It has been suggested recently that the extent of learning in perceptual tasks can be predicted well from the initial performance according to a Weber-like law. However, the exact relationship between initial thresholds and the amount of learning and the link between learning and generalization still remained unclear. In three perceptual learning paradigms, we tested (1) how initial thresholds influence learning, (2) how the amount of learning influences generalization, and (3) how general these relationships are across different paradigms of perceptual learning. Using a 5-day training protocol in each paradigm, separate groups of observers were trained to discriminate around two different reference values: at 73 or 30% in contrast, at 45 or 15 degrees in orientation, and at 88 or 33 dots in magnitude discrimination task. In each paradigm, initial thresholds were significantly higher at the high reference (73% contrast, 45 degrees, and 88 dots) than those at the low reference (ps< 0.05). Within conditions in each paradigm, we found strong correlations between subjects' initial threshold and their percent improvement, (rs=0.63-0.82, ps< 0.01), but their relationship did not conform the proposed Weber-like law. In contrast, across conditions in each paradigm, both the average absolute improvement and the mean percent improvement confirmed the Weber-like relationship showing no difference in percent improvement between the conditions (Bayes Factors= 2-2.3). Finally, generalization of learning was proportional to the amount of learning (linear regression slopes= 0.74-0.92, r2s= 0.45-0.83). This pattern of result suggests that (1) individual variations in perceptual learning are not related to the learning process but to other factors such as motivation, (2) regardless of individual differences and testing paradigms, the amount of perceptual learning conditioned on visual attributes is proportional to the initial thresholds following a Weber-like law, and (3) generalization is linearly proportional to the amount of learning within the task.