1. A neural network circuit including a plurality of neural network circuit elements which are interconnected, wherein each of the plurality of neural network circuit elements includes: at least one synapse circuit which receives as an input a first input signal output from another neural network circuit element; and one neuron circuit which receives as an input a signal output from the at least one synapse circuit; wherein the synapse circuit includes a variable resistance element; wherein the variable resistance element includes a first terminal, a second terminal, and a third terminal; wherein a resistance value between the first terminal and the second terminal changes in response to an electric potential difference between the first terminal and the third terminal; wherein the neuron circuit includes a waveform generating circuit for generating an analog pulse voltage having a specified waveform, which is output to the synapse circuit of the neural network circuit element including the neuron circuit, and a switching pulse voltage which has a waveform with a specified duration and is input as the first input signal to the synapse circuit of the another neural network circuit element; wherein the synapse circuit is configured such that the analog pulse voltage generated in the neuron circuit of the neural network circuit element including the synapse circuit is input to the third terminal of the variable resistance element of the synapse circuit, for a permissible input period with the specified duration, as the first input signal from the another neural network circuit element; and wherein the synapse circuit is configured such that the resistance value of the variable resistance element is changed in response to an electric potential difference between the first terminal and the third terminal, which occurs depending on a magnitude of the analog pulse voltage for the permissible input period.