Gradient Descent: Visualizing the Foundations of Machine Learning
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Editor’s note: This article is a part of our series on visualizing the foundations of machine learning.
Welcome to the first entry in our series on visualizing the foundations of machine learning. In this series, we will aim to break down important and often complex technical concepts into intuitive, visual guides to help you master the core principles of the field. Our first entry focuses on the engine of machine learning optimization: gradient descent.
The Engine of Optimization
Gradient descent is often considered the engine of machine learning optimization. At its core, it is an iterative optimization algorithm used to minimize a cost (or loss) function by strategically adjusting model parameters. By refining these parameters, the algorithm helps models learn from data and improve their performance over time.
To understand how this works, imagine the process of descending the mountain of error. The goal is to find the global minimum, which is the lowest point of error on the cost surface. To reach this nadir, you must take small steps in the direction of the steepest descent. This journey is guided by three main factors: the model parameters, the cost (or loss) function, and the learning rate, which determines your step size.
Our visualizer highlights the generalized three-step cycle for optimization:
- Cost function: This component measures how “wrong” the model’s predictions are; the objective is to minimize this value
- Gradient: This step involves calculating the slope (the derivative) at the current position, which points uphill
- Update parameters: Finally, the model parameters are moved in the opposite direction of the gradient, multiplied by the learning rate, to move closer to the minimum
Depending on your data and computational needs, there are three primary types of gradient descent to consider. Batch GD uses the entire dataset for each step, which is slow but stable. On the other end of the spectrum, stochastic GD (SGD) uses just one data point per step, making it fast but noisy. For many, mini-batch GD offers the best of both worlds, using a small subset of data to achieve a balance of speed and stability.
Gradient descent is crucial for training neural networks and many other machine learning models. Keep in mind that the learning rate is a critical hyperparameter that dictates success of the optimization. The mathematical foundation follows the formula
\[
\theta_{new} = \theta_{old} – a \cdot \nabla J(\theta),
\]
where the ultimate goal is to find the optimal weights and biases to minimize error.
The visualizer below provides a concise summary of this information for quick reference.
![Gradient Descent: Visualizing the Foundations of Machine Learning [Infographic]](https://machinelearningmastery.com/wp-content/uploads/2026/01/mlm-visualizing-foundations-ml-gradient-descent-infographic-scaled.png)
Gradient Descent: Visualizing the Foundations of Machine Learning (click to enlarge)
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You can click here to download a PDF of the infographic in high resolution.
Machine Learning Mastery Resources
These are some selected resources for learning more about gradient descent:
- Gradient Descent For Machine Learning – This beginner-level article provides a practical introduction to gradient descent, explaining its fundamental procedure and variations like stochastic gradient descent to help learners effectively optimize machine learning model coefficients.
Key takeaway: Understanding the difference between batch and stochastic gradient descent. - How to Implement Gradient Descent Optimization from Scratch – This practical, beginner-level tutorial provides a step-by-step guide to implementing the gradient descent optimization algorithm from scratch in Python, illustrating how to navigate a function’s derivative to locate its minimum through worked examples and visualizations.
Key takeaway: How to translate the logic into a working algorithm and how hyperparameters affect results. - A Gentle Introduction To Gradient Descent Procedure – This intermediate-level article provides a practical introduction to the gradient descent procedure, detailing the mathematical notation and providing a solved step-by-step example of minimizing a multivariate function for machine learning applications.
Key takeaway: Mastering the mathematical notation and handling complex, multi-variable problems.
Be on the lookout for for additional entries in our series on visualizing the foundations of machine learning.
About Matthew Mayo
Matthew Mayo (@mattmayo13) holds a master’s degree in computer science and a graduate diploma in data mining. As managing editor of KDnuggets & Statology, and contributing editor at Machine Learning Mastery, Matthew aims to make complex data science concepts accessible. His professional interests include natural language processing, language models, machine learning algorithms, and exploring emerging AI. He is driven by a mission to democratize knowledge in the data science community. Matthew has been coding since he was 6 years old.