One of our graduate students is thrilled about this paper, although he tends to do that with any new CS advance that seems sensational and that we barely understand (we do bioinformatics). He said that it stood to reason that if it can mmult 100GB/s/core, then we could matrix multiply 12TB in a minute!

Could you translate into practitioner-level language what are the practical limitations of this method; specifically, what would the error rates induced by approximation be under some practical scenarios, when would it make sense and not make sense to use it, etc? There is a complex equation in the paper describing the theoretical error bounds, but I have no idea whether in some practical scenario multiplying some normally distributed variables, whether that would mean a 0.1%, 1%, 5%, 10% error.

Personally I think it only makes sense to use this kind of method in some real-time algorithm where speed is of the essence, the downstream results of the mmult are themselves used in some other approximation (like many ML applications), and emphatically not to make the process of drawing biological conclusions from painstakingly derived data a few minutes faster for the analyst.

I fear that you have made an impressive, but dangerous, tool to people who don't know what they're doing.