We can now measure the connectivity of every neuron in a neural circuit, but we are still blind to other biological details, including the dynamical characteristics of each neuron. The degree to which connectivity measurements alone can inform understanding of neural computation is an open question. Here we show that with experimental measurements of only the connectivity of a biological neural network, we can predict the neural activity underlying a specified neural computation. We constructed a model neural network with the experimentally determined connectivity for 64 cell types in the motion pathways of the fruit fly optic lobe but with unknown parameters for the single-neuron and single-synapse properties. We then optimized the values of these unknown parameters using techniques from deep learning, to allow the model network to detect visual motion. Our mechanistic model makes detailed, experimentally testable, predictions for each neuron in the connectome. We found that model predictions agreed with experimental measurements of neural activity across 26 studies. Our work demonstrates a strategy for generating detailed hypotheses about the mechanisms of neural circuit function from connectivity measurements. We show that this strategy is more likely to be successful when neurons are sparsely connected—a universally observed feature of biological neural networks across species and brain regions.