  We present a simple proof for the benefit of depth in multi-layer feedforward
network with rectified activation ("depth separation"). Specifically we present
a sequence of classification problems indexed by $m$ such that (a) for any
fixed depth rectified network there exist an $m$ above which classifying
problem $m$ correctly requires exponential number of parameters (in $m$); and
(b) for any problem in the sequence, we present a concrete neural network with
linear depth (in $m$) and small constant width ($\leq 4$) that classifies the
problem with zero error.
  The constructive proof is based on geometric arguments and a space folding
construction.
  While stronger bounds and results exist, our proof uses substantially simpler
tools and techniques, and should be accessible to undergraduate students in
computer science and people with similar backgrounds.
