Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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FEEDFORWARD NEURAL NETWORKS AND SEPARATION OF GEOMETRIC REGIONS

  • 투고 : 2019.02.12
  • 심사 : 2019.03.26
  • 발행 : 2019.05.30
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초록

We investigate how a feedforward neural network works to separate a geometric region from its complement. Our investigations are restricted to regions in ${\mathbb{R}}$ or ${\mathbb{R}}^2$ including an interval, a triangular region, a disk and the union of two disjoint disks. We also examine what happens at each layer of the network.

키워드

E1MCA9_2019_v37n3_4_271_f0001.png 이미지

FIGURE 1. The outputs of a network which separates [-1, 1]

E1MCA9_2019_v37n3_4_271_f0002.png 이미지

FIGURE 2. Inputs and First outputs of a network which separates the first quadrant

E1MCA9_2019_v37n3_4_271_f0003.png 이미지

FIGURE 3. Separation of a triangular region and a circular region

E1MCA9_2019_v37n3_4_271_f0004.png 이미지

FIGURE 4. Parametrization of networks

E1MCA9_2019_v37n3_4_271_f0005.png 이미지

FIGURE 5. Separation of the union of two disjoint disks solid line: the level curve of $y^{(2)}_{3}$ at level 0.5 dashed line: four lines F(1)(x) = 0

참고문헌

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