Welcome back to part two of our exploration into activation functions and convolutional neural networks. In this article, we will continue our discussion on activation functions by delving into some of the popular ones used in deep learning.
Contents
The Rectified Linear Unit (ReLU)
One of the most famous examples is the Rectified Linear Unit (ReLU). The idea behind ReLU is to set the negative half space to zero and the positive half space to x. This piecewise linearity results in derivatives of one for the positive half space and zero everywhere else. ReLU offers a significant speed up as it does not require the use of slow exponential functions. Additionally, it overcomes the vanishing gradient problem prevalent in classical machine learning neural networks.
Leaky ReLU and Parametric ReLU
While ReLU has proven to be effective, it does have its limitations. One such limitation is the “dying ReLU” problem, where neurons with weights and biases trained to yield negative results always result in a zero derivative. To mitigate this issue, the Leaky ReLU and Parametric ReLU were introduced.
In Leaky ReLU, the negative half space is set to a scaled small number (alpha * x), where alpha is typically set to 0.01. This approach provides a similar effect to ReLU but eliminates the dying ReLU problem, as the derivative is never zero.
Parametric ReLU takes Leaky ReLU a step further by making alpha a trainable parameter. This allows the activation function to adapt its behavior according to the data, further enhancing its effectiveness.
Exponential Linear Units (ELUs)
Exponential Linear Units (ELUs) are another variant of activation functions that aim to address the limitations of ReLU. ELUs find a smooth function on the negative half space that slowly decays, resulting in derivatives of one for positive values and alpha exponent x for negative values. This approach provides a saturating effect and reduces the shift in activations. By choosing specific values for alpha and lambda, ELUs maintain a zero mean and unit variance for inputs, effectively eliminating the issue of internal covariate shift.
Batch Normalization and Other Activation Functions
Another technique to combat the covariate shift problem is batch normalization. We will cover this topic in more detail in a future article.
Other activation functions worth mentioning include the Maxout function, which learns the activation function, and radio basis functions. There is also the Softplus function, a logarithm of 1 plus e to the power of x, but it has been found to be less efficient than ReLU.
The Search for the Optimal Activation Function
Some researchers have gone to great lengths to find the optimal activation function using reinforcement learning search. However, the computational cost and complexity of this approach make it impractical for most applications. In their search, they tested various unary and binary functions, combining them in different ways. One noteworthy result is the “switch function” (x * sigma(8 * beta * x)), which has been proposed as the Sigmoid Weighted Linear Unit (SWiLU).
While these findings are interesting, it is important to consider the significance of the changes. The rectified linear unit (ReLU) consistently performs well across various tasks, making it a reliable choice. However, the scaled exponential linear unit (SELU) is also worth considering, thanks to its self-adaptation property. As a general recommendation, start with ReLU and incorporate batch normalization if needed.
In conclusion, finding the perfect activation function is an ongoing challenge, and the existing options are sufficient for most applications. Good activation functions exhibit almost linear areas to prevent vanishing gradients, have saturating areas for non-linearity, and should be monotonic to aid optimization.
FAQs
Q: What is the Rectified Linear Unit (ReLU)?
A: ReLU is an activation function that sets the negative half space to zero and the positive half space to x. It overcomes the vanishing gradient problem and allows for the training of deep neural networks.
Q: What are Leaky ReLU and Parametric ReLU?
A: Leaky ReLU sets the negative half space to a scaled small number (alpha * x), while Parametric ReLU makes alpha a trainable parameter. These variants address the dying ReLU problem and provide improved performance.
Q: What are Exponential Linear Units (ELUs)?
A: ELUs are activation functions that find a smooth function on the negative half space, providing a saturating effect and reducing the shift in activations. They also eliminate the internal covariate shift problem.
Q: Are there other activation functions worth considering?
A: Yes, some other activation functions include Maxout, radio basis functions, and softplus. However, ReLU remains the go-to choice for most applications.
Conclusion
In this article, we explored different activation functions used in deep learning, including ReLU, Leaky ReLU, Parametric ReLU, ELUs, and more. While the search for the optimal activation function continues, ReLU and its variants have proven to be effective and reliable choices. Remember to experiment and incorporate batch normalization when necessary. Stay tuned for our next article on convolutional neural networks!
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