for higher-order singular-value derivatives of rectangular matrices.
Derives a primal-dual MLSVD formulation for multilinear data.
A new method selects regions of interest in GC-MS data without prior target selection.
Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools. However, in many practical applications such as collaborative filtering and network analysis, we only get a partial observation.…
Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recen…
Stochastic gradient descent regularizes least squares problems by smoothing large singular values.
In the early 1980's Almgren developed a theory of Dirichlet energy minimizing multi-valued functions, proving that the Hausdorff dimension of the singular set (including branch points) of such a function is at most where is the dimension of its domain. Almgren used this result in an essential way to show t…
Informed by recent work on tensor singular value decomposition and circulant algebra matrices, this paper presents a new theoretical bridge that unifies the hypercomplex and tensor-based approaches to singular value decomposition and robust principal component analysis. We begin our work by extending the principal comp…
Random matrix analysis reveals that neural network weights are mostly random, with some indicating learned information.
Paper studies tensor models using random matrix theory.
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analys…
The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the (unobservable)_denoising_ problem of how to best approximate a low-rank signal matrix bur…
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is…
It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network's input-output Jacobian is is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condi…
S2D selectively decays large singular values to improve quantization of neural activations.
The paper sharpens the analysis of sketch-and-project methods using randomized singular value decomposition.
Study analyzes accuracy of tensor deflation in noisy conditions.
Improved SVD for shifted matrices without explicit matrix construction.
New algorithms improve RPCA for large matrices with upper rank bounds.
A new PCR method using SVD with sparse regularization.
Note on minimal maps' uniqueness via singular values.
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to approximate the tensor rank with the norm of singular values based on its …
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsit…
Study inequalities for singular values of rectangular matrices.
The paper establishes criteria for spacetime inextendibility using asymptotic volume-distance-ratio analysis.
The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.
Study differentiable maps on hypersurface links, finding fold maps with circle singular value sets.
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is com…
Study on games with degenerate diffusion matrices, proving value existence and convergence.
Study evaluates thresholds for removing noise from DNN weights using random matrix theory.
A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries. Reconstruction of X from the singular values and singular vectors of the contaminated matrix Y is a key problem in machine learning, computer vision and data science. In this paper we show that common…
Deterministic bounds for tensor singular values and vectors, differing from matrix cases.
The paper analyzes how random perturbations affect RSVD and its applications.
In this paper, we introduce the algorithms of Orthogonal Deep Neural Networks (OrthDNNs) to connect with recent interest of spectrally regularized deep learning methods. OrthDNNs are theoretically motivated by generalization analysis of modern DNNs, with the aim to find solution properties of network weights that guara…
We introduce the concept of singular values for the Riemann curvature tensor, a central mathematical tool in Einstein's theory of general relativity. We study the properties related to the singular values, and investigate five typical cases to show its relationship to the Ricci scalar and other invariants.