16,837 research outputs found
Artificial Neural Network Methods in Quantum Mechanics
In a previous article we have shown how one can employ Artificial Neural
Networks (ANNs) in order to solve non-homogeneous ordinary and partial
differential equations. In the present work we consider the solution of
eigenvalue problems for differential and integrodifferential operators, using
ANNs. We start by considering the Schr\"odinger equation for the Morse
potential that has an analytically known solution, to test the accuracy of the
method. We then proceed with the Schr\"odinger and the Dirac equations for a
muonic atom, as well as with a non-local Schr\"odinger integrodifferential
equation that models the system in the framework of the resonating
group method. In two dimensions we consider the well studied Henon-Heiles
Hamiltonian and in three dimensions the model problem of three coupled
anharmonic oscillators. The method in all of the treated cases proved to be
highly accurate, robust and efficient. Hence it is a promising tool for
tackling problems of higher complexity and dimensionality.Comment: Latex file, 29pages, 11 psfigs, submitted in CP
Deep Exponential Families
We describe \textit{deep exponential families} (DEFs), a class of latent
variable models that are inspired by the hidden structures used in deep neural
networks. DEFs capture a hierarchy of dependencies between latent variables,
and are easily generalized to many settings through exponential families. We
perform inference using recent "black box" variational inference techniques. We
then evaluate various DEFs on text and combine multiple DEFs into a model for
pairwise recommendation data. In an extensive study, we show that going beyond
one layer improves predictions for DEFs. We demonstrate that DEFs find
interesting exploratory structure in large data sets, and give better
predictive performance than state-of-the-art models
Study and optimization of the spatial resolution for detectors with binary readout
Using simulations and analytical approaches, we have studied single hit
resolutions obtained with a binary readout, which is often proposed for high
granularity detectors to reduce the generated data volume. Our simulations
considering several parameters (e.g. strip pitch) show that the detector
geometry and an electronics parameter of the binary readout chips could be
optimized for binary readout to offer an equivalent spatial resolution to the
one with an analogue readout. To understand the behavior as a function of
simulation parameters, we developed analytical models that reproduce simulation
results with a few parameters. The models can be used to optimize detector
designs and operation conditions with regard to the spatial resolution.Comment: 21 pages, 20 figure
A survey on modern trainable activation functions
In neural networks literature, there is a strong interest in identifying and
defining activation functions which can improve neural network performance. In
recent years there has been a renovated interest of the scientific community in
investigating activation functions which can be trained during the learning
process, usually referred to as "trainable", "learnable" or "adaptable"
activation functions. They appear to lead to better network performance.
Diverse and heterogeneous models of trainable activation function have been
proposed in the literature. In this paper, we present a survey of these models.
Starting from a discussion on the use of the term "activation function" in
literature, we propose a taxonomy of trainable activation functions, highlight
common and distinctive proprieties of recent and past models, and discuss main
advantages and limitations of this type of approach. We show that many of the
proposed approaches are equivalent to adding neuron layers which use fixed
(non-trainable) activation functions and some simple local rule that
constraints the corresponding weight layers.Comment: Published in "Neural Networks" journal (Elsevier
- …