> In this section, we show that L-Mul is more precise than fp8 e4m3 multiplications
> To be concise, we do not consider the rounding to nearest even mode in both error analysis and complexity estimation for both Mul and L-Mul
These two statements together are non-sensical. Sure, if you analyze accuracy while ignoring the part of the algorithm that gives you accuracy in the baseline you can derive whatever cherry-picked result you want.
The multiplication of two floating point values if you round to nearest even will be the correctly rounded result of multiplying the original values at infinite precision, this is how floating point rounding usually works and what IEEE 754 mandates for fundamental operations if you choose to follow those guidelines (e.g., multiplication here). But not rounding to nearest even will result in a lot more quantization noise, and biased noise at that too.
> applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by elementwise floating point tensor multiplications and 80% energy cost of dot products
A good chunk of the energy cost is simply moving data between memories (especially external DRAM/HBM/whatever) and along wires, buffering values in SRAMs and flip-flops and the like. Combinational logic cost is usually not a big deal. While having a ton of fixed-function matrix multipliers does raise the cost of combinational logic quite a bit, at most what they have will probably cut the power of an overall accelerator by 10-20% or so.
> In this section, we demonstrate that L-Mul can replace tensor multiplications in the attention mechanism without any loss of performance, whereas using fp8 multiplications for the same purpose degrades inference accuracy
I may have missed it in the paper, but they have provided no details on (re)scaling and/or using higher precision accumulation for intermediate results as one would experience on an H100 for instance. Without this information, I don't trust these evaluation results either.