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Context: Scientific paper targeting at computer scientists, engineers and mathematicians

I am searching for a word similar to "promote", "push", "force", "enforce", "implement" or "ensure".

Example 1: We introduced this mechanism into our algorithm to "forces" the variable x to be larger or equal than zero. Example 2: We add this loss to tour loss function to force our model to learn ... instead of .... Example 3(abstract): A forces that B is fulfilled.

My question: I am worried that "forces" or "enforces" might be misunderstood in a mathematical context. We don't want to say we have a mathematical proof that it always succeeds in reaching the goal in mathematically exact way. Does "force"/"enforce" in a technical/Mathematical context mean that the goal is always exactly reached? "Promote" feels for me more like we are slowly moving in the direction of the goal, but we might be quite far away from reaching our goal. We want to say more something along the lines without A, B would not be fulfilled at all, but with A we ensure that B is in almost all situations fulfilled to a sufficient extend for practical applications. For our purposes B is solved sufficiently well by A. If B is not fulfilled sufficiently well in a certain situation, one could use A with different parameters to obtain B again. This is just a very small detail of the paper and it would take pages many to explain in detail under which conditions A actually ensures that B is fulfilled, but we only have one short sentence for the detail, that should say A takes care of B sufficiently well such that B won't make any problems in the remainder of the paper (while B would be a big problem without A, A is critical and could not be left away).

Maybe in German the word "forcieren" would fit quite well.

So I am looking for a word that is as strong as possible without implying that we have a 100% perfect mathematical guarantee. Is "force" a valid choice? Does "force" imply a 100% success rate? I think I would rather prefer something slightly weaker.

I think the 4 most important dimensions for this word are:

  1. the success rate: I want to imply a very high but not 100% success rate of B, when A is applied. (most important dimension in this context)
  2. relative success rate: B is much more likly sucessfully fulfilled with A than without A, but the success-rate of B without A is not 0%. (maybe even more important than 1.)
  3. the effort/force that is applied: I want rather strong force, rather pushy. (but less important than 1. and 2.)
  4. Emotionally positive or negative: I want a positive emotion. B is very desirable. It was sad that B was not possible without A, but now with A, finally B is (almost perfectly) fulfilled as we desire. (but the emotional dimension is also less important than 1. and 2. in the scientific context, neutral would also be fine)

I would also be interested in the position with respect to these dimensions of suggested words.

For example the word "enable" would kind of imply 0% success-rate of B without A (i.e., a very high second dimension), while not implying enough success-rate of B with A (too small in the first dimension). 3. rather neutral, 4. positive/neutral

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    Requires? It's stronger than promotes but actually less pushy. Commented Aug 9, 2022 at 23:26
  • In a mathematical context "A requires B to be fulfilled" would usually be interpreted as "A is only true if B is fulfilled" or "A only works if B is fulfilled". I think this would lead to misunderstandings in this context, but I agree taht in other contexts "require" can fit quite well.
    – Jakob
    Commented Aug 9, 2022 at 23:33
  • ... to limit x to values equal to or greater than zero. Commented Aug 9, 2022 at 23:35
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    @Jakob Since there's an emotional dimension, encourage positive values. Or discourage negative ones. Commented Aug 10, 2022 at 0:59
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    I agree with @YosefBaskin -- require works: We introduced this mechanism to require that the variable x be larger or equal than zero. You can require a teen to be home by midnight, but that doesn't necessarily mean it's going to happen. If require is still too strong, try ask. Commented Aug 10, 2022 at 2:18

2 Answers 2

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You could say that the algorithm biases towards a positive value for the variable

If you are willing to talk about the results rather than the action, you could say that positive values prevail or dominate.

But in the case you are describing, it is more often said that the algorithm guarantees something; in this case, that positive values prevail, or are almost always obtained.

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  • A algorithm that makes x>0 in 51% of the cases instead of 50% of the cases it also biases towards a positive value. We want to express something more in the lines of "our algorithm ensures positive x in ~99% of all cases and in the rare cases where x>0, it is just slightly below 0 which is sufficient for our application."
    – Jakob
    Commented Aug 10, 2022 at 21:39
  • Thanks for the clarification. I've edited my answer with some more suggestions. Guarantees is a verb that we use a lot to describe algorithms when we can't formally prove a property like optimality.
    – djs
    Commented Aug 10, 2022 at 22:38
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Not a single word, but the easiest way of expressing the concept is with a purpose clause.

For example:

We introduced this mechanism into our algorithm so that the variable x will nearly always be larger or equal than zero.

I'd avoid the term "almost always" since "almost all" has a specific meaning in mathematics (see Wikipedia).

Incidentally: rather than "larger or equal than zero," the correct English idiom would be "greater than or equal to zero" (example from CueMath). You could even just nonnegative, which means "being either positive or zero" (see Merriam-Webster).

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