>> we can replace elementwise products in each dot product (a₁b₁ + a₂b₂ ...) with elementwise additions (a₁+b₁ + a₂+b₂ ...), in which signs depend on each value
Thinking out loud here. If you encode 64 weights in 2 64-bit words you can have the bits in one word indicating +1 if they're 1, and the bits in the other word indicating -1 if they are 1. You should be able to do the "products" with a few boolean operations on these 2 words to get a pair of 64 bit words for the result. Then summing becomes a matter of using a count-of-1's instruction on each word and subtracting the "negative" count from the positive. If AVX instructions can do this too, it seems like equivalent of 10-100 TOPS might be possible on a multi-core CPU.
Yes. More generally, this will enable implementation via crazy-cheap bit-wise ops in binary hardware, and possibly, maybe, via crazy-cheap trit-wise ops in ternary hardware that manipulates ternary digits, or trits. Note that any binary op over trits has only nine possible (trit, trit) input pairs and only three possible trit outputs. Maybe ternary hardware for AI will become a thing?
Fleshing out my thought above. If we want to multiply A*B = C and all operands are stored in 2 separate bits Ap and An (Ap = 1 if A = +1 while An = 1 if A = -1). We can do a product with:
Cp = (Ap & Bp) | (An & Bn)
Cn = (An & Bp) | (Ap & Bn)
So 64 products in 6 instructions, or 256 in 6 instructions with AVX2, or 512 in six instructions using AVX512. If you can execute 2 instructions at a time on different words, this becomes 1024 "products" in 6 cycles or between 0.5 and 1 TOP per core.
The summing still involves using popcount on the positive and negative bits - I doubt AVX supports that but its still a fast way to "sum" individual bits. I don't see custom hardware for this as a short term thing - they need to prove out the quantization concept more first.
Thinking out loud here. If you encode 64 weights in 2 64-bit words you can have the bits in one word indicating +1 if they're 1, and the bits in the other word indicating -1 if they are 1. You should be able to do the "products" with a few boolean operations on these 2 words to get a pair of 64 bit words for the result. Then summing becomes a matter of using a count-of-1's instruction on each word and subtracting the "negative" count from the positive. If AVX instructions can do this too, it seems like equivalent of 10-100 TOPS might be possible on a multi-core CPU.