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.

pre(a)⊆s  ⟹  δ(s,a)=(s∖del(a))∪add(a)\mathrm{pre}(a) \subseteq s \;\Longrightarrow\; \delta(s,a) = \big(s \setminus \mathrm{del}(a)\big) \cup \mathrm{add}(a)

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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RMSNorm(x)j=xjRMS(x) gj,RMS(x)=1d∑k=1dxk2+ϵ\mathrm{RMSNorm}(x)_j = \frac{x_j}{\mathrm{RMS}(x)}\, g_j, \qquad \mathrm{RMS}(x) = \sqrt{\frac{1}{d}\sum_{k=1}^{d} x_k^2 + \epsilon}

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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SEcluster=SEnaive×1+(m−1)ρ\mathrm{SE}_{\text{cluster}} = \mathrm{SE}_{\text{naive}} \times \sqrt{1 + (m - 1)\rho}

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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∇θJ(θ)=Eπ ⁣[∑t=0T∇θlog⁡πθ(at∣st)(∑t′≥trt′)]\nabla_\theta J(\theta) = \mathbb{E}_\pi\!\left[\sum_{t=0}^{T} \nabla_\theta \log \pi_\theta(a_t \mid s_t) \left(\sum_{t' \ge t} r_{t'}\right)\right]

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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ϕ(fθ,x)≠ϕ(fθrand,x)for typical x\phi(f_\theta, x) \neq \phi(f_{\theta_{\mathrm{rand}}}, x) \quad \text{for typical } x

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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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}

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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backoff(n)=min⁡ ⁣(cap, base⋅2 n)\text{backoff}(n) = \min\!\left(\text{cap},\ \text{base} \cdot 2^{\,n}\right)

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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Cost(ni,no)={ni piL+no poL,ni<Tni piH+no poH,ni≥T\text{Cost}(n_i, n_o) = \begin{cases} n_i\, p_i^{L} + n_o\, p_o^{L}, & n_i < T \\ n_i\, p_i^{H} + n_o\, p_o^{H}, & n_i \geq T \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 →