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Published equation contexts

weff=w+skw_{\mathrm{eff}} = w + \frac{s}{k}

Why this formula appears here

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 weff=w+skw_{\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 weffw_{\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 weffw_{\mathrm{eff}} ≈\approx 4.5 bits per…

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weffw_{\mathrm{eff}}

Symbol w_eff

wew_eff is part of the quantity the equation computes from the expression on the right.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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weff=w+skw_{\mathrm{eff}} = w + \frac{s}{k}

Equation 9 · Semiconductors

AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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 weff=w+skw_{\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 weffw_{\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 weffw_{\mathrm{eff}} ≈\approx 4.5 bits per…

Meanings in this article

  • kk: the block size.
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