JAX Autograd and XLA Framework

JAX is a Python library for high-performance numerical computing and machine learning research, developed by Google. JAX combines Autograd (automatic differentiation of Python and NumPy code) with XLA (Accelerated Linear Algebra) for compiling and running numerical code on accelerators including GPUs and TPUs. Key features: automatic differentiation via grad, value_and_grad, and jacfwd/jacrev for computing gradients of arbitrary-order derivatives of Python functions, supporting forward-mode and reverse-mode autodiff. Just-In-Time (JIT) compilation via jit decorator that compiles Python numerical functions to optimized XLA kernels for GPU and TPU execution, achieving C++-level performance from Python code. Vectorization via vmap for automatic batching of operations, enabling efficient parallel computation without manual loop writing. Parallel computation via pmap for distributing computations across multiple GPU or TPU devices with single-program multiple-data (SPMD) parallelism. Functional programming paradigm where functions are pure and stateless, enabling safe compilation, parallelization, and differentiation. NumPy-compatible API (jax.numpy) that mirrors numpy functions but with device-agnostic execution on CPU, GPU, and TPU. Hardware acceleration transparently dispatching operations to the best available accelerator. Tree data structures (pytrees) for handling nested Python data structures like dictionaries and tuples in transformations. Optax and Flax libraries built on JAX for neural network optimization and model construction. Haiku and Stax for neural network module abstractions. Diffrax for numerical differential equation solving. Used by Google DeepMind for AlphaFold and RL research. Cross-platform on Linux with NVIDIA GPUs, Google Cloud TPUs, and Apple Silicon via Metal.