Block Size or Scale Format? A Backward-Error Decomposition of MXFP4 and NVFP4

NVIDIA reports that MXFP4 needs 36% more training tokens than NVFP4 to reach thesame pretraining loss on its own 8B model, but the two formats differ in two ways at once,block size and scale format, so that result cannot say which choice is responsible. This workseparates them. Backward error of a quantized GEMM is measured under exact accumulation,isolating input quantization from accumulator rounding, within a framework in the traditionof classical rounding-error analysis but adapted where that analysis no longer applies. Blocksize and scale format are crossed in a two-by-two design and swept over operand tail weightand contraction length. The scale format moves measured error more than the block sizedoes at every canonical cell, and the ranking survives stochastic rounding and a randomHadamard transform; the margin narrows sharply at the heaviest tail without crossing. Theoriginally planned comparison, locating the tail index at which the derived bound first fails,proved uninformative: the bound is broken across the entire tested range, which motivatedthe magnitude-based analysis reported here. Against GPT-2 activations the predictionstransfer closely at two of three layers, with the third showing a mismatch consistent withchannel-concentrated outliers, not established as causal here.