3,301 research outputs found
Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere
Among the various architectures of Recurrent Neural Networks, Echo State
Networks (ESNs) emerged due to their simplified and inexpensive training
procedure. These networks are known to be sensitive to the setting of
hyper-parameters, which critically affect their behaviour. Results show that
their performance is usually maximized in a narrow region of hyper-parameter
space called edge of chaos. Finding such a region requires searching in
hyper-parameter space in a sensible way: hyper-parameter configurations
marginally outside such a region might yield networks exhibiting fully
developed chaos, hence producing unreliable computations. The performance gain
due to optimizing hyper-parameters can be studied by considering the
memory--nonlinearity trade-off, i.e., the fact that increasing the nonlinear
behavior of the network degrades its ability to remember past inputs, and
vice-versa. In this paper, we propose a model of ESNs that eliminates critical
dependence on hyper-parameters, resulting in networks that provably cannot
enter a chaotic regime and, at the same time, denotes nonlinear behaviour in
phase space characterised by a large memory of past inputs, comparable to the
one of linear networks. Our contribution is supported by experiments
corroborating our theoretical findings, showing that the proposed model
displays dynamics that are rich-enough to approximate many common nonlinear
systems used for benchmarking
Meteorological time series forecasting based on MLP modelling using heterogeneous transfer functions
In this paper, we propose to study four meteorological and seasonal time
series coupled with a multi-layer perceptron (MLP) modeling. We chose to
combine two transfer functions for the nodes of the hidden layer, and to use a
temporal indicator (time index as input) in order to take into account the
seasonal aspect of the studied time series. The results of the prediction
concern two years of measurements and the learning step, eight independent
years. We show that this methodology can improve the accuracy of meteorological
data estimation compared to a classical MLP modelling with a homogenous
transfer function
Global Deterministic Optimization with Artificial Neural Networks Embedded
Artificial neural networks (ANNs) are used in various applications for
data-driven black-box modeling and subsequent optimization. Herein, we present
an efficient method for deterministic global optimization of ANN embedded
optimization problems. The proposed method is based on relaxations of
algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20
(2009), pp. 573-601] including the convex and concave envelopes of the
nonlinear activation function of ANNs. The optimization problem is solved using
our in-house global deterministic solver MAiNGO. The performance of the
proposed method is shown in four optimization examples: an illustrative
function, a fermentation process, a compressor plant and a chemical process
optimization. The results show that computational solution time is favorable
compared to the global general-purpose optimization solver BARON.Comment: J Optim Theory Appl (2018
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