Live mathematical reference

Mathematical compendium

A live index of the equations in published articles. Each entry leads to its article, equation guide, and the terms explained there. New or edited published articles appear automatically.

1676 equations across 1477 symbols.

error(m)  =  Pr⁡[tool⋆∉Sm]⏟retrieval gap, shrinks as m grows  +  Pr⁡[miscall∣tool⋆∈Sm]⏟confusion gap, grows as m grows\mathrm{error}(m) \;=\; \underbrace{\Pr[\mathrm{tool}^\star \notin S_m]}_{\text{retrieval gap, shrinks as } m \text{ grows}} \;+\; \underbrace{\Pr[\text{miscall} \mid \mathrm{tool}^\star \in S_m]}_{\text{confusion gap, grows as } m \text{ grows}}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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PGR  =  perf(fw→s)−perf(fw)perf(fs→s)−perf(fw)\mathrm{PGR} \;=\; \frac{\mathrm{perf}(f_{w\to s}) - \mathrm{perf}(f_w)}{\mathrm{perf}(f_{s\to s}) - \mathrm{perf}(f_w)}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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max⁡π1  min⁡π2    Eτ∼(π1,π2)[Judge(τ)]\max_{\pi_1}\;\min_{\pi_2}\;\; \mathbb{E}_{\tau\sim(\pi_1,\pi_2)}\big[\mathrm{Judge}(\tau)\big]

1 published occurrence

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

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max⁡θ  Ex, y∼πθ[rϕ(x,y)]  −  β DKL(πθ ∥ πref)\max_\theta \; \mathbb{E}_{x,\, y\sim\pi_\theta}\big[r_\phi(x,y)\big] \;-\; \beta \, D_{\mathrm{KL}}\big(\pi_\theta \,\Vert\, \pi_{\mathrm{ref}}\big)

1 published occurrence

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

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decision(c)={deny,c∈Dask,c∉D and c∈Aallow,c∉D∪A and c∈Wask (default),otherwise\text{decision}(c) = \begin{cases} \text{deny}, & c \in D \\ \text{ask}, & c \notin D \text{ and } c \in A \\ \text{allow}, & c \notin D \cup A \text{ and } c \in W \\ \text{ask (default)}, & \text{otherwise} \end{cases}

1 published occurrence

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Trust(s)={certified,ϵ^(s)≤ϵmax⁡ and ϵ^(s) independently auditedunverified,otherwise\text{Trust}(s) = \begin{cases} \text{certified}, & \hat\epsilon(s) \le \epsilon_{\max} \ \text{and} \ \hat\epsilon(s) \ \text{independently audited} \\ \text{unverified}, & \text{otherwise} \end{cases}

1 published occurrence

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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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