Related papers: p-Adic Statistical Field Theory and Convolutional …

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…

Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…

Artificial neural networks (ANNs) are at the core of most Deep learning (DL) algorithms that successfully tackle complex problems like image recognition, autonomous driving, and natural language processing. However, unlike biological brains…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Restricted Boltzmann machines (RBM) and deep Boltzmann machines (DBM) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between…

Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…

Deep neural networks (DNNs) have shown exceptional performances in a wide range of tasks and have become the go-to method for problems requiring high-level predictive power. There has been extensive research on how DNNs arrive at their…

We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Deep Boltzmann Machines (DBMs) are generative neural networks with these desired properties. We integrate a DBM…

This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…

Noncommutative field theory (NCFT) is an extension of quantum field theory (QFT) that redefines spacetime, replacing commuting coordinates with a noncommutative structure. This shift fundamentally alters the way fields, interactions, and…

The self-consistent field (SCF) generation of the three-dimensional (3D) electron density distribution ($\rho$) represents a fundamental aspect of density functional theory (DFT) and related first-principles calculations, and how one can…

The landscape of condensed matter physics is facing an unprecedented data surge driven by high-throughput ab initio workflows and rapidly expanding experimental datasets. Traditional first-principles methods such as Density Functional…

In this paper, we study complex-valued neural network (CVNNs) with tensor-valued hidden-to-output weights within the framework of neural-network quantum field theory (NN-QFT). For standard CVNNs with scalar weights, we derive the generating…

Training large-scale deep neural networks (DNNs) is resource-intensive, making model compression a practical necessity. The widely accepted ''learning as compression'' hypothesis posits that training induces structure in network weights,…

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of…

Predicting interfacial thermodynamics across molecular and continuum scales remains a central challenge in computational science. Classical density functional theory (cDFT) provides a first-principles route to connect microscopic…

Stacking-based deep neural network (S-DNN), in general, denotes a deep neural network (DNN) resemblance in terms of its very deep, feedforward network architecture. The typical S-DNN aggregates a variable number of individually learnable…

((1+1)-dimensional ${\cal N}=1$ super-symmetric field theory and (3+1)-dimensional ${\cal N}=2$ super-symmetric gauge theory are discussed in a, more or less, unified way, designed to identify the quantum BPS states in both systems.…