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This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where…

We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error $\mathcal{O}\big((K^{-1}+J^{-1/2})^{\frac{1}{2}}\big)$, for…

The article is devoted to the study of neural networks with one hidden layer and a modified activation function for solving physical problems. A rectified sigmoid activation function has been proposed to solve physical problems described by…

Understanding the inner working mechanism of deep neural networks (DNNs) is essential and important for researchers to design and improve the performance of DNNs. In this work, the entropy analysis is leveraged to study the neurons…

We introduce a novel scheme to train binary convolutional neural networks (CNNs) -- CNNs with weights and activations constrained to {-1,+1} at run-time. It has been known that using binary weights and activations drastically reduce memory…

We characterize the computational power of neural networks that follow the graph neural network (GNN) architecture, not restricted to aggregate-combine GNNs or other particular types. We establish an exact correspondence between the…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…

Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…

Single hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

We study the universality of complex-valued neural networks with bounded widths and arbitrary depths. Under mild assumptions, we give a full description of those activation functions $\varrho:\mathbb{C}\to \mathbb{C}$ that have the property…

Neural networks are powerful functions with widespread use, but the theoretical behaviour of these functions is not fully understood. Creating deep neural networks by stacking many layers has achieved exceptional performance in many…

Activation functions play an essential role in neural networks. They provide the non-linearity for the networks. Therefore, their properties are important for neural networks' accuracy and running performance. In this paper, we present a…

Whatever information a deep neural network has gleaned from training data is encoded in its weights. How this information affects the response of the network to future data remains largely an open question. Indeed, even defining and…

The weights of neural networks (NNs) have recently gained prominence as a new data modality in machine learning, with applications ranging from accuracy and hyperparameter prediction to representation learning or weight generation. One…

A neural network works as an associative memory device if it has large storage capacity and the quality of the retrieval is good enough. The learning and attractor abilities of the network both can be measured by the mutual information…

The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components, we apply a…

Despite broad interest in applying deep learning techniques to scientific discovery, learning interpretable formulas that accurately describe scientific data is very challenging because of the vast landscape of possible functions and the…