It's nice to see sparse interpretable LLMs being made.
This is similar to factor rotation in factor analysis (or PCA). A varimax rotation, for example, can produce an equivalent factor analysis with sparse loadings, and which is generally more interpretable. Fortunately for us the world is not just a complete mess, and sparse loadings can often be found. There seem to be "natural" concepts that we have observed rather than invented.
(Many examples in other simple machine learning methods too, I am sure.)
My dad is in his 80s. He keeps careful notes on how to use devices like tablets and TVs. There might be a touch of engineer-brain at work here, but the struggle is very real. He generally wouldn't take in all of the text and symbols on a screen if there is a lot of going on, or might get hung up on the wrong parts of it. He generally wouldn't find a modern interface at all "intuitive".
Any change to an interface is going to disrupt this, so one thing would be to change the interface only very rarely and carefully.
For linear models, least squares leads to the BLUE estimator: Best Linear Unbiassed Estimator. This acronym is doing a lot of work with each of the words having a specific technical meaning.
Fitting the model is also "nice" mathematically. It's a convex optimization problem, and in fact fairly straightforward linear algebra. The estimated coefficients are linear in y, and this also makes it easy to give standard errors and such for the coefficients!
Also, this is what you would do if you were doing Maximum Likelihood assuming Gaussian distributed noise in y, which is a sensible assumption (but not a strict assumption in order to use least squares).
Also, in a geometric sense, it means you are finding the model that puts its predictions closest to y in terms of Euclidean distance. So if you draw a diagram of what is going on, least squares seems like a reasonable choice. The geometry also helps you understand things like "degrees of freedom".
The least squares model will produce unbiassed predictions of y given x, i.e. predictions for which the average error is zero. This is the usual technical definition of unbiassed in statistics, but may not correspond to common usage.
Whether x is a noisy measurement or not is sort of irrelevant to this -- you make the prediction with the information you have.
R is so good in part because of the efforts of people like Di Cook, Hadley Wickham, and Yihui Xie to create an software environment that they like working in.
It also helps that in R any function can completely change how its arguments are evaluated, allowing the tidyverse packages to do things like evaluate arguments in the context of a data frame or add a pipe operator as a new language feature. This is a very dangerous feature to put in the hands of statisticians, but it allows more syntactic innovation than is possible in Python.
Producing a diverse list of results may still help in a couple of ways here.
* If there are a lot of lexical matches, real semantic matches may still be in the list but far down the list. A diverse set of, say, 20 results may have a better chance of including a semantic match than the top 20 results by some score.
* There might be a lot of semantic matches, but a vast majority of the semantic matches follow a particular viewpoint. A diverse set of results has a better chance of including the viewpoint that solves the problem.
Yes, semantic matching is important, but this is solving an orthogonal and complementary problem. Both are important.
This is similar to factor rotation in factor analysis (or PCA). A varimax rotation, for example, can produce an equivalent factor analysis with sparse loadings, and which is generally more interpretable. Fortunately for us the world is not just a complete mess, and sparse loadings can often be found. There seem to be "natural" concepts that we have observed rather than invented.
(Many examples in other simple machine learning methods too, I am sure.)