Leaky ReLU

Leaky Rectified Linear Unit (Leaky ReLU) is an activation function commonly used in artificial neural networks. It is a variant of the popular Rectified Linear Unit (ReLU) activation function. Leaky ReLU addresses the issue of dying ReLU neurons by allowing a small, non-zero gradient when the input is negative.

Definition

The Leaky ReLU activation function is defined as:

f(x) = { x, if x > 0;
ax, if x <= 0; }

where a is a small constant, usually in the range of 0.01 to 0.2. This small gradient for negative inputs prevents neurons from dying, as they can still learn and update their weights even when the input is negative.

Advantages of Leaky ReLU

Leaky ReLU offers several advantages over the standard ReLU activation function:

1. Prevents Dying Neurons: The main advantage of Leaky ReLU is that it prevents neurons from dying, which can occur when the gradient of the ReLU function is zero for negative inputs. By allowing a small gradient for negative inputs, Leaky ReLU ensures that neurons can still contribute to the learning process.
2. Improved Learning: Leaky ReLU has been shown to improve the learning process in deep neural networks by addressing the issue of dying neurons. This can lead to faster convergence and better overall performance of the network.
3. Non-Zero Output: Unlike ReLU, which outputs zero for negative inputs, Leaky ReLU outputs a non-zero value for negative inputs. This can be beneficial in certain cases where the network needs to capture information from negative inputs.
4. Easy Implementation: Implementing Leaky ReLU is straightforward, as it only requires a simple modification to the ReLU function by adding a small slope for negative inputs.

Disadvantages of Leaky ReLU

While Leaky ReLU offers several advantages, it also has some drawbacks:

1. Additional Hyperparameter: The slope parameter 'a' in the Leaky ReLU function is an additional hyperparameter that needs to be tuned. Choosing the right value for 'a' can impact the performance of the network.
2. Not Monotonic: Unlike the ReLU function, which is a simple threshold function, Leaky ReLU is not strictly monotonic. This can introduce non-convexities in the network, which may affect optimization.
3. Complexity: Introducing a non-zero slope for negative inputs adds complexity to the activation function, which can make it harder to analyze and understand compared to simpler activation functions.

Comparison with Other Activation Functions

Leaky ReLU is one of several activation functions used in neural networks. Here is a comparison of Leaky ReLU with other popular activation functions: