As highlighted in the chapter introduction, tools like jax.jit and jax.vmap significantly boost performance, but primarily within the confines of a single computational device (like one GPU or one TPU core). When you have access to multiple accelerators, how can you leverage them all simultaneously to tackle larger datasets or more complex models even faster? This is where data parallelism comes into play.

Data parallelism is a common strategy in high-performance computing and machine learning. The core idea is straightforward: if you have a large dataset and multiple processing units, you can split the data among the units and have each unit perform the same computation on its assigned chunk of data.

The SPMD Model

The execution model underlying jax.pmap and many data parallelism implementations is known as SPMD, which stands for Single Program, Multiple Data.

Think of it like this:

Single Program: You write one piece of code, one function, that defines the computation you want to perform (e.g., a neural network forward pass, a physics simulation step).
Multiple Data: Your input data (like a large batch of images or simulation parameters) is split into smaller pieces or shards.
Parallel Execution: Each available device (GPU, TPU core) executes the exact same program (your function), but operates only on its assigned shard of the data.

This contrasts with other parallel models like MIMD (Multiple Instruction, Multiple Data), where different processors might be running entirely different programs. SPMD simplifies the programming model because you only need to reason about a single program structure. The parallelism comes from applying this single program to different data concurrently.

Imagine you have a function process_data(x) and a large dataset X. If you have 4 devices, the SPMD approach would look something like this:

Data is split (sharded) across multiple devices. Each device executes the same program (process_data) on its own data shard in parallel. Results are often combined afterward.

Why SPMD for JAX?

The SPMD model aligns well with JAX's functional programming approach and its focus on function transformations. jax.pmap is essentially a function transformation that takes a standard Python function written for a single data instance (or batch) and transforms it into an SPMD program that runs across multiple devices.

Key advantages of this approach include:

Code Reusability: You often write code very similar to what you'd write for a single device, and pmap handles the parallel execution details.
Scalability: It provides a direct path to scaling computations to multiple accelerators, which is essential for training large machine learning models or processing massive datasets.
Efficiency: By processing data shards concurrently, you can significantly reduce the total computation time compared to processing the entire dataset sequentially on a single device.

Of course, effective data parallelism involves more than just splitting the data. Often, devices need to communicate during the computation, for example, to aggregate results (like gradients in machine learning training) or exchange boundary information in simulations. JAX provides mechanisms called "collective operations" (like jax.lax.psum for summing values across all devices) that work seamlessly within pmap-transformed functions to handle this inter-device communication. We will explore these later in the chapter.

Understanding the SPMD concept is fundamental to using pmap effectively. It shapes how you structure your data inputs and how you think about the flow of computation across your available hardware resources. The following sections will show you how to apply this model in practice using jax.pmap.