Is this true? If it can add, it can probably subtract? If it can add and subtract it may be able to multiply (repeated addition) and divide? If it can multiply it can do exponents?

I don’t know, but cannot jump to your conclusion without much more domain knowledge.

> If it can add and subtract it may be able to multiply (repeated addition) and divide? If it can multiply it can do exponents?

It was just a simple feed-forward network. It can't do arbitrary amounts of repeated addition (nor repeat any other operation arbitrarily often).

None of these require arbitrary amounts of repeated addition though. E.g. multiplying two 8 bit numbers requires at most 7 additions.

Yeah I did not mean a loop, repeated in the network.

Are you doing the equivalent of repeated squaring here?

Otherwise, you'd need up to 255 (or so) additions to multiply two 8 bit numbers, I think?

An 8x8 bit multiplication only requires 7 additions, either in parallel or sequentially. Remember long-form multiplication? [1] It's the same principle. Of course, high-speed digital multiplication circuits use a much more optimized, much more complex implementation.

[1] https://en.wikipedia.org/wiki/Multiplication_algorithm#Examp...

OK. It sounded to me like the comment I originally replied to (https://news.ycombinator.com/item?id=34400296) suggested to implement multiplication as naive repeated addition.

Repeated additions may be hard, but computing a*b as exp(log(a)+log(b)) should be learnable.