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.
A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.
Kaczmarz++ accelerates convergence for ill-conditioned systems.
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
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…
KBB algorithm reduces sample complexity for policy evaluation in general state spaces.
A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.
We establish Evans-Krylov estimates for certain nonconvex fully nonlinear elliptic and parabolic equations by exploiting partial Legendre transformations. The equations under consideration arise in part from the study of the "pluriclosed flow" introduced by the first author and Tian
We describe how to use the perturbation theory of Caffarelli to prove Evans-Krylov type estimates for solutions of nonlinear elliptic equations in complex geometry, assuming a bound on the Laplacian of the solution. Our results can be used to replace the various Evans-Krylov type arguments in the complex geom…
New method for directed graphs using learnable spectral positional encodings.
In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a …
A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.
Note on advancements in nonlinear elliptic equations' regularity theory.
A new method for faster optimization in high dimensions.
Enhances gradient estimates for Hermitian Monge-Ampère equations.
Efficiently computes matrix square roots and their inverses for large matrices.
Hessian-free training has become a popular parallel second or- der optimization technique for Deep Neural Network training. This study aims at speeding up Hessian-free training, both by means of decreasing the amount of data used for training, as well as through reduction of the number of Krylov subspace solver iterati…
Paper proposes a new method for efficient second-order neural network training.
Unified framework for multi-view learning with orthogonal projections.
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random…
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
New method speeds up kernel-based machine learning for force field reconstruction.
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitting method, whose convergence is proved based on the Barles-Souganidis…
In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski problem in convex geometry. We will also study the Dirichlet problem of the corresponding degenerate equations as an extension of the equat…
This paper tackles unpaired data in multi-view learning, proposing a new framework and models.
Paper solves Hessian equations on Kähler manifolds.
In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the…
New lower bounds for sampling from log-concave distributions in higher dimensions.
Local Neural Operators enable efficient system-level analysis of complex PDEs.
We study the task of semi-supervised learning on multilayer graphs by taking into account both labeled and unlabeled observations together with the information encoded by each individual graph layer. We propose a regularizer based on the generalized matrix mean, which is a one-parameter family of matrix means that incl…
We study -SVD that is to obtain the first singular vectors of a matrix . Recently, a few breakthroughs have been discovered on -SVD: Musco and Musco [1] proved the first gap-free convergence result using the block Krylov method, Shamir [2] discovered the first variance-reduction stochastic method, and Bhoj…
We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It decouples the nonlinear optimization problem in MLR into three steps that can be solv…
Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML). However, the scalability of these optimization methods is inhibited by the cost of communicating and synchronizing processors in a parallel setting. Iterative ML metho…
Proposes iVDFM for identifying latent factors in multivariate time series.
The study proves inequalities for complex operators on curved spaces.
Fast and accurate methods for low-rank learning problems.
This article presents an analysis of the normalized Yamabe flow starting at and preserving a class of compact Riemannian manifolds with incomplete edge singularities and negative Yamabe invariant. Our main results include uniqueness, long-time existence and convergence of the edge Yamabe flow starting at a metric with …
A new model uses Toeplitz matrices to analyze time-series data transitions.
New method uses quantum computing to process classical data efficiently.
We prove a uniform C^alpha estimate for collapsing Calabi-Yau metrics on the total space of a proper holomorphic submersion over the unit ball in C^m. The usual methods of Calabi, Evans-Krylov, and Caffarelli do not apply to this setting because the background geometry degenerates. We instead rely on blowup arguments a…
New method improves subspace iteration for eigenvectors in machine learning.
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and deep architectures have not been sufficiently exploited. In this paper, we theor…
The regularity theory for pluriclosed flow hinges on obtaining regularity for the metric assuming uniform equivalence to a background metric. This estimate was established in \cite{StreetsPCFBI} by an adaptation of ideas from Evans-Krylov, the key input being a sharp differential inequality satisfied by the assoc…
This study examines the relationship between PLS and OLS regression using eigenvalue distributions.
Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral embedding provides a low-dimensional parametrization of the data manifold which…
In this work, we present direction-of-arrival (DoA) estimation algorithms based on the Krylov subspace that effectively exploit prior knowledge of the signals that impinge on a sensor array. The proposed multi-step knowledge-aided iterative conjugate gradient (CG) (MS-KAI-CG) algorithms perform subtraction of the unwan…