how to understand sigmoid(x+y)- sigmoid(x-y)
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As shown in the following graph, why does function sigmoid(x+y)- sigmoid(x-y) has smooth instead of sharp edges around (0,1) in the contour plot? Could you please explain it both intuitive and mathematically?
analysis intuition
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
$endgroup$
add a comment |
$begingroup$
As shown in the following graph, why does function sigmoid(x+y)- sigmoid(x-y) has smooth instead of sharp edges around (0,1) in the contour plot? Could you please explain it both intuitive and mathematically?
analysis intuition
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
$endgroup$
add a comment |
$begingroup$
As shown in the following graph, why does function sigmoid(x+y)- sigmoid(x-y) has smooth instead of sharp edges around (0,1) in the contour plot? Could you please explain it both intuitive and mathematically?
analysis intuition
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
$endgroup$
As shown in the following graph, why does function sigmoid(x+y)- sigmoid(x-y) has smooth instead of sharp edges around (0,1) in the contour plot? Could you please explain it both intuitive and mathematically?
analysis intuition
analysis intuition
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
edited Dec 24 '18 at 15:18
Shaun
10.3k113686
10.3k113686
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
asked Dec 24 '18 at 14:33
user7586189user7586189
1294
1294
add a comment |
add a comment |
1 Answer
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I think you confused sigmoid function with signum function. Sigmoid function is a function continuous everywhere. There are many possible sigmoid functions. One example is ${e^xover e^x+1}$.
https://en.m.wikipedia.org/wiki/Sigmoid_function
So unsurprisingly, the plot is continuous, and smooth, since being continuous is implied by differentiability, which is a common characteristic of smooth functions.
A signum plot on the other hand, would be discontinuous and "sharp" like you predicted:
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
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active
oldest
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active
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$begingroup$
I think you confused sigmoid function with signum function. Sigmoid function is a function continuous everywhere. There are many possible sigmoid functions. One example is ${e^xover e^x+1}$.
https://en.m.wikipedia.org/wiki/Sigmoid_function
So unsurprisingly, the plot is continuous, and smooth, since being continuous is implied by differentiability, which is a common characteristic of smooth functions.
A signum plot on the other hand, would be discontinuous and "sharp" like you predicted:
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
$endgroup$
add a comment |
$begingroup$
I think you confused sigmoid function with signum function. Sigmoid function is a function continuous everywhere. There are many possible sigmoid functions. One example is ${e^xover e^x+1}$.
https://en.m.wikipedia.org/wiki/Sigmoid_function
So unsurprisingly, the plot is continuous, and smooth, since being continuous is implied by differentiability, which is a common characteristic of smooth functions.
A signum plot on the other hand, would be discontinuous and "sharp" like you predicted:
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
$endgroup$
add a comment |
$begingroup$
I think you confused sigmoid function with signum function. Sigmoid function is a function continuous everywhere. There are many possible sigmoid functions. One example is ${e^xover e^x+1}$.
https://en.m.wikipedia.org/wiki/Sigmoid_function
So unsurprisingly, the plot is continuous, and smooth, since being continuous is implied by differentiability, which is a common characteristic of smooth functions.
A signum plot on the other hand, would be discontinuous and "sharp" like you predicted:
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
$endgroup$
I think you confused sigmoid function with signum function. Sigmoid function is a function continuous everywhere. There are many possible sigmoid functions. One example is ${e^xover e^x+1}$.
https://en.m.wikipedia.org/wiki/Sigmoid_function
So unsurprisingly, the plot is continuous, and smooth, since being continuous is implied by differentiability, which is a common characteristic of smooth functions.
A signum plot on the other hand, would be discontinuous and "sharp" like you predicted:
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
edited Dec 24 '18 at 15:28
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
answered Dec 24 '18 at 15:23
KKZiomekKKZiomek
2,2441641
2,2441641
add a comment |
add a comment |
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