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.

Ct=(πθ,t,Ht,Tt,Pt,Et,Vt,Ut)\mathcal C_t = (\pi_{\theta,t}, H_t, \mathcal T_t, P_t, E_t, V_t, U_t)

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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J(θ)=Ex∼D, y∼πθ(⋅∣x)[r(x,y)]\mathcal{J}(\theta) = \mathbb{E}_{x \sim \mathcal{D},\ y \sim \pi_\theta(\cdot \mid x)}\left[ r(x, y) \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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L=−1B∑i=1Blog⁡exp⁡(⟨ui,vi⟩/τ)∑j=1Bexp⁡(⟨ui,vj⟩/τ)\mathcal{L} = -\frac{1}{B} \sum_{i=1}^{B} \log \frac{\exp(\langle u_i, v_i \rangle / \tau)}{\sum_{j=1}^{B} \exp(\langle u_i, v_j \rangle / \tau)}

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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Attention(Q,K,V)=softmax ⁣(QK⊤dk)V\mathrm{Attention}(Q, K, V) = \mathrm{softmax}\!\left(\frac{QK^{\top}}{\sqrt{d_k}}\right)V

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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PUE=EfacilityEIT=1+Ecooling+Edistribution+EotherEIT\mathrm{PUE} = \frac{E_{\mathrm{facility}}}{E_{\mathrm{IT}}} = 1 + \frac{E_{\mathrm{cooling}} + E_{\mathrm{distribution}} + E_{\mathrm{other}}}{E_{\mathrm{IT}}}

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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accept⁡(s′)=1 ⁣[⋀i=1mvi(s′)=1]⋅u(s′)\operatorname{accept}(s') = \mathbb{1}\!\left[ \bigwedge_{i=1}^{m} v_i(s')=1 \right] \cdot u(s')

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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logit⁡(pir)=α+ur+β⊤xir,ur∼N(0,σr2)\operatorname{logit}(p_{ir})=\alpha+u_r+\beta^\top x_{ir}, \qquad u_r\sim\mathcal N(0,\sigma_r^2)

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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Risk⁡(a)=P(unsafe proposal)⋅P(authorization∣proposal)⋅P(escape detection)⋅L(a)\operatorname{Risk}(a)= P(\text{unsafe proposal}) \cdot P(\text{authorization}\mid\text{proposal}) \cdot P(\text{escape detection}) \cdot L(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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