You drop the memory throughput requirements because of the packed representation of bits so an FMA can become the bottleneck, and you bypass the problem of needing to upscale the bits to whatever FP the FMA instruction needs.
replytypically for 1-bit matmul, you can get away with xors and pop_counts which should have a better throughput profile than FMA when taking into account the SIMD nature of the inputs/outputs.
yes but this is not 1 bit matmul, it's 1.58 bits with expensive unpacking
replyThe title and the repo uses 1-bit when it means 1.58 bits tertiary values, it doesn't change any of my arguments (still xors and pop_counts).
replyHow do you do ternary matmul with popcnt on 1.58 bit packed data?
replyAssuming 2 bit per values (first bit is sign and second bit is value).
replyactv = A[_:1] & B[_:1]
sign = A[_:0] ^ B[_:0]
dot = pop_count(actv & !sign) - pop_count(actv & sign)
It can probably be made more efficient by taking a column-first format.
Since we are in CPU land, we mostly deal with dot products that match the cache size, I don't assume we have a tiled matmul instruction which is unlikely to support this weird 1-bit format.
Haven't looked closely, but on modern x86 CPUs it might be possible to do much better with the gf2affineqb instructions, which let us do 8x8 bit matrix multiplications efficiently. Not sure how you'd handle the 2-bit part, of course.
replyThe win is in how many weights you process per instruction and how much data you load.
replySo it's not that individual ops are faster — it's that the packed representation lets each instruction do more useful work, and you're moving far less data from memory to do it.
Bitnet encoding more information dense per byte perhaps? CPUs have slow buses so would eke out more use of bandwidth?
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