39,322 research outputs found
Input-to-State Representation in linear reservoirs dynamics
Reservoir computing is a popular approach to design recurrent neural
networks, due to its training simplicity and approximation performance. The
recurrent part of these networks is not trained (e.g., via gradient descent),
making them appealing for analytical studies by a large community of
researchers with backgrounds spanning from dynamical systems to neuroscience.
However, even in the simple linear case, the working principle of these
networks is not fully understood and their design is usually driven by
heuristics. A novel analysis of the dynamics of such networks is proposed,
which allows the investigator to express the state evolution using the
controllability matrix. Such a matrix encodes salient characteristics of the
network dynamics; in particular, its rank represents an input-indepedent
measure of the memory capacity of the network. Using the proposed approach, it
is possible to compare different reservoir architectures and explain why a
cyclic topology achieves favourable results as verified by practitioners
A Theoretically Grounded Application of Dropout in Recurrent Neural Networks
Recurrent neural networks (RNNs) stand at the forefront of many recent
developments in deep learning. Yet a major difficulty with these models is
their tendency to overfit, with dropout shown to fail when applied to recurrent
layers. Recent results at the intersection of Bayesian modelling and deep
learning offer a Bayesian interpretation of common deep learning techniques
such as dropout. This grounding of dropout in approximate Bayesian inference
suggests an extension of the theoretical results, offering insights into the
use of dropout with RNN models. We apply this new variational inference based
dropout technique in LSTM and GRU models, assessing it on language modelling
and sentiment analysis tasks. The new approach outperforms existing techniques,
and to the best of our knowledge improves on the single model state-of-the-art
in language modelling with the Penn Treebank (73.4 test perplexity). This
extends our arsenal of variational tools in deep learning.Comment: Added clarifications; Published in NIPS 201
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
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