253 research outputs found
Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuli
In this paper, we investigate convergence dynamics of almost periodic
encoded patterns of general neural networks (GNNs) subjected to external almost
periodic stimuli, including almost periodic delays. Invariant regions are
established for the existence of almost periodic encoded patterns under
two classes of activation functions. By employing the property of
-cone and inequality technique, attracting basins are estimated
and some criteria are derived for the networks to converge exponentially toward
almost periodic encoded patterns. The obtained results are new, they
extend and generalize the corresponding results existing in previous
literature.Comment: 28 pages, 4 figure
Hierarchical neural networks perform both serial and parallel processing
In this work we study a Hebbian neural network, where neurons are arranged
according to a hierarchical architecture such that their couplings scale with
their reciprocal distance. As a full statistical mechanics solution is not yet
available, after a streamlined introduction to the state of the art via that
route, the problem is consistently approached through signal- to-noise
technique and extensive numerical simulations. Focusing on the low-storage
regime, where the amount of stored patterns grows at most logarithmical with
the system size, we prove that these non-mean-field Hopfield-like networks
display a richer phase diagram than their classical counterparts. In
particular, these networks are able to perform serial processing (i.e. retrieve
one pattern at a time through a complete rearrangement of the whole ensemble of
neurons) as well as parallel processing (i.e. retrieve several patterns
simultaneously, delegating the management of diff erent patterns to diverse
communities that build network). The tune between the two regimes is given by
the rate of the coupling decay and by the level of noise affecting the system.
The price to pay for those remarkable capabilities lies in a network's capacity
smaller than the mean field counterpart, thus yielding a new budget principle:
the wider the multitasking capabilities, the lower the network load and
viceversa. This may have important implications in our understanding of
biological complexity
Convergence under dynamical thresholds with delays
Necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential equations modeling the action of a neuron with dynamical threshold effects
Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations
© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe
Collective stability of networks of winner-take-all circuits
The neocortex has a remarkably uniform neuronal organization, suggesting that
common principles of processing are employed throughout its extent. In
particular, the patterns of connectivity observed in the superficial layers of
the visual cortex are consistent with the recurrent excitation and inhibitory
feedback required for cooperative-competitive circuits such as the soft
winner-take-all (WTA). WTA circuits offer interesting computational properties
such as selective amplification, signal restoration, and decision making. But,
these properties depend on the signal gain derived from positive feedback, and
so there is a critical trade-off between providing feedback strong enough to
support the sophisticated computations, while maintaining overall circuit
stability. We consider the question of how to reason about stability in very
large distributed networks of such circuits. We approach this problem by
approximating the regular cortical architecture as many interconnected
cooperative-competitive modules. We demonstrate that by properly understanding
the behavior of this small computational module, one can reason over the
stability and convergence of very large networks composed of these modules. We
obtain parameter ranges in which the WTA circuit operates in a high-gain
regime, is stable, and can be aggregated arbitrarily to form large stable
networks. We use nonlinear Contraction Theory to establish conditions for
stability in the fully nonlinear case, and verify these solutions using
numerical simulations. The derived bounds allow modes of operation in which the
WTA network is multi-stable and exhibits state-dependent persistent activities.
Our approach is sufficiently general to reason systematically about the
stability of any network, biological or technological, composed of networks of
small modules that express competition through shared inhibition.Comment: 7 Figure
Stochastic Neural Networks with the Weighted Hebb Rule
Neural networks with synaptic weights constructed according to the weighted
Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of
noise(finite temperature), when the number of stored patterns is finite and in
the limit that the number of neurons . The fact that different patterns enter the synaptic rule with
different weights changes the configuration of the free energy surface. For a
general choice of weights not all of the patterns are stored as {\sl global}
minima of the free energy function. However, as for the case of the usual Hebb
rule, there exists a temperature range in which only the stored patterns are
minima of the free energy. In particular, in the presence of a single extra
pattern stored with an appropriate weight in the synaptic rule, the temperature
at which the spurious minima of the free energy are eliminated is significantly
lower than for a similar network without this extra pattern. The convergence
time of the network, together with the overlaps of the equilibria of the
network with the stored patterns, can thereby be improved considerably.Comment: 14 pages, OKHEP 93-00
Solving constraint-satisfaction problems with distributed neocortical-like neuronal networks
Finding actions that satisfy the constraints imposed by both external inputs
and internal representations is central to decision making. We demonstrate that
some important classes of constraint satisfaction problems (CSPs) can be solved
by networks composed of homogeneous cooperative-competitive modules that have
connectivity similar to motifs observed in the superficial layers of neocortex.
The winner-take-all modules are sparsely coupled by programming neurons that
embed the constraints onto the otherwise homogeneous modular computational
substrate. We show rules that embed any instance of the CSPs planar four-color
graph coloring, maximum independent set, and Sudoku on this substrate, and
provide mathematical proofs that guarantee these graph coloring problems will
convergence to a solution. The network is composed of non-saturating linear
threshold neurons. Their lack of right saturation allows the overall network to
explore the problem space driven through the unstable dynamics generated by
recurrent excitation. The direction of exploration is steered by the constraint
neurons. While many problems can be solved using only linear inhibitory
constraints, network performance on hard problems benefits significantly when
these negative constraints are implemented by non-linear multiplicative
inhibition. Overall, our results demonstrate the importance of instability
rather than stability in network computation, and also offer insight into the
computational role of dual inhibitory mechanisms in neural circuits.Comment: Accepted manuscript, in press, Neural Computation (2018
Design of exponential state estimators for neural networks with mixed time delays
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China under Grants 05KJB110154 and BK2006064, and the National Natural Science Foundation of China under Grants 10471119 and 10671172
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