Updated demo to work with newer version of JAX

[vinayak19th]

Since new versions of JAX don't support the abstraction using __jax_array__ anymore, the old method of passing keras.Variables to jax.jit compiled functions doesn't work.

This change fixes that by manually extracting the underlying jax arrays

[gemini-code-assist]

Summary of Changes

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This pull request updates the JAX custom training loop guide to ensure compatibility with recent JAX versions. It addresses a breaking change where the implicit __jax_array__ abstraction for Keras variables is no longer supported, by explicitly extracting the raw JAX array values.

Highlights

• JAX Compatibility Update: Modified the demo to align with newer JAX versions that no longer support the __jax_array__ abstraction for keras.Variables.
• Explicit Variable Extraction: Implemented manual extraction of underlying JAX arrays from keras.Variables for trainable, non-trainable, and optimizer variables to ensure proper functionality.

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Changelog

• guides/writing_a_custom_training_loop_in_jax.py
  • Updated variable handling to explicitly extract JAX array values from Keras variables.

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[gemini-code-assist]

Code Review

This pull request updates the JAX custom training loop guide for compatibility with newer JAX versions by extracting JAX arrays from Keras variables. No security vulnerabilities were found. However, the change is incomplete as a similar variable initialization for the second training loop example (including metrics) around line 415 in guides/writing_a_custom_training_loop_in_jax.py was missed, which will cause the guide to fail. Please apply the same fix to that section to ensure the entire guide is functional.