431 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
Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
A new class of non-homogeneous state-affine systems is introduced for use in
reservoir computing. Sufficient conditions are identified that guarantee first,
that the associated reservoir computers with linear readouts are causal,
time-invariant, and satisfy the fading memory property and second, that a
subset of this class is universal in the category of fading memory filters with
stochastic almost surely uniformly bounded inputs. This means that any
discrete-time filter that satisfies the fading memory property with random
inputs of that type can be uniformly approximated by elements in the
non-homogeneous state-affine family.Comment: 41 page
Liquid Time-constant Networks
We introduce a new class of time-continuous recurrent neural network models.
Instead of declaring a learning system's dynamics by implicit nonlinearities,
we construct networks of linear first-order dynamical systems modulated via
nonlinear interlinked gates. The resulting models represent dynamical systems
with varying (i.e., liquid) time-constants coupled to their hidden state, with
outputs being computed by numerical differential equation solvers. These neural
networks exhibit stable and bounded behavior, yield superior expressivity
within the family of neural ordinary differential equations, and give rise to
improved performance on time-series prediction tasks. To demonstrate these
properties, we first take a theoretical approach to find bounds over their
dynamics and compute their expressive power by the trajectory length measure in
latent trajectory space. We then conduct a series of time-series prediction
experiments to manifest the approximation capability of Liquid Time-Constant
Networks (LTCs) compared to classical and modern RNNs. Code and data are
available at https://github.com/raminmh/liquid_time_constant_networksComment: Accepted to the Thirty-Fifth AAAI Conference on Artificial
Intelligence (AAAI-21
Musical instrument mapping design with Echo State Networks
Echo State Networks (ESNs), a form of recurrent neural network developed in the field of Reservoir Computing, show significant potential for use as a tool in the design of mappings for digital musical instruments. They have, however, seldom been used in this area, so this paper explores their possible applications. This project contributes a new open source library, which was developed to allow ESNs to run in the Pure Data dataflow environment. Several use cases were explored, focusing on addressing current issues in mapping research. ESNs were found to work successfully in scenarios of pattern classification, multiparametric control, explorative mapping and the design of nonlinearities and uncontrol. 'Un-trained' behaviours are proposed, as augmentations to the conventional reservoir system that allow the player to introduce potentially interesting non-linearities and uncontrol into the reservoir. Interactive evolution style controls are proposed as strategies to help design these behaviours, which are otherwise dependent on arbitrary values and coarse global controls. A study on sound classification showed that ESNs could reliably differentiate between two drum sounds, and also generalise to other similar input. Following evaluation of the use cases, heuristics are proposed to aid the use of ESNs in computer music scenarios
Liquid State Machine with Dendritically Enhanced Readout for Low-power, Neuromorphic VLSI Implementations
In this paper, we describe a new neuro-inspired, hardware-friendly readout
stage for the liquid state machine (LSM), a popular model for reservoir
computing. Compared to the parallel perceptron architecture trained by the
p-delta algorithm, which is the state of the art in terms of performance of
readout stages, our readout architecture and learning algorithm can attain
better performance with significantly less synaptic resources making it
attractive for VLSI implementation. Inspired by the nonlinear properties of
dendrites in biological neurons, our readout stage incorporates neurons having
multiple dendrites with a lumped nonlinearity. The number of synaptic
connections on each branch is significantly lower than the total number of
connections from the liquid neurons and the learning algorithm tries to find
the best 'combination' of input connections on each branch to reduce the error.
Hence, the learning involves network rewiring (NRW) of the readout network
similar to structural plasticity observed in its biological counterparts. We
show that compared to a single perceptron using analog weights, this
architecture for the readout can attain, even by using the same number of
binary valued synapses, up to 3.3 times less error for a two-class spike train
classification problem and 2.4 times less error for an input rate approximation
task. Even with 60 times larger synapses, a group of 60 parallel perceptrons
cannot attain the performance of the proposed dendritically enhanced readout.
An additional advantage of this method for hardware implementations is that the
'choice' of connectivity can be easily implemented exploiting address event
representation (AER) protocols commonly used in current neuromorphic systems
where the connection matrix is stored in memory. Also, due to the use of binary
synapses, our proposed method is more robust against statistical variations.Comment: 14 pages, 19 figures, Journa
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