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.

A≻B  ⟺  sA≥sB,  cA≤cB,  lA≤lB,  with at least one inequality strict.A \succ B \iff s_A \ge s_B,\ \ c_A \le c_B,\ \ l_A \le l_B,\ \ \text{with at least one inequality strict.}

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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a∗=arg⁡min⁡a∈A Lval(w∗(a), a)subject tog(a)≤B,w∗(a)=arg⁡min⁡w Ltrain(w,a)a^* = \arg\min_{a \in \mathcal{A}} \ \mathcal{L}_{\text{val}}\big(w^*(a),\, a\big) \quad \text{subject to} \quad g(a) \le B, \qquad w^*(a) = \arg\min_{w} \ \mathcal{L}_{\text{train}}(w, a)

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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b′(s′)=η O(o∣s′,a)∑sT(s′∣s,a) b(s)b'(s') = \eta \, O(o \mid s', a) \sum_{s} T(s' \mid s, a)\, b(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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Clifetime=Creuse⏟compress  +  Ccurate+Ctrain⏟train small  +  Csearch⏟NAS  +  Q⋅cˉtok,withMresident≤BmemC_{\text{lifetime}} = \underbrace{C_{\text{reuse}}}_{\text{compress}} \;+\; \underbrace{C_{\text{curate}} + C_{\text{train}}}_{\text{train small}} \;+\; \underbrace{C_{\text{search}}}_{\text{NAS}} \;+\; Q \cdot \bar c_{\text{tok}}, \qquad \text{with} \quad M_{\text{resident}} \le B_{\text{mem}}

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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Ci  =  κi[(1−hi) piin+hi piin γi]  +  ρi pioutC_i \;=\; \kappa_i\Big[(1-h_i)\,p^{\text{in}}_i + h_i\, p^{\text{in}}_i\,\gamma_i\Big] \;+\; \rho_i\, p^{\text{out}}_i

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.

All uses →Latest guide →Latest article →