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State aggregation aims to reduce the computational complexity of solving Markov Decision Processes (MDPs) while preserving the performance of the original system. A fundamental challenge lies in optimizing policies within the aggregated, or…
Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…
Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
Max-product belief propagation is a local, iterative algorithm to find the mode/MAP estimate of a probability distribution. While it has been successfully employed in a wide variety of applications, there are relatively few theoretical…
Molecular conformer generation (MCG) is an important task in cheminformatics and drug discovery. The ability to efficiently generate low-energy 3D structures can avoid expensive quantum mechanical simulations, leading to accelerated virtual…
In this paper, we introduce a novel method for merging the weights of multiple pre-trained neural networks using a genetic algorithm called MeGA. Traditional techniques, such as weight averaging and ensemble methods, often fail to fully…
Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep…
Retrieving similar images from a large dataset based on the image content has been a very active research area and is a very challenging task. Studies have shown that retrieving similar images based on their shape is a very effective…
Current graph clustering methods emphasize individual node and edge con nections, while ignoring higher-order organization at the level of motif. Re cently, higher-order graph clustering approaches have been designed by motif based…
This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…
The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Large language models (LLMs) demonstrate strong performance in math reasoning benchmarks, but their performance varies inconsistently across problems with varying levels of difficulty. This paper describes Adaptive Multi-Expert Reasoning…
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via $L_2$…
Graph embeddings are a ubiquitous tool for machine learning tasks, such as node classification and link prediction, on graph-structured data. However, computing the embeddings for large-scale graphs is prohibitively inefficient even if we…
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…
Adaptive mesh refinement (AMR) is indispensable for efficient finite element analyses. However, its performance depends not only on the refinement itself but also on strategy to mark elements for refinement and the way it is tuned. This…
We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…
The arithmetic mean/geometric mean-inequality (AM/GM-inequality) facilitates classes of non-negativity certificates and of relaxation techniques for polynomials and, more generally, for exponential sums. Here, we present a first systematic…