2,452 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
Fluctuations between high- and low-modularity topology in time-resolved functional connectivity
Modularity is an important topological attribute for functional brain
networks. Recent studies have reported that modularity of functional networks
varies not only across individuals being related to demographics and cognitive
performance, but also within individuals co-occurring with fluctuations in
network properties of functional connectivity, estimated over short time
intervals. However, characteristics of these time-resolved functional networks
during periods of high and low modularity have remained largely unexplored. In
this study we investigate spatiotemporal properties of time-resolved networks
in the high and low modularity periods during rest, with a particular focus on
their spatial connectivity patterns, temporal homogeneity and test-retest
reliability. We show that spatial connectivity patterns of time-resolved
networks in the high and low modularity periods are represented by increased
and decreased dissociation of the default mode network module from
task-positive network modules, respectively. We also find that the instances of
time-resolved functional connectivity sampled from within the high (low)
modularity period are relatively homogeneous (heterogeneous) over time,
indicating that during the low modularity period the default mode network
interacts with other networks in a variable manner. We confirmed that the
occurrence of the high and low modularity periods varies across individuals
with moderate inter-session test-retest reliability and that it is correlated
with previously-reported individual differences in the modularity of functional
connectivity estimated over longer timescales. Our findings illustrate how
time-resolved functional networks are spatiotemporally organized during periods
of high and low modularity, allowing one to trace individual differences in
long-timescale modularity to the variable occurrence of network configurations
at shorter timescales.Comment: Reorganized the paper; to appear in NeuroImage; arXiv abstract
shortened to fit within character limit
Multiplex visibility graphs to investigate recurrent neural network dynamics
Source at https://doi.org/10.1038/srep44037 .A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning them properly may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize internal dynamics of a class of RNNs called echo state networks (ESNs). We design principled unsupervised methods to derive hyperparameters configurations yielding maximal ESN performance, expressed in terms of prediction error and memory capacity. In particular, we propose to model time series generated by each neuron activations with a horizontal visibility graph, whose topological properties have been shown to be related to the underlying system dynamics. Successively, horizontal visibility graphs associated with all neurons become layers of a larger structure called a multiplex. We show that topological properties of such a multiplex reflect important features of ESN dynamics that can be used to guide the tuning of its hyperparamers. Results obtained on several benchmarks and a real-world dataset of telephone call data records show the effectiveness of the proposed methods
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