# Winnow versus Perceptron - Why adding irrelevant features increases L2(X) but not L∞(X)?

Intuitively, if “n” is large but most features are irrelevant (i.e. target is sparse but examples are dense), then Winnow is better because adding irrelevant features increases L2(X) but not L∞(X). On the other hand, if the target is dense and examples are sparse, then Perceptron is better.

Why adding irrelevant features increases L2(X) but not L∞(X)?