# 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?

• Do you know what non-linear functions and how they're different that linear functions? Oct 22 '17 at 19:38
• @Seanny123 Probably not in the mathematical sense. I think of science from a physical standpoint rather than a mathematical one. Oct 22 '17 at 20:22
• Ok I read up on the difference between linear functions and non-linear functions in math (Yeah, I know, I should know that already), but I'm not exactly clear on how this translates to neural patterns. Oct 22 '17 at 21:25
• It's not really the neural patterns that are non-linear, as much as the function being computed by the neurons that are non-linear. Basically, there's a non-linear mapping between the input (visual stimuli) and the output (object). It's really just a way of saying "complicated" in this context. Oct 22 '17 at 22:10

## 1 Answer

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 $\alpha$.

• Could you explain it in a physical manner? Unlike many (who prefer it explained this way), I think of science purely in the physical sense, for example: when I think about a chemical reaction, I think about how the molecules are interacting, not about a formula representing it. Same with neuroscience. The math is fine, most scientists prefer to speak in terms of math, but I've never cared to use it, instead focusing on the actual physical states and interactions. Oct 22 '17 at 20:26
• @Viziionary I could, but there are tons of books that will do a better job of it. The thing I found important in your question was the fact that you wanted to know about linear/non-linear systems in the context of neuroscience, for which the answer is that it is the same as in all science and any textbook you like will work. Oct 22 '17 at 20:28
• Ok. So you're saying it would take a text-book chapter, not an SE answer, to explain it in that manner? I'm not arguing, just asking for clarification. Oct 22 '17 at 20:29
• +1 for your answer, but, perhaps, could you add a source to the answer to allow users to background read on this? Linear systems theory is quite an essential topic for many disciplines and a good web source or reference as a background would really help I guess, given OP's comments.
– AliceD
Oct 22 '17 at 21:42
• I did read up on the difference between linear functions and non-linear, but I was still confused about how that related to the neural patterns in this context. Seanny123's comment really answered my question: "It's not really the neural patterns that are non-linear, as much as the function being computed by the neurons that are non-linear. Basically, there's a non-linear mapping between the input (visual stimuli) and the output (object). It's really just a way of saying "complicated" in this context." Oct 22 '17 at 22:21