fraction

The passage around this formula

Fact. The move from FP8 to sub-8-bit formats has already happened once, and the mechanism by which it happened exposes the trade-off that will decide whether it happens again. A microscaling format with element width w bits, block size k , and a shared scale of s bits carries an effective per-element cost of $w_{\mathrm{eff}} = w + \frac{s}{k}$. with the second term the amortised metadata tax. The OCP MX alliance’s MXFP4 uses w = 4 , k = 32 , and an 8-bit shared scale, for $w_{\mathrm{eff}}$ = 4.25 bits per element — a roughly 6% tax [ 4 ] . NVIDIA’s NVFP4 instead uses a smaller block, k = 16 , with the same 8-bit block scale plus a near-negligible per-tensor term, for $w_{\mathrm{eff}}$ $\approx$ 4.5 bits per…

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