Our ability to compare sensory stimuli is a fundamental cognitive function, which is known to be affected by two biases: choice bias, which reflects a preference for a given response, and contraction bias, which reflects a tendency to perceive stimuli as similar to previous ones. To test whether both reflect supervised processes, we designed feedback protocols aimed to modify them and tested them in human participants. Choice bias was readily modifiable. However, contraction bias was not. To compare these results to those predicted from an optimal supervised process, we studied a noise-matched optimal linear discriminator (Perceptron). In this model, both biases were substantially modified, indicating that the “resilience” of contraction bias to feedback does not maximize performance. These results suggest that perceptual discrimination is a hierarchical, two-stage process. In the first, stimulus statistics are learned and integrated with representations in an unsupervised process that is impenetrable to external feedback. In the second, a binary judgment, learned in a supervised way, is applied to the combined percept.