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aa

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Used in 72 equations

Judge(a)={automated,ϵ^(a)≤ϵmax⁡(a) and ϵ^(a) externally auditedhuman required,otherwise\text{Judge}(a) = \begin{cases} \text{automated}, & \hat\epsilon(a) \le \epsilon_{\max}(a) \ \text{and}\ \hat\epsilon(a)\ \text{externally audited} \\ \text{human required}, & \text{otherwise} \end{cases}

Agent Evaluation in 2035: Two Axes, Four Scenarios, and What Would Falsify Them · Equation 4

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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Q(st,at)←Q(st,at)+α[rt+1+γmax⁡aQ(st+1,a)−Q(st,at)].Q(s_t,a_t) \leftarrow Q(s_t,a_t) + \alpha\Big[r_{t+1} + \gamma \max_{a} Q(s_{t+1},a) - Q(s_t,a_t)\Big].

From Scripted Bots to Autonomous Agents: A History of AI Agent Architecture · Equation 9

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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g(i)∼πsuper(g∣task),at(i)∼πworker(i)(a∣o≤t(i), ht(i), g(i)).g^{(i)} \sim \pi_{\text{super}}(g \mid \text{task}), \qquad a_t^{(i)} \sim \pi_{\text{worker}}^{(i)}\bigl(a \mid o_{\le t}^{(i)},\ h_t^{(i)},\ g^{(i)}\bigr).

Comparing the Main Approaches to AI Agent Architecture · Equation 8

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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Approval(a)={automatic,p(a) S(a)≤Bhuman required,p(a) S(a)>B\text{Approval}(a) = \begin{cases} \text{automatic}, & p(a)\, S(a) \le B \\ \text{human required}, & p(a)\, S(a) > B \end{cases}

AI Agent Architecture in 2035: Four Scenarios, Their Signals, and What Would Falsify Them · Equation 5

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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