8,188 research outputs found
Asymptotic stability of impulsive high-order Hopfield typeneural networks
AbstractIn this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method
Recognition of partially occluded threat objects using the annealed Hopefield network
Recognition of partially occluded objects has been an important issue to airport security because occlusion causes significant problems in identifying and locating objects during baggage inspection. The neural network approach is suitable for the problems in the sense that the inherent parallelism of neural networks pursues many hypotheses in parallel resulting in high computation rates. Moreover, they provide a greater degree of robustness or fault tolerance than conventional computers. The annealed Hopfield network which is derived from the mean field annealing (MFA) has been developed to find global solutions of a nonlinear system. In the study, it has been proven that the system temperature of MFA is equivalent to the gain of the sigmoid function of a Hopfield network. In our early work, we developed the hybrid Hopfield network (HHN) for fast and reliable matching. However, HHN doesn't guarantee global solutions and yields false matching under heavily occluded conditions because HHN is dependent on initial states by its nature. In this paper, we present the annealed Hopfield network (AHN) for occluded object matching problems. In AHN, the mean field theory is applied to the hybird Hopfield network in order to improve computational complexity of the annealed Hopfield network and provide reliable matching under heavily occluded conditions. AHN is slower than HHN. However, AHN provides near global solutions without initial restrictions and provides less false matching than HHN. In conclusion, a new algorithm based upon a neural network approach was developed to demonstrate the feasibility of the automated inspection of threat objects from x-ray images. The robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features
Neural Distributed Autoassociative Memories: A Survey
Introduction. Neural network models of autoassociative, distributed memory
allow storage and retrieval of many items (vectors) where the number of stored
items can exceed the vector dimension (the number of neurons in the network).
This opens the possibility of a sublinear time search (in the number of stored
items) for approximate nearest neighbors among vectors of high dimension. The
purpose of this paper is to review models of autoassociative, distributed
memory that can be naturally implemented by neural networks (mainly with local
learning rules and iterative dynamics based on information locally available to
neurons). Scope. The survey is focused mainly on the networks of Hopfield,
Willshaw and Potts, that have connections between pairs of neurons and operate
on sparse binary vectors. We discuss not only autoassociative memory, but also
the generalization properties of these networks. We also consider neural
networks with higher-order connections and networks with a bipartite graph
structure for non-binary data with linear constraints. Conclusions. In
conclusion we discuss the relations to similarity search, advantages and
drawbacks of these techniques, and topics for further research. An interesting
and still not completely resolved question is whether neural autoassociative
memories can search for approximate nearest neighbors faster than other index
structures for similarity search, in particular for the case of very high
dimensional vectors.Comment: 31 page
The Relativistic Hopfield network: rigorous results
The relativistic Hopfield model constitutes a generalization of the standard
Hopfield model that is derived by the formal analogy between the
statistical-mechanic framework embedding neural networks and the Lagrangian
mechanics describing a fictitious single-particle motion in the space of the
tuneable parameters of the network itself. In this analogy the cost-function of
the Hopfield model plays as the standard kinetic-energy term and its related
Mattis overlap (naturally bounded by one) plays as the velocity. The
Hamiltonian of the relativisitc model, once Taylor-expanded, results in a
P-spin series with alternate signs: the attractive contributions enhance the
information-storage capabilities of the network, while the repulsive
contributions allow for an easier unlearning of spurious states, conferring
overall more robustness to the system as a whole. Here we do not deepen the
information processing skills of this generalized Hopfield network, rather we
focus on its statistical mechanical foundation. In particular, relying on
Guerra's interpolation techniques, we prove the existence of the infinite
volume limit for the model free-energy and we give its explicit expression in
terms of the Mattis overlaps. By extremizing the free energy over the latter we
get the generalized self-consistent equations for these overlaps, as well as a
picture of criticality that is further corroborated by a fluctuation analysis.
These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur
Global exponential stability of impulsive high-order Hopfield typeneural networks with delays
AbstractIn this paper, we investigate the global exponential stability of impulsive high-order Hopfield type neural networks with delays. By establishing the impulsive delay differential inequalities and using the Lyapunov method, two sufficient conditions that guarantee global exponential stability of these networks are given, and the exponential convergence rate is also obtained. A numerical example is given to demonstrate the validity of the results
Dynamical Analysis for High-Order Delayed Hopfield Neural Networks with Impulses
The global exponential stability and uniform stability of the equilibrium point for high-order delayed Hopfield neural networks with impulses are studied. By utilizing Lyapunov functional method, the quality of negative definite matrix, and the linear matrix inequality approach, some new stability criteria for such system are derived. The results are related to the size of delays and impulses. Two examples are also given to illustrate the effectiveness of our results
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