Skip to main content

What is activation Function? Explain ReLU, Sigmoid, and Softmax.

 

What are Activation Functions?

Activation functions are mathematical functions applied to the output of neurons in a neural network. They introduce non-linearity to the model, enabling it to learn complex patterns and relationships in the data. Without activation functions, the entire neural network would behave like a linear model, regardless of its depth, limiting its ability to model real-world problems.

Types of Activation Functions

Activation functions can be broadly categorized into:

  1. Linear Activation Functions: Outputs are proportional to the input. Rarely used because they can't model non-linear relationships.
  2. Non-Linear Activation Functions: Essential for deep learning, allowing the network to learn complex mappings. Examples include ReLU, Sigmoid, and Softmax.

ReLU (Rectified Linear Unit)

Formula:

f(x)=max⁡(0,x)f(x) = \max(0, x)
  • If x>0x > 0, f(x)=xf(x) = x.
  • If x≤0x \leq 0, f(x)=0f(x) = 0.

Characteristics:

  • Introduces non-linearity by zeroing out negative inputs.
  • Efficient computation, making it widely used in hidden layers.

Advantages:

  • Solves the vanishing gradient problem (common in older functions like Sigmoid).
  • Sparse activation: Only activates neurons with positive inputs, making computations efficient.

Disadvantages:

  • Dying ReLU Problem: Neurons can "die" (output zero for all inputs), becoming inactive during training.

Applications:

  • Commonly used in hidden layers of deep neural networks.

Sigmoid

Formula:

f(x)=11+e−xf(x) = \frac{1}{1 + e^{-x}}
  • Outputs values in the range (0,1)(0, 1).

Characteristics:

  • Maps input to a probability-like value.
  • Produces a smooth curve.

Advantages:

  • Interpretable outputs, making it suitable for binary classification tasks.

Disadvantages:

  • Vanishing Gradient Problem: Gradients become very small for large positive or negative inputs, slowing down learning in deeper networks.
  • Non-zero centered output: Causes inefficiencies in gradient updates.

Applications:

  • Used in binary classification tasks, typically in the output layer.

Softmax

Formula:

f(xi)=exi∑j=1nexjf(x_i) = \frac{e^{x_i}}{\sum_{j=1}^{n} e^{x_j}}
  • Converts a vector of logits into a probability distribution where:
    • Each output is between (0,1)(0, 1).
    • Outputs sum to 1.

Characteristics:

  • Normalizes outputs to represent probabilities across multiple classes.

Advantages:

  • Useful for multi-class classification tasks.
  • Emphasizes the largest input values, helping in decision-making.

Disadvantages:

  • Computationally expensive for a large number of classes.
  • Sensitive to large input values (numerical instability mitigated by subtracting the max logit before exponentiation).

Applications:

  • Used in the output layer of neural networks for multi-class classification.

Comparison Table

Function Formula Range Primary Use Advantages Limitations
ReLU max⁡(0,x)\max(0, x) [0,∞)[0, \infty) Hidden layers Efficient, avoids vanishing gradient Dying neurons (output always zero)
Sigmoid 11+e−x\frac{1}{1 + e^{-x}} (0,1)(0, 1) Binary classification Probabilistic output Vanishing gradient, non-zero mean
Softmax exi∑exj\frac{e^{x_i}}{\sum e^{x_j}} (0,1)(0, 1) Multi-class classification Probability distribution Computational cost

Summary

  • ReLU is used in hidden layers for its efficiency and ability to handle deep networks effectively.
  • Sigmoid is used in binary classification tasks, providing probabilistic outputs.
  • Softmax is used in multi-class classification to output probabilities over multiple classes.

Choosing the right activation function is critical to the success of a neural network and depends on the problem's requirements and network architecture.

Comments

Post a Comment

Popular posts from this blog

Simple Linear Regression - and Related Regression Loss Functions

Today's Topics: a. Regression Algorithms  b. Outliers - Explained in Simple Terms c. Common Regression Metrics Explained d. Overfitting and Underfitting e. How are Linear and Non Linear Regression Algorithms used in Neural Networks [Future study topics] Regression Algorithms Regression algorithms are a category of machine learning methods used to predict a continuous numerical value. Linear regression is a simple, powerful, and interpretable algorithm for this type of problem. Quick Example: These are the scores of students vs. the hours they spent studying. Looking at this dataset of student scores and their corresponding study hours, can we determine what score someone might achieve after studying for a random number of hours? Example: From the graph, we can estimate that 4 hours of daily study would result in a score near 80. It is a simple example, but for more complex tasks the underlying concept will be similar. If you understand this graph, you will understand this blog. Sim...
Post a Comment
Read more

What problems can AI Neural Networks solve

How does AI Neural Networks solve Problems? What problems can AI Neural Networks solve? Based on effectiveness and common usage, here's the ranking from best to least suitable for neural networks (Classification Problems, Regression Problems and Optimization Problems.) But first some Math, background and related topics as how the Neural Network Learn by training (Supervised Learning and Unsupervised Learning.)  Background Note - Mathematical Precision vs. Practical AI Solutions. Math can solve all these problems with very accurate results. While Math can theoretically solve classification, regression, and optimization problems with perfect accuracy, such calculations often require impractical amounts of time—hours, days, or even years for complex real-world scenarios. In practice, we rarely need absolute precision; instead, we need actionable results quickly enough to make timely decisions. Neural networks excel at this trade-off, providing "good enough" solutions in seco...
Post a Comment
Read more

Activation Functions in Neural Networks

  A Guide to Activation Functions in Neural Networks 🧠 Question: Without activation function can a neural network with many layers be non-linear? Answer: Provided at the end of this document. Activation functions are a crucial component of neural networks. Their primary purpose is to introduce non-linearity , which allows the network to learn the complex, winding patterns found in real-world data. Without them, a neural network, no matter how deep, would just be a simple linear model. In the diagram below the f is the activation function that receives input and send output to next layers. Commonly used activation functions. 1. Sigmoid Function 2. Tanh (Hyperbolic Tangent) 3. ReLU (Rectified Linear Unit - Like an Electronic Diode) 4. Leaky ReLU & PReLU 5. ELU (Exponential Linear Unit) 6. Softmax 7. GELU, Swish, and SiLU 1. Sigmoid Function                       The classic "S-curve," Sigmoid squashes any input value t...
Post a Comment
Read more