Often in numerical computation and machine learning, you need to apply the same function to multiple data points simultaneously, a process commonly referred to as batching. While you could write explicit loops or rely on functions designed for batch operations, these approaches can sometimes be verbose or require careful manual management of array dimensions.

JAX offers a transformation, jax.vmap, designed specifically for automatic vectorization. It allows you to take a function written to operate on a single data point and efficiently apply it across an entire batch (or multiple batches) of data, often without needing to rewrite the original function's logic. vmap effectively adds a "batch dimension" to your computations automatically.

In this chapter, you will learn:

• What vectorization means and why it's useful for performance.
• How to use jax.vmap to vectorize functions operating on single or multiple arguments.
• To control which axes are mapped using the in_axes and out_axes arguments.
• How to handle more complex scenarios by nesting vmap calls.
• How vmap interacts with other JAX transformations like jit and grad.
• Practical considerations for using vmap effectively.

By the end of this chapter, you'll be able to use vmap to simplify and often accelerate your batch processing code in JAX.