How can several weak signals combine to activate a neuron in a neural net?

In automata theory, a neuron functions based on a threshold mechanism, where it remains quiescent unless it receives sufficient excitation to fire an impulse. When individual incoming signals are too weak to trigger this response on their own, they can combine to activate the neuron through a process of summation.1

In this mathematical model, a neuron $N$ with a defined threshold $h$ will fire if the total excitation received from connected neurons meets or exceeds that threshold at a given time. Specifically:1

• Summation: Multiple incoming impulses, each individually inadequate to excite the neuron, can combine to provide the necessary threshold stimulus.1
• Weighted Inputs: In many artificial neural network models, each connection has an associated "weight" representing its relative importance. The total weighted input is calculated by summing the weights of all active (firing) connections. If this total sum equals or exceeds the neuron's threshold, the neuron fires.23
• Inhibition: This process is conditional; the neuron will not fire if an inhibitory signal is simultaneously received, regardless of the total excitatory input.1