[fabiospampinato]

I would guess that having 2 zeros is not that useful for NNs, but in general with 2 bits we could encode 4 states, so are there 4 possible states that would be useful to encode? Sure, but would this be better than encoding 3 states? That's the entire question imo. I would guess that 3 states are probably better, because negative/neutral/positive seems the minimal signal that we need these weights to provide.

[eru]

You could use a negative-two base, and encode {-2, -1, 0, 1}. See https://en.wikipedia.org/wiki/Negative_base

Or you could use the regular positive-two base and encode {-2, -1, 0, 1} the normal way with two's complement.