Clipped Relu

Rectified Linear Unit (ReLU) Activation Function with Learnable Threshold

Introduction

The Rectified Linear Unit (ReLU) activation function is a commonly used activation function in deep learning models. It is defined as follows:

``` f(x) = max(0, x) ```

where x is the input to the function.

ReLU is a simple and efficient activation function that has been shown to work well in a variety of applications. However, it can suffer from the problem of dying ReLUs, where the gradient of the function is zero for negative inputs. This can lead to vanishing gradients and make it difficult to train deep models.

One way to address the problem of dying ReLUs is to use a ReLU activation function with a learnable threshold. This threshold is a parameter of the activation function that can be learned during training. The threshold determines the point at which the activation function begins to saturate.

Implementation

The following code shows how to implement a ReLU activation function with a learnable threshold in Keras:

```python import tensorflow as tf class LeakyReLU(tf.keras.layers.Layer): def __init__(self, threshold=0.0, **kwargs): super(LeakyReLU, self).__init__(**kwargs) self.threshold = threshold def call(self, inputs): return tf.maximum(self.threshold * inputs, inputs) ```

This layer can be used in any Keras model just like any other activation function.

Benefits

Using a ReLU activation function with a learnable threshold can provide several benefits, including:

• Reduced risk of dying ReLUs: The learnable threshold allows the activation function to be more sensitive to negative inputs, which can help to prevent dying ReLUs.
• Improved training stability: The learnable threshold can help to stabilize the training process by preventing vanishing gradients.
• Increased accuracy: In some cases, using a ReLU activation function with a learnable threshold can lead to improved accuracy on downstream tasks.

Conclusion

The ReLU activation function with a learnable threshold is a simple and effective way to improve the performance of deep learning models. This activation function can help to reduce the risk of dying ReLUs, improve training stability, and increase accuracy.