Given basic elements of a neuron(as below) with a bias value:

[![neuron structure][1]][1]

 [1]: https://i.sstatic.net/KPDLCRyG.png

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I learnt that, a bias value allows you to shift the activation function(say **sigmoid function**) to the left or right, which may be **critical for successful learning**. Yet to understand, why?


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Mathematically, when we change an argument of a function(say sigmoid function in this case) by adding or subtracting a constant, then the output values shift to left or right accordingly, as shown below:


[![sigmoid function][2]][2]

[2]: https://i.sstatic.net/wcaUpgY8.png

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My understanding is that, binary classification problems(example - image recognition), use neural network based AI solutions. This is the reason, a neuron runs an activation function like sigmoid function that takes a summation of all inputs(with weights) and provide a output value within interval [0,1]

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**Question:**

1)
 Given any argument(input) to a function(sigmoid), how shifting of output values(left or right) using bias **critical to** successful learning(training) in artificial neural network?

2) 
 Mathematically, a function must have one domain and one range. For successful learning, why sigmoid function(single variable function) **use linear combiner**(Σ) for all the inputs(synapsesXparameters)? Because summation of synapsesXparameters may not provide uniqueness, if parameters(weights) have negative value