Randomized Leaky Rectified Linear Units

In the world of machine learning, there is a concept called activation functions. These functions help to determine the output of a neural network. One popular activation function is called Randomized Leaky Rectified Linear Units, or RReLU for short.

What is RReLU?

RReLU is a type of activation function that randomly samples the negative slope for activation values. The function was first introduced and used in the Kaggle NDSB Competition. During training, a random number is sampled from a uniform distribution and used as part of the function.

The mathematical formula for RReLU is as follows:

yji = xji if xji ≥ 0yji = aji * xji if xji < 0αij ∼ U(l, u), l < u and l, u ∈ [0, 1)

Where xji represents the input value, and yji represents the output value. aji is the random number sampled from the uniform distribution. The values of l and u are also part of the distribution.

How Does RReLU Work?

RReLU works by randomly selecting a negative slope value during the training phase. During training, the random value aji sampled from the uniform distribution is used as part of the function. If the input value is positive, the function returns xji. If the input value is negative, the function multiplies the input value by aji.

The purpose of randomly selecting a negative slope value is to avoid overfitting. Overfitting is a common problem in machine learning that occurs when a model is too complex and fits too closely to the training data. By introducing randomness to the function, RReLU helps to reduce the risk of overfitting and improve the model's performance on unseen data.

How is RReLU Used in Testing?

During testing, the average of all aji values from the training phase is taken. This average is then used to set aji to a deterministic result. By doing this, the function produces consistent results in testing. The formula used during testing is:

yji = xji / ((l+u)/2)

Where xji is the input value, and l and u are the values used in the uniform distribution during training.

Advantages of RReLU

RReLU provides several advantages over other activation functions:

  • Reduced Overfitting: By introducing random negative slope values during training, RReLU helps to reduce the risk of overfitting and improve the model's performance on unseen data.
  • Improved Performance: RReLU has been shown to improve the performance of neural networks compared to other activation functions.
  • Easy to Implement: RReLU is easy to implement and can be used with a variety of neural network architectures.

RReLU is a powerful activation function that provides significant benefits over other functions. It helps to reduce the risk of overfitting, improve model performance, and is easy to implement. By introducing random negative slope values during training, RReLU provides an effective way to improve the performance of neural networks and advance the field of machine learning.

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