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.

1676 equations across 1477 symbols.

p^θ(y∣aℓ)=σ ⁣(w⊤aℓ+b),θ={w,b}\hat p_\theta(y \mid a_\ell) = \sigma\!\left(w^{\top} a_\ell + b\right), \qquad \theta = \{w, b\}

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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x^=Wdf(x)+bd,f(x)=JumpReLUθ(Wex+be),L(x)=∥x−x^∥22+λ∥f(x)∥0\hat x = W_d f(x) + b_d, \qquad f(x) = \mathrm{JumpReLU}_\theta\big(W_e x + b_e\big), \qquad \mathcal L(x) = \lVert x - \hat x \rVert_2^2 + \lambda \lVert f(x) \rVert_0

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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⟨RΘ,m q,  RΘ,n k⟩  =  ⟨RΘ, m−n q,  k⟩\langle R_{\Theta,m}\,q,\; R_{\Theta,n}\,k\rangle \;=\; \langle R_{\Theta,\,m-n}\,q,\; k\rangle

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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=−12B∑i=1B[log⁡exp⁡(⟨ui,vi⟩/τ)∑j=1Bexp⁡(⟨ui,vj⟩/τ)+log⁡exp⁡(⟨ui,vi⟩/τ)∑j=1Bexp⁡(⟨uj,vi⟩/τ)]\mathcal{L} = -\frac{1}{2B}\sum_{i=1}^{B}\left[\log\frac{\exp(\langle u_i, v_i\rangle/\tau)}{\sum_{j=1}^{B}\exp(\langle u_i, v_j\rangle/\tau)} + \log\frac{\exp(\langle u_i, v_i\rangle/\tau)}{\sum_{j=1}^{B}\exp(\langle u_j, v_i\rangle/\tau)}\right]

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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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LKD=α LCE(y,σ(zs))+(1−α) T2 KL(σ(zt/T) ∥ σ(zs/T))\mathcal{L}_{\mathrm{KD}} = \alpha \, \mathcal{L}_{\mathrm{CE}}\left(y, \sigma(z_s)\right) + (1-\alpha)\, T^2 \, \mathrm{KL}\left(\sigma(z_t / T) \,\Vert\, \sigma(z_s / T)\right)

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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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