Identifying and characterizing the wiring rules of neural circuits is critical for our understanding of the computations that they perform and how they learn. The reconstruction of complete connectivity maps of neural networks at the single cell resolution make the quantitative study of their design principles possible. We examined the detailed connectivity of a column of the mouse visual cortex with a generative model that predicts connectivity based on explicit biological and physical features: excitatory or inhibitory cell type, the distance between cell bodies, and cell's depth, which is correlated with neuronal birth times and cortical layers. This model was relatively accurate in predicting individual synapses, but failed to reproduce the observed degree distributions and connectivity patterns between layers. While adding features or cell types would potentially improve the model, it is not clear that neural circuits are wired according to features we can name or immediately identify or measure. Indeed, a model that used 10 cell types did not perform significantly better. We, therefore, explored a representation learning approach, simultaneously learning an abstract representation of neurons ("embedding") and a simple Artificial Neural Network (ANN) that predicts the connection probability of neurons given their embedding ("connector"). Surprisingly, a single layer feed-forward connector with embedding in a handful of dimensions is highly accurate in predicting individual synapses, in-degree and out-degree distributions, inter-layer connectivity, and small network motifs. We further find that the learned embedding corresponds to cortical layers and cell types. Our results suggest a framework for learning minimal generative models for connectomes. Importantly, the simplicity of our embedding and connector suggests a way to infer the features and wiring rules that govern the structure of neural circuits - offering computational bounds on the wiring design, and directions for deciphering the genetic and physical processes that implement them.