What does "non-linear processing" mean, exactly? In the following sentence from "How does the brain solve visual object recognition?" by DiCarlo et al.:


  In sum, our view is that the “output” of the ventral stream is
  reflexively expressed in neuronal firing rates across a short interval
  of time (~50 ms), is an “explicit” object representation (i.e., object
  identity is easily decodable), and the rapid production of this
  representation is consistent with a largely feedforward, non-linear
  processing of the visual input.


I'm familiar with "feed-forward" but not with the meaning of "non-linear processing" in a neuroscience context. What does "non-linear processing" mean, exactly?
The idea of linear/non-linear in neuroscience is the same as in mathematics. A process $f(x)$ is linear if $f(\alpha x) = \alpha f(x)$ and $f(x+y) = f(x)+f(y)$ for all $x$, $y$, and $\alpha$.