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ScalingMultiple choiceHard

You fit ten noisy samples of a smooth curve with a sum of sine waves, sized by the number of waves, and measure test error against the true curve between the points.

Six waves give a smooth fit with test error 0.03; ten waves, one per point, pass through every point with test error 1.6; a thousand waves also pass through every point, with test error 0.02.

What causes the spike at ten?