What is CosLU?
CosLU, short for Cosine Linear Unit, is an activation function used in Artificial Neural Networks. It uses a combination of trainable parameters and the cosine function to map the input data to a non-linear output.
CosLU is defined using the following formula:
$$CosLU(x) = (x + \alpha \cos(\beta x))\sigma(x)$$
Where $\alpha$ and $\beta$ are multiplier parameters that are learned during training, and $\sigma(x)$ is a standard activation function like the sigmoid or the rectified linear unit function. The CosLU function can be seen as a variation of the rectified linear unit (ReLu) function where the linear part of the function is replaced with a cosine wave.
How does CosLU work?
The Cosine Linear Unit function takes an input value $x$ and adds a cosine wave of the form $\alpha \cos(\beta x)$ to it. The amplitude and frequency of the cosine wave are determined by the learned parameters $\alpha$ and $\beta$ respectively.
The output of the CosLU function is then multiplied by a standard activation function like the sigmoid function, which maps the output to a non-linear range.
By using a combination of cosine waves and standard activation functions, the CosLU function is able to capture complex patterns in the input data and transform them into a non-linear output.
What are the advantages of using CosLU?
One of the main advantages of using the Cosine Linear Unit function is its ability to capture non-linear patterns in the input data. The cosine wave component of the function allows it to capture cyclic patterns that might be present in the input data.
Another advantage of using CosLU is that it is differentiable, meaning that it can be used in backpropagation algorithms to train neural networks. The trainable parameters $\alpha$ and $\beta$ can be updated during training to optimize the performance of the network.
Finally, CosLU has been shown to be effective in a variety of applications, including image recognition, speech recognition, and natural language processing. In some cases, it has been shown to outperform other activation functions like the sigmoid function or the ReLu function.
CosLU is a powerful activation function that is able to capture complex, non-linear patterns in input data. By using a combination of trainable parameters and the cosine function, CosLU is able to optimize its performance during training and outperform other activation functions in some cases.
If you are working with Artificial Neural Networks and want to explore new ways of capturing complex patterns in your input data, consider trying the Cosine Linear Unit function.
