Exploring Automatic Differentiation with TensorFlow's GradientTape

Problem Statement and Goal of Project

This project is a hands-on exploration of one of the most fundamental concepts in deep learning: automatic differentiation. The goal is to understand and demonstrate how TensorFlow's tf.GradientTape can be used to compute gradients—the cornerstone of training neural networks via backpropagation. This notebook serves as a practical guide to the mechanics of gradient computation, moving from simple mathematical functions to more complex scenarios involving multiple variables and persistent tapes.

Solution Approach

The project systematically explores the functionalities of tf.GradientTape through a series of clear, commented examples:

1. Basic Gradient Calculation: The notebook starts by computing the gradient of a simple function, $y = x^2$, and verifying that the result ($2x$) matches the analytical solution.
2. Trainable vs. Non-Trainable Tensors: It demonstrates the difference between using tf.Variable (which is automatically "watched" by the tape) and tf.constant (which is not). It then shows how to explicitly use tape.watch() to compute gradients with respect to a constant tensor.
3. Complex Functions and Visualization: The gradient of the sigmoid function is computed over a range of inputs, and the results are plotted using Matplotlib to visualize the relationship between the function and its derivative.
4. Gradients with Multiple Variables: The project extends the concept to a simple linear model ($y = xW + b$), calculating the gradients of a loss function with respect to multiple trainable variables (weights W and bias b).
5. Persistent Tapes: Finally, it showcases the use of a persistent=True GradientTape to compute multiple gradients from the same set of recorded operations, which is useful for more advanced models or for debugging purposes.

Technologies & Libraries

• TensorFlow: For all tensor operations and automatic differentiation using tf.GradientTape.
• Matplotlib: For visualizing the sigmoid function and its gradient.
• Jupyter Notebook: For interactive development and clear presentation of the concepts.

Description about Dataset

This project does not use a formal dataset. Instead, it relies on programmatically generated tf.Tensor objects (variables and constants) to clearly and concisely demonstrate the mathematical principles of gradient computation without the overhead of data loading and preprocessing.

Installation & Execution Guide

1. Clone the repository:

   git clone <repository-url>
   cd <repository-directory>

2. Install the required libraries:

   pip install tensorflow matplotlib

3. Run the Jupyter Notebook:

   jupyter notebook gradients.ipynb

Key Results / Performance

This project was focused on demonstrating a core machine learning concept rather than training a model for performance. The key results are the successful computations of gradients, which were verified against known analytical solutions.

For example, the gradient of $y = x^2$ at $x = 3.0$ was correctly computed as 6.0. The notebook also successfully produced the characteristic bell-shaped curve for the derivative of the sigmoid function.

Screenshots / Sample Output

Visualization of the Sigmoid Function and its Gradient

The plot below clearly illustrates the relationship between the sigmoid activation function and its derivative, computed using tf.GradientTape.

Additional Learnings / Reflections

This project was a deep dive into the mechanics of backpropagation and provided a solid foundation for understanding how neural networks learn.

• Understanding tf.GradientTape: I gained a practical and intuitive understanding of how the GradientTape API works, including the importance of "watching" variables and the flexibility offered by persistent tapes.
• Trainable Variables: The distinction between tf.Variable and tf.constant in the context of automatic differentiation is now much clearer. This knowledge is essential for building custom layers and models where I need to define which parameters should be trained.
• Foundation for Custom Training: This exercise is a direct prerequisite for creating custom training loops. By mastering gradient computation, I can now move beyond the high-level model.fit() API to implement more complex training logic for advanced architectures like GANs or Siamese Networks.

---

💡 Some interactive outputs (e.g., plots, widgets) may not display correctly on GitHub. If so, please view this notebook via nbviewer.org for full rendering.

👤 Author

Mehran Asgari

Email: imehranasgari@gmail.com.

GitHub: https://github.com/imehranasgari.

---

📄 License

This project is licensed under the Apache 2.0 License – see the LICENSE file for details.