  In this work, we introduce the concept of bandlimiting into the theory of
machine learning because all physical processes are bandlimited by nature,
including real-world machine learning tasks. After the bandlimiting constraint
is taken into account, our theoretical analysis has shown that all practical
machine learning tasks are asymptotically solvable in a perfect sense.
Furthermore, the key towards this solvability almost solely relies on two
factors: i) a sufficiently large amount of training samples beyond a threshold
determined by a difficulty measurement of the underlying task; ii) a
sufficiently complex and bandlimited model. Moreover, for some special cases,
we have derived new error bounds for perfect learning, which can quantify the
difficulty of learning. These generalization bounds are not only asymptotically
convergent but also irrelevant to model complexity. Our new results on
generalization have provided a new perspective to explain the recent successes
of large-scale supervised learning using complex models like neural networks.
