Huh? Diffeomorphisms are dimensionality preserving. You can't have a diffeomorphism between Rn to R2 unless n=2. That's the only way your differential mapping is bijective

So I am not sure how the diffeomorphisms guarantee that you can have lossless dimensionality reduction.

What can happen is that if your data inherently lies on a lower dimensional manifold. For instance if you have A subset of Rn that has an inherent dimensionality of just 2 then you can trivially just represent it in 2 dimensions. For example if you have a 3d space where the 3rd dimension is an exact linear combination of the 1st and 2nd then it's inherent dimensionality is 2 and you can obviously losslessly reduce it to 2d.

But most definitely not all datasets have an inherent dimensionality of 2.

That's not PCA's fault. No matter what kind of technique you use, if you try to represent a 768d vector in a 2d plane by using dimensionality reduction, you will lose lots of explainabilility.

The real question is about what properties do you care to preserve when doing dimensionality reduction and validating that your technique tries to preserve as much of it as possible.

I was focusing more on the Leetcode side of things. The memorization thing was obviously worse and I don't know of any big company that does it either.

I am an NLP Researcher with good research experience. Leetcode is not going to be helpful for me at all. Sure I can take some time and grind leetcode for a month. I used to do competitive programming back when I was in college so it shouldn't be a problem. But I have a full time job and a life. So it just feels like a waste of time for me.

I rarely ever interview for big companies these days for the exact same reason. They are so rigidly stuck to their outdated interviewing process, it's not for me. I have a well paying job that I love already. Who has time to grind leetcode and brush up a bunch of algorithms that I have no interest in that I am never going to use in my everyday work.

At least some of the new up and coming startups seem to have a much more interesting interview process. I know some people hate them but small take home assessments are the best, especially if it's an interesting problem and does not take more than 3-4 hours to solve.