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Local Lyapunov exponents of deep echo state networks

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Academic year: 2021

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(a) 0.5 1 1.5 Spectral Radius ( ) 10 5 1 -0.8 -0.6 -0.4 -0.2 0 (b) 1 0.5 0.1

Leaking Rate (a) 10 5 1 -0.2 -0.15 -0.1 -0.05 (c) 1 0.5 0.1

Input Scaling (scalein) 10 5 1 -0.15 -0.1 -0.05 (d) 1 0.5 0.1

Inter-layer Scaling (scaleil) 10 5 1 -0.15 -0.1 -0.05 0

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0.5

0.7

0.9

1.1

1.3

1.5

Spectral Radius ( )

-0.8

-0.6

-0.4

-0.2

0

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20 layers deepESN

10 layers deepESN

5 layers deepESN

shallow ESN

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Number of Recurrent Units

-0.3

-0.25

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-0.15

-0.1

-0.05

0

deepESN

groupedESN

shallow ESN

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-0.8

-0.6

-0.4

-0.2

0

0.2

max

0

10

20

30

40

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(a)

0.5

1

1.5

Spectral Radius ( )

100

50

10

10 15 20 25 30

(b)

0.5

1

1.5

Spectral Radius ( )

100

50

10

10 15 20 25 30

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(a) 0.5 1 1.5 Spectral Radius ( ) 10 5 1 -0.8 -0.6 -0.4 -0.2 0 (b) 1 0.5 0.1

Leaking Rate (a)

10 5 1 -0.15 -0.1 -0.05 (c) 1 0.5 0.1

Input Scaling (scalein)

10 5 1 -0.15 -0.1 -0.05 (d) 1 0.5 0.1

Inter-layer Scaling (scaleil)

10 5 1 -0.15 -0.1 -0.05 0

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(a) 0.5 1 1.5 Spectral Radius ( ) 10 5 1 -0.8 -0.6 -0.4 -0.2 0 (b) 1 0.5 0.1

Leaking Rate (a)

10 5 1 -0.15 -0.1 -0.05 (c) 1 0.5 0.1

Input Scaling (scalein)

10 5 1 -0.15 -0.1 -0.05 (d) 1 0.5 0.1

Inter-layer Scaling (scaleil)

10 5 1 -0.15 -0.1 -0.05 0

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