Statistical factorization in motor control: Opposing biases from statistics on different timescales enable fast and accurate behavior

Motor planning is fundamentally constrained by the speed-accuracy tradeoff: a single optimization that balances time and error costs, such that longer preparation yields more accurate movements while faster ones incur greater error. Here we propose that the motor system exploits environmental statistics to reshape this relationship, using two complementary computations that rely on distinct statistical information. The first leverages the marginal statistics of the target distribution, learned by integrating slowly over many trials, to modify the initial preparation state, accelerating planning for frequently encountered targets; this simultaneously speeds decisions and reduces planning variability, but introduces an attractive bias toward the mean of the target distribution. Strikingly, a second process tracks the sequential statistics of the environment over only the last few trials, producing a repulsive sequential bias whose persistence is tuned to the temporal autocorrelation and selectively counteracting the attractive bias introduced by the first. These results reveal that the motor system applies statistical factorization, estimating marginal and sequential statistics on their own timescales to shape movement preparation, thereby escaping the speed-accuracy tradeoff and producing movements that are both faster and more accurate.