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There may be several misperceptions in some researchers like me due to the wrong understanding of concepts in the early days.

For toy example, if we see the following equation

$$y = x \theta$$

I used to imagine all variables in the above equation have real numbers. Once I encounter such equations in calculating gradients, it becomes difficult for me to imagine the things and hence it takes more time for me to understand how to imagine things.

The question related to this example can be as follows:

How do researchers imagine or perceive the variables in understanding the equations like $$y = x \theta$$

With this context, is it allowed to ask in our main site the questions about the perceptions or imaginations that are followed by the researchers in AI?

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The question is your example is a bit vague/ambiguous because it's not clear what you mean by "perceive variables". So, that's the first problem with that question.

Having said that, generally, I think that questions in the context of understanding theoretical AI/ML concepts (which includes mathematical notation and terminology used in AI) should be on-topic here, provided they have an objective answer and don't lead to just opinions.

You already asked a question here that falls into the category you're describing. How do people in AI imagine higher dimensions or objects in higher-dimensional spaces? The reason why this question is on-topic here is that you're specifically interested in how "AI researchers" approach this problem (so you assume that AI researchers approach this problem differently than other researchers, which may or not be the case), but, generally, an answer to these questions may also be applicable to other cases.

So, here are my recommendations

  • Don't ask mathematical questions (like "what is a vector space?") and just put them in the context of machine learning as an excuse for making it on-topic here. If something is just purely mathematical, it may be a good idea to ask your question on Math Stack Exchange. It depends also on the type of answer you're looking for. Of course, on AI SE, you may find people with a different background than on Math SE, so you may get different types of answers here. If you think that something is done differently in AI or ML than in other fields, then you should ask your question here. For example, if you think that a "vector space" may have different connotations in AI/ML than in other fields (e.g. statistics) then you probably should clarify this in your post (e.g. I found that this article describes X as Y, but I thought X was Z in mathematics), so that people know why you're asking that question, which apparently is a question that should be asked on Math SE.

  • Try to formulate your questions so that they do not lead to opinions, but, preferably, for example, common practices/guidelines. If a question can lead to answers like "In my opinion, I think you should view higher dimensions as X", then your question might have been formulated incorrectly or could be closed as opinion-based.

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  • $\begingroup$ Sure, I will follow all. $\endgroup$
    – hanugm
    Nov 17 '21 at 14:58

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