91,407 research outputs found
Neural Networks with Non-Uniform Embedding and Explicit Validation Phase to Assess Granger Causality
A challenging problem when studying a dynamical system is to find the
interdependencies among its individual components. Several algorithms have been
proposed to detect directed dynamical influences between time series. Two of
the most used approaches are a model-free one (transfer entropy) and a
model-based one (Granger causality). Several pitfalls are related to the
presence or absence of assumptions in modeling the relevant features of the
data. We tried to overcome those pitfalls using a neural network approach in
which a model is built without any a priori assumptions. In this sense this
method can be seen as a bridge between model-free and model-based approaches.
The experiments performed will show that the method presented in this work can
detect the correct dynamical information flows occurring in a system of time
series. Additionally we adopt a non-uniform embedding framework according to
which only the past states that actually help the prediction are entered into
the model, improving the prediction and avoiding the risk of overfitting. This
method also leads to a further improvement with respect to traditional Granger
causality approaches when redundant variables (i.e. variables sharing the same
information about the future of the system) are involved. Neural networks are
also able to recognize dynamics in data sets completely different from the ones
used during the training phase
A multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics
The dynamics of a collection of resonant atoms embedded inside an
inhomogeneous nondispersive and lossless dielectric is described with a dipole
Hamiltonian that is based on a canonical quantization theory. The dielectric is
described macroscopically by a position-dependent dielectric function and the
atoms as microscopic harmonic oscillators. We identify and discuss the role of
several types of Green tensors that describe the spatio-temporal propagation of
field operators. After integrating out the atomic degrees of freedom, a
multiple-scattering formalism emerges in which an exact Lippmann-Schwinger
equation for the electric field operator plays a central role. The equation
describes atoms as point sources and point scatterers for light. First,
single-atom properties are calculated such as position-dependent
spontaneous-emission rates as well as differential cross sections for elastic
scattering and for resonance fluorescence. Secondly, multi-atom processes are
studied. It is shown that the medium modifies both the resonant and the static
parts of the dipole-dipole interactions. These interatomic interactions may
cause the atoms to scatter and emit light cooperatively. Unlike in free space,
differences in position-dependent emission rates and radiative line shifts
influence cooperative decay in the dielectric. As a generic example, it is
shown that near a partially reflecting plane there is a sharp transition from
two-atom superradiance to single-atom emission as the atomic positions are
varied.Comment: 18 pages, 4 figures, to appear in Physical Review
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A Double Error Dynamic Asymptote Model of Associative Learning
In this paper a formal model of associative learning is presented which incorporates representational and computational mechanisms that, as a coherent corpus, empower it to make accurate predictions of a wide variety of phenomena that so far have eluded a unified account in learning theory. In particular, the Double Error Dynamic Asymptote (DDA) model introduces: 1) a fully-connected network architecture in which stimuli are represented as temporally clustered elements that associate to each other, so that elements of one cluster engender activity on other clusters, which naturally implements neutral stimuli associations and mediated learning; 2) a predictor error term within the traditional error correction rule (the double error), which reduces the rate of learning for expected predictors; 3) a revaluation associability rate that operates on the assumption that the outcome predictiveness is tracked over time so that prolonged uncertainty is learned, reducing the levels of attention to initially surprising outcomes; and critically 4) a biologically plausible variable asymptote, which encapsulates the principle of Hebbian learning, leading to stronger associations for similar levels of cluster activity. The outputs of a set of simulations of the DDA model are presented along with empirical results from the literature. Finally, the predictive scope of the model is discussed
Latent Multi-task Architecture Learning
Multi-task learning (MTL) allows deep neural networks to learn from related
tasks by sharing parameters with other networks. In practice, however, MTL
involves searching an enormous space of possible parameter sharing
architectures to find (a) the layers or subspaces that benefit from sharing,
(b) the appropriate amount of sharing, and (c) the appropriate relative weights
of the different task losses. Recent work has addressed each of the above
problems in isolation. In this work we present an approach that learns a latent
multi-task architecture that jointly addresses (a)--(c). We present experiments
on synthetic data and data from OntoNotes 5.0, including four different tasks
and seven different domains. Our extension consistently outperforms previous
approaches to learning latent architectures for multi-task problems and
achieves up to 15% average error reductions over common approaches to MTL.Comment: To appear in Proceedings of AAAI 201
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