← Back to article

Equation 40 · AI Feeds on the Distance Between an Intention and an Outcome

What does this equation mean?

dtd_t

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

dtd_t

Symbol d_t

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

Understand this part →

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.

Understand this part →

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Here qtrq_{tr} is supplied input-context length in tokens, not tokens consumed after the agent has begun acting; using post-attempt expenditure would contaminate the predictor with behavior. The term dtd_t is a predeclared ordinary benchmark-difficulty score based only on endpoint-side, redaction-invariant features such as repository size band, static dependency reach, test-suite scope, and selected task-family label. It is deliberately conventional and admittedly imperfect. The terms urepo(t)u_{\mathrm{repo}(t)} and utu_t are repository and task random effects, while αm\alpha_m represents model or agent-configuration identity. The baseline includes model identity, token length, ordinary difficulty, and task…
Read the full surrounding passage
Here qtrq_{tr} is supplied input-context length in tokens, not tokens consumed after the agent has begun acting; using post-attempt expenditure would contaminate the predictor with behavior. The term dtd_t is a predeclared ordinary benchmark-difficulty score based only on endpoint-side, redaction-invariant features such as repository size band, static dependency reach, test-suite scope, and selected task-family label. It is deliberately conventional and admittedly imperfect. The terms urepo(t)u_{\mathrm{repo}(t)} and utu_t are repository and task random effects, while αm\alpha_m represents model or agent-configuration identity. The baseline includes model identity, token length, ordinary difficulty, and task horizon exactly so that the new variable cannot win by repeating any one of them.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to AI Feeds on the Distance Between an Intention and an Outcome

Browse the mathematical compendium →