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.
New Krylov subspace methods speed up mixed-effects models with crossed random effects.
A new method for spectral positional encodings in directed graphs using Hermitian block Krylov subspaces.
A new method for faster optimization in high dimensions.
A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.
Kaczmarz++ accelerates convergence for ill-conditioned systems.
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 …
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…
New method for directed graphs using learnable spectral positional encodings.
Unified framework for multi-view learning with orthogonal projections.
This paper tackles unpaired data in multi-view learning, proposing a new framework and models.
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…
Efficiently computes matrix square roots and their inverses for large matrices.
New method improves subspace iteration for eigenvectors in machine learning.
New method speeds up kernel-based machine learning for force field reconstruction.
Efficiently maps indoor magnetic fields with SKI and D-SKI.
AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.
Local Neural Operators enable efficient system-level analysis of complex PDEs.
ISOKANN learns collective variables and effective dynamics for metastable transitions.
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…
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…
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
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix computations, and as multiresolution analysis in wavelets constructions. They are comm…
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…
KBB algorithm reduces sample complexity for policy evaluation in general state spaces.
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…
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…
A new model uses Toeplitz matrices to analyze time-series data transitions.
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…
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…
Deep neural networks are usually trained with stochastic gradient descent (SGD), which minimizes objective function using very rough approximations of gradient, only averaging to the real gradient. Standard approaches like momentum or ADAM only consider a single direction, and do not try to model distance from extremum…
Fast and accurate methods for low-rank learning problems.
Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations , e.g., gradient descent can be viewed as iteratively applying the operation . It is known that Anderson acceleration is quite efficient in practice and can be viewed…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and a…
The paper shows how to stabilize off-policy reinforcement learning using specific state representations.
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…
The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it ma…
Paper solves Hessian equations on Kähler manifolds.
The memory capacity of linear echo state networks is accurately calculated using new numerical methods.
Paper proposes a new method for efficient second-order neural network training.
New lower bounds for sampling from log-concave distributions in higher dimensions.
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…
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…
The study proves inequalities for complex operators on curved spaces.