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.

W=W0+ΔW=W0+BA,B∈Rd×r, A∈Rr×k, r≪min⁡(d,k)W = W_0 + \Delta W = W_0 + BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, k)

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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W′=arg min⁡∥W′∥0≤k∥WX−W′X∥22W' = \operatorname*{arg\,min}_{\|W'\|_0 \le k} \|WX - W'X\|_2^2

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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xq=clip(⌊xs⌉+z, qmin⁡, qmax⁡),x^=s(xq−z)x_q = \mathrm{clip}\left(\left\lfloor \frac{x}{s} \right\rceil + z,\ q_{\min},\ q_{\max}\right), \qquad \hat{x} = s\left(x_q - z\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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y(x)=∑i∈TopK(G(x))G(x)i⋅Ei(x),Ctok≈kE⋅Ctokdense(Ntotal)y(x) = \sum_{i \in \mathrm{TopK}(G(x))} G(x)_i \cdot E_i(x), \qquad C_{\text{tok}} \approx \frac{k}{E} \cdot C_{\text{tok}}^{\text{dense}}(N_{\text{total}})

1 published occurrence

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

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(IDF)k=⌈log⁡2n⌉−⌈log⁡2dk⌉+1(\mathrm{IDF})_k = \lceil \log_2 n \rceil - \lceil \log_2 d_k \rceil + 1

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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