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Gemma-2 uses the (approximated) GeGLU activation in every feed-forward (MLP) block.

  1. Definition (KaTeX notation only)

Split the input vector xx of size d_modeld\_{model} into two halves x_ax\_a and x_bx\_b (each size d_modeld\_{model}).
The linear layer projects each half to size d_ffd\_{ff}, giving h_a,  h_bRd_ffh\_a,\;h\_b\in\mathbb R^{d\_{ff}}.

GeGLU(x)=GELU(h_a)    h_b\text{GeGLU}(x)=\text{GELU}(h\_a)\;\odot\;h\_b

where \odot is element-wise multiplication, and GELU is the Gaussian Error Linear Unit

GELU(z)=0.5z(1+tanh ⁣[2/π(z+0.044715z3)]).\text{GELU}(z)=0.5\,z\left(1+\tanh\!\bigl[ \sqrt{2/\pi}\,(z+0.044715\,z^{3}) \bigr]\right).

(The “approximated” qualifier refers to using the tanh-based approximation of GELU shown above, which avoids the exact error-function call.)

  1. Why GeGLU was chosen

• Gating improves expressiveness. Multiplying one branch by a nonlinear gate lets the MLP model input-dependent feature selection, which simple ReLU or GELU alone cannot do.

• Higher parameter efficiency. With a gate the projected dimension can be kept large (Gemma-2 uses d_ffd\_{ff} much larger than d_modeld\_{model}) without destabilising training, giving more capacity per parameter than a plain linear-GELU block.

• Empirical gains. Prior work (e.g.\ in LLaMA, PaLM, Gemini) showed that GeGLU or its sibling SwiGLU yields better perplexity for the same compute; the Gemma-2 ablations confirmed the same trend.

• Stable gradients. GELU’s smoothness plus the gating term reduces activation variance compared to ReLU, helping very deep networks (Gemma-2 has up to 46 layers) train reliably.

• Fast to compute. The tanh approximation is implemented with elementary ops that vectorise well on TPUs/GPUs, so GeGLU adds negligible latency compared with ReLU or GELU alone.

In short, Gemma-2 keeps the strong empirical performance of recent gated activations while remaining computationally lightweight, hence the choice of approximated GeGLU.

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