What does this equation mean?

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: $\mathrm{FFN}_{\mathrm{SwiGLU}}(x) = \big(\mathrm{Swish}_1(xW_1) \odot xW_3\big)\,W_2, \qquad \mathrm{Swish}_1(z) = z \cdot \sigma(z)$. 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 language modelling and fine-tuning tasks tested, at matched parameter and compute budgets [ 6 ] . Because the gate consumes an extra weight matrix, Llama’s feed-forward hidden dimension is set below the naive 4d multiplier used in the original transformer, to hold total parameters roughly constant against a non-gated block of the same width — an accounting detail visible in the hyperparameter tables of Meta’s own papers rather than a claim requiring independent verification here.