The Squared ReLU activation function is a nonlinear mathematical function used in the Primer architecture within the Transformer layer. It is simply the activation function created by squaring the Rectified Linear Unit (ReLU) activations.

What is an Activation Function?

In artificial neural networks, the decision-making process of a neuron is modeled with the help of mathematical functions called activation functions. The input signal is given to the neuron, and the activation function decides whether to fire or not, based on the decision threshold.

In the context of artificial intelligence, the activation function is an elementary computational unit that performs a specific data transformation operation.

What is the Rectified Linear Unit (ReLU)?

The Rectified Linear Unit (ReLU) activation function consists of a linear function that outputs the input directly if it is positive, but if the input is negative, it outputs zero. It is one of the most common activation functions used in deep learning, as it offers a simple computational structure and allows efficient neural network optimization. However, ReLU has some limitations, including the dying ReLU problem, where some neurons cease to activate after a period of training because their output remains consistently negative.

What is Squared ReLU?

Squared ReLU, as mentioned above, is the ReLU activation function squared. It is a non-monotonic function, meaning that it is not consistently increasing or decreasing as the input values change. However, it has been shown to be an effective replacement to other commonly used activation functions such as GELU and Swish.

Why use Squared ReLU?

Squared ReLU has been found to deliver better quality results than other activation functions, without the addition of extra parameters or complicated computations. It has also been observed that higher order polynomials such as squared ReLU are effective in improving the performance of neural networks, as they capture more intricate nonlinearities in the input signal that would otherwise be difficult to model.

Furthermore, squared ReLU differs from other commonly used activation functions such as ReLU, GELU, and Swish in terms of its asymptotic behavior as the inputs get increasingly large. Squared ReLU has distinctly different asymptotics, which means that it behaves differently from other activation functions as the input values get very large.

Conclusion:

Squared ReLU is a simple yet effective non-linear activation function used in deep learning models, particularly in the Primer architecture of the Transformer layer. It is simply the ReLU activation function squared and has demonstrated better quality results compared to other typical activation functions with its higher-order polynomial structure. It is also invariant under linear transformations and has a different asymptotic behavior than other common activation functions, which makes it a suitable replacement in deep learning models where the quality of results is a prime concern.

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