It's enough to have only one mlp layer to classify moons

moons classification multilayer perceptron.py

from matplotlib.pyplot import *
from numpy import *
from sklearn.datasets import make_moons

# def plot_line(k=3, b=0, label=None, ax=None):
#     def pred(x, y, k, b):
#         y_pred = k * x + b
#         return 1 / (1 + exp((y - y_pred) * 10))
#
#     x, y = meshgrid(linspace(-1, 1), linspace(-1, 1))
#
#     ax = ax or gca()
#     ax.pcolormesh(x, y, pred(x, y, k, b), label=label)
T = array([
    [-0.676, -3.347],
    [0.554, -0.557],
])
bias = array([0.193, 1.778])


figure(figsize=(10, 5), dpi=150)
subplot(1, 3, 1, title='Moons (dataset)')
Xy, c = make_moons()
scatter(*Xy.T, c=c)

line = linspace(-40, 40, 100_000_000) * 0.05
plot(*((arctanh(stack([line, line * 1.5]).T)-bias)@ linalg.inv(T)).T)

subplot(1, 3, 2, title='Applied(Linear transform)')
# 1. Linear

scatter(*(Xy @ T + bias).T, c=c)
line = linspace(-1, 1, 100000) + 0.001
plot(*(arctanh(stack([line, line * 1.5]).T)).T)

subplot(1, 3, 3, title='Applied(Linear transform)')
scatter(*(tanh(Xy @ T + bias)).T, c=c)
line = linspace(-1, 1)
plot(*stack([line, line * 1.5]))
#
# subplot(1, 4, 4, title='Applied(Linear transform)')
# # plot_line(1.5, 0, trans=lambda x: )
# plot(line, line * 1.5)
# scatter(*(tanh(Xy @ T + bias)).T, c=c)

show()

The output: