A New Perspective on Machine Learning: How to do Perfect Supervised Learning

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 model that is properly bandlimited. Moreover, for some special cases, we have derived new error bounds for perfect learning, which can quantify the difficulty of learning. These case-specific bounds are much tighter than the uniform bounds in conventional learning theory. Our results have provided a new perspective to explain the recent successes of large-scale supervised learning using complex models like neural networks.