Straight Line, Curved Squeeze

Logistic regression predicts $P(y=1|x) = \text{sigmoid}(w \cdot x + b)$ and classifies using threshold $0.5$ . What is the shape of the resulting decision boundary in the original feature space?

It varies in shape depending on how steep the sigmoid is

Linear (a hyperplane), since $\text{sigmoid}(z)=0.5$ exactly when the linear score $w \cdot x+b$ equals $0$

A quadratic curve, because the sigmoid function itself is curved

A circle centered at the origin