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.

bmax⁡≈Mdevice−MweightsMkv(s)b_{\max} \approx \frac{M_{\mathrm{device}} - M_{\mathrm{weights}}}{M_{\mathrm{kv}}(s)}

2 published occurrences

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

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Bj=(Ntokens,Nturns,Ntools,twall,Ccompute,kattempts)B_j=(N_{\mathrm{tokens}},N_{\mathrm{turns}},N_{\mathrm{tools}},t_{\mathrm{wall}},C_{\mathrm{compute}},k_{\mathrm{attempts}})

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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c=pinn+pcww+pcrr+pout(y+z)c = p_{\mathrm{in}} n + p_{\mathrm{cw}} w + p_{\mathrm{cr}} r + p_{\mathrm{out}} \left( y + 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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creq=cin (tfresh+α tcached)+creason treason+cout toutc_{\mathrm{req}} = c_{\mathrm{in}}\,(t_{\mathrm{fresh}} + \alpha\, t_{\mathrm{cached}}) + c_{\mathrm{reason}}\, t_{\mathrm{reason}} + c_{\mathrm{out}}\, t_{\mathrm{out}}

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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Ctotal=Cpre+Cpost+Q⋅cˉinfC_{\mathrm{total}} = C_{\mathrm{pre}} + C_{\mathrm{post}} + Q \cdot \bar{c}_{\mathrm{inf}}

1 published occurrence

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The total compute bill has three parts: pretraining, post-training, and all the requests served afterwards.

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Cℓ=12ℓ+1∑m=−ℓℓ∣aℓm∣2C_\ell = \frac{1}{2\ell+1}\sum_{m=-\ell}^{\ell} \left|a_{\ell m}\right|^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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ci=∑j=1Txαijhj,αij=exp⁡(eij)∑k=1Txexp⁡(eik)c_i = \sum_{j=1}^{T_x} \alpha_{ij} h_j, \qquad \alpha_{ij} = \frac{\exp(e_{ij})}{\sum_{k=1}^{T_x} \exp(e_{ik})}

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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CAC=Clicenses+Cusage+Cruntime+Chuman+Crework+CincidentsNaccepted,quality−adjustedCAC=\frac{ C_{\mathrm{licenses}}+C_{\mathrm{usage}}+C_{\mathrm{runtime}} +C_{\mathrm{human}}+C_{\mathrm{rework}}+C_{\mathrm{incidents}} }{N_{\mathrm{accepted,quality-adjusted}}}

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 →