People use rich prior knowledge about the world in order to efficiently learn new concepts. These priors-also known as “inductive biases”-pertain to the space of internal models considered by a learner, and they help the learner make inferences that go beyond the observed data. A recent study found that deep neural networks optimized for object recognition develop the shape bias (Ritter et al., 2017), an inductive bias possessed by children that plays an important role in early word learning. However, these networks use unrealistically large quantities of training data, and the conditions required for these biases to develop are not well understood. Moreover, it is unclear how the learning dynamics of these networks relate to developmental processes in childhood. We investigate the development and influence of the shape bias in neural networks using controlled datasets of abstract patterns and synthetic images, allowing us to systematically vary the quantity and form of the experience provided to the learning algorithms. We find that simple neural networks develop a shape bias after seeing as few as 3 examples of 4 object categories. The development of these biases predicts the onset of vocabulary acceleration in our networks, consistent with the developmental process in children.