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Equation 4 · The Hardest Unsolved Problems in Evaluating xAI's Claims

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u3≈31.6u_3 \approx 31.6

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This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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u3u_3

Symbol u_3

u3u_3 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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≈

≈

Approximately equal to; the equality is not exact.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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Its accuracy depends on the assumptions and range of use described in the article.

What the article says around this equation

giving u1u_1 ≈\approx 3.16 , u2u_2 = 10 , and u3u_3 ≈\approx 31.6 — which is a formal way of saying that even a well-resourced independent estimate of a frontier training run can be off by an order of magnitude or more, and everyone doing the estimating knows it going in. Epoch’s own account of its Grok 4 figures is direct about why: “the FLOP and GPU-hour estimates for Grok-4 are largely based on public statements from xAI, which are often vague,” producing significant uncertainty in the resulting compute total [ 4 ] . Their published point estimate — roughly 5.0×10²⁶ FLOP, built from about 246 million H100-hours — is a best reconstruction, not a confirmed figure, and Epoch says so on the page.

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