When is logit function preferred over sigmoid? I found out that logit and sigmoid functions are inverse of one another, and are used in binary classification, but is there a preference of one over another in any circumstances, or can they be used interchangeably? or do they have the same effect?
 A: In general you may use any function that looks like this:

Src: Wikipedia
You just need to adjust them to [0,1] interval by adding 1 and dividing by 2. Depending on the underlying distribution there is always a function that will perform better, so it is a good idea to do combinatoric search as well.
A: It would not make sense to use the logit in place of the sigmoid in classification problems.
The sigmoid (*) function is used because it maps the interval $[-\infty, \infty]$ monotonically onto $[0, 1]$, and additionally has some nice mathematical properties that are useful for fitting and interpreting models.  It is important that the image is $[0, 1]$, because most classification models work by estimating probabilities.
The logit, on the other hand, being the inverse, maps $[0, 1]$ onto $[-\infty, \infty]$.  It certainly cannot be used in place of the sigmoid, as it does not output values interpretable as probabilities.
(*) As @seanv507 mentions in the comment above, I'm taking sigmid to mean the logistic function $f(t) = \frac{1}{1 + e^{-t}}$.  Generally, it's often used to refer to any S shaped curve with $\lim_{t \rightarrow \infty} f(t) = 1$ and $\lim_{t \rightarrow -\infty} f(t) = 0$.
