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 Krylov subspace methods speed up mixed-effects models with crossed random effects.
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.
A new diffusion sampling method combines Krylov subspace and diffusion models for faster and more efficient inverse problems.
New method for directed graphs using learnable spectral positional encodings.
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
Kaczmarz++ accelerates convergence for ill-conditioned systems.
A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.
Note on advancements in nonlinear elliptic equations' regularity theory.
Enhances gradient estimates for Hermitian Monge-Ampère equations.
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…
Paper solves Hessian equations on Kähler manifolds.
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
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…
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…
Efficiently maps indoor magnetic fields with SKI and D-SKI.
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 for faster optimization in high dimensions.
Proposes iVDFM for identifying latent factors in multivariate time series.
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…
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
Efficiently computes matrix square roots and their inverses for large matrices.
Unified framework for multi-view learning with orthogonal projections.
Paper proposes a new method for efficient second-order neural network training.
New lower bounds for sampling from log-concave distributions in higher dimensions.
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…
We prove long time existence and convergence results for the pluriclosed flow, which imply geometric and topological classification theorems for generalized Kähler structures. Our approach centers on the reduction of pluriclosed flow to a degenerate parabolic equation for a -form, introduced in \cite{ST2}. We ob…
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…
New method speeds up kernel-based machine learning for force field reconstruction.
We show that the pluriclosed flow preserves generalized Kähler structures with the extra condition , a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a nonconvex fully nonlinear parabolic flow of a scalar potential function. We prove a num…
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…
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
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 study proves inequalities for complex operators on curved spaces.
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…
Local Neural Operators enable efficient system-level analysis of complex PDEs.
This paper tackles unpaired data in multi-view learning, proposing a new framework and models.
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…
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 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…
The Liouville theorem and -estimate for Calabi-Yau cones establish uniqueness and asymptotic behavior of metrics.
The graph Laplacian is a standard tool in data science, machine learning, and image processing. The corresponding matrix inherits the complex structure of the underlying network and is in certain applications densely populated. This makes computations, in particular matrix-vector products, with the graph Laplacian a ha…
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…
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…
New method computes affine normal directions efficiently for sparse polynomials.
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 …