[VogonPoetry]

This is an analogy. a^2 - b^2 = aa - bb. This can be factored to (a+b)(a-b). In the first expression there are two multiplies, in the factored version there is only one.

However, from a numerical analysis / accuracy standpoint, evaluating the factored expression can result in loss of precision in the result when a is close to b. This is especially true if you repeatedly and sequentially do a lot of these operations. Loss of precision can be a problem in numeral modeling (like climate simulation) -- long term predictions diverge.

Given that there is a drive to use greatly reduced precision in ML engines, loss of precision might have an effect on how a model performs. Then again, it might not. I haven't read a lot of papers on ML, but I don't recall seeing ones that try to quantify how sensitive a model is to error propagation. (I am making a distinction between tests where the precision is reduced to see where it breaks down v.s. calculating / understanding what the error level actually is in a model)

[jart]

With LLMs they start showing signs of brain damage once the errors get too high. In my experience it reduces their ability to reason, they stop counting correctly, and they start homogenizing categories, like calling a lemur a monkey. Compare this with quantizing weights, which instead of brain damage leads to ignorance, forcing them to hallucinate more.