Jax Training Recipe

Produce an implementable JAX, Flax, and Optax training recipe with explicit PRNG management, pure functions, jit/vmap/pmap usage, gradient computation, Flax state handling, checkpointing, and debugging checks. Use when implementing a model in JAX/Flax, porting from PyTorch, debugging tracing/shape/NaN issues, or designing research code that uses JAX transformations.

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