How does a neuron’s threshold affect whether it fires in a neural-net model?

In automata theory, a neuron’s threshold acts as a critical gate for its activation, reflecting the "all or none" nature of neural signaling.1

In a neural network model, a neuron $N$ with a threshold $h$ functions based on the inputs it receives from connected neurons:

• Firing Condition: A neuron will fire an impulse if the total excitation it receives meets or exceeds its threshold $h$ at a given time. In models using weighted connections, this means the sum of the weights of all firing input neurons must be greater than or equal to the threshold.12
• Quiescent State: If the total stimulus is absent, inadequate, or inhibited by other neurons, the threshold is not reached, and the neuron remains quiescent (does not fire).12

Specifically, in the model established by Warren S. McCulloch and Walter Pitts, a neuron is excited only if the number of excitatory inputs meets the threshold and no inhibitory inputs are active. This mechanism allows neural nets to perform logical operations and process information in quantized, pulsed steps.1