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Extracting a connectome from an electron microscopy (EM) data set requires identification of neurons and determination of connections (synapses) between neurons. As manual extraction of this information is very time-consuming, there has been extensive research efforts to automatically segment the neurons to help guide and eventually replace manual tracing. Until recently, there has been comparatively little research on automatic detection of the actual synapses between neurons. This discrepancy can, in part, be attributed to several factors: obtaining neuronal shapes is a prerequisite for the first step in extracting a connectome, manual tracing is much more time-consuming than annotating synapses, and neuronal contact area can be used as a proxy for synapses in determining connections. However, recent research has demonstrated that contact area alone is not a sufficient predictor of a synaptic connection. Moreover, as segmentation improved, we observed that synapse annotation consumes a more significant fraction of overall reconstruction time (upwards of 50% of total effort). This ratio will only get worse as segmentation improves, gating the overall possible speed-up. Therefore, we address this problem by developing algorithms that automatically detect presynaptic neurons and their postsynaptic partners. In particular, presynaptic structures are detected using a U-Net convolutional neural network (CNN), and postsynaptic partners are detected using a multilayer perceptron (MLP) with features conditioned on the local segmentation. This work is novel because it requires minimal amount of training, leverages advances in image segmentation directly, and provides a complete solution for polyadic synapse detection. We further introduce novel metrics to evaluate our algorithm on connectomes of meaningful size. When applied to the output of our method on EM data from Drosphila, these metrics demonstrate that a completely automatic prediction can be used to effectively characterize most of the connectivity correctly.