Quantum-Inspired Complex-Valued Multidirectional Associative Memory

Complex-valued neuron is one of the significant and effective innovation in artificial neural networks. It is able to deal with multi-valued pattern and oscillator models. With regard as associative memory, several types of complex-valued artificial neural associative memories have developed, and confirmed its superior abilities. Conventionally, we have developed Quantum-Inspired Mulitidirectional Associative Memory (QMAM). This model demonstrates quantum information processing in neural structures results in an exponential increase in storage capacity and can explain the extensive memory and inferencing capabilities of humans. This model is applied a fuzzy inference to weight matrix to satisfy parallelism and unitarity. In this paper, we introduce Quantum-Inspired Complex-Valued Multidirectional Associative Memory (QCMAM) to handle multi-valued information. In addition, the mathematical proofs of parallelism and unitarity for a complex-valued model are presented. The simulation experiments show that QCMAM has superior abilities comparing with conventional model.

[1]  Raymond S. T. Lee.  A transient-chaotic autoassociative network (TCAN) based on Lee oscillators , 2004, IEEE Transactions on Neural Networks.

[2]  V. Srinivasa Chakravarthy,et al.  Chaotic Synchronization Using a Network of Neural oscillators , 2008, Int. J. Neural Syst..

[3]  Tetsuo Matsui,et al.  Quantum gauged neural network: U(1) gauge theory , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[4]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[5]  Bart Kosko.  Constructing an associative memory , 1987 .

[6]  Masaki Kobayashi,et al.  Pseudo-Relaxation Learning Algorithm for Complex-Valued Associative Memory , 2008, Int. J. Neural Syst..

[7]  D.-L. Lee,et al.  Improvements of Complex-Valued Hopfield Associative Memory by Using Generalized Projection Rules , 2006, IEEE Transactions on Neural Networks.

[8]  Gerasimos G. Rigatos,et al.  Stochastic Processes and Neuronal Modelling: Quantum Harmonic Oscillator Dynamics in Neural Structures , 2010, Neural Processing Letters.

[9]  C. S. Leung.  Encoding method for bidirectional associative memory using projection on convex sets , 1993, IEEE Trans. Neural Networks.

[10]  Jacek M. Zurada,et al.  Complex-valued multistate neural associative memory , 1996, IEEE Trans. Neural Networks.

[11]  E. Villaseñor.  Introduction to Quantum Mechanics , 2008, Nature.

[12]  Hoon Kang.  Multilayer associative neural networks (MANN's): storage capacity versus perfect recall , 1994, IEEE Trans. Neural Networks.

[13]  Chu Kiong Loo,et al.  Affective communication robot partners using associative memory with mood congruency effects , 2014, 2014 IEEE Symposium on Robotic Intelligence in Informationally Structured Space (RiiSS).

[14]  Spyros G. Tzafestas,et al.  Quantum learning for neural associative memories , 2006, Fuzzy Sets Syst..

[15]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[16]  H.J. Levy,et al.  A feedforward artificial neural network based on quantum effect vector-matrix multipliers , 1993, IEEE Trans. Neural Networks.

[17]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Masafumi Hagiwara.  Multidirectional associative memory , 1990 .

[19]  Noest.  Discrete-state phasor neural networks. , 1988, Physical review. A, General physics.

[20]  G. Reeke.  Marvin Minsky, The Society of Mind , 1991, Artif. Intell..

[21]  T. Martin McGinnity,et al.  Quantum Neural Network-Based EEG Filtering for a Brain–Computer Interface , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Masao Nakagawa,et al.  Quick learning for bidirectional associative memory , 1994 .

[23]  Wen-June Wang,et al.  A multivalued bidirectional associative memory operating on a complex domain , 1998, Neural Networks.

[24]  Masaki Kobayashi,et al.  Complex-valued Multidirectional Associative Memory , 2005 .

[25]  G. Bower,et al.  Human Associative Memory , 1973 .

[26]  M. Eysenck.  Psychology : an integrated approach , 1998 .

[27]  Spyros G. Tzafestas,et al.  Parallelization of a fuzzy control algorithm using quantum computation , 2002, IEEE Trans. Fuzzy Syst..

[28]  Jose B. Cruz,et al.  Guaranteed recall of all training pairs for bidirectional associative memory , 1991, IEEE Trans. Neural Networks.

[29]  W. Marsden.  I and J , 2012 .