Where Lambda is a real number...

Recently have read something similar like "where Lambda is a real number", in an academic journal article (not exclusive to mathematicians). This was related to the following equation:





$$ f(x) = \frac{1}{1+e^{-\lambda x}}$$

Lambda is a Greek letter and the little triangle thing ($\lambda$) in the equation.

I am not particularly gifted in mathematics. Therefore, to me the information that Lambda should be a real number is rather cynical. It is like saying: "Tomorrow is going to be weather." You are probably better off not saying anything about it if you are not willing to or capable* of saying what it is really supposed to be doing.

Luckily, several sources cited the equation (with more or less similar explanations for Lambda**) and gave different recommendations for a value of Lambda (but without a why!). I also knew that my x values can also be only in the range of [-1,1]. Hence I could plug the values into Excel and see the effects on a graph. I started with $\lambda=1$

"Okay, that is unexpected", I thought to myself. Tried $\lambda=5$

That was the aha-moment. See how the curve stays within 0 and 1 on the Y-axis? That is the point. The purpose in this case is to fit a set of input values into (ideally) the [0,1] interval. The value 5 for Lambda does it well enough.

So why can you not just write something like:

"where Lambda ($\lambda = 5$) maps the input values on to the (0,1)*** interval"

Adapt where appropriate to more mathematical jargon. There is no excuse for "is a real number".

Meanwhile I have also found an article that did bother to explain the purpose of Lambda. Too late for me but oh well. Reminded me that Excel is neat little DIY / self-help tool.

For the sake of completeness, the equation above is a sigmoid function (https://en.wikipedia.org/wiki/Sigmoid_function); this one in particular "the special case of the logistic function" (https://en.wikipedia.org/wiki/Logistic_function). It was used as an activation function in neural networks / fuzzy cognitive maps.

*The risk of not revealing it, even if it is obvious to you, is that you can cause the impression that you do not understand your own equations. 

**"Steepness" as suggested by Wiki (https://en.wikipedia.org/wiki/Logistic_function) was not among the academic sources.

***The ideal interval is [0,1] including 0 and 1 whereas the equation can only provide (0,1) excluding 0 and 1.