Cortical information processing requires synergistic integration of input. Understanding the determinants of synergistic integration-a form of computation-in cortical circuits is therefore a critical step in understanding the functional principles underlying cortical information processing. We established previously that synergistic integration varies directly with the strength of feedforward connectivity. What relationship recurrent and feedback connectivity have with synergistic integration remains unknown. To address this, we analyzed the spiking activity of hundreds of well-isolated neurons in organotypic cultures of mouse somatosensory cortex, recorded using a high-density 512-channel microelectrode array. We asked how empirically observed synergistic integration, quantified through partial information decomposition, varied with local functional network structure. Toward that end, local functional network structure was categorized into motifs with varying recurrent and feedback connectivity. We found that synergistic integration was elevated in motifs with greater recurrent connectivity and was decreased in motifs with greater feedback connectivity. These results indicate that the directionality of local connectivity, beyond feedforward connections, has distinct influences on neural computation. Specifically, more upstream recurrence predicts greater downstream computation, but more feedback predicts lesser computation.