An Approach for the Realization of Threshold Functions of Order r

Hwa, H. R.; Sheng, C. L.

doi:10.1109/t-c.1969.222548

Cited by 11 publications

(8 citation statements)

References 20 publications

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“…Therefore, there is only one true vector for the n-variable function f 1 expressed in Eq. (5). Given that a pair of true vectors does not exist in regard to f 1 , f 1 is a threshold function, from Theorem 1.…”

Section: Extending the Order Of High-order Threshold Functionsmentioning

confidence: 99%

“…Because the conditions attached to functions contribute to network optimization, there have also been studies focusing on the characteristics of threshold functions [3], [4]. However, because functions realizable by single-threshold functions are restricted to the linearly separable class, studies are being carried out on high-order threshold functions in which terms that consist of the product of input variables are being attached to the threshold function [5]- [8]. This approach allows arbitrary logical functions to be realized.…”

Section: Introductionmentioning

confidence: 99%

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Generating High-Order Threshold Functions with Multiple Thresholds

Kamada,

Miyasaki

2013

Preprint

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In this paper, we consider situations in which a given logical function is realized by a multithreshold threshold function. In such situations, constant functions can be easily obtained from multithreshold threshold functions, and therefore, we can show that it becomes possible to optimize a class of high-order neural networks. We begin by proposing a generating method for threshold functions in which we use a vector that determines the boundary between the linearly separable function and the high-order threshold function. By applying this method to high-order threshold functions, we show that functions with the same weight as, but a different threshold than, a threshold function generated by the generation process can be easily obtained. We also show that the order of the entire network can be extended while maintaining the structure of given functions.

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Section: Extending the Order Of High-order Threshold Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating High-Order Threshold Functions with Multiple Thresholds

Kamada,

Miyasaki

2013

Preprint

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show abstract

“…Rich and initially unexpected phenomenology has emerged in the "intermediate p T " region (p T ∼ 2 − 5 GeV/c) of nuclear collisions at RHIC. The enhancement of baryon relative to meson yields [ 18,19], the approximate scaling of elliptic flow v 2 with the number of constituent quarks [ 20], and correlation measurements in this region [ 21] suggest an interplay between hadronization of hard partons and the bulk medium, as discussed extensively elsewhere at the conference [ 20,22]. Here we will concentrate on the region p T ∼ > 6 GeV, i.e.…”

Section: Rhic: Inclusive Yieldsmentioning

confidence: 99%

High pT in Nuclear Collisions at the SPS, RHIC, and LHC

Jacobs

Leeuwen

2006

Nuclear Physics A

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“…Another point to note is that the threshold function cannot realize an arbitrary logic function. From that viewpoint, the high-order threshold function, extending the conventional threshold function so that any logic function can be realized, has been proposed [4].…”

Section: Introductionmentioning

confidence: 99%

“…As regards the structure of the high-order threshold function, there is a study which discusses the relation between monotonicity and the high-order terms from the viewpoint of linearity [5]. However, there is still insufficient theoretical study of the structural analysis of high-order threshold functions [4].…”

Section: Introductionmentioning

confidence: 99%

Generation of threshold functions of high‐order satisfying monotonicities

Kamada¹,

Miyasaki²

2007

Systems & Computers in Japan

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SUMMARYThis paper presents a generation procedure for highorder threshold functions, considering the high-order neighbor vector and the monotonic property. Specifically, it is first shown that the high-order neighbor vector can be derived from an input vector which is noncomparable by the high-order threshold function. Then, it is shown that a monotonic function of a high-order variable can easily be generated from the given monotonic function. Based on the generation process for the monotonic function, the generation procedure for high-order threshold functions is derived. It is also shown that if a given high-order threshold function preserves monotonicity, the generated high-order threshold function also preserves monotonicity, and also the high-order terms.

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An Approach for the Realization of Threshold Functions of Order r

Cited by 11 publications

References 20 publications

Generating High-Order Threshold Functions with Multiple Thresholds

Generating High-Order Threshold Functions with Multiple Thresholds

High pT in Nuclear Collisions at the SPS, RHIC, and LHC

Generation of threshold functions of high‐order satisfying monotonicities

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