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Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…

The problem of modeling forest tree growth curves with an artificial neural network (NN) is examined. The NN parametric form is shown to be a suitable model if each forest tree plot is assumed to consist of several differently growing…

This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does…

Neural networks are very successful tools in for example advanced classification. From a statistical point of view, fitting a neural network may be seen as a kind of regression, where we seek a function from the input space to a space of…

The varying cortical geometry of the brain creates numerous challenges for its analysis. Recent developments have enabled learning surface data directly across multiple brain surfaces via graph convolutions on cortical data. However,…

In this paper we propose a deep learning approach for segmenting sub-cortical structures of the human brain in Magnetic Resonance (MR) image data. We draw inspiration from a state-of-the-art Fully-Convolutional Neural Network (F-CNN)…

Modern artificial neural networks, including convolutional neural networks and vision transformers, have mastered several computer vision tasks, including object recognition. However, there are many significant differences between the…

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively…

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…

Neural representations have emerged as a new paradigm for applications in rendering, imaging, geometric modeling, and simulation. Compared to traditional representations such as meshes, point clouds, or volumes they can be flexibly…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

Boundary representation (B-rep) models are the standard way 3D shapes are described in Computer-Aided Design (CAD) applications. They combine lightweight parametric curves and surfaces with topological information which connects the…

Human brains lie at the core of complex neurobiological systems, where the neurons, circuits, and subsystems interact in enigmatic ways. Understanding the structural and functional mechanisms of the brain has long been an intriguing pursuit…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

In order to better understand feature learning in neural networks, we propose a framework for understanding linear models in tangent feature space where the features are allowed to be transformed during training. We consider linear…

Cytoarchitectonic parcellations of the human brain serve as anatomical references in multimodal atlas frameworks. They are based on analysis of cell-body stained histological sections and the identification of borders between brain areas.…

Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…

We introduce a flexible setup allowing for a neural network to learn both its size and topology during the course of a standard gradient-based training. The resulting network has the structure of a graph tailored to the particular learning…

This work presents a procedure to extract morphological information from neuronal cells based on the variation of shape functionals as the cell geometry undergoes a dilation through a wide interval of spatial scales. The targeted shapes are…

Network analysis is rapidly becoming a standard tool for studying functional magnetic resonance imaging (fMRI) data. In this framework, different brain areas are mapped to the nodes of a network, whose links depict functional dependencies…