To effectively use PyTorch for complex tasks, it helps to understand what happens behind the scenes. This chapter focuses on the foundational elements: PyTorch tensors, the mechanism for automatic differentiation (autograd), and the computational graphs that link them.

We will look at the structure of tensors and how they manage memory. You'll see how PyTorch dynamically builds computational graphs as operations execute and how the autograd engine traverses these graphs to compute gradients, like $\frac{\partial L}{\partial w}$ for a loss $L$ and weight $w$.

Key topics include:

• The internal structure of torch.Tensor.
• How dynamic computational graphs are created and used.
• The step-by-step process of the autograd engine during the backward pass.
• Implementing custom operations by defining forward and backward methods via torch.autograd.Function.
• Calculating higher-order gradients.
• Techniques for inspecting gradients and visualizing computation graphs.
• Considerations for efficient memory usage in PyTorch.

Gaining familiarity with these core components is essential for debugging complex models, optimizing performance, and implementing custom functionalities beyond the standard library offerings. We'll conclude with a practical exercise in building your own autograd function.