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Equation 15 · Part 11 · The Hardest Unsolved Problems in AI Agent Evaluation and Reliability

Ending index or upper bound: n

R=1−∑i=1nwi⋅1[trial i failed],R = 1 - \sum_{i=1}^{n} w_i \cdot \mathbb{1}[\text{trial } i \text{ failed}],
nn

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

and contrast it with a severity-weighted version, R=1−∑i=1nwi⋅1[trial i failed]R = 1 - \sum_{i=1}^{n} w_i \cdot \mathbb{1}[\text{trial } i \text{ failed}]. where wiw_i scales each failure by how costly it actually was. Two agents can share an identical p^\hat{p} of, say, ninety-five percent, while one of them fails harmlessly - an unhelpful but reversible answer - and the other fails catastrophically - an irreversible transaction, a deleted repository, a wrong medical dosage recommendation - on that same five percent. No standard agent benchmark publishes R , because assigning a defensible wiw_i requires a judgment about real-world consequence that a replayable, sandboxed task suite is not built to carry, and because the tasks that would carry the highest weights are, not…

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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the article section

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