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Equation 17 · Part 2 · The Hardest Unsolved Problems in Frontier AI Model Comparisons

Symbol v

qA(v)≷qB(v),where the sign can flip as the operating-point vector v varies.q_A(v) \gtrless q_B(v), \quad \text{where the sign can flip as the operating-point vector } v \text{ varies}.
vv

What this part means

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

Its job in the formula

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

The passage around this formula

More fundamentally, even a perfectly executed, continuously updated tracker cannot make the comparison one-dimensional, because quality at a given cost and latency is a function of a whole vector of settings — reasoning effort, context length used, modality, batching — and two systems compared at one point in that vector can reverse their relative standing at another point: qA(v)≷qB(v),where the sign can flip as the operating-point vector v variesq_A(v) \gtrless q_B(v), \quad \text{where the sign can flip as the operating-point vector } v \text{ varies}. A model that leads at high cost and maximum reasoning effort is not guaranteed to lead at the low-cost, low-latency point a production deployment actually needs, and a comparison that quotes only one of those two points without saying which is not wrong so much as silently incomplete. No published…

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