Multilayer Perceptron Explained And How To Train & Optimise MLPs

by | Feb 20, 2024 | Artificial Intelligence, Machine Learning

What is a Multilayer perceptron (MLP)?

In artificial intelligence and machine learning, the Multilayer Perceptron (MLP) stands as one of the foundational architectures, wielding remarkable versatility and power in solving many complex problems. Within the vast landscape of neural networks, the MLP serves as a cornerstone, offering a structured framework for processing and learning from data.

In this blog post, we embark on a journey to unravel the intricacies of the Multilayer Perceptron, delving into its architecture, functionalities, and applications. Whether you’re a seasoned machine learning practitioner seeking a more profound understanding or a newcomer eager to explore the world of neural networks, this comprehensive guide will provide invaluable insights into the inner workings of the MLP.

We’ll begin by establishing a solid foundation in neural network fundamentals, gradually progressing to dissect the anatomy of an MLP and comprehensively understanding its mechanisms. From forward propagation to backpropagation, we’ll navigate through the essential algorithms driving the training and optimisation of MLPs.

Furthermore, we’ll explore the diverse landscape of activation functions, crucial elements that dictate the behaviour and expressiveness of MLPs. Through practical examples and theoretical discussions, we’ll shed light on the strengths and limitations of various activation functions, empowering you to make informed choices in model design.

Moreover, we’ll delve into the nuances of training MLPs, unravelling the intricacies of data preprocessing, hyperparameter tuning, and regularisation techniques. Armed with this knowledge, you’ll be equipped to navigate the complexities of model training with confidence and precision.

Throughout this exploration, we’ll illuminate the real-world applications of MLPs across diverse domains, from image recognition and natural language processing to financial forecasting and beyond. By showcasing the tangible impact of MLPs in solving real-world challenges, we’ll underscore their significance as indispensable tools in the modern machine learning arsenal.

In essence, this blog post serves as a beacon of knowledge, guiding you through the fascinating landscape of Multilayer Perceptrons. Whether you’re seeking theoretical insights or practical applications, join us on this enlightening journey as we unravel the mysteries and unveil the potential of MLPs in shaping the future of artificial intelligence.

Fundamentals of Neural Networks

Neural networks represent a powerful paradigm in machine learning, drawing inspiration from the intricate connections of neurons in the human brain to process information. In this section, we’ll delve into the core concepts that form the foundation of neural networks:

Artificial Neural Networks (ANNs)

  • ANNs are computational models composed of interconnected nodes, or neurons, organised into layers.
  • These layers typically include an input layer, one or more hidden layers, and an output layer.
  • Each neuron receives input signals, performs computations, and produces an output signal.
In the 1990s, neural networks were used to develop generative AI models

A neural network consists of an input layer, one or more hidden layers, and an output layer.

Neurons and Layers

  • Neurons are the basic building blocks of neural networks, characterised by parameters such as weights and biases.
  • Layers are collections of neurons that process data sequentially.
  • The input layer receives raw data, while the output layer produces the network’s final output.
  • Hidden layers, positioned between the input and output layers, facilitate complex transformations of the input data.

Activation Functions

  • Activation functions introduce non-linearity into the neural network, enabling it to model complex relationships in data.
  • Standard activation functions include sigmoid, tanh, ReLU (Rectified Linear Unit), and softmax.
  • These functions govern the output of each neuron based on its input, allowing neural networks to capture intricate patterns in the data.
sigmoid function

The Sigmoid function

Feedforward Propagation

  • Feedforward propagation describes transmitting input data through the network to produce an output prediction.
  • It involves computing the output of each neuron in successive layers, starting from the input layer and moving towards the output layer.
  • The output of each neuron serves as the input to the neurons in the subsequent layer.


  • Backpropagation is a fundamental algorithm for training neural networks by adjusting the network’s parameters to minimise prediction errors.
  • It works by computing the gradient of the loss function concerning the network’s parameters and then updating these parameters in the opposite direction of the gradient.
  • This iterative process allows the network to learn from its mistakes and improve its performance over time.
Backpropagation is essential for image classification

By grasping these fundamental concepts, we lay the groundwork for understanding more advanced neural network architectures such as the Multilayer Perceptron (MLP). In the following sections, we’ll explore the intricacies of MLPs and their role in solving complex machine learning tasks.

Anatomy of a Multilayer Perceptron Algorithm

The Multilayer Perceptron (MLP) represents a fundamental architecture within neural networks characterised by its ability to handle complex nonlinear relationships in data.

Multilayer Perceptron Architecture

Multilayer Perceptron Architecture

In this section, we’ll dissect the anatomy of an MLP, examining its structure and components in detail:

Input Layer:

  • The input layer serves as the entry point for data into the neural network.
  • Each neuron in the input layer corresponds to a feature or input variable in the dataset.
  • The dimensionality of the input data determines the number of neurons in the input layer.

Hidden Layers

  • Hidden layers are intermediate between the input and output layers, where complex computations and transformations occur.
  • Each neuron in a hidden layer receives inputs from the neurons in the previous layer and produces an output based on a weighted sum of these inputs.
  • The number of hidden layers and the number of neurons in each hidden layer are configurable hyperparameters, which can vary based on the problem’s complexity and the data’s characteristics.

Output Layer

  • The output layer is responsible for producing the neural network’s final output.
  • The number of neurons in the output layer depends on the nature of the prediction task.
  • For binary classification tasks, a single neuron with a sigmoid activation function may be used to produce a probability score.
  • For multi-class classification tasks, the output layer may consist of multiple neurons with a softmax activation function to output class probabilities.
  • In regression tasks, the output layer typically contains a single neuron with a linear activation function to produce continuous-valued predictions.

Weighted Connections

  • Each neuron in the MLP is connected to every neuron in the subsequent layer via weighted connections.
  • These weights determine the strength of the connections between neurons and govern the influence of each input on the neuron’s output.
  • During training, the weights are adjusted through the backpropagation process to minimise prediction errors and improve the network’s performance.

Bias Neurons

  • Bias neurons are additional neurons in each layer of the MLP that introduce a constant value, known as the bias, to the weighted sum of inputs.
  • The bias allows the network to learn an offset from zero and helps improve the flexibility and expressiveness of the model.

Understanding the architecture of an MLP is essential for grasping its capabilities and limitations.

In the subsequent sections, we’ll delve deeper into the mechanisms of forward propagation, backpropagation, and training strategies employed in MLPs to harness their full potential in solving real-world problems.

What is Forward Propagation?

Forward propagation is a fundamental process in neural networks, including Multilayer Perceptrons (MLPs), where input data is sequentially passed through the network layers to produce an output prediction.

In this section, we’ll explore the mechanics of forward propagation in an MLP:

Input Data Transmission

  • Forward propagation begins with the transmission of input data through the network.
  • Each neuron in the input layer receives one feature of the input data.
  • The input values are then multiplied by the corresponding weights associated with the connections between the input layer neurons and the neurons in the first hidden layer.

Activation Function Application

  • After computing the weighted sum of inputs, each neuron applies an activation function to introduce non-linearity into the network.
  • Standard activation functions include sigmoid, tanh, ReLU, and softmax, each serving specific purposes based on the task.
  • The output of each neuron in the hidden layers becomes the input to the neurons in the subsequent layer, following the same process of weighted summation and activation function application.

Propagation Through Hidden Layers

  • The weighted summation and activation function application process is repeated for each hidden layer in the MLP.
  • Each hidden layer performs complex transformations on the input data, extracting higher-level features and representations.
  • The output of the last hidden layer serves as the input to the output layer.

Output Layer Prediction

  • In the output layer, the computed values are further processed to produce the final output prediction of the network.
  • Depending on the nature of the task (e.g., classification or regression), different configurations of neurons and activation functions may be used.
  • For instance, a single neuron with a sigmoid activation function may be employed in binary classification tasks to output a probability score.
  • In contrast, for multi-class classification tasks, the output layer may consist of multiple neurons with a softmax activation function to output class probabilities.

Output Interpretation

  • The output produced by the MLP can be interpreted based on the task’s requirements.
  • In classification tasks, the class with the highest probability score is typically chosen as the predicted class.
  • In regression tasks, the output represents the predicted continuous value.

Forward propagation enables the MLP to process input data and generate predictions efficiently. However, we rely on the backpropagation algorithm to refine these predictions and improve the model’s performance, which we’ll explore in the following section.

What is the Backpropagation Algorithm?

The backpropagation algorithm is a cornerstone of training neural networks, including Multilayer Perceptrons (MLPs), by iteratively adjusting the network’s parameters to minimise prediction errors. In this section, we’ll delve into the mechanics of the backpropagation algorithm:

Error Calculation

  • The backpropagation process begins with calculating prediction errors for each data point in the training set.
  • The error is typically measured using a loss function such as Mean Squared Error (MSE) or Mean Absolute Error (MAE) for regression tasks.
  • Cross-entropy loss functions are commonly used for classification tasks to measure the discrepancy between predicted and actual class labels.

Gradient Computation

  • Once the prediction errors are computed, the gradient of the loss function concerning each network parameter (weights and biases) is calculated.
  • This gradient represents the direction and magnitude of the steepest ascent in the loss function’s space.

Backward Propagation

  • The computed gradients are then propagated backwards through the network, starting from the output layer and moving towards the input layer.
  • At each layer, the gradients are used to update the parameters (weights and biases) using gradient descent or its variants (e.g., stochastic gradient descent, Adam optimiser).
  • The magnitude of the parameter updates is determined by the learning rate, which controls the step size in the parameter space.

Weight and Bias Updates

  • The gradients are used in each layer to update the weights and biases according to the gradient descent algorithm.
  • The weights are adjusted in the direction that minimises the loss function, while the biases provide an additional degree of freedom to shift the activation function’s output.

Iterative Refinement

  • The backpropagation algorithm is applied iteratively over multiple epochs, each representing a complete pass through the training data.
  • During training, the network’s parameters are gradually adjusted to minimise prediction errors and improve the model’s performance.
  • The training continues until a stopping criterion is met, such as reaching a specified number of epochs or observing negligible improvements in validation loss.

By iteratively applying the backpropagation algorithm, the MLP learns to make more accurate predictions by refining its internal parameters. This iterative optimisation process is essential for training deep neural networks to capture complex patterns and relationships in data effectively.

Training a Multilayer Perceptron (MLP)

Training a Multilayer Perceptron (MLP) involves adjusting its parameters, such as weights and biases, to minimise prediction errors and improve performance on a given task. In this section, we’ll explore the process of training an MLP:

1. Data Preprocessing

2. Splitting Data

  • The available dataset is typically split into training, validation, and test sets.
  • The training set is used to train the MLP, while the validation set is used to tune hyperparameters and monitor the model’s performance during training.
  • The test set is used to evaluate the final performance of the trained model on unseen data.

3. Initialisation

  • The parameters of the Multilayer Perceptron, including weights and biases, are initialised using appropriate strategies.
  • Standard initialisation techniques include random initialisation with small weights drawn from a uniform or normal distribution.
the gaussian or normal distribution

The normal distribution

4. Forward Propagation and Backpropagation

  • The training begins with forward propagation, passing input data through the network to generate predictions.
  • Prediction errors are then calculated using a suitable loss function, such as Mean Squared Error (MSE) for regression or cross-entropy loss for classification tasks.
  • The backpropagation algorithm is applied to compute the gradients of the loss function concerning the network’s parameters.
  • These gradients are used to update the parameters using optimisation algorithms such as gradient descent, stochastic gradient descent (SGD), or Adam.

5. Hyperparameter Tuning

  • Hyperparameters, such as learning rate, batch size, number of hidden layers, and number of neurons per layer, significantly impact the performance of the Multilayer Perceptron.
  • Hyperparameter tuning involves experimenting with different values for these hyperparameters to find the configuration that results in the best performance on the validation set.
  • Techniques such as grid search, random search, or Bayesian optimisation can be employed for hyperparameter tuning.

6. Monitoring Training Progress

  • Throughout the training process, monitoring various metrics, such as training loss and validation loss, is crucial to assessing the model’s performance and preventing overfitting.
  • Overfitting occurs when the model learns to memorise the training data instead of generalising it to unseen data.
  • Techniques such as early stopping, regularisation, and dropout can help mitigate overfitting and improve the model’s generalisation ability.

7. Evaluation

  • Once training is complete, the final trained model is evaluated on the test set to assess its performance on unseen data.
  • Evaluation metrics depend on the specific task but may include accuracy, precision, recall, F1-score, or mean squared error.

Following these steps, we can effectively train an MLP to learn from data and accurately predict various tasks. However, training an MLP requires careful consideration of multiple factors, including data preprocessing, hyperparameter tuning, and monitoring training progress, to ensure optimal performance and generalisation ability.

A Multilayer Perceptron Classifier Example In Python With Sklearn

Here’s a simple example of implementing a Multilayer Perceptron (MLP) using Python and the popular machine learning library, scikit-learn, to solve a binary classification problem:

# Importing necessary libraries
from sklearn.neural_network import MLPClassifier
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# Generating a synthetic dataset for binary classification
X, y = make_classification(n_samples=1000, n_features=20, n_classes=2, random_state=42)

# Splitting the dataset into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Initializing and training the MLP classifier
mlp_classifier = MLPClassifier(hidden_layer_sizes=(64, 32), activation='relu', solver='adam', max_iter=1000, random_state=42), y_train)

# Making predictions on the test set
y_pred = mlp_classifier.predict(X_test)

# Evaluating the performance of the MLP classifier
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
  • We first import the necessary libraries: MLPClassifier from scikit-learn for creating the MLP model, make_classification to generate a synthetic dataset for binary classification, train_test_split for splitting the dataset into training and testing sets, and accuracy_score for evaluating the performance of the model.
  • We generate a synthetic dataset with 1000 samples and 20 features using make_classification.
  • We split the dataset into training and testing sets using train_test_split, with 80% of the data used for training and 20% for testing.
  • We initialise the MLP classifier with two hidden layers containing 64 and 32 neurons, respectively, using the MLPClassifier class. We specify the activation function as ReLU (‘relu’) and the solver as Adam (‘adam’) and set the maximum number of iterations to 1000. These parameters can be adjusted based on the specific problem and dataset.
  • We train the MLP classifier on the training data using the fit method.
  • We make predictions on the test set using the prediction method.
  • Finally, we evaluate the MLP classifier’s performance by calculating the test set’s accuracy score and printing the result.

This example demonstrates creating, training, and evaluating a simple MLP classifier using scikit-learn for a binary classification task. You can further customise the model by adjusting hyperparameters, adding more layers, or trying different activation functions to improve its performance on your dataset.

5 Common Activation Functions For Multilayer Perceptron

Activation functions play a crucial role in neural networks, including Multilayer Perceptrons (MLPs), by introducing non-linearity into the network’s computations. In this section, we’ll explore some standard activation functions used in MLPs and discuss their characteristics:

1. Sigmoid Function

  • The sigmoid activation or logistic function squashes input values into the range [0, 1].
  • The formula:
sigmoid function used in Multilayer Perceptron
  • Sigmoid functions are commonly used in the output layer of binary classification tasks, where they interpret the output as probabilities.
  • However, sigmoid functions suffer from the vanishing gradient problem, making them less suitable for deep networks.

2. Tanh Function

  • The hyperbolic tangent (tanh) activation function is similar to the sigmoid function but squashes input values into the range [-1, 1].
  • The formula:
tanh function used in Multilayer Perceptron
  • Tanh functions are often used in hidden layers of neural networks because they produce zero-centred outputs, which can help mitigate the vanishing gradient problem compared to sigmoid functions.

3. ReLU (Rectified Linear Unit)

  • The ReLU activation function replaces negative input values with zero and leaves positive values unchanged.
  • It is defined as:
relu fuction used in Multilayer Perceptron
  • ReLU functions are computationally efficient and help mitigate the vanishing gradient problem.
  • However, they are susceptible to the “dying ReLU” problem, where neurons may become inactive during training and stop learning.

4. Leaky ReLU

  • Leaky ReLU is a variant of the ReLU activation function that allows a slight, non-zero gradient for negative input values.
  • It is defined as
leaky relu function used in Multilayer Perceptron

a is a small positive constant (e.g., 0.01)

  • Leaky ReLU helps address the dying ReLU problem by preventing neurons from becoming completely inactive.

5. Softmax Function

  • The softmax activation function is commonly used in the output layer of multi-class classification tasks to produce class probabilities.
  • It inputs a vector of arbitrary real-valued scores and outputs a probability distribution over multiple classes.
  • Softmax is:
softmax function used in Multilayer Perceptron

where xi​ is the score for class i and the sum is taken over all classes.

Understanding the characteristics and behaviours of these standard activation functions is essential for designing effective neural network architectures and achieving optimal performance in various machine learning tasks. Depending on the problem at hand, different activation functions may be more suitable, and experimentation is often necessary to determine the most appropriate choice for a given scenario.

What about Overfitting and Regularisation?

Overfitting is a common challenge in machine learning, including neural networks such as Multilayer Perceptrons (MLPs), where the model learns to memorise the training data instead of generalising well to unseen data.

In this section, we’ll explore overfitting and discuss regularisation techniques to mitigate its effects:

Understanding Overfitting

  • Overfitting occurs when a model captures noise or random fluctuations in the training data, leading to poor performance on new, unseen data.
  • It manifests as excessively complex models performing well on the training set but generalising poorly to unseen examples.
  • Overfitting can occur in MLPs when the model has too many parameters relative to the size of the training data, allowing it to memorise the training examples rather than learn underlying patterns.

Regularisation Techniques

Regularisation is a set of techniques to prevent overfitting by imposing constraints on the model’s parameters during training.

Standard regularisation techniques for MLPs include:

  1. L1 Regularization (Lasso):
    • L1 regularisation adds a penalty term to the loss function proportional to the absolute value of the weights.
    • It encourages sparsity in the model by driving some weights to precisely zero, effectively reducing the model’s complexity.
    • The regularisation term is given by λi​∣wi​∣, where λ is the regularisation parameter and wi​ are the model weights.
  2. L2 Regularization (Ridge):
    • L2 regularisation adds a penalty term to the loss function proportional to the square of the weights.
    • It discourages large weights and helps prevent overfitting by smoothing the model’s learned function.
    • The regularisation term is given by 2λiwi2​, where λ is the regularisation parameter and wi​ are the model weights.
  3. Dropout:
    • Dropout is a regularisation technique that randomly deactivates a fraction of neurons in the network during training.
    • It forces the network to learn redundant representations and prevents it from relying too heavily on any single neuron.
    • Dropout effectively creates an ensemble of smaller networks, which tend to generalise better.
  4. Early Stopping:
    • Early stopping is a simple yet effective regularisation technique that halts the training process when the performance on a validation set stops improving.
    • It prevents the model from overfitting by terminating training before memorising the training data.
    • Early stopping relies on monitoring a validation metric, such as validation loss or accuracy, and stopping training when the metric starts to degrade.

Choosing the Right Regularization Strategy

  • The choice of regularisation strategy depends on the specific characteristics of the dataset and the model architecture.
  • Experimentation and validation on a separate validation set are crucial for determining the most effective regularisation technique for a given problem.

By employing appropriate regularisation techniques, we can prevent overfitting in MLPs and improve their ability to generalise new, unseen data, leading to more robust and reliable models. Regularisation plays a vital role in training, ensuring MLPs learn meaningful patterns from data rather than memorise the data.

Applications of Multilayer Perceptron (MLP)

Multilayer Perceptrons (MLPs) have emerged as versatile and powerful tools in machine learning, finding applications across various domains. In this section, we will explore some of the critical applications of MLPs and how they have contributed to advancements in multiple fields:

1. Image Recognition and Classification

  • MLPs have been widely used in image recognition tasks, such as object detection, face recognition, and digit classification.
  • By processing pixel values as input features, MLPs can learn to identify patterns and features within images, making them essential components of computer vision systems.

2. Natural Language Processing (NLP)

  • MLPs have found applications in natural language processing tasks, including sentiment analysis, language translation, and text classification.
  • By processing text data as sequences of words or characters, MLPs can learn to extract semantic information and understand the underlying meaning of textual content.

3. Financial Forecasting

  • MLPs are utilised in financial forecasting tasks, such as stock price prediction, risk assessment, and algorithmic trading.
  • By analysing historical financial data and market trends, MLPs can learn to predict future price movements and identify profitable trading opportunities.

4. Healthcare and Biomedicine

  • In healthcare and biomedicine, MLPs are employed for disease diagnosis, medical imaging analysis, and drug discovery.
  • By analysing patient data, medical images, and genetic sequences, MLPs can assist healthcare professionals in making accurate diagnoses and developing personalised treatment plans.

5. Time Series Forecasting

  • MLPs are effective in time series forecasting tasks, such as weather prediction, demand forecasting, and anomaly detection.
  • By analysing historical time series data, MLPs can learn to predict future trends and detect abnormal patterns, enabling proactive decision-making in various domains.

6. Customer Relationship Management (CRM)

  • MLPs are utilised in CRM systems for customer segmentation, churn prediction, and recommendation systems.
  • By analysing customer behaviour and transactional data, MLPs can help businesses understand their customers’ needs and preferences, leading to more targeted marketing strategies and improved customer satisfaction.

7. Robotics and Autonomous Systems

  • MLPs are used for sensor fusion, motion planning, and control tasks in robotics and autonomous systems.
  • By processing sensor data and environmental inputs, MLPs can enable robots and autonomous vehicles to navigate complex environments and perform tasks autonomously.

8. Game Playing and Reinforcement Learning

  • MLPs are employed in game-playing and reinforcement learning tasks, such as training agents to play video games or control robotic systems.
  • By learning from trial and error, MLPs can adapt their behaviour to achieve specific goals and objectives.

These applications represent just a fraction of the vast possibilities enabled by Multilayer Perceptrons. As machine learning continues to evolve, MLPs are poised to play an increasingly integral role in driving innovation and unlocking new opportunities across diverse domains.


In this comprehensive exploration of Multilayer Perceptrons (MLPs), we’ve delved into the intricacies of one of the foundational architectures in neural networks. From understanding the fundamentals of neural networks to dissecting the anatomy of MLPs and exploring training strategies and regularisation techniques, we’ve covered many topics essential for mastering this powerful machine-learning tool.

MLPs have demonstrated remarkable versatility and effectiveness across various domains, from image classification and natural language processing to time series forecasting. Their ability to capture complex patterns and relationships in data makes them indispensable in the modern machine learning landscape.

As we’ve seen, the success of MLPs hinges on a deep understanding of their architecture, mechanisms, and training methodologies. By grasping concepts such as forward propagation, backpropagation, and regularisation, we can harness the full potential of MLPs to tackle real-world challenges with confidence and precision.

However, it’s essential to approach MLPs critically, recognising their limitations and the potential pitfalls such as overfitting. Experimentation, validation, and continuous refinement are vital to building robust and reliable MLP models that generalise unseen data and provide meaningful insights.

MLPs remain a cornerstone as machine learning evolves, offering a solid foundation for exploring more advanced architectures and techniques. By mastering the principles and practices outlined in this guide, practitioners can embark on a journey of innovation and discovery, leveraging MLPs to unlock new possibilities and drive impactful solutions in diverse domains.

In conclusion, Multilayer Perceptrons stand as a testament to the enduring power of neural networks in shaping the future of artificial intelligence and revolutionising how we approach complex problems in the digital age.

About the Author

Neri Van Otten

Neri Van Otten

Neri Van Otten is the founder of Spot Intelligence, a machine learning engineer with over 12 years of experience specialising in Natural Language Processing (NLP) and deep learning innovation. Dedicated to making your projects succeed.

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