The logistic function (the function on the bottom right) is used rather than say a step function for binary classification because it is differentiable, which is important in many machine learning calculations.
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We can see the biological inspiration of a neural network, in that each unit behaves similarly to a neuron. The neuron gets inputs as electrical signals along the dendrites, and the axion will fire based on the combination of input signals, which is what the unit is doing with its variable inputs.
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Function $f$ is one of the most important parts of a neural network, as it provides non-linearity (otherwise the DNN is simply a series of linear transformations).
The logistic function (the function on the bottom right) is used rather than say a step function for binary classification because it is differentiable, which is important in many machine learning calculations.
We can see the biological inspiration of a neural network, in that each unit behaves similarly to a neuron. The neuron gets inputs as electrical signals along the dendrites, and the axion will fire based on the combination of input signals, which is what the unit is doing with its variable inputs.
Function $f$ is one of the most important parts of a neural network, as it provides non-linearity (otherwise the DNN is simply a series of linear transformations).