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Successful point cloud registration relies on accurate correspondences established upon powerful descriptors. However, existing neural descriptors either leverage a rotation-variant backbone whose performance declines under large rotations,…

One important feature of complex systems are problem domains that have many local minima and substructure. Biological systems manage these local minima by switching between different subsystems depending on their environmental or…

The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…

In this paper, we consider a class of nonconvex-linear minimax problems on Riemannian manifolds, which find wide applications in machine learning and signal processing. For solving this class of problems, we develop a flexible Riemannian…

Retrieval augmented generation (RAG) has transformed text based question answering, yet its extension to visual domains remains hindered by fundamental challenges: bridging the modality gap between image queries and text heavy knowledge…

We conducted a reproducibility study on Integrated Gradients (IG) based methods and the Important Direction Gradient Integration (IDGI) framework. IDGI eliminates the explanation noise in each step of the computation of IG-based methods…

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals---appearing in quantum field theoretic calculations---to a set of master integrals. We extend existing approaches by using an…

SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such…

Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problem, it tests if a region contains eigenvalues using an approximate…

We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

Integrated Gradients (IG) is a widely used algorithm for attributing the outputs of a deep neural network to its input features. Due to the absence of closed-form integrals for deep learning models, inaccurate Riemann Sum approximations are…

Information geometric optimization (IGO) is a general framework for stochastic optimization problems aiming at limiting the influence of arbitrary parametrization choices. The initial problem is transformed into the optimization of a smooth…

An algorithm for the numerical inversion of large matrices, the biconjugate gradient algorithm (BGA), is investigated in view of its use for Monte Carlo simulations of fermionic field theories. It is compared with the usual conjugate…

The alignment of two similar graphs from different domains is a well-studied problem. In many practical usages, there is no reliable information or labels over the vertices or edges, leaving structural similarity as the only information…

The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount…

This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…

This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…

We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…