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Symbol in context

σ\sigma

This entry links every published equation using this exact notation. Its meaning may change between equations.

Meanings in context

Used in 41 equations

⟨σv⟩3α  ∝  ΓαΓ Γrad  exp⁡ ⁣(−ERkBT)\langle \sigma v \rangle_{3\alpha} \;\propto\; \frac{\Gamma_\alpha}{\Gamma}\,\Gamma_{\mathrm{rad}}\; \exp\!\left(-\frac{E_R}{k_{B}T}\right)

The Resonance That Selected Carbon, and the Universes That Couldn't · Equation 1

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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FFNSwiGLU(x)=(Swish1(xW1)⊙xW3) W2,Swish1(z)=z⋅σ(z).\mathrm{FFN}_{\mathrm{SwiGLU}}(x) = \big(\mathrm{Swish}_1(xW_1) \odot xW_3\big)\,W_2, \qquad \mathrm{Swish}_1(z) = z \cdot \sigma(z).

How Llama's Architecture Actually Works, Generation by Generation · Equation 16

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Ldistill=(1−α) CE(y, σ(zs))  +  α T2 CE(σ(zt/T), σ(zs/T))\mathcal{L}_{\text{distill}} = (1-\alpha)\,\mathrm{CE}\big(y,\ \sigma(z_s)\big) \;+\; \alpha\, T^2\,\mathrm{CE}\big(\sigma(z_t/T),\ \sigma(z_s/T)\big)

Shrink It, Train It Small, or Search for It: The Main Strategies for Small Models, Compared · Equation 1

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)

How a Model Actually Gets Small Enough to Run on a Phone · Equation 7

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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C(r)=∫tntfT(t) σ(r(t)) c(r(t),d) dt,T(t)=exp⁡ ⁣(−∫tntσ(r(s)) ds),C(\mathbf{r}) = \int_{t_n}^{t_f} T(t)\, \sigma(\mathbf{r}(t))\, \mathbf{c}(\mathbf{r}(t), \mathbf{d})\, dt, \qquad T(t) = \exp\!\left(-\int_{t_n}^{t} \sigma(\mathbf{r}(s))\, ds\right),

How Multimodal Models Actually Handle Video, Audio, and Space · Equation 13

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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Cn=∑i=1nci=n pin(τ+δ)+pin σ n(n−1)2+n pout oˉC_n = \sum_{i=1}^{n} c_i = n\,p_{\text{in}}(\tau+\delta) + p_{\text{in}}\,\sigma\,\frac{n(n-1)}{2} + n\,p_{\text{out}}\,\bar{o}

The Economics and Physical Limits of Running AI Agents at Scale · Equation 19

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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