Expose the same neuron to the same input N times and you won't get a randomly distributed range of outputs, you'll get a signal that is either attenuated or pot

Expose the same neuron to the same input N times and you won't get a randomly distributed range of outputs, you'll get a signal that is either attenuated or potentiated. That's not noise, that's the simplest form of neuroplasticity at work (which is why static parameters can never represent ion channels).