Tolerance of a Binary Associative Memory Towards Stuck-at-Faults

Rueckert, Ulrich; Surmann, Hartmut

doi:10.1016/b978-0-444-89178-5.50050-6

Cited by 10 publications

(9 citation statements)

References 2 publications

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“…Iterative retrieval in the Willshaw model (2) can be described by the Lyapunov function (12) since it is easy to show that asynchronous application of the Willshaw update in (2) sets to if (13) We call the method for setting the threshold during the course of iterations the threshold strategy.…”

Section: A Retrieval As Constraint Satisfactionmentioning

confidence: 99%

“…The Lyapunov function (14) is equivalent (up to a constant factor and a constant offset) to (12) for . The terms in (14) can be interpreted as constraint terms on : The first term punishes pairs of 1-components in that coincide with a matrix element .…”

Section: A Retrieval As Constraint Satisfactionmentioning

confidence: 99%

“…However, it has not been so widely used since its performance degrades significantly if there are errors in the initial patterns presented or if there are errors in the synaptic weight matrix [12]. Both sorts of error are highly likely in large-scale hardware implementations in silicon or optical devices and also in networks of biological neurons.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian retrieval in associative memories with storage errors

Sommer

Dayan

1998

IEEE Trans. Neural Netw.

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Abstract-It is well known that for finite-sized networks, onestep retrieval in the autoassociative Willshaw net is a suboptimal way to extract the information stored in the synapses. Iterative retrieval strategies are much better, but have hitherto only had heuristic justification. We show how they emerge naturally from considerations of probabilistic inference under conditions of noisy and partial input and a corrupted weight matrix. We start from the conditional probability distribution over possible patterns for retrieval. This contains all possible information that is available to an observer of the network and the initial input. Since this distribution is over exponentially many patterns, we use it to develop two approximate, but tractable, iterative retrieval methods. One performs maximum likelihood inference to find the single most likely pattern, using the (negative log of the) conditional probability as a Lyapunov function for retrieval. In physics terms, if storage errors are present, then the modified iterative update equations contain an additional antiferromagnetic interaction term and site dependent threshold values. The second method makes a mean field assumption to optimize a tractable estimate of the full conditional probability distribution. This leads to iterative mean field equations which can be interpreted in terms of a network of neurons with sigmoidal responses but with the same interactions and thresholds as in the maximum likelihood update equations. In the absence of storage errors, both models become very similiar to the Willshaw model, where standard retrieval is iterated using a particular form of linear threshold strategy.

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Section: A Retrieval As Constraint Satisfactionmentioning

confidence: 99%

Section: A Retrieval As Constraint Satisfactionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian retrieval in associative memories with storage errors

Sommer

Dayan

1998

IEEE Trans. Neural Netw.

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“…The basic operation of NAMs (Kohonen 1984) are pattern mapping (heteroassociative recall) and pattern completion (autoassociative recall). In addition NAMs have the capability of fault tolerance as described in Palm (1982), Rückert and Surmann (1991), and Kohonen (1984). There are two phases in working with NAMs.…”

Section: Associative Memory With Neural Architecturementioning

confidence: 99%

Parallel Implementation of Neural Associative Memories on RISC Processors

Rückert¹,

Rüping²,

Naroska³

1994

VLSI for Neural Networks and Artificial Intelligence

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“…Thus, these systems have to be designed carefully in order to guarantee reliable operation under changing and noisy environment. In order to fulfill these requirements neural networks have to be fault-tolerant to malfunctioning neurons [2] and to be robust to noise corrupted weights and inputs [4]. Technical implementations have always to face malfunctioning elements [5], especially in future nanoelectronic realizations [6] and noise is always present [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Fault-Tolerance of Basis Function Networks using Tensor Product Stabilizers

Eickhoff

Rückert

2005 IEEE International Conference on Systems, Man and Cybernetics

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Neural networks are intended to be used in future nanoelectronics since these architectures seem to be fault-tolerant to malfunctioning elements and robust to noise. In this paper, the robustness to noise of Basis Function networks using tensor product stabilizers is analyzed and upper bounds of the mean square error under noise contaminated weights or inputs are determined. Furthermore, consequences of permanently malfunctioning neurons are investigated and their impact on the mean squared error is analyzed. To achieve a reliable operation of the neural network necessary restrictions are introduced. Finally, the impact of technical realizations is investigated and its complexity is compared to Radial Basis Functions.

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Tolerance of a Binary Associative Memory Towards Stuck-at-Faults

Cited by 10 publications

References 2 publications

Bayesian retrieval in associative memories with storage errors

Bayesian retrieval in associative memories with storage errors

Parallel Implementation of Neural Associative Memories on RISC Processors

Fault-Tolerance of Basis Function Networks using Tensor Product Stabilizers

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