Activation Functions: Linear vs. Nonlinear for Deep Learning Success

What are activation functions?

Activation functions are mathematical equations that determine the output of a neural network. They decide to deactivate neurons or activate them to get the desired output, thus the name, activation functions. In a neural network, the weighted sum of inputs is passed through the activation function.

Y = Activation function(∑ (weights*input + bias))

Importance of Activation functions

1. Introduce non-linearity for capturing complex patterns.

2. Enable complex mapping between inputs and outputs.

3. Enhance model expressiveness for better representation.

4. Support gradient-based optimization during training.

5. Handle input variability and adapt to different data distributions.

6. Control neuron activation and selective response to inputs.

7. Mitigate vanishing and exploding gradients.

8. Provide regularization effects to prevent overfitting.

9. Improve computational efficiency in large-scale models.

10. Offer flexibility for customization and adaptation to specific tasks and data characteristics.

Linear Vs Nonlinear Activation functions

Linear Activation Functions:

1. Linear activation functions produce a linear relationship between inputs and outputs.

2. The output of a linear activation function is a weighted sum of the inputs, without any nonlinearity applied.

3. Linear activation functions do not introduce nonlinearity into the network, limiting the model's expressive power.

4. Common examples of linear activation functions include Identity function and Linear function.

5. Linear activation functions are primarily used in regression tasks where the output needs to be a linear combination of the inputs.

Nonlinear Activation Functions:

1. Nonlinear activation functions introduce nonlinearity into the neural network model.

2. Nonlinear activation functions allow the network to learn and represent complex patterns and relationships in the data.

3. Nonlinear activation functions are crucial for handling nonlinear problems such as classification, image recognition, and language processing.

4. Popular examples of nonlinear activation functions include Sigmoid, Tanh, ReLU (Rectified Linear Unit), Leaky ReLU, and Softmax.

5. Nonlinear activation functions help the network learn nonlinear decision boundaries and capture intricate data patterns.

Commonly used activation functions in deep learning include:

1. Sigmoid: It squashes the input values between 0 and 1, providing a smooth non-linear transformation.

2. Tanh (Hyperbolic Tangent): Similar to the sigmoid function, it maps the input values to the range -1 to 1, introducing non-linearity.

3. ReLU (Rectified Linear Unit): It sets negative input values to zero and keeps positive values unchanged, providing a simple and effective non-linear activation.

4. Leaky ReLU: Similar to ReLU, but allows a small negative slope for negative input values, addressing the "dying ReLU" problem.

5. Softmax: It converts a vector of real values into a probability distribution, commonly used for multi-class classification problems.

6. Swish: It is a self-gated activation function that has a smooth non-linearity and has shown promising results in deep learning models.

Conclusion

Activation functions are crucial in deep learning, enabling networks to capture complex patterns and non-linear relationships. Nonlinear activations enhance model expressiveness, support gradient-based optimization, and mitigate gradient issues. Choosing the right activation function is key to achieving high-performance in various tasks.