Symbol i
i appears in the bound of this product. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Published equation contexts
Why this formula appears here
Single-turn model quality can hide long-horizon fragility. Suppose a task has n dependent stages and each stage succeeds with conditional probability given that all previous stages succeeded. Then . If one makes the deliberately crude assumption =p , a 98% reliable stage repeated 50 times yields 0.98^{50}0.364 . Real agent steps are neither independent nor identically distributed: an early mistake can corrupt later observations, while a test can expose and reverse it. The simple product is useful because it reveals the architecture’s burden. Long tasks require mechanisms that change conditional probabilities after observing evidence , not merely a model with…
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Symbol p_i
is an input to the expression that computes the quantity on the left.
Read this term in its guide →Probability operator
The probability operator gives the chance of the event named inside its brackets or parentheses.
Read this term in its guide →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: n
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
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Published contexts (1)
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Equation 12 · AI Agents & Systems
Reliable AI Agents Are Control Systems, Not Chatbots
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Single-turn model quality can hide long-horizon fragility. Suppose a task has n dependent stages and each stage succeeds with conditional probability given that all previous stages succeeded. Then . If one makes the deliberately crude assumption =p , a 98% reliable stage repeated 50 times yields 0.98^{50}0.364 . Real agent steps are neither independent nor identically distributed: an early mistake can corrupt later observations, while a test can expose and reverse it. The simple product is useful because it reveals the architecture’s burden. Long tasks require mechanisms that change conditional probabilities after observing evidence , not merely a model with…