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$w_{\mathrm{eff}} \approx 4.5$

Why this formula appears here

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 element — a roughly 12.5% tax [ 5 ] . The smaller block buys better local adaptation to each block’s dynamic range, which is the stated reason NVIDIA gives for its accuracy results at 4-bit precision [ 5 ] ; the price is paid in the overhead fraction, s/(kw) , which is exactly double NVFP4’s block-16 tax at block-32. Analysis. That…

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w_{\mathrm{eff}}

Symbol w_eff

$w_e$ ff is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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w_{\mathrm{eff}} \approx 4.5

Equation 14 · Semiconductors

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

This equation gives an approximation: it relates the quantities while allowing an approximation.

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 element — a roughly 12.5% tax [ 5 ] . The smaller block buys better local adaptation to each block’s dynamic range, which is the stated reason NVIDIA gives for its accuracy results at 4-bit precision [ 5 ] ; the price is paid in the overhead fraction, s/(kw) , which is exactly double NVFP4’s block-16 tax at block-32. Analysis. That…

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weff≈4.5w_{\mathrm{eff}} \approx 4.5weff​≈4.5