How are sensory representations learned via experience? Deep learning offers a theoretical toolkit for studying how neural codes emerge under different learning rules. Studies suggesting that representations in deep networks resemble those in biological brains have mostly relied on one specific learning rule: gradient descent, the workhorse behind modern deep learning. However, it remains unclear how robust these emergent representations in deep networks are to this specific choice of learning algorithm. Here we present a continuous two-dimensional space of candidate learning rules, parameterized by levels of top-down feedback and Hebbian learning. We show that this space contains five important candidate learning algorithms as specific points--Gradient Descent, Contrastive Hebbian, quasi-Predictive Coding, Hebbian & Anti-Hebbian. Next, we exhaustively characterize the properties of each rule during learning about hierarchically structured data, and identify zones within this space where deep networks exhibit qualitative signatures of biological learning. We find that while a large set of algorithms achieve zero training error at convergence, only a subset show hallmarks of human semantic development like progressive differentiation and illusory correlations. Further, only a subset adjust intermediate neural representations toward task-relevant representations, indicative of backpropagation-like behavior. Finally, we show that algorithms can dramatically differ in their learned neural representations and dynamics, providing experimentally testable hallmarks of different learning principles. Our findings provide a framework linking diverse neural representational geometries to learning principles which can guide future experiments, and offer evidence about the learning rules likely to be at work in biology.