相关论文: A Clifford Algebra approach to the Discretizable M…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

There are many ways to represent a molecule as input to a machine learning model and each is associated with loss and retention of certain kinds of information. In the interest of preserving three-dimensional spatial information, including…

We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which…

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…

Accurate boundary detection in high-dimensional data remains a central challenge in unsupervised learning, particularly in the presence of non-linear structures and heterogeneous densities. In this work, we introduce Mean Curvature Boundary…

We study the problem of reconstructing a hidden graph given access to a distance oracle. We design randomized algorithms for the following problems: reconstruction of a degree bounded graph with query complexity $\tilde{O}(n^{3/2})$;…

We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…

In this paper, we propose a new Deep Neural Network (DNN) testing algorithm called the Constrained Gradient Descent (CGD) method, and an implementation we call CGDTest aimed at exposing security and robustness issues such as adversarial…

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…

In this paper, a new algorithm to solve the discrete logarithm problem is presented which is similar to the usual baby-step giant-step algorithm. Our algorithm exploits the order of the discrete logarithm in the multiplicative group of a…

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is a recent embedding method that has been used to solve a…

In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally Lipschitz differentiable (possibly nonconvex) function,…

We develop a combined machine learning (ML) and quantum mechanics approach that enables data-efficient reconstruction of flexible molecular force fields from high-level ab initio calculations, through the consideration of fundamental…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…

Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with the stiff Poisson equations. In this article we use CGP for the first…

The prosperity of computer vision (CV) and natural language procession (NLP) in recent years has spurred the development of deep learning in many other domains. The advancement in machine learning provides us with an alternative option…

A generalization of the term "generalized Clifford algebras" (as appears in papers on advances in applied Clifford algebras) is introduced. This algebra is studied by means of structure theory of central simple algebras. A graph theoretical…

Molecular representation pretraining is critical in various applications for drug and material discovery due to the limited number of labeled molecules, and most existing work focuses on pretraining on 2D molecular graphs. However, the…