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The availability of large-scale neuronal population datasets necessitates new methods to model population dynamics and extract interpretable, scientifically translatable insights. Existing deep learning methods often overlook the biological…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

The neuronal networks in the mammals cortex are characterized by the coexistence of hierarchy, modularity, short and long range interactions, spatial correlations, and topographical connections. Particularly interesting, the latter type of…

Objective: To improve accelerated MRI reconstruction through a densely connected cascading deep learning reconstruction framework. Materials and Methods: A cascading deep learning reconstruction framework (baseline model) was modified by…

Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input…

In this paper, we explore the structure of the penultimate Gram matrix in deep neural networks, which contains the pairwise inner products of outputs corresponding to a batch of inputs. In several architectures it has been observed that…

We propose the APTx Neuron, a novel, unified neural computation unit that integrates non-linear activation and linear transformation into a single trainable expression. The APTx Neuron is derived from the APTx activation function, thereby…

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

Global brain activity self-organizes into discrete patterns characterized by distinct behavioral observables and modes of information processing. The human thalamocortical system is a densely connected network where local neural activation…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Convolution is a central operation in Convolutional Neural Networks (CNNs), which applies a kernel to overlapping regions shifted across the image. However, because of the strong correlations in real-world image data, convolutional kernels…

Aims: The aim of this work is to study the application of the artificial neural networks guided by the autoencoder architecture as a method for precise reconstruction of the neutron star equation of state, using their observable parameters:…

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to…

Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a…

Understanding how segmentation performance scales with training data is fundamental for developing data-efficient medical AI systems. In this study, we systematically revisit data scaling behavior across 15 anatomical segmentation tasks…

We prove some new results concerning the approximation rate of neural networks with general activation functions. Our first result concerns the rate of approximation of a two layer neural network with a polynomially-decaying non-sigmoidal…

Artificial neural networks (ANN), typically referred to as neural networks, are a class of Machine Learning algorithms and have achieved widespread success, having been inspired by the biological structure of the human brain. Neural…

This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the…

Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. This leads either to an…

Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…