<p>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 $\alpha$.</p>

CC BY-SA 3.0
2017-10-27T21:41:05.427Z
@Seanny123 By his lack of elaboration by now I think he's made it pretty clear that he doesn't intend to improve his answer.
J.Todd
CC BY-SA 3.0
2017-10-22T20:26:12.300Z
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.
J.Todd
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2017-10-22T20:28:36.743Z
@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.
StrongBad
CC BY-SA 3.0
2017-10-22T20:29:44.993Z
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.
J.Todd
CC BY-SA 3.0
2017-10-22T21:42:04.750Z
+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
CC BY-SA 3.0
2017-10-22T22:21:32.343Z
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."
J.Todd
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2017-10-23T17:20:48.020Z
@StrongBad do you want to add my comment to your answer so we can delete all this discussion? It personally feels kind of messy to me.
Seanny123
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2017-10-22T20:12:22.723Z
2017-10-22T20:12:22.723Z
StrongBad
<p>In the following sentence from "<a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3306444/" rel="noreferrer">How does the brain solve visual object recognition?</a>" by DiCarlo et al.:</p>

<blockquote>
  <p>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, <strong>non-linear</strong>
  processing of the visual input.</p>
</blockquote>

<p>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?</p>

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2017-10-22T19:38:32.180Z
Do you know what non-linear functions and how they're different that linear functions?
Seanny123
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2017-10-22T20:22:36.263Z
@Seanny123 Probably not in the mathematical sense. I think of science from a physical standpoint rather than a mathematical one.
J.Todd
CC BY-SA 3.0
2017-10-22T21:25:33.270Z
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.
J.Todd
CC BY-SA 3.0
2017-10-22T22:10:15.073Z
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.
Seanny123
<cognitive-neuroscience>
What does "non-linear processing" mean, exactly?
J.Todd
# What does "non-linear processing" mean, exactly?

(Asked by: username_0 on 2017-10-22)

In the following sentence from "[How does the brain solve visual object recognition?](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3306444/)" 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?

**Tags:** cognitive-neuroscience

> **Comments:**
> **username_1**: Do you know what non-linear functions and how they're different that linear functions?  
> **username_0**: @username_1 Probably not in the mathematical sense. I think of science from a physical standpoint rather than a mathematical one.  
> **username_0**: 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.  
> **username_1**: 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.  

---

## 1 answers

### Answer by username_2 on 2017-10-22. Score: 5

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 $\alpha$.

> **Comments:**
> **username_0**: 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.  
> **username_2**: @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.  
> **username_0**: 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.  
> **username_3**: +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.  
> **username_0**: 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. username_1'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."  
> **username_1**: @username_2 do you want to add my comment to your answer so we can delete all this discussion? It personally feels kind of messy to me.  
> **username_0**: @username_1 By his lack of elaboration by now I think he's made it pretty clear that he doesn't intend to improve his answer.  

---

