# ELU Activation Function

Exponential Linear Unit is a popular machine learning activation function that speeds up training and increases model performance.
Domas Bitvinskas
Jul 21, 2020
Exponential Linear Unit (ELU) is a popular activation function that speeds up learning and produces more accurate results. This article is an introduction to ELU and its position when compared to other popular activation functions. It also includes an interactive example and usage with PyTorch and Tensorflow.
Djork-Arné Clevert, Thomas Unterthiner, Sepp Hochreiter introduced ELU in Nov 2015. It outperformed ReLU-based CIFAR-100 networks at the time. To this day, ELUs are still popular among Machine Learning engineers and are well studied by now.

## What is ELU?

ELU is an activation function based on ReLU that has an extra alpha constant (α) that defines function smoothness when inputs are negative. Play with an interactive example below to understand how α influences the curve for the negative part of the function.
ELU activation
Interactive chart
Alpha constant (α)
1
Drag the slider to adjust the alpha constant.

### ELU calculation

$\text{ELU}(x) = \begin{cases} {x} & {if } x >= 0\\ {\alpha (e^x-1)} & {if } x < 0 \end{cases}$
The ELU output for positive input is the input (identity). If the input is negative, the output curve is slightly smoothed towards the alpha constant (α). The higher the alpha constant, the more negative the output for negative inputs gets.

### ELU vs ReLU

ELU and ReLU are the most popular activation functions used. Here are the advantages and disadvantages of using it when compared to other popular activation functions.

• Tend to converge faster than ReLU (because mean ELU activations are closer to zero)
• Better generalization performance than ReLU
• Fully continuous
• Fully differentiable
• Does not have a
problem
• Does not have an
problem
• Does not have a
problem

• Slower to compute (because of non-linearity for negative input values)
ELU is slower to compute, but ELU compensates this by faster convergence during training. During test time ELU is slower to compute than ReLU though.

## Usage in machine learning frameworks

### PyTorch ELU usage

To use ELU in PyTorch, use
torch.nn.ELU
function. Here's an example model that uses ELU:
import torchfrom torch import nnclass Model(nn.Module):    def __init__(self, dataset):        super(Model, self).__init__()        self.layer1 = nn.Sequential(            nn.Conv3d(in_channels=4, out_channels=2, kernel_size=2),            nn.ELU(alpha=2.0)        )    def forward(self, x):        return self.layer1(x)
Note that
alpha
is
1

### TensorFlow ELU usage

The easiest way to use ELU in TensorFlow is to use Keras layers. Example TensorFlow model below that uses ELU:
import tensorflow as tfclass Model(tf.keras.Model):    def __init__(self):        super(Model, self).__init__()        self.layer1 = tf.keras.models.Sequential([            tf.keras.layers.Conv2D(4, kernel_size=(2, 2), input_shape=(6, 6, 1)),            tf.keras.layers.ELU(alpha=2.0)        ])    def call(self, x):        return self.layer1(x)
Note that
alpha
is
1
by default. More details in TensorFlow ELU documentation.

## Next steps

Now you know how ELU works and where it stands compared to other popular activation functions.
Here's what you can do next:
alpha