The limit is in the design

Move the line. Turn it. Try every angle.

At best, three mushrooms land on the correct side. Fix the fourth and another slips across.

Those three are not the three that share a side. The line always cuts the map so that one mushroom sits alone and three sit together. The lone one is correct. Among the three, two are correct and one is on the wrong side.

The problem is not finding the right settings. For this neuron, the right settings do not exist.

Training can move and turn the boundary. It cannot give one neuron a second boundary, or make its one boundary change direction halfway across the map.

So how could the machine separate all four mushrooms?