Location specific perceptual learning can transfer to a new location if the new location is trained with a secondary task that by itself does not impact the performance of the primary learning task (double training). Learning may also transfer to other locations when double training is performed at the same location. Here we investigated the mechanisms underlying double-training enabled learning and transfer with an external noise paradigm. Specifically, we measured the Vernier thresholds at various external noise contrasts before and after double training. Double training mainly vertically downshifts the TvC functions at the training and transfer locations, which may be interpreted as improved sampling efficiency in a linear amplifier model or a combination of internal noise reduction and external noise exclusion in a perceptual template model at both locations. The change of the TvC functions appears to be a high-level process that can be remapped from a training location to a new location after double training.