Discovering SwiGLU: The Activation Function Powering Modern LLMs

Activation functions are the unsung heroes of deep learning. They’re at the core of every neural network, influencing how the model learns, generalizes, and predicts. Among them, ReLU (Rectified Linear Unit) has been the gold standard for years, thanks to its simplicity and effectiveness. ??

But times are changing. The latest Large Language Models (LLMs) like LLaMA and Google’s PaLM are adopting a newer activation function: SwiGLU.

So, why the shift? Let’s explore.

The Limitations of ReLU ??

While ReLU has proven itself, it’s not without drawbacks:

1?? Not Differentiable at Zero ReLU’s gradient is undefined at x=0, which can lead to optimization issues.

2?? Saturation on the Negative Side For negative values, ReLU outputs a constant zero, causing the “Dying ReLU” problem where certain neurons never activate.

3?? Monotonicity ReLU is strictly increasing, which can sometimes limit the expressiveness of the network.

Enter SwiGLU: A Game-Changer in Activation Functions ?

SwiGLU, short for Swish-Gated Linear Unit, combines two innovative ideas:

1. Swish Activation Function: A smoother, more expressive activation function compared to ReLU.
2. GLU (Gated Linear Unit): A gating mechanism that adds more control over which parts of the input get activated.

Together, they form an activation powerhouse that’s both efficient and expressive.

Let’s Break It Down

What is GLU (Gated Linear Unit)? ??

The Gated Linear Unit (GLU) is an activation mechanism designed to improve the learning dynamics of deep models by introducing gating

Here’s how it works:

The Formula for GLU

The GLU layer takes an input vector x and computes the output as:

GLU(x)= (xW1+b1)? σ (xW2+b2)

Here’s what the terms mean:

• x: Input vector.
• W1,W2: Weight matrices for two linear transformations.
• b1,b2: Bias terms for each transformation.
• σ: Sigmoid activation function.
• ?: Element-wise multiplication.

In SwiGlu, we use Swish activation function in the place sigmoid activation function.

What is the Swish Activation Function? ??

The Swish function is defined as:

Where:

σ(x)= 1/1 + e^{-x}

It’s a smooth, non-monotonic activation function that blends linear and non-linear behaviors.

Key Properties of Swish:

• Non-zero gradients for negative inputs: Unlike ReLU, Swish doesn’t discard negative values entirely, allowing more nuanced learning.
• Smoothness: The curve is differentiable everywhere, making optimization easier.
• Expressiveness: Swish captures richer patterns in data than simple activation functions like ReLU.

Comparison of ReLU and Swish

While SwiGLU (and Swish) often outperforms ReLU in modern models, ReLU still has its edge in some scenarios:

1?? Simplicity & Efficiency: ReLU is lightweight and computationally simple with its straightforward operation: ReLU(x) = max(0, x). In contrast, SwiGLU introduces extra steps like sigmoid and element-wise multiplication, making ReLU faster for simpler models or real-time systems.

2?? Sparsity & Robustness: ReLU naturally produces sparse activations (many zero outputs), which can be beneficial for specific architectures and scenarios where sparsity improves learning or reduces overfitting.

So while SwiGLU shines in LLMs, ReLU remains a solid choice for certain tasks and smaller models!