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Today's scientific simulations require a significant reduction of data volume because of extremely large amounts of data they produce and the limited I/O bandwidth and storage space. Error-bounded lossy compression has been considered one…
Most machine learning classifiers only concern classification accuracy, while certain applications (such as medical diagnosis, meteorological forecasting, and computation advertising) require the model to predict the true probability, known…
The brain performs intelligent tasks with extremely low energy consumption. This work takes inspiration from two strategies used by the brain to achieve this energy efficiency: the absence of separation between computing and memory…
An implicit method for the ohmic dissipation is proposed. The proposed method is based on the Crank-Nicolson method and exhibits second-order accuracy in time and space. The proposed method has been implemented in the SFUMATO adaptive mesh…
Coordinated multi-robot motion planning at intersections is key for safe mobility in roads, factories and warehouses. The rapidly exploring random tree (RRT) algorithms are popular in multi-robot motion planning. However, generating the…
In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and…
An efficient method for finding all real roots of a univariate function in a given bounded domain is formulated. The proposed method uses adaptive mesh refinement to locate bracketing intervals based on bisection criterion for root finding.…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
This paper studies the "explanation problem" for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose…
This paper presents strong worst-case iteration and operation complexity guarantees for Riemannian adaptive regularized Newton methods, a unified framework encompassing both Riemannian adaptive regularization (RAR) methods and Riemannian…
Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature…
Optical neural networks (ONN) based on micro-ring resonators (MRR) have emerged as a promising alternative to significantly accelerating the massive matrix-vector multiplication (MVM) operations in artificial intelligence (AI) applications.…
The zeroth-order optimization has been widely used in machine learning applications. However, the theoretical study of the zeroth-order optimization focus on the algorithms which approximate (first-order) gradients using (zeroth-order)…
Tree kernels have been proposed to be used in many areas as the automatic learning of natural language applications. In this paper, we propose a new linear time algorithm based on the concept of weighted tree automata for SubTree kernel…
The adoption of the distributed paradigm has allowed applications to increase their scalability, robustness and fault tolerance, but it has also complicated their structure, leading to an exponential growth of the applications'…
Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…
The $k^2$-tree is a compact data structure designed to efficiently store sparse binary matrices by leveraging both sparsity and clustering of nonzero elements. This representation supports efficiently navigational operations and complex…
Retrieval-Augmented Generation (RAG), by integrating non-parametric knowledge from external knowledge bases into models, has emerged as a promising approach to enhancing response accuracy while mitigating factual errors and hallucinations.…
This paper presents an octree construction method, called Cornerstone, that facilitates global domain decomposition and interactions between particles in mesh-free numerical simulations. Our method is based on algorithms developed for 3D…
The decision tree recursively partitions the input space into regions and derives axis-aligned decision boundaries from data. Despite its simplicity and interpretability, decision trees lack parameterized representation, which makes it…