Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

Xu, Zong Ben; Qiao, Chen

doi:10.1007/s10114-011-0598-2

Cited by 7 publications

(14 citation statements)

References 43 publications

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“…Thus, the UPPAM RNNs are called as the unified RNNs. Further, it is guessed that only the study of the dynamics of the UPPAM RNNs may achieve the outcome that we can discriminate the similarity and redundant of the dynamics results among those known RNNs individuals, and which is affirmed following in [22,23] for discrete-time RNNs as well as for continuous-time RNNs, respectively.…”

Section: Introductionmentioning

confidence: 98%

“…In [22], it is shown that most of the common nonlinear activation operators have the uniformly antimonotonous properties, such as the nearest point projection operator, the linear saturating operator, the signum operator, and the pseudoprojection operator.…”

Section: Basic Definitionmentioning

confidence: 99%

“…Definition 1 (see [22]). The nonlinear activation operator : R → R is said to be an -uniformly antimonotonous operator if there is a constant positive number such that…”

Section: Basic Definitionmentioning

confidence: 99%

“…Definition 2 (see [22]). An operator is said to be a pseudoprojection if there exists a positive define diagonal matrix = diag{ 1 , 2 , .…”

Section: Basic Definitionmentioning

confidence: 99%

“…On the other hand, in order to discover some more indepth characters other than the bound and monotonically nondecreasing properties of the common used activation operators, [22] provides two novel concepts: the uniformly pseudoprojection antimonotone (UPPAM) operator and the UPPAM RNNs. The UPPAM operator can formalize most of the activation operators, and the UPPAM RNNs can be the representation of most of the RNNs individuals too.…”

Section: Introductionmentioning

confidence: 99%

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Without Diagonal Nonlinear Requirements: The More GeneralP-Critical Dynamical Analysis for UPPAM Recurrent Neural Networks

Chen

Mao

Qiao

2013

Mathematical Problems in Engineering

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Continuous-time recurrent neural networks (RNNs) play an important part in practical applications. Recently, due to the ability of assuring the convergence of the equilibriums on the boundary line between stable and unstable, the study on the critical dynamics behaviors of RNNs has drawn especial attentions. In this paper, a new asymptotical stable theorem and two corollaries are presented for the unified RNNs, that is, the UPPAM RNNs. The analysis results given in this paper are under the generally -critical conditions, which improve substantially upon the existing relevant critical convergence and stability results, and most important, the compulsory requirement of diagonally nonlinear activation mapping in most recent researches is removed. As a result, the theory in this paper can be applied more generally.

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Section: Introductionmentioning

confidence: 98%

Section: Basic Definitionmentioning

confidence: 99%

“…Definition 1 (see [22]). The nonlinear activation operator : R → R is said to be an -uniformly antimonotonous operator if there is a constant positive number such that…”

Section: Basic Definitionmentioning

confidence: 99%

“…Definition 2 (see [22]). An operator is said to be a pseudoprojection if there exists a positive define diagonal matrix = diag{ 1 , 2 , .…”

Section: Basic Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations