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SwiGLU is a variant within the Gated Linear Unit (GLU) family of activation functions. It is formed by using the Swish function as the internal non-linear activation, denoted as σ(·) in the general GLU formula.

SwiGLU (Swish-based Gated Linear Unit)

The SwiGLU function is a specific implementation of the Gated Linear Unit (GLU) where the non-linear activation function, $\sigma(\cdot)$, is the Swish function. The formula is defined as:

$\sigma_{\text{swiglu}}(\mathbf{h}) = \sigma_{\text{swish}}(\mathbf{hW}_1 + \mathbf{b}_1) \odot (\mathbf{hW}_2 + \mathbf{b}_2)$

Where:
* $\mathbf{h}$ is the input vector.
* $\sigma_{\text{swish}}$ is the Swish activation function.
* $\mathbf{W}_1, \mathbf{W}_2$ are weight matrices and $\mathbf{b}_1, \mathbf{b}_2$ are bias vectors, which are learnable parameters.
* $\odot$ denotes the element-wise product.

SwiGLU (Swish-based Gated Linear Unit) Formula

The SwiGLU (Swish-based Gated Linear Unit) activation function is integral to the architecture of several influential Large Language Models. Notably, it is employed in both the PaLM and LLaMA series of models.

Applications of SwiGLU in Large Language Models

The family of Gated Linear Unit (GLU) activation functions creates different variants by incorporating a specific non-linear function to control an information 'gate'. Based on this principle, what is the key distinguishing feature of the SwiGLU variant compared to other possible variants in the same family?

Deconstruct the name 'SwiGLU' (Swish-based Gated Linear Unit). For each component of the name ('Swi', 'G', 'L', 'U'), explain what it signifies about the function's structure and operation within a neural network.

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