Three Value

The Three Value rule extends the behavior of a binary neuron by allowing three distinct activation states. A neuron’s activation is determined by comparing its input (plus a fixed bias) to two thresholds:

\[x = \text{input} + \text{bias}\]

The neuron’s output is then:

\[a = \begin{cases} \text{Lower Value}, & x < \text{Lower Threshold} \\ \text{Upper Value}, & x > \text{Upper Threshold} \\ \text{Middle Value}, & \text{otherwise} \end{cases}\]

This rule allows for a ternary decision model useful in systems requiring an explicit “neutral” or “no response” state between excitatory and inhibitory thresholds.

Parameters

• Bias: A constant value added to the input before threshold comparisons.
• Lower Threshold: If the input plus bias is less than this value, the activation is set to the lower value.
• Upper Threshold: If the input plus bias is greater than this value, the activation is set to the upper value.
• Lower Value: The activation value when input is below the lower threshold.
• Middle Value: The activation value when input falls between the two thresholds.
• Upper Value: The activation value when input exceeds the upper threshold.

For all other parameters, see common neuron properties