The neocortex is composed of spiking neurons interconnected in a sparse, recurrent network. Spiking within neocortical networks drives the computational processes that convert sensory inputs into suitable behavioral responses. In this study, we train biologically realistic recurrent spiking neural network (SNN) models and identify the architectural changes following training which enable task-appropriate computations. Specifically, we employ a binary state change detection task, where each state is defined by motion entropy. This task mirrors behavioral paradigms that are performed in the lab. SNNs are composed of interconnected excitatory and inhibitory units with connection likelihoods and strengths matched to mouse neocortex. Following training, we discover that SNNs selectively adjust firing rates depending on motion entropy state, and that excitatory and inhibitory connectivity between input and recurrent layers change in accordance with this rate modulation. Recurrent inhibitory units which positively modulate firing rates to one input strengthened their connections to recurrent units of the opposite modulation. This specific pattern of cross-modulation inhibition emerged as the solution regardless of the output encoding schemes when imposing Dale’s law throughout training of the SNNs. Disrupting spike times and recurrent excitatory connectivity significantly impaired performance, indicating that precise spike coordination and recurrent excitation are critical for the network's behavior. Using a one-hot output encoding resulted in balanced spike rates in response to the two different motion entropy states. With this balance, the same cross-modulation inhibition solution emerged. This work underscores the crucial role of interneurons and specific inhibitory architectural patterns in shaping dynamics and enabling information processing within neocortical circuits.