[shawntan]

Generally, literature on the computational power of the SAME neural architecture can differ on their conclusions based on their premises. Assuming finite precision will give a more restrictive result, and assuming arbitrary precision can give you Turing completeness.

From a quick skim this seems like it's making finite precision assumptions? Which doesn't actually tighten previous bounds, it just makes different starting assumptions.

Am author of [1].

[krackers]

Ah my bad, great catch! I've updated my comment accordingly.

[shawntan]

You can't really be blamed though, the language in the paper does seem to state what you originally said. Might be a matter of taste but I don't think it's quite accurate.

The prior work they referenced actually did account for finite precision cases and why they didn't think it was useful to prove the result with those premises.

In this work they simply argued from their own perspective why finite precision made more sense.

The whole sub-field is kinda messy and I get quoted differing results all the time.

Edit: Also, your original point stands, obviously. Sorry for nitpicking on your post, but I also just thought people should know more about the nuances of this stuff.