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Learning entails preserving the features of the external world in the neuronal representations of the brain, and manifests itself in the form of strengthened interactions between neurons within assemblies. Hebbian synaptic plasticity is thought to be one mechanism by which correlations in spiking promote assembly formation during learning. While spike timing dependent plasticity (STDP) rules for excitatory synapses have been well characterized, inhibitory STDP rules remain incomplete, particularly with respect to sub-classes of inhibitory interneurons. Here, we report that in layer 2/3 of the orbitofrontal cortex of mice, inhibition from parvalbumin (PV) interneurons onto excitatory (E) neurons follows a symmetric STDP function and mediates homeostasis in E-neuron firing rates. However, inhibition from somatostatin (SOM) interneurons follows an asymmetric, Hebbian STDP rule. We incorporate these findings in both large scale simulations and mean-field models to investigate how these differences in plasticity impact network dynamics and assembly formation. We find that plasticity of SOM inhibition builds lateral inhibitory connections and increases competition between assemblies. This is reflected in amplified correlations between neurons within assembly and anti-correlations between assemblies. An additional finding is that the emergence of tuned PV inhibition depends on the interaction between SOM and PV STDP rules. Altogether, we show that incorporation of differential inhibitory STDP rules promotes assembly formation through competition, while enhanced inhibition both within and between assemblies protects new representations from …