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Equation 16 · Part 6 · How Llama's Architecture Actually Works, Generation by Generation

Symbol σ

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).
σ\sigma

What this part means

σ is one factor in the product that computes the quantity on the left.

Its job in the formula

σ is one factor in the product that computes the quantity on the left.

The passage around this formula

Shazeer’s paper on gated linear unit variants tested several replacements for the standard ReLU or GELU feed-forward block, in which two linear projections are combined so that one, passed through a nonlinearity, gates the other [ 6 ] . The variant that stuck across the field, and that Llama adopts in every generation, uses the Swish (SiLU) nonlinearity as the gate: 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). Two independent linear projections of the residual stream are formed; one is passed through the gate and multiplied element-wise ( ⊙\odot ) against the other; the product is projected back down. Shazeer’s own results reported the gated variants outperforming the plain ReLU feed-forward block across the…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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