A circuit implementing a spiking neural network that includes a learning component that can learn from temporal correlations in the spikes regardless of correlations in the rates. In some embodiments, the learning component comprises a rate-discounting component. In some embodiments, the learning rule computes a rate-normalized covariance (normcov) matrix, detects clusters in this matrix, and sets the synaptic weights according to these clusters. In some embodiments, a synapse with a long-term plasticity rule has an efficacy that is composed by a weight and a fatiguing component. In some embodiments, A Hebbian plasticity component modifies the weight component and a short-term fatigue plasticity component modifies the fatiguing component. The fatigue component increases with increases in the presynaptic spike rate. In some embodiments, the fatigue component increases are implemented in a spike-based manner. In some embodiments, the Hebbian plasticity is a spike-timing-dependent plasticity (STDP), resulting in a fatiguing STDP (FSTDP) synapse.