ML optimization algorithms generally do require proper handling of very,very small numbers for e.g. calculation of gradients.

There's a bunch of work on discretization of models after you've done optimizing them - that works, you can get high-performance inference with low-bit fixed point numbers; but that's after the learning has been done using proper floating point (however, you don't necessarily need high accuracy floating point, e.g. single precision may work betted than double precision simply because it's twice less bytes to copy over).