Related papers: A Multi-Layer Regression based Predicable Function…

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential…

Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between…

In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

The remarkable capability of Transformers to do reasoning and few-shot learning, without any fine-tuning, is widely conjectured to stem from their ability to implicitly simulate a multi-step algorithms -- such as gradient descent -- with…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that…

Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…

This article studies (multilayer perceptron) neural networks with an emphasis on the transformations involved --- both forward and backward --- in order to develop a semantical/logical perspective that is in line with standard program…

Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…

We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a…

The Forward-Forward algorithm is an alternative learning method which consists of two forward passes rather than a forward and backward pass employed by backpropagation. Forward-Forward networks employ layer local loss functions which are…

This paper presents a new artificial neuron model capable of learning its receptive field in the topological domain of inputs. The model provides adaptive and differentiable local connectivity (plasticity) applicable to any domain. It…

Bolted joints are critical in engineering for maintaining structural integrity and reliability. Accurate prediction of parameters influencing their function and behavior is essential for optimal performance. Traditional methods often fail…

The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…

Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns…

Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…