掲載種別：研究論文（その他学術会議資料等）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

We provide a rigorous account of the equivalence between the complex-valued widely linear estimation method and the quaternion involution widely linear estimation method with their vector-valued real linear estimation counterparts. This is achieved by an account of degrees of freedom and by providing matrix mappings between a complex variable and an isomorphic bivariate real vector, and a quaternion variable versus a quadri-variate real vector. Furthermore, we show that the parameters in the complex-valued linear estimation method, the complex-valued widely linear estimation method, the quaternion linear estimation method, the quaternion semi-widely linear estimation method, and the quaternion involution widely linear estimation method include distinct geometric structures imposed on complex numbers and quaternions, respectively, whereas the real-valued linear estimation methods do not exhibit any structure. This key difference explains, both in theoretical and practical terms, the advantage of estimation in division algebras (complex, quaternion) over their multivariate real vector counterparts. In addition, we discuss the computational complexities of the estimators of the hypercomplex widely linear estimation methods.

DOI： 10.1109/TSP.2019.2922151

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：WILEY  

It has been reported that training deep neural networks is more difficult than training shallow neural networks. Hinton etal. proposed deep belief networks with a learning algorithm that trains one layer at a time. A much better generalization can be achieved when pre-training each layer with an unsupervised learning algorithm. Since then, deep neural networks have been extensively studied. On the other hand, it has been revealed that singular points affect the training dynamics of the learning models such as neural networks and cause a standstill of training. Naturally, training deep neural networks suffer singular points. As described in this paper, we present a deep neural network model that has fewer singular points than the usual one. First, we demonstrate that some singular points in the deep real-valued neural network, which is equivalent to a deep complex-valued neural network, have been resolved as its inherent property. Such deep neural networks are less likely to become trapped in local minima or plateaus caused by critical points. Results of experiments on the two spirals problem, which has an extreme nonlinearity, support our theory. Copyright (c) 2017 John Wiley & Sons, Ltd.

DOI： 10.1002/mma.4434

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

In this paper, we first extend the Wirtinger derivative which is defined for complex functions to hyperbolic functions, and derive the hyperbolic gradient operator yielding the steepest descent direction by using it. Next, we derive the hyperbolic backpropagation learning algorithms for some multilayered hyperbolic neural networks (NNs) using the hyperbolic gradient operator. It is shown that the use of the Wirtinger derivative reduces the effort necessary for the derivation of the learning algorithms by half, simplifies the representation of the learning algorithms, and makes their computer programs easier to code. In addition, we discuss the differences between the derived Hyperbolic-BP rules and the complex-valued backpropagation learning rule (Complex-BP). Finally, we make some experiments with the derived learning algorithms. As a result, we find that the convergence rates of the Hyperbolic-BP learning algorithms are high even if the fully activation functions are used, and discover that the Hyperbolic-BP learning algorithm for the hyperbolic NN with the split-type hyperbolic activation function has an ability to learn hyperbolic rotation as its inherent property.

DOI： 10.1109/TNNLS.2017.2677446

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担当区分：筆頭著者,　責任著者  

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その他リンク： https://dblp.uni-trier.de/db/journals/corr/corr1806.html#abs-1806-04884

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

We present a theoretical analysis of singular points of artificial deep neural networks, resulting in providing deep neural network models having no critical points introduced by a hierarchical structure. It is considered that such deep neural network models have good nature for gradient-based optimization. First, we show that there exist a large number of critical points introduced by a hierarchical structure in deep neural networks as straight lines, depending on the number of hidden layers and the number of hidden neurons. Second, we derive a sufficient condition for deep neural networks having no critical points introduced by a hierarchical structure, which can be applied to general deep neural networks. It is also shown that the existence of critical points introduced by a hierarchical structure is determined by the rank and the regularity of weight matrices for a specific class of deep neural networks. Finally, two kinds of implementation methods of the sufficient conditions to have no critical points are provided. One is a learning algorithm that can avoid critical points introduced by the hierarchical structure during learning (called avoidant learning algorithm). The other is a neural network that does not have some critical points introduced by the hierarchical structure as an inherent property (called avoidant neural network).

DOI： 10.1109/TNNLS.2016.2580741

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：SPRINGER INT PUBLISHING AG  

In this paper, we analyze a deep neural network model from the viewpoint of singularities. First, we show that there exist a large number of critical points introduced by a hierarchical structure in the deep neural network as straight lines. Next, we derive sufficient conditions for the deep neural network having no critical points introduced by a hierarchical structure.

DOI： 10.1007/978-3-319-46681-1_47

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC  

The quaternion widely linear (WL) estimator has been recently introduced for optimal second-order modeling of the generality of quaternion data, both second-order circular (proper) and second-order noncircular (improper). Experimental evidence exists of its performance advantage over the conventional strictly linear (SL) as well as the semi-WL (SWL) estimators for improper data. However, rigorous theoretical and practical performance bounds are still missing in the literature, yet this is crucial for the development of quaternion valued learning systems for 3-D and 4-D data. To this end, based on the orthogonality principle, we introduce a rigorous closed-form solution to quantify the degree of performance benefits, in terms of the mean square error, obtained when using the WL models. The cases when the optimal WL estimation can simplify into the SWL or the SL estimation are also discussed.

DOI： 10.1109/TNNLS.2015.2388782

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担当区分：筆頭著者,　責任著者   記述言語：英語   出版者・発行元：KOWSAR CORP  

Context: Recently, the singular points of neural networks have attracted attention from the artificial intelligence community, and their interesting properties have been demonstrated. The objective of this study is to provide an overview of studies on the singularities of complex-valued neural networks.Evidence Acquisition: This review is based on the relevant literature on complex-valued neural networks and singular points.Results: Review of the studies and available literature on the subject area shows that the singular points of complex-valued neural networks have negative effects on learning, as do those of real-valued neural networks. However, the nature of the singular points in complex-valued neural networks is superior in quality, and the methods for improving the learning performance have been proposed.Conclusions: A complex-valued neural network could be a promising learning method from the viewpoint of a singularity.

DOI： 10.5812/archneurosci.27461

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担当区分：筆頭著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MIT PRESS  

This letter investigates the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron). The parameters of the polar variable complex-valued neuron are unidentifiable. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron. Furthermore, computer simulations suggest that a single polar variable complex-valued neuron has the following characteristics in the case of using the steepest gradient-descent method with square error: (1) unidentifiable parameters (singular points) degrade the learning speed and (2) a plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to become stuck. However, computer simulations also show that the steepest gradient-descent method with amplitude-phase error and the complex-valued natural gradient method could reduce the effects of the singular points. The learning dynamics near singular points depends on the error functions and the training algorithms used.

DOI： 10.1162/NECO_a_00729

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：SciTePress  

In this paper, the characteristics of the complex-valued neuron model with parameters represented by polar coordinates (called polar variable complex-valued neuron) are investigated. The main results are as reported below. The polar variable complex-valued neuron is unidentifiable: there exists a parameter that does not affect the output value of the neuron and one cannot identify its value. The plateau phenomenon can occur during learning of the polar variable complex-valued neuron: the learning error does not decrease in a period. Furthermore, it is suggested by computer simulations that a single polar variable complex-valued neuron has the following characteristics: (a) Unidentifiable parameters (singular points) degrade the learning speed. (b) A plateau can occur during learning. When the weight is attracted to the singular point, the learning tends to be stuck.

DOI： 10.5220/0004887905260531

Scopus

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その他リンク： https://dblp.uni-trier.de/db/conf/icaart/icaart2014-1.html#Nitta14

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：PERGAMON-ELSEVIER SCIENCE LTD  

Most of local minima caused by the hierarchical structure can be resolved by extending the real-valued neural network to complex numbers. It was proved in 2000 that a critical point of the real-valued neural network with H - 1 hidden neurons always gives many critical points of the real-valued neural network with H hidden neurons. These critical points consist of many lines in the parameter space which could be local minima or saddle points. Local minima cause plateaus which have a strong negative influence on learning. However, most of the critical points of complex-valued neural network are saddle points unlike those of the real-valued neural network. This is a prominent property of the complex-valued neural network. (c) 2013 Elsevier Ltd. All rights reserved.

DOI： 10.1016/j.neunet.2013.02.002

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：SPRINGER BASEL AG  

We survey the development of Clifford's geometric algebra and some of its
engineering applications during the last 15 years. Several recently developed
applications and their merits are discussed in some detail. We thus hope to
clearly demonstrate the benefit of developing problem solutions in a unified
framework for algebra and geometry with the widest possible scope: from quantum
computing and electromagnetism to satellite navigation, from neural computing
to camera geometry, image processing, robotics and beyond.

DOI： 10.1007/s00006-013-0378-4

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その他リンク： http://arxiv.org/pdf/1305.5663v1

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：ELSEVIER SCIENCE BV  

A critical point is a point on which the derivatives of an error function are all zero. It has been shown in the literatures that the critical points caused by the hierarchical structure of the real-valued neural network could be local minima or saddle points, whereas most of the critical points caused by the hierarchical structure are saddle points in the case of complex-valued neural networks. Several studies have demonstrated that that kind of singularity has a negative effect on learning dynamics in neural networks. In this paper, we will demonstrate via some examples that the decomposition of high-dimensional NNs into real-valued NNs equivalent to the original NNs yields the NNs that do not have critical points based on the hierarchical structure. (C) 2013 The Authors. Published by Elsevier B.V.

DOI： 10.1016/j.procs.2013.09.103

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.4018/joci.2012040103

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：SPRINGER-VERLAG BERLIN  

In this paper, we formulate a Clifford-valued widely linear estimation framework. Clifford number is a hypercomplex number that generalizes real, complex numbers, quaternions, and higher dimensional numbers. And also, as a first step, we will give a theoretical foundation for a quaternion-valued widely linear estimation framework. The estimation error obtained with the quaternion-valued widely linear estimation method is proven to be smaller than that obtained using the usual quaternion-valued linear estimation method.

DOI： 10.1007/978-3-642-24955-6_62

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その他リンク： https://dblp.uni-trier.de/db/conf/iconip/iconip2011-1.html#Nitta11

担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：WORLD SCIENTIFIC PUBL CO PTE LTD  

This paper will prove the uniqueness theorem for 3-layered complex-valued neural networks where the threshold parameters of the hidden neurons can take non-zeros. That is, if a 3-layered complex-valued neural network is irreducible, the 3-layered complex-valued neural network that approximates a given complex-valued function is uniquely determined up to a finite group on the transformations of the learnable parameters of the complex-valued neural network.

DOI： 10.1142/S0129065708001439

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IEEE  

In this paper, the basic properties, especially decision boundary, of the hyperbolic neurons used in the hyperbolic neural networks are investigated. And also, a non-split hyperbolic sigmoid activation function is proposed.

DOI： 10.1109/IJCNN.2008.4634216

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：MIT PRESS  

This letter presents some results of an analysis on the decision boundaries of complex-valued neural networks whose weights, threshold values, input and output signals are all complex numbers. The main results may be summarized as follows. (1) A decision boundary of a single complex-valued neuron consists of two hypersurfaces that intersect orthogonally, and divides a decision region into four equal sections. The XOR problem and the detection of symmetry problem that cannot be solved with two-layered real-valued neural networks, can be solved by two-layered complex-valued neural networks with the orthogonal decision boundaries, which reveals a potent computational power of complex-valued neural nets. Furthermore, the fading equalization problem can be successfully solved by the two-layered complex-valued neural network with the highest generalization ability. (2) A decision boundary of a three-layered complex-valued neural network has the orthogonal property as a basic structure, and its two hypersurfaces approach orthogonality as all the net inputs to each hidden neuron grow. In particular, most of the decision boundaries in the three-layered complex-valued neural network inetersect orthogonally when the network is trained using Complex-BP algorithm. As a result, the orthogonality of the decision boundaries improves its generalization ability. (3) The average of the learning speed of the Complex-BP is several times faster than that of the Real-BP. The standard deviation of the learning speed of the Complex-BP is smaller than that of the Real-BP. It seems that the complex-valued neural network and the related algorithm are natural for learning complex-valued patterns for the above reasons.

DOI： 10.1162/08997660460734001

PubMed

CiNii Article

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その他リンク： https://dblp.uni-trier.de/db/journals/neco/neco16.html#Nitta04

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Springer  

DOI： 10.1007/3-540-44989-2_118

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その他リンク： https://dblp.uni-trier.de/db/conf/icann/icann2003.html#Nitta03

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：PERGAMON-ELSEVIER SCIENCE LTD  

This letter presents some results on the computational power of complex-valued neurons. The main results may be summarized as follows. The XOR problem and the detection of symmetry problem which cannot be solved with a single real-valued neuron (i.e. a two-layered real-valued neural network), can be solved with a single complex-valued neuron (i.e. a two-layered complex-valued neural network) with the orthogonal decision boundaries, which reveals the potent computational power of complex-valued neurons. Furthermore, the fading equalization problem can be successfully solved with a single complex-valued neuron with the highest generalization ability. (C) 2003 Elsevier Ltd. All rights reserved.

DOI： 10.1016/S0893-6080(03)00168-0

PubMed

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その他リンク： https://dblp.uni-trier.de/db/journals/nn/nn16.html#Nitta03

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

A complex neural network is obtained from an ordinary network by extending the (real-valued) parameters, such as the weights and the thresholds, to complex values. Applications to problems involving complex numbers, such as communications systems, are expected. This paper presents the following uniqueness theorem. When a complex function is given, the three-layered neural network that approximates the function is uniquely determined by a certain finite group, if it is irreducible. The above finite group specifies the redundancy of the parameters in the complex neural network, but has a structure which is different from that of the real-valued neural network. The order of the finite group is examined, and it is shown that the redundancy of the complex-valued neural network is an exponent multiple of the redundancy of the real-valued neural network. Analysis of the redundancy is important in the theoretical investigation of the basic characteristics of complex-valued neural networks, such as the local minimum property. A sufficient condition is derived for the given three-layered complex-valued neural network to be minimal. The above results are shown, in essence, by extending the approach of Sussmann for real-valued neural networks.

DOI： 10.1002/scj.10363

Scopus

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

This paper shows the differences between the real-valued neural network and the complex-valued neural network by analyzing their fundamental properties from the view of architectures. The main results may be summarized as follows: (a) A single complex-valued neuron with n-inputs is equivalent to two real-valued neurons with 2n-inputs which have a restriction on a set of weight parameters. (b) The decision boundary of a single complex-valued neuron consists of two hypersurfaces which intersect orthogonally. (c) The decision boundary of a three-layered complex-valued neural network has the orthogonal structure. (d) The orthogonality of the decision boundary in the three-layered Complex-BP network can improve its generalization ability. (e) The average of the learning speed of the Complex-BP is several times faster than that of the Real-BP, and the standard deviation of the learning speed of the Complex-BP is smaller than that of the Real-BP. (C) 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0925-2312(02)00568-4

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：ELSEVIER SCIENCE BV  

In this letter, we will clarify the redundancy of the parameters of the complex-valued neural network. The results may be summarized as follows. There exist the four transformations which can cause the redundancy of the parameters of the complex-valued neural network, including the two transformations which can cause the redundancy of the parameters of the real-valued neural network (i.e., the interchange of the two hidden neurons and the sign flip of the parameters on the hidden neurons). (C) 2002 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0925-2312(02)00669-0

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

In human memory, impressive objects (those with attachments to strong emotions, such as happiness and sadness) are retained easily, while non-impressive objects (those without attachments to strong emotions) are not. Furthermore, one can easily acquire systematic knowledge about a favorite field, while it is difficult to acquire such knowledge about a non-favorite field. Emotions thus seem to play an important role in retaining the memory of an object and in forming a conceptual memory of objects. We have therefore developed an emotion-memory model, and in this paper, we present a simulation result on concept forming.

Scopus

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1023/A:1026582217675

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

In this paper, we propose a computational model of personality (called personality model) for the purpose of implementing non-intellectual functions of human mind on computer systems. The personality model will be formulated based on psychoanalysis, assuming that defensive mechanism plays an essential role in a personality. Inductive probability will be employed for modeling defense mechanism. The personality model is useful for the expression of feelings, and will be used in virtual reality, computer game characters, agent secretaries, and robotics.

Scopus

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

This paper describes a new model of neuron, named neuron-oid, that can detect the 'coincidence with delays'. A neuronoid is modeled as a collection of chemicals. Each Chemical belongs to either 'rover' category or 'borderer' category. The interaction of chemicals between these two categories leads to the decision of a neuronoid to fire or not.

Scopus

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IASTED/ACTA Press  

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その他リンク： https://dblp.uni-trier.de/db/conf/appinf/appinf1999.html#NishidaNT99

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IOA Press  

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その他リンク： https://dblp.uni-trier.de/db/conf/iconip/iconip1998.html#Nitta98

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：Springer  

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その他リンク： https://dblp.uni-trier.de/db/conf/iconip/iconip1997-1.html#Nitta97

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1016/S0893-6080(97)00036-1

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その他リンク： https://dblp.uni-trier.de/db/journals/nn/nn10.html#Nitta97

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IEEE  

It has been discovered by computational experiments that the `Complex-BP' algorithm can transform geometrical figures (e.g. rotation, similar transformation and parallel displacement), and reported that this ability can be successfully applied to computer vision. In this paper, the ability of the `Complex-BP' algorithm to learn similar transformation of geometrical figures is analyzed. A Complex-BP network which has learned similar transformation, has the ability to generalize the similitude ratio with a distance error which is represented by the sine of the difference between the argument of the test pattern and that of the training pattern.

DOI： 10.1109/ICNN.1995.487386

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その他リンク： https://dblp.uni-trier.de/db/conf/icnn/icnn1995.html#Nitta95

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IEEE  

DOI： 10.1109/ICNN.1995.488166

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J-GLOBAL

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その他リンク： https://dblp.uni-trier.de/db/conf/icnn/icnn1995.html#Nitta95a

担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

DOI： 10.1109/icnn.1994.374173

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J-GLOBAL

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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J-GLOBAL

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

The 3D vector version of the back-propagation algorithm (called '3DV-BP') is a natural extension of the complex-valued version of the back-propagation algorithm (called 'Complex-BP'). The Complex-BP can be applied to multi-layered neural networks whose weights, threshold values, input and output signals are all complex numbers, and the 3DV-BP can be applied to multi-layered neural networks whose threshold values, input and output signals are all 3D real valued vectors, and whose weights are all 3D orthogonal matrices. It has already been reported that an inherent property of the Complex-BP is its ability to learn '2D motion'. This paper shows in computational experiments that the 3DV-BP has the ability to learn '3D motion', which corresponds to the ability of the Complex-BP to learn '2D motion'.

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

This paper introduces a complex numbered version of the back-propagation algorithm, which can be applied to neural networks whose weights, threshold values, input and output signals are all complex numbers. This new algorithm can be used to learn complex numbered patterns in a natural way. We show that ″Complex-BP″ can transform geometrical figures.

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

A 3D vector version of the back-propagation algorithm is proposed for multi-layered neural networks in which vector product operation is performed, and whose weights, threshold values, input and output signals are all 3D real numbered vectors. This new algorithm can be used to learn patterns consisted of 3D vectors in a natural way. The XOR problem was used to successfully test the new formulation.

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）   出版者・発行元：IEEE Computer Society  

A SD vector version of the back-propagation algorithm is proposed for multi-layered neural networks in which vector product operation is performed, and whose weights, threshold values, input and output signals are all 3D real numbered vectors. This new algorithm can be used to learn patterns consisted of 3D vectors in a natural way. A 3D-example was used to successfully test the new formulation.

DOI： 10.1109/TAI.1993.634002

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その他リンク： https://dblp.uni-trier.de/db/conf/ictai/ictai1993.html#Nitta93

担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：一般社団法人情報処理学会  

近年 階層型ニューラルネットワークの学習方式として提案されたバックプロパゲーション学習アルゴリズム(BP)が注目され 様々な分野に応用されている.複素パターンに対する学習アルゴリズムとして提案された複素BPは その学習パラメータがすべて複素数となっており 実数値を用いる通常のBPを複素数に拡張したものであると言える.複素BPには 従来のBPには見られない2次元運動学習能力が備わっていることは既に報告した.本稿では ネットワークアーキテクチャの観点から 複素BPの基本特性を解析的 実験的に調べ 従来のBPとの差異を明確にしたので報告する.得られた主要な結果は 次のとおりである(1)複素BPネットワークにおける重み係数は 従来のBPネットワークにおけるそれとは異なり 2次元運動に関係した制約を持っており 学習は基本的にその制約を保ちつつ行われる.(2)複素ニューロンの実部の決定表面と虚部の決定表面とは互いに直交しており 決定領域を均等に4つに分割する3層の複素BPネットワークにおける決定表面は基本的にこの構造を内包しており 中間ニューロンヘの総入力が十分大きいときに直交する.この意味で 複素BPは複素パターンに対する自然な学習アルゴリズムであると思われる・これらの特性は意図されたものではなく 複素数への拡張の結果として自ずと現れてきたものであることに注意されたい.

CiNii Article

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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記述言語：英語   掲載種別：研究論文（国際会議プロシーディングス）  

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）   出版者・発行元：公益社団法人日本オペレーションズ・リサーチ学会  

本稿では、確率的資源配分モデルを扱う。生産関数は、[7]における生産関数g(x)=xを拡張したものである。資源を消費と生産に対して逐次配分することにより、各段階において効用が得られる。問題となるのは、全段階に渡って得られる効用の総和の期待値、すなわち、期待全効用を最大にするような配分方法である。最適配分が存在した場合に、それが満たすべき必要十分条件がmartingaleで表現される。任意に配分を行った場合に得られる条件付期待全効用の上限はsupemartingaleを形成するが、その配分が最適であるためには、条件付期待全効用の上限がmartingaleであることで必要十分である。更に、得られた上記の十分条件を利用することにより、対数効用関数と非線形生産関数g(x)=x^p(p>0)を持つモデルにおける最適配分を求めた。その結果は[7]で得られている最適配分を包含した形のものとなっている。

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担当区分：筆頭著者,　責任著者   記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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記述言語：日本語   掲載種別：研究論文（学術雑誌）  

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担当区分：筆頭著者,　責任著者   記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：公益社団法人日本オペレーションズ・リサーチ学会  

This paper deals with stochastic models of an optimal sequential allocation of resources between consumption and production. We obtain the following results by means of the theory of martingales. For a model of resource allocation we establish the dynamic programming equation and show that a supermartingale characterizes the composition of the model and clear the composition of the optimality, representing the sufficient condition for an allocation to be optimal via a martingale. Further, we show the following three results as the application of the above result. (1) For the Kennedy's model we give another proof for the fact on an optimal allocation. (2) For a model with a convex utility function, we represent an optimal allocation via a supelmartingale. (3) For a model with a logarithmic utility function, we obtain an explicit optimal allocation.

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記述言語：日本語   出版者・発行元：一般社団法人電子情報通信学会  

海馬に関する形態学的構造と生理学的知見に基づいて構成した、海馬の三次元神経回路による連想記憶モデルを提案する。このモデルは、海馬の垂直方向の結線を考慮し、CA1には直交パターンの復号化と関係連合の学習の2つの機能があり、海馬台には関係の復号化の機能があるとしている。このモデル化により、連想記憶の基本である1対多、多対多、多対1の連想や慨念の形成ができることを計算機シミュレーションによって示す。また、時系列の連想・連合機能があることを示す。

CiNii Article

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記述言語：日本語  

CiNii Article

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記述言語：日本語   出版者・発行元：一般社団法人情報処理学会  

人間の記憶は、次々と新しい事例を記憶し、それを失うことなく類似の事例をまとめて概念化していくことができる。そして、頻繁に利用される記憶は想起しやすくなるなどの優れた機能を持っている。また、人間の記憶には、嬉しかった事悲しかった事など、何らかの感情を伴った事例は記憶されやすいという特徴がある。本稿では、感情の記憶における働きに着目し、感情を記憶に対する制御信号と捉えた感情記憶システムを提案する。感情記憶システムでは、感情の活性化により記憶事例の獲得や記憶の概念化が実現でき、学習により頻繁にアクセスされる記憶は想起しやすくなるなど、人間の記憶機能をうまく再現できる。In this paper we propose a memory system which employs emotion as a control signal for memory. This Emotional Memory system can learn concepts without losing memory instances, and frequently accessed memories become easily associated.

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記述言語：日本語  

本稿では、従来のニューラルネットワークの結合の重みと各ノードが持つしきい値を複素数に拡張し、複素パターンに対する自然な学習を可能にするバックプロパゲーション学習アルゴリズム(以下、複素BPと呼ぶ)を提案する。その学習収束性については、甘利[1]による学習識別理論を複素数に拡張することによって保証される。さらに、従来のBP[2]には見られない図形変換能力があることを確認し、そのふるまいと複素解析における一致の定理との関係について述べる。

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記述言語：日本語  

本論文ではフィードバックリンクを持つ多層ニューラルネット(以下、FMネットと略)を提案する。これは相互結合型の血種であるが、相互接続が限定されており、バックプロパゲーション(BP)学習が使える他、意図的に安定点を作り易いという特長がある。以下では、先ずFMネットの構成を示し、次に典型的な利用形態と学習法を示す。

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総ページ数：xxi, 423p   記述言語：日本語

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