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Equation 11 · Part 9 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

addition

logit⁡(pir)=α+ur+β⊤xir,ur∼N(0,σr2),\operatorname{logit}(p_{ir})=\alpha+u_r+\beta^\top x_{ir}, \qquad u_r\sim\mathcal N(0,\sigma_r^2),
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

A hierarchical model can represent repository effects: logit⁡(pir)=α+ur+β⊤xir,ur∼N(0,σr2)\operatorname{logit}(p_{ir})=\alpha+u_r+\beta^\top x_{ir}, \qquad u_r\sim\mathcal N(0,\sigma_r^2). where r indexes repositories and xirx_{ir} task characteristics. The estimate can then expose between-repository variance rather than hiding it inside a global mean. Bootstrap intervals should resample at relevant task-family or repository levels when generalization across those units is the target.

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

Open the illustrated addition and subtraction in an equation guide →

The article lists its research sources here.