Visualizes very simple error functions of neural networks with tanh activation functions and sum of squared errors.

error.gnuplot

reset
set pm3d
set hidden3d
set isosample 100, 100
unset surface
unset xtics
unset ytics
unset ztics
unset border
unset key
unset colorbox
r = 20
set xrange [-r:r]
set yrange [-r:r]

max(x, y) = x > y ? x : y
relu(a) = max(a, 0)
logit(a) = 1/(1+exp(-a))

#set view 43, 54
#y(x, w1, w2) = w1+w2*x
#set view 46, 36
#y(x, w1, w2) = w1+tanh(w2*x)
#set view 62, 166
#y(x, w1, w2) = tanh(w1+tanh(w2*x))
#splot (y(0,x,y)-1)**2+(y(1,x,y)-2)**2+(y(2.5,x,y)-1.5)**2 t ""

#y(x1, x2, w1, w2) = tanh(w1+tanh(w2*x1+2*x2)+3*tanh(-2*x1+2*x2)-2*tanh(x1-2*x2))
#y(x1, x2, w1, w2) = max(0, w1+max(0, w2*x1+2*x2)+3*max(0, -2*x1+2*x2)-2*max(0, x1-2*x2))
#splot (y(0,1,x,y)-1)**2+(y(1,0,x,y)-2)**2+(y(0.5,0.5,x,y)-1.5)**2 t ""

#y(x1, x2, w1, w2) = logit(0.2*logit(w1*x1+w2*x2+0.2) + -0.2*logit(-0.1*x1+0.25*x2-0.1) + 0.1)
#y(x1, x2, w1, w2) = logit(0.2*logit(0.2*x1-0.1*x2+0.2) + w1*logit(-0.1*x1+w2*x2-0.1) + 0.1)
#y(x1, x2, w1, w2) = logit(w1*logit(0.2*x1-0.1*x2+0.2) + w2*logit(-0.1*x1+0.25*x2-0.1) + 0.1)
y(x1, x2, w1, w2) = relu(w1*relu(0.2*x1-0.1*x2+0.2) + w2*relu(-0.1*x1+0.25*x2-0.1) + 0.1)
splot (y(0,1,x,y)-1)**2+(y(1,0,x,y)-1)**2+(y(0,0,x,y)-0)**2+(y(1,1,x,y)-0)**2