I'm also sure that fp8 is small enough that multiplication can really be done in a much simpler circuit than larger fp formats. Even smaller formats like fp4 would be able to just use a lookup table, and that makes them more like sort-of-standardized quantization schemes.
i suspect that you could do fp8 with log tables and interpolation if you really wanted to (compared to the memory required for the model it's peanuts), it just turns into a LUT (log table look up) and bit shift (interpolation). so again, memory bandwidth is the limiting factor for transformers (as far as energy is concerned).
This time though LUT exists in a circuit, which is much more efficient than typical memory lookup. Such LUT would have to exist per each ALU though, so it can't be too large.
fp4/fp8 for neural networks don't work the way you think they do - they are merely compression formats - a set of, say, 256 fp32 weights from 1 neuron are lossily turned into 1 max value (stored in fp32 precision) and 256 fp4/fp8 numbers. Those compressed numbers are multiplied by the fp32 number at runtime to restore the original weights and full fp32 multiplication + additions are executed.
You are correct that the accumulation (i.e. additions in dot products) has to be done in a higher precision, however the multiplication can still be done via LUT. (Source: I currently work at a hardware-accelerated ML hardware startup.)
The goal of this type of quantization is to move the multiplication by the fp32 rescale factor outside of the dot-product accumulation.
So the multiplications+additions are done on fp8/int8/int4/whatever (when the hardware support those operators of course) and accumulated in a fp32 or similar, and only the final accumulator is multiplied by the rescale factor in fp32.
That's how Nvidia's mixed precision training worked with FP32-FP16, but it isn't the case for Bfloat16 on TPUs and maybe (I'm not sure) FP8 training on Nvidia Hopper GPUs.
I’m not a binary guy that much, but iirc all floats are 1.m*2^e — “1.” is always there except for subnormals. There’s also SEEE FP4 which is basically +-2^([u?]int3).
