Neuronal tuning changes over time, even in the absence of obvious signs of learning or changes in behaviour. This representational drift causes fixed readouts from a neural population to gradually deteriorate, suggesting that downstream populations adapt to these tuning changes. Many statistical distributions of tuning curve changes can produce comparable population-wide drift. We argue that heavy-tailed drift statistics, in which populations exhibit sparse and sudden changes in neuronal tuning, are relatively easy to adapt to. We present preliminary evidence that neural populations favour such distributions from existing in-vivo measurements of representational drift. Neural populations have no access to a ground truth. Instead, cortical populations must build up a representation of the external world through statistical regularities in upstream activity. We present an adaptive decoder capable of producing a drift-invariant readout over many days that relies exclusively on exploiting those statistical regularities, without recourse to an error signal or ground truth. We use this decoder as a model for a neural population that compensates for non-stationary tuning curve changes in an upstream population. We show that, in simulation of such models, drift processes with different underlying statistics (Fig. a) at the level of individual neurons are not equally easy to compensate for, even if they have identical drift rates at the level of entire populations (Fig. b). When drift is mediated by a few individual neurons making sudden jumps in tuning, rather than many neurons simultaneously making gradual incremental changes, it becomes easier to distinguish tuning adjustments from statistical fluctuations (Fig. c). The heavy tail of sudden drift distributions is an advantage (Fig. d, e). We present analyses of two existing in-vivo datasets exhibiting representational drift (Driscoll et al. 2017 and Marks & Goard 2021). We examine the distributions of the magnitudes of tuning changes and find the statistics of individual neurons reminiscent of a Lévy flight. Population-wide representations change gradually, but individual neurons undergo both jumps in tuning and incremental adjustments (Fig. f, g). We speculate that, as in our simulated model, the heavy tail of such drift processes facilitates the implementation of stable readouts in downstream brain regions.