python-jax

JAX's `jax.grad` function computes automatic differentiation by transforming your code to generate gradient functions. Pass a function to `jax.grad` and it returns a new function that computes gradients with respect to the first argument, enabling gradient-based optimization and machine-learning workflows.

JAX provides GPU/TPU acceleration with minimal code changes through `jax.jit` for JIT compilation and seamless hardware offloading. Compile numerical kernels once and run them on accelerators automatically, achieving high-performance computation without rewriting your NumPy-compatible array operations.

JAX's `jax.vmap` applies automatic vectorization to transform scalar functions into batched operations, eliminating explicit loops. Use `vmap` to automatically batch across any dimension and combine it with `jit` for compiled, vectorized performance on GPU/TPU.

JAX's `jax.pmap` enables data parallelism across multiple devices by distributing array slices to each device and collecting results. Combine `pmap` with `vmap` and `grad` for scalable distributed machine-learning pipelines with multi-device parallelism.

JAX supports composing transformations: nest `grad` calls for higher-order derivatives, combine `grad` with `vmap` and `jit` for batched gradients, and use nested pytrees to handle complex data structures. This enables building sophisticated gradient-based algorithms and research workflows.

JAX uses a NumPy-like API with immutable arrays and explicit random-key management as key differences. Functional programming with `jax.grad`, `jax.jit`, and `jax.vmap` adds concepts, but NumPy familiarity transfers directly—start with a simple function and apply transformations incrementally.