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Deep neural networks (DNNs) frequently present behaviorally irregular patterns, significantly limiting their practical potentials and theoretical validity in travel behavior modeling. This study proposes strong and weak behavioral…
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe; training a deep model on a very large dataset of supervised examples. However, this approach is rather…
We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of…
Optimizing fluid-dynamic performance is an important engineering task. Traditionally, experts design shapes based on empirical estimations and verify them through expensive experiments. This costly process, both in terms of time and space,…
Two dimensional (2D) peak finding is a common practice in data analysis for physics experiments, which is typically achieved by computing the local derivatives. However, this method is inherently unstable when the local landscape is…
Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear.…
We introduce a notion of emergence for coarse-grained macroscopic variables associated with highly-multivariate microscopic dynamical processes, in the context of a coupled dynamical environment. Dynamical independence instantiates the…
A fairly comprehensive analysis is presented for the gradient descent dynamics for training two-layer neural network models in the situation when the parameters in both layers are updated. General initialization schemes as well as general…
In complex systems, information propagation can be defined as diffused or delocalized, weakly localized, and strongly localized. This study investigates the application of graph neural network models to learn the behavior of a linear…
We show how to calculate the likelihood of dynamical large deviations using evolutionary reinforcement learning. An agent, a stochastic model, propagates a continuous-time Monte Carlo trajectory and receives a reward conditioned upon the…
Deep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with…
With the development of end-to-end control based on deep learning, it is important to study new system modeling techniques to realize dynamics modeling with high-dimensional inputs. In this paper, a novel Koopman-based deep convolutional…
Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…
In this paper, we introduce two deterministic models aimed at capturing the dynamics of congested Internet connections. The first model is a continuous-time model that combines a system of differential equations with a sudden change in one…
Efficient downscaling of large ensembles of coarse-scale information is crucial in several applications, such as oceanic and atmospheric modeling. The determining form map is a theoretical lifting function from the low-resolution solution…
We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability…