Artificial neural networks (ANNs) have undergone a revolution, catalyzed by better supervised learning algorithms. However, in stark contrast to young animals (including humans), training such networks requires enormous numbers of labeled examples, leading to the belief that animals must rely instead mainly on unsupervised learning. Here we argue that most animal behavior is not the result of clever learning algorithms—supervised or unsupervised—but is encoded in the genome. Specifically, animals are born with highly structured brain connectivity, which enables them to learn very rapidly. Because the wiring diagram is far too complex to be specified explicitly in the genome, it must be compressed through a "genomic bottleneck". The genomic bottleneck suggests a path toward ANNs capable of rapid learning.