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Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the…

We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar…

Popular PEFT methods reduce trainable parameter count for fine-tuning by parameterizing new low-rank or sparse trainable weights in parallel to the frozen pre-trained weights $W$. However, these weights are trained from scratch, and there…

A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be…

In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…

There is growing interest in learning Fourier domain sampling strategies (particularly for magnetic resonance imaging, MRI) using optimization approaches. For non-Cartesian sampling patterns, the system models typically involve non-uniform…

Diffusion policies are becoming mainstream in robotic manipulation but suffer from hard negative class imbalance due to uniform sampling and lack of sample difficulty awareness, leading to slow training convergence and frequent inference…

The broadband line-by-line analysis of radiative transfer in the atmosphere is extremely demanding with regard to computational resources. As a remedy, we present here the calculation of uniform error bounds for approximating the classical…

Interpreting a nonparametric regression model with many predictors is known to be a challenging problem. There has been renewed interest in this topic due to the extensive use of machine learning algorithms and the difficulty in…

Recent advancements in source code summarization have leveraged transformer-based pre-trained models, including Large Language Models of Code (LLMCs), to automate and improve the generation of code summaries. However, existing methods often…

The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for…

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…

Hyper-parameter selection remains a daunting task when building a pattern recognition architecture which performs well, particularly in recently constructed visual pipeline models for feature extraction. We re-formulate pooling in an…

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…

The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered…

In this paper, we propose an adaptive pruning method. This method can cut off the channel and layer adaptively. The proportion of the layer and the channel to be cut is learned adaptively. The pruning method proposed in this paper can…

Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…

Machine learning software accounts for a significant amount of energy consumed in data centers. These algorithms are usually optimized towards predictive performance, i.e. accuracy, and scalability. This is the case of data stream mining…

Additive models offer accurate and interpretable predictions for tabular data, a critical tool for statistical modeling. Recent advances in Neural Additive Models (NAMs) allow these models to handle complex machine learning tasks, including…