What Are Activation Functions in Neural Networks? Functioning, Types, Real-world Examples, Challenge

Ever wondered how neural networks mimic the human brain to solve real-world problems? The secret lies in activation functions. These mathematical functions breathe life into neural networks, enabling them to learn, make decisions, and tackle complex tasks. 

Just as neurons in your brain fire signals to interpret and react, activation functions empower neural networks to process data, unlocking their ability to recognize patterns, and power technologies like voice assistants and facial recognition. You see, this has a tremendous effect on industries worldwide, thus pushing you to learn more about it.

By the end of this blog, you’ll understand what activation function in neural network are, types of activation function in neural network, real-world impact, challenges, and the potential to transform industries. 

Let’s begin!

What is an Activation Function in a Neural Network?

An activation function in a neural network acts like a “transfer function,” determining the output of a neuron by deciding which signals to pass forward. Think of it as a filter: it ensures only relevant signals move deeper into the network, just like how your brain’s neurons fire signals based on the strength of an input. 

Without this mechanism, neural networks wouldn’t have the power to process complex patterns or solve intricate problems.

Why Are Activation Functions Essential?

Activation functions are the backbone of neural networks, enabling them to process data in a way that mimics real-world decision-making. Without them, neural networks would lose their ability to handle non-linear relationships.

And why do you think neural networks need activation functions?

• They introduce non-linearity, enabling the network to learn from complex datasets.
• Without them, networks behave like linear regression models, making them unsuitable for tasks like image or speech recognition.
• Linear models struggle with non-linear relationships, limiting their ability to solve real-world problems.

By introducing activation functions, neural networks gain the power to empower innovations across industries.

How Do Activation Functions in Neural Networks Work?

The activation function mechanism is at the core of a neural network's power. After summing the weights and biases, these functions transform inputs into meaningful outputs by applying mathematical operations. This transformation enables neurons to decide whether to "activate" or remain dormant, allowing the network to detect patterns and make predictions. 

Activation functions act as decision-makers, ensuring that relevant signals progress through the network while irrelevant ones are filtered out. Let's briefly discuss its functioning.

Feedforward and Backpropagation: A Glimpse Into Functioning

To truly understand how activation functions work, you must explore two fundamental processes: feedforward and backpropagation. These mechanisms enable a neural network to process data and refine its learning. Let us break it down.

1. Feedforward: Passing Data Through Layers

• Mechanism: Data flows from the input layer, through hidden layers, to the output layer.
• Role of Activation Functions: At each neuron, the activation function transforms the intermediate output (weighted sum + bias) into a non-linear form, making it suitable for complex problem-solving.
• Purpose: Ensures the network can model non-linear relationships in data.

2. Backpropagation: Refining Through Learning

• Mechanism: After the network predicts an output, the error (difference from the target output) is calculated.
• Role of Activation Functions: Gradients (slopes) of the activation function are computed to adjust weights and biases, minimizing errors during subsequent iterations.
• Differentiability: Essential for this process, as it enables the calculation of gradients needed to fine-tune the network.

A neural network cannot learn effectively without the ability to calculate gradients. Differentiability ensures the network can adjust its weights and biases during training, enabling it to improve accuracy and tackle non-linear problems. 

Let’s break this down further in a tabular form:

Aspect	Without Differentiability	With Differentiability
Learning Process	Gradients cannot be computed, halting weight updates.	Gradients guide adjustments to weights and biases.
Accuracy	Limited learning, leading to poor model performance.	Higher accuracy through iterative learning.
Non-linear Problems	Cannot solve non-linear relationships effectively.	Excels in modeling non-linear and complex patterns.

Having explored how activation functions operate, the next step is understanding the types of activation function in neural network and their significance.

Also Read: The Role of Bias in Neural Networks

What are the Primary Two Types of Activation Functions in Neural Networks?

Activation functions are categorized into linear and non-linear types. Each serves a distinct purpose in determining how a neural network processes and learns from data.

• Linear Activation Functions: These functions preserve the linearity of inputs, making them easy to compute but limiting their ability to handle complex patterns.
• Non-Linear Activation Functions: These functions introduce non-linearity, enabling the network to capture intricate patterns and solve real-world problems. This makes them the dominant choice in modern neural networks.

Let’s understand each type of activation function in neural network in brief. 

Linear Activation Function in Neural Network

A linear activation function directly scales the input without altering its nature. Its simplicity makes it computationally efficient and beneficial for linear regression tasks or in output layers for specific problems.

Mathematical Formula

f(x)=ax      Here, a is a constant that scales the input x.

Range: The output can range from -∞ to +∞, meaning it has no upper or lower bound.

The key drawbacks of linear activation functions are as below:

Aspects	Limitations
Non-linearity	Cannot capture non-linear relationships in data.
Learning Depth	Fails to enable multi-layer networks to learn effectively.
Backpropagation	Gradients remain constant, limiting weight adjustments.

Also Read: Neural Network Model: Brief Introduction, Glossary & Backpropagation

Now that you know the linear functions, let’s understand non-linear activation functions.

Non-Linear Activation Functions

Non-linear activation functions apply transformations that enable networks to model complex patterns, classify data effectively, and solve non-linear problems.

The key importance of non-linear activation functions are:

• Capturing Complexity: Handle non-linear relationships in real-world data. 

Example: A non-linear activation function like ReLU allows a neural network to capture the relationship between ad spend and revenue, which isn’t strictly linear.

• Feature Learning: Allow deeper layers to learn hierarchical patterns.

Example: In an image recognition task, non-linear functions help learn edges in early layers and more complex shapes like faces in deeper layers.

• Gradient Flow: Ensure gradients remain meaningful during backpropagation.

Non-linear functions like Leaky ReLU prevent the vanishing gradient problem, allowing networks to learn effectively in deep architectures.

• Universal Approximation: Enable neural networks to approximate any function.

Sigmoid or Tanh functions allow networks to approximate non-linear functions like sine waves or complex classification boundaries.

Now, let’s explore the types of non-linear activation functions commonly used, along with their mathematical formulas and unique characteristics. This will give you a clearer picture of their work and why they’re so impactful.

What are the Common Non-Linear Activation Functions You Should Know?

Over the past decade, researchers have introduced over 400 non-linear activation functions to enhance neural network performance. While many are specialized, several have become foundational in deep learning applications.

Now, here are the most commonly used non-linear activation functions:

• Sigmoid (Logistic) Activation Function
• Tanh (Hyperbolic Tangent) Activation Function
• ReLU (Rectified Linear Unit)
• Leaky ReLU

Additionally, advanced activation functions have emerged to address specific challenges:

• Swish
• GELU (Gaussian Error Linear Unit)
• PReLU (Parametric ReLU)
• ELU (Exponential Linear Unit)
• SELU (Scaled Exponential Linear Unit)

Also Read: Deep Learning vs Neural Networks: Difference Between Deep Learning and Neural Networks

Up next, we will learn the formulas, characteristics, and real-world applications of activation functions.

Sigmoid (Logistic) Activation Function in Neural Network

The Sigmoid activation function compresses the input into a range between 0 and 1, making it ideal for probabilistic predictions. It transforms the weighted sum of inputs into a probability-like output.

Mathematical Formula: f(x)=1/(1+e-x)​

Range: (0, 1)

Look at the table below to understand what works and what doesn't in this function:

Advantages	Limitations
Smooth probability output for binary classification.	Prone to the vanishing gradient problem during backpropagation.
Well-suited for the final layer in binary output models.	Gradients are close to zero for extreme input values.

The use cases are as follows:

Domain	Use Case	Examples
Healthcare	Diagnosing diseases with binary outcomes.	Predict diabetes risk from patient health data.
Education	Predicting binary learning outcomes.	Determine whether a student will pass or fail based on study habits.
Finance	Fraud detection (fraud/not fraud).	Classify transactions as fraudulent or legitimate using transaction history.

Also Read: Fraud Detection in Machine Learning: What You Need To Know [2024]

Tanh (Hyperbolic Tangent) Activation Function

Tanh scales inputs from −1 to 1, making it a centered function. It is often used in hidden layers to normalize outputs closer to zero, facilitating better optimization.

Mathematical Formula: f(x)=tanh(x)=(ex-e-x)/(ex+e-x)

Range: (-1, 1)

The pros and cons of Tanh function are:

Advantages	Limitations
Zero-centered output improves optimization.	Suffers from vanishing gradients for large inputs.
Better suited for hidden layers than Sigmoid.	Computationally more expensive than ReLU.

The use cases are as follows:

Domain	Use Case	Examples
NLP	Sentiment analysis in text data.	Classify customer reviews as positive or negative.
Robotics	Control systems for precise movements.	Enable a robotic arm to adjust movements based on feedback loops.
Retail	Customer segmentation in e-commerce platforms.	Group customers based on purchasing behavior for targeted marketing.

ReLU (Rectified Linear Unit)

ReLU is the most widely used activation function in neural networks due to its simplicity and efficiency. It sets all negative inputs to zero while passing positive inputs unchanged.

Mathematical Formula: f(x)=max(0,x)

Range: [0, ∞)

ReLU’s pros and cons are as follows:

Advantages	Limitations
Computationally efficient and fast.	Prone to "dying ReLU" (neurons stuck at zero).
Handles non-linear relationships effectively.	Outputs are unbounded, leading to potential instability.

The use cases are as follows:

Domain	Use Case	Examples
Computer Vision	Object detection and image recognition.	Identify faces in images for security systems.
Gaming	AI in real-time strategy games.	Train AI to make strategic moves based on game scenarios.
Speech Processing	Speech-to-text systems.	Convert spoken words into text for virtual assistants.

Also Read: How To Convert Speech to Text with Python [Step-by-Step Process]

Leaky ReLU

Leaky ReLU solves the "dying ReLU" problem by allowing small, non-zero gradients for negative inputs. This ensures that neurons remain active during training and prevents gradient vanishing issues.

Mathematical Formula: f(x) = max(0.01*x, x)

Range: (-∞, ∞)

Below are the merits and demerits of the Leaky ReLU function: 

Advantages	Limitations
Prevents neurons from becoming inactive.	May cause instability sometimes.
Suitable for networks with sparse activations.	Slightly more complex than standard ReLU.

The use cases are as follows:

Domain	Use Case	Examples
Finance	Risk analysis and stock trend prediction.	Predict market risks and stock price movements using historical data.
Healthcare	Anomaly detection in patient data.	Identify irregularities in ECG data to detect heart conditions.
Marketing	Predicting customer churn.	Forecast which customers are likely to leave based on engagement patterns.

Advanced Activation Functions

Advanced activation functions address the limitations of simpler ones like ReLU, introducing features to improve gradient flow, enhance stability, and optimize performance in deeper neural networks. 

Explore some of the most popular advanced activation functions and their unique contributions.

Function	Unique Feature	Use Case
Swish	Smooth, non-monotonic activation with self-gating.	Deep reinforcement learning and robotics.
GELU ((Gaussian Error Linear Unit)	Combines ReLU and probabilistic smoothness.	Transformer models like BERT in NLP.
PReLU (Parametric ReLU)	Parametric slope for negative inputs, trainable.	Advanced computer vision networks.
ELU (Exponential Linear Unit)	Exponential transformation for gradient stability.	Stabilizing training in recurrent networks.
SELU (Scaled Exponential Linear Unit)	Self-normalizing behavior to control activations.	Extremely deep neural network architectures.

Now, let us discover some practical applications of these activation functions.

What are Some Practical Examples of Activation Functions?

Activation functions play a pivotal role in powering AI applications across various industries. Their ability to handle complex data has revolutionized fields such as medical diagnosis, autonomous systems, and content recommendation.

Let’s explore how different activation functions are applied in practical scenarios across diverse domains. 

Read World Examples

Here’s a quick look at their real-world applications for all the activation functions:

Activation Function	Application	Example
Sigmoid	Binary classification	Predicting spam emails or medical diagnoses.
Tanh	Sentiment analysis	Categorizing tweets as positive or negative.
ReLU	Image classification	CNNs for object detection and recognition.
Leaky ReLU	Generative Adversarial Networks (GANs)	Creating realistic images like human faces.
Softmax	Multi-class classification	Handwriting digit recognition.
GELU	Natural Language Processing (NLP) tasks	Models like BERT and ChatGPT for language understanding.
ELU	Speech recognition	Handling negative values in sound wave modeling.

These examples showcase how activation functions in neural networks transform industries by driving innovation in critical applications. 

How to Ensure You Choose the Right Activation Function?

Choosing the right activation function in neural networks is critical to achieving optimal learning and performance. Using the wrong activation function can lead to poor understanding, slower convergence, or even a complete generalization failure. 

The selection depends on the network’s architecture and the specific task. Keep reading ahead to better understand it by categorizing it into layers.

For Hidden Layers

The activation function in hidden layers introduces non-linearity, enabling the network to capture complex patterns in data. Without non-linear activation functions, the network would behave like a linear model, limiting its ability to solve non-linear problems.

Which Types Work Best?

• ReLU: Most widely used due to its simplicity and efficiency in avoiding vanishing gradients.
• Leaky ReLU: Useful for preventing dead neurons by allowing a small gradient for negative values.
• Tanh: Effective for centered data when deeper feature representations are needed.

Let’s head to the other layer category.

For Output Layers

The activation function in the output layer transforms the raw output into a format that aligns with the task type. For example, binary classification requires probabilities, while regression tasks need absolute values.

Which Types Work Best?

• Sigmoid: Ideal for binary classification problems.
• Softmax: Best for multi-class classification as it distributes probabilities across classes.
• Linear: Used in regression tasks where the output can take any real value.

Also Read: Top 10 Neural Network Architectures in 2024 ML Engineers Need to Learn

Transitioning from choosing the proper activation function, it’s essential to address the challenges of implementing them. Let’s talk about some of them.

What are the Common Challenges with Activation Functions?

Activation functions are key to unlocking a neural network's potential, but they also come with challenges that can hinder its performance. Addressing these issues ensures the network learns effectively and converges to optimal solutions. 

Below are some of the most common challenges faced when using activation functions in neural networks, along with practical solutions to mitigate them.

1. Vanishing Gradient Problem
The vanishing gradient problem occurs when gradients become extremely small as they propagate backward through the network. This slows or even halts learning, especially in deeper networks.

Have a look below at how to solve this problem:

Approach	Description
Use ReLU or its Variants	Functions like ReLU and Leaky ReLU avoid vanishing gradients by keeping gradients constant for positive inputs.
Batch Normalization	Normalizing input distributions reduces gradient shrinkage.
Careful Weight Initialization	Ensures weights are not too small, preventing rapid gradient diminishment.

2. Exploding Gradient Problem
The exploding gradient problem occurs when gradients become excessively large, leading to unstable weight updates and divergence during training. This is particularly prevalent in deep networks or those with poorly initialized weights.

Have a look below at how to solve this problem:

Approach	Description
Gradient Clipping	Caps gradients to prevent them from exceeding a certain threshold.
Use Optimizers like Adam	Adaptive optimizers can mitigate gradient instability.
Weight Regularization	Techniques like L2 regularization control weight magnitudes.

3. Dead Neurons

Dead neurons occur when activation functions like ReLU output zero for all inputs, causing the neurons to stop contributing to learning. Once a neuron becomes "dead," it can no longer recover, impacting network performance.

Have a look below at how to solve this problem:

Approach	Description
Leaky ReLU or PReLU	These variants allow a slight gradient for negative inputs, preventing neurons from becoming inactive.
Monitor Learning Rate	A lower learning rate prevents excessive updates that could deactivate neurons.
Xavier Initialization	Proper initialization avoids extreme weight values leading to dead neurons.

To consolidate your understanding, here’s a concise cheat sheet for quick reference.

Cheat Sheet for Activation Functions

With so many options available, deciding which one best suits your task can be challenging. This cheat sheet provides a quick overview of commonly used activation functions in neural networks, including their equations, ranges, and applications. 

Use it to make informed choices while designing your models.

Function Name	Equation	Range	Applications
Sigmoid	f(x) = 1 / (1 + e^(-x))	(0, 1)	Binary classification, medical diagnosis
Tanh	f(x) = tanh(x)	(-1, 1)	Sentiment analysis, robotics
ReLU	f(x) = max(0, x)	[0, ∞)	Image recognition, speech-to-text
Leaky ReLU	f(x) = x if x > 0,  f(x) = αx if x ≤ 0	(-∞, ∞)	GANs, stock prediction
Softmax	f(x_i) = e^(x_i) / ∑ e^(x_j)	(0, 1)	Multi-class classification, handwriting recognition
GELU	f(x) = 0.5x(1 + tanh(√(2/π)(x + 0.044715x^3)))	(-∞, ∞)	NLP models (e.g., BERT)
ELU	f(x) = x if x > 0,  f(x) = α(e^x - 1) if x ≤ 0	(-α, ∞)	Speech recognition, regression tasks
Swish	f(x) = x * σ(x)	(-∞, ∞)	Deep learning, reinforcement learning
SELU	f(x) = λx if x > 0,  f(x) = λ * α(e^x - 1) if x ≤ 0	(-∞, ∞)	Deep networks, big data tasks

This cheat sheet consolidates everything you need about activation functions, helping you select the most effective one for your neural network’s architecture and task!

Also, for a fun read, go through 16 Best Neural Network Project Ideas & Topics for Beginners [2025].

Conclusion

Activation functions shape how machines "think" and solve problems. Imagine solving a puzzle with only straight-edged pieces — without activation functions, that’s how a neural network would behave. 

But by choosing the right function, you transform your network into a versatile problem-solver capable of recognizing patterns in anything from cat photos to financial forecasts. 

So, if mastering these concepts excites you, upGrad's online artificial intelligence & machine learning programs are the perfect next steps. 

 

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