[fheinsen]

The manuscript formally defines GOOMs as a set of mathematical objects, shows that floating-point formats are a special case of GOOMs, and notes that they extend prior work on logarithmic number systems (LNSs), which go back to at least the early 1970's. That is, LNSs are a special case of GOOMs too. Defining and naming GOOMs enables reasoning about all possible special cases in the abstract. In practice, each implementation makes different trade-offs.

The formal definition stops short of inducing an isomorphism between GOOMs and R, to allow for the possibility of transformations that leverage the structure of the complex plane, e.g., deep learning models that process data in C and apply a final transformation from C to GOOMs, thereby allowing the data to be exponentiated to R. The library in this repository makes implementing such a model trivial, because it ensures that backpropagation works seamlessly over C, over GOOMs, and across mappings between C, GOOMs, and floats.

Take a look at the selective-resetting algorithm in the manuscript too. To the best of our knowledge, it's a new algorithm, but we opted not to claim as much, out of an abundance of caution. You will appreciate reading about it.

[LolWolf]

ok I think I see where you’re going, though many (if not most) of the special cases and properties here seem to be essentially a consequence of each of these systems.

I’ll take a peek at the algorithm which I did admittedly skip, but curious if it gains us something !