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Consider a perceptron where $w_0=1$ and $w_1=1$: Perceptron Now, say we use an activation function

$f(x)=1,~for~x=1$

$~~~~~~~~~~~~~0, otherwise$

The output is then summarised as:

$x_0~~~~~x_1~~~~~w_0*x_0 + w_1*x1~~~~~f(.)$

$0~~~~~~~0~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~0$

$0~~~~~~~1~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~~~~~~~~~1$

$1~~~~~~~0~~~~~~~~~~~~~~1~~~~~~~~~~~~~~~~~~~~~~~~~~~~1$

$1~~~~~~~1~~~~~~~~~~~~~~2~~~~~~~~~~~~~~~~~~~~~~~~~~~~0$

Someone tell Rosenblatt I solved his problem ...

...or have I?

Is there something wrong with the way I've defined the activation function?

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1 Answer 1

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Your function

0,otherwise 1

is not a linear combination of the inputs.

From the definition of single layer perceptronL

A single layer perceptron (SLP) is a feed-forward network based on a threshold transfer function

Your function has two thresholds: one for < 1 another for >1

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