Why bandwidth decides speed

reads the weights once per token and does about 1 to 2 FLOP per byte, so the memory bus finishes last and sets the pace. This is why speeds things up at all: integer and float multiplies run at similar rates on a modern GPU, so the gain is not cheaper arithmetic but fewer bytes to fetch. Memory bandwidth utilization, or MBU, is the share of peak the actually reaches, and no reaches all of it.

Formula

Worked example: RTX 4090 with an 8B Q4 model

The 4090 peaks at 1008 GB/s. Reading 4.6 GB per token at 70 percent of peak lands at 153 tokens per second, inside the measured 140 to 180 band. Note what does not appear in this formula: FLOPS. Doubling the card's arithmetic throughput would not move the answer.

Try a current model on the RTX 4090