Atypical forgetting functions have been demonstrated in several recent studies of delayed matching to sample, in which experimental conditions are altered partway through the retention interval. The forgetting functions are atypical in that accuracy or discriminability is not always a negatively accelerated monotonic function of increasing retention interval duration, but may increase at later times in the retention interval. Atypical forgetting functions reflect changes in levels of discrimination. A switch from a lower level to a higher level of discrimination, or vice versa, can occur at any time in the retention interval. The behavioral theories of remembering proposed by Nevin, Davison, Odum, and Shahan (2007), and White and Brown (2014), offer quantitative predictions of forgetting functions that differ in intercept or slope. Both theories are able to account for atypical forgetting functions, by assuming time-independent changes in the mediating effect of attending to sample and comparison stimuli (in Nevin et al.'s model) or in the direct effect of the context of reinforcement of the conditional discrimination (in White & Brown's model). Despite differences in their main assumptions, the theories have an edge over any theory that assumes that forgetting is time-dependent.