Abstract
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 unimodal
data distributions, we have derived a new error bound for perfect learning,
which can quantify the difficulty of learning. This case-specific bound is much
tighter than the uniform bounds in conventional learning theory.
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