autograd

Handles complex code structures like loops, conditionals, and recursion automatically, as demonstrated in the examples with neural networks and fluid simulations, without requiring manual gradient rules.

Supports both reverse-mode (backpropagation) and forward-mode differentiation, which can be composed arbitrarily for efficient gradient computation, ideal for scalar-valued functions with array inputs.

Provides a thinly-wrapped version of NumPy, allowing users to write familiar NumPy code while enabling automatic differentiation, as shown in the basic tutorial and examples.

Can compute derivatives multiple times (e.g., second, third, fourth derivatives) using functions like `egrad`, enabling advanced optimization and analysis beyond first-order gradients.