1. A spike timing dependent plasticity (STDP) apparatus comprising: a first input transconductance amplifier to receive and amplify a first spike signal; a first leaky integrator connected to an output of the first input transconductance amplifier to receive and integrate the amplified first spike signal, an output of the first leaky integrator being gated to produce a first gated integrated signal; a second input transconductance amplifier to receive and amplify a second spike signal; a second leaky integrator connected to an output of the second input transconductance amplifier to receive and integrate the amplified second spike signal, an output of the second leaky integrator being gated to produce a second gated integrated signal; and an output integrator to integrate a difference of the first gated integrated signal and the second gated integrated signal to produce a weighted signal at an output of the STDP apparatus, wherein the first leaky integrator output is gated according to the second spike signal and the second leaky integrator output is gated according to the first spike signal, and wherein one or more of the first leaky integrator, the second leaky integrator and the output integrator is implemented using a physical circuit.