1.3 A single neuron with one input
How does a single neuron with one input calculate its output?
Artificial neurons receive an input, process it, and generate an output (see the IPO model described in the introduction). They usually output a decimal number between 0 and 1. This output is calculated by multiplying the input values by their corresponding weights, adding them up, and then subtracting the threshold (bias). The neuron’s output therefore depends on the following factors: the input, the weights, and the threshold.
In this interactive figure, you can observe the influence these three factors have on the output of the neuron. The slider can be used to set the input x to values between 0 and 1. The weight and the threshold value can be changed using the plus and minus signs. Each change to one of these three factors results in a change to the neuron’s output, which is displayed graphically. In the lower part of the figure, black vertical lines indicate which values the neuron can output with the currently set values at all. This part of the figure contains the actual mathematical sigmoid function with which the neuron's output is calculated.
The intention here is to just give you a rough idea of how artificial neurons work, but it is also possible to recalculate all steps in detail: The activation of the neuron is x⋅w. The further the activation is below the threshold, the less the neuron fires. The further the activation is above the threshold, the more the neuron fires. To recalculate exactly how the neuron calculates its output, you can also simply enter the result of the subtraction (activation minus threshold) as input value x in the calculation input field at the bottom of the page and click on Calculate.
Instructions
- Drag the slider back and forth to move the input x to values between 0 and 1.
- Click on the minus or plus signs to change the values for the weight w or the threshold value b.
- The neuron’s output o is calculated at all times.
- In the figure, blue stands for negative values and red stands for positive values.
Tasks
- Adjust the neuron’s threshold value in such a way that the neuron only outputs values close to 0 for each input x, i.e. hardly fires at all.
- Adjust the neuron’s threshold value in such a way that the neuron only outputs values close to 1 for each input x, i.e. fires almost continuously.
- Adjust the neuron’s weight and threshold value in such a way that the neuron fires for small x-values (input slider on the left), but no longer fires for large x-values (input slider on the right).
Calculate activation function:
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