A Projection Rule for Complex‐Valued Associative Memory with Partial Connections

2020 ◽  
Vol 15 (9) ◽  
pp. 1327-1336
Author(s):  
Masayuki Tsuji ◽  
Teijiro Isokawa ◽  
Masaki Kobayashi ◽  
Nobuyuki Matsui ◽  
Naotake Kamiura
Keyword(s):  
Associative Memory ◽  
Complex Valued ◽  
Projection Rule

Bicomplex Projection Rule for Complex-Valued Hopfield Neural Networks

2020 ◽  
Vol 32 (11) ◽  
pp. 2237-2248
Author(s):  
Masaki Kobayashi
Keyword(s):  
Neural Networks ◽  
Computer Simulations ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Hopfield Neural Networks ◽  
Noise Tolerance ◽  
Synchronous Mode ◽  
Memory Resources ◽  
Complex Valued ◽  
Projection Rule

A complex-valued Hopfield neural network (CHNN) with a multistate activation function is a multistate model of neural associative memory. The weight parameters need a lot of memory resources. Twin-multistate activation functions were introduced to quaternion- and bicomplex-valued Hopfield neural networks. Since their architectures are much more complicated than that of CHNN, the architecture should be simplified. In this work, the number of weight parameters is reduced by bicomplex projection rule for CHNNs, which is given by the decomposition of bicomplex-valued Hopfield neural networks. Computer simulations support that the noise tolerance of CHNN with a bicomplex projection rule is equal to or even better than that of quaternion- and bicomplex-valued Hopfield neural networks. By computer simulations, we find that the projection rule for hyperbolic-valued Hopfield neural networks in synchronous mode maintains a high noise tolerance.

Complex-valued multistate neural associative memory

1996 ◽  
Vol 7 (6) ◽  
pp. 1491-1496 ◽  
Author(s):  
S. Jankowski ◽  
A. Lozowski ◽  
J.M. Zurada
Keyword(s):  
Associative Memory ◽  
Complex Valued

Storage Capacity of Quaternion-Valued Hopfield Neural Networks with Dual Connections

2021 ◽  
pp. 1-15
Author(s):  
Masaki Kobayashi
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Stochastic Analysis ◽  
Storage Capacity ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Hopfield Neural Networks ◽  
Noise Tolerance ◽  
Complex Valued ◽  
Projection Rule

Abstract A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of projection rule for QHNNs with DCs is half of that for CHNNs and equals that of conventional QHNNs. The small storage capacity of QHNNs with DCs is caused by projection rule, not the architecture. In this work, the ebbian rule is introduced and proved by stochastic analysis that the storage capacity of a QHNN with DCs is 0.8 times as many as that of a CHNN.

A complex-valued associative memory for storing patterns as oscillatory states

1996 ◽  
Vol 75 (3) ◽  
pp. 229-238 ◽  
Author(s):  
Srinivasa V. Chakravarthy ◽  
Joydeep Ghosh
Keyword(s):  
Associative Memory ◽  
Complex Valued
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