Inferred mechanisms of learning, such as those involved in improvements resulting from perceptual training, are reliant on (and reflect) the functional forms that models of learning take. However, previous investigations of the functional forms of perceptual learning have been limited in ways that are incompatible with the known mechanisms of learning. For instance, previous work has overwhelmingly aggregated learning data across learning participants, learning trials, or both. Here we approach the study of the functional form of perceptual learning on the by-person and by-trial levels at which the mechanisms of learning are expected to act. Each participant completed one of two visual perceptual learning tasks over the course of two days, with the first 75% of task performance using a single reference stimulus (i.e., "training") and the last 25% using an orthogonal reference stimulus (to test generalization). Five learning functions, coming from either the exponential or the power family, were fit to each participant's data. The exponential family was uniformly supported by Bayesian Information Criteria (BIC) model comparisons. The simplest exponential function was the best fit to learning on a texture oddball detection task, while a Weibull (augmented exponential) function tended to be the best fit to learning on a dot-motion discrimination task. The support for the exponential family corroborated previous by-person investigations of the functional form of learning, while the novel evidence supporting the Weibull learning model has implications for both the analysis and the mechanistic bases of the learning.