tf.saved_model.save gives error with concrete function
Hi @shashwatj07 ,

I have replicated the reported error. Attaching [gist](https://colab.sandbox.google.com/gist/SuryanarayanaY/59315c17842502f5f9d89d1ab67793e9/62231.ipynb) here for reference. Will look into the issue and keep you posted.

Thanks! Thanks! @SuryanarayanaY 
Is there any updated documentation I could see to use AOT XLA Compilation? Hi @shashwatj07 ,

Apologies for the delay. As per the documentation of tf.saved_model.save the first argument "obj" should be a trackable object such as tf.Module or tf.train.Checkpoint or tf.keras.Model etc. In your code its just a function which might not be trackable object. Hence the problem.

I have rewritten the code to make it as trackable object and its works fine. Please refer modified code and its execution in the attached [gist](https://colab.sandbox.google.com/gist/SuryanarayanaY/83e378262931c9616231c91affce94d8/62231_r1.ipynb) here .

Thanks! This issue is stale because it has been open for 7 days with no activity. It will be closed if no further activity occurs. Thank you. This issue was closed because it has been inactive for 7 days since being marked as stale. Please reopen if you'd like to work on this further. Are you satisfied with the resolution of your issue?
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### Issue type

Support

### Have you reproduced the bug with TensorFlow Nightly?

Yes

### Source

source

### TensorFlow version

v2.11.0-rc2-17-gd5b57ca93e5

### Custom code

Yes

### OS platform and distribution

CentOS 7 (Core)

### Mobile device

_No response_

### Python version

3.10.13

### Bazel version

_No response_

### GCC/compiler version

_No response_

### CUDA/cuDNN version

11.2.2/8.1.0.77

### GPU model and memory

NVIDIA RTX A4500 20470MiB - 4x

### Current behavior?

I am trying to use TensorFlow XLA AOT Compilation. I see the error below when running the code below. I could reproduce the issue with tf-nightly as well.

### Standalone code to reproduce the issue

```shell
"""
Save the code below as create_model.py
Script that creates a dummy graph as a SavedModel named "my_model" in the same directory.
Run as:
> TF_XLA_FLAGS="--tf_xla_auto_jit=2 --tf_xla_cpu_global_jit" python create_model.py
"""


import tensorflow as tf


@tf.function(jit_compile=True)
def my_model(x):
    """
    Dummy model that does nothing expect for reducing axis 1 via sum.
    """
    return tf.reduce_sum(x, axis=1)


if __name__ == "__main__":
    import os

    this_dir = os.path.dirname(os.path.abspath(__file__))
    model_dir = os.path.join(this_dir, "my_model")

    # save the model with a concrete signature
    tf.saved_model.save(my_model, model_dir, signatures={
        "default": my_model.get_concrete_function(tf.TensorSpec(shape=[2, 5], dtype=tf.float32))
    })
```


### Relevant log output

```shell
Traceback (most recent call last):
  File "/home/sj74/xla_analysis/create_model.py", line 28, in <module>
    tf.saved_model.save(my_model, model_dir, signatures={
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 1231, in save
    save_and_return_nodes(obj, export_dir, signatures, options)
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 1267, in save_and_return_nodes
    _build_meta_graph(obj, signatures, options, meta_graph_def))
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 1440, in _build_meta_graph
    return _build_meta_graph_impl(obj, signatures, options, meta_graph_def)
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 1404, in _build_meta_graph_impl
    object_graph_proto = _serialize_object_graph(saveable_view,
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 972, in _serialize_object_graph
    _write_object_proto(obj, obj_proto, asset_file_def_index,
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/save.py", line 987, in _write_object_proto
    function_serialization.serialize_function(
  File "/home/sj74/anaconda3/envs/xla_analysis3/lib/python3.10/site-packages/tensorflow/python/saved_model/function_serialization.py", line 103, in serialize_function
    proto.concrete_functions.append(concrete_function.name)
AttributeError: '_SignatureMap' object has no attribute 'name'
```
