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.

1680 equations across 1484 symbols.

judge alone≈NP,judge+debate (polynomially many rounds)≈PSPACE\text{judge alone} \approx \mathrm{NP}, \qquad \text{judge} + \text{debate (polynomially many rounds)} \approx \mathrm{PSPACE}

1 published occurrence

View equation in context

This equation gives an approximation: it relates the quantities while allowing an approximation.

All uses →Latest guide →Latest article →
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}

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
passk  :=  Etasks ⁣[ (ck)(nk) ]\text{pass}^{k} \;:=\; \mathbb{E}_{\text{tasks}}\!\left[\, \frac{\binom{c}{k}}{\binom{n}{k}} \,\right]

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
passdeterministick=pass1for every k\text{pass}^k_{\text{deterministic}} = \text{pass}^1 \quad \text{for every } k

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
passk(t)=∏i=1k1 ⁣[trial i on task t succeeds]\text{pass}^k(t) = \prod_{i=1}^{k} \mathbb{1}\!\left[\text{trial } i \text{ on task } t \text{ succeeds}\right]

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
pass@k  :=  Etasks ⁣[ 1  −  (n−ck)(nk) ]\text{pass@}k \;:=\; \mathbb{E}_{\text{tasks}}\!\left[\, 1 \;-\; \frac{\binom{n-c}{k}}{\binom{n}{k}} \,\right]

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
pass@k  =  Eproblems ⁣[ 1−(n−ck)(nk) ]\text{pass@}k \;=\; \mathbb{E}_{\text{problems}}\!\left[\,1 - \frac{\binom{n-c}{k}}{\binom{n}{k}}\,\right]

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
Precision=TPR⋅πTPR⋅π+FPR⋅(1−π)\text{Precision} = \frac{\mathrm{TPR} \cdot \pi}{\mathrm{TPR} \cdot \pi + \mathrm{FPR} \cdot (1 - \pi)}

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
score(C)=mpatch(C)−mcorruptmclean−mcorrupt\text{score}(\mathcal C) = \frac{m_{\text{patch}}(\mathcal C) - m_{\text{corrupt}}}{m_{\text{clean}} - m_{\text{corrupt}}}

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
selectivity=acctask−acccontrol\text{selectivity} = \mathrm{acc}_{\text{task}} - \mathrm{acc}_{\text{control}}

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
sleep(n)=Uniform ⁣(0, backoff(n))\text{sleep}(n) = \mathrm{Uniform}\!\left(0,\ \text{backoff}(n)\right)

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
θ(t+1)=θ(t)−η⋅1 ⁣[θ∈θbridge]⊙∇θ L(θ(t))\theta^{(t+1)} = \theta^{(t)} - \eta \cdot \mathbb{1}\!\left[\theta \in \theta_{\text{bridge}}\right] \odot \nabla_\theta \, \mathcal{L}(\theta^{(t)})

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →
∣ct∣>τ⋅Cmax  ⟹  ct→c^t,∣c^t∣≪∣ct∣|c_t| > \tau \cdot C_{\mathrm{max}} \implies c_t \to \hat{c}_t, \quad |\hat{c}_t| \ll |c_t|

1 published occurrence

View equation in context

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

All uses →Latest guide →Latest article →