A neuromorphic memory circuit including a memory cell with a programmable resistive memory element. A postsynaptic capacitor builds up a leaky integrate and fire (LIF) charge. An axon LIF pulse generator activates a LIF discharge path from the postsynaptic capacitor through the resistive memory element when the axon LIF pulse generator generates axon LIF pulses. A postsynaptic comparator compares the capacitor voltage to a threshold voltage and generates postsynaptic output pulses when the capacitor voltage passes the threshold voltage. The postsynaptic output pulses include a postsynaptic firing characteristic dependent on a frequency of the axon LIF pulses. A refractory circuit prevents the postsynaptic comparator from generating additional postsynaptic output pulses until a refractory time passes since a preceding postsynaptic output pulse. A training circuit adjusts the postsynaptic firing characteristic to match a target firing characteristic.