Four basis functions.

Four basis functions.

To build the MSE dataset I used four basis functions: 1, t, sin(50t), cos(50t). Why these four?

𐂅 Constant never hurts — it lets the curve shift up or down.
𐂅Linear captures any overall trend.
𐂅sin and cos with the same frequency come as a pair: by mixing their weights you set both amplitude and phase (i.e., you can place the peaks where you need them).

Why 50?
Because on 𝑡∈[0,1] the period 2π/50 roughly matches the width of the letters in the title I’m approximating, so the oscillations align with the letter shapes.