Repository: tensorflow
Issue: ExtensionType does not allow creating tf.function methods
Labels: stat:awaiting tensorflower,type:bug,comp:tf.function,TF 2.13

### Issue type

Bug

### Have you reproduced the bug with TensorFlow Nightly?

Yes

### Source

binary

### TensorFlow version

tf 2.13.0, tf 2.12.0

### Custom code

Yes

### OS platform and distribution

Colab, Mac

### Mobile device

_No response_

### Python version

3.11.3

### Bazel version

_No response_

### GCC/compiler version

_No response_

### CUDA/cuDNN version

_No response_

### GPU model and memory

_No response_

### Current behavior?

When calling a method on ExtensionType, it seems that `self` is flattened, making it incompatible with `tf.function` and `input_signature`. Is this the intended behavior?

### Standalone code to reproduce the issue

Colab: https://colab.research.google.com/drive/19b65SIbsUgV4CKGX0DGgS0IcbXeOsOw9?usp=sharing

```shell
import tensorflow as tf

print("tf.__version__:", tf.__version__)

class A(tf.experimental.ExtensionType):
    x1: tf.Tensor
    x2: tf.Tensor

_a = A.Spec(tf.TensorSpec((5, 6)), tf.TensorSpec((5, 6)))

class B(tf.experimental.ExtensionType):
    y1: tf.Tensor
    y2: tf.Tensor
    y3: int

_b = B.Spec(tf.TensorSpec((7, 8)), tf.TensorSpec((7, 8)), 9)

class C(tf.experimental.ExtensionType):
    a1: A
    a2: A
    a3: A
    a4: A

    @tf.function(input_signature=[_b])
    def f(self, b: B):
        return b

x = tf.zeros((5, 6))
y = tf.zeros((7, 8))
a = A(x, x)
b = B(y, y, 9)
c = C(a, a, a, a)
c.f(b)
```


### Relevant log output

Colab:
```
tf.__version__: 2.12.0
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-1-6a3d1772c2f1> in <cell line: 33>()
     31 b = B(y, y, 9)
     32 c = C(a, a, a, a)
---> 33 c.f(b)

1 frames
/usr/local/lib/python3.10/dist-packages/tensorflow/python/eager/polymorphic_function/function_spec.py in cast_inputs_to_signature(inputs, input_signature)
    538         check_types=False)  # lists are convert to tuples for `tf.data`.
    539   except ValueError:
--> 540     raise ValueError("Structure of Python function inputs does not match "
    541                      "input_signature:\n"
    542                      f"{format_error_message(inputs, input_signature)}.")

ValueError: Structure of Python function inputs does not match input_signature:
  inputs: (
    C(a1=A(x1=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>, x2=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>), a2=A(x1=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>, x2=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>), a3=A(x1=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>, x2=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>), a4=A(x1=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>, x2=<tf.Tensor: shape=(5, 6), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0.]], dtype=float32)>)),
    B(y1=<tf.Tensor: shape=(7, 8), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.]], dtype=float32)>, y2=<tf.Tensor: shape=(7, 8), dtype=float32, numpy=
array([[0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0., 0., 0., 0.]], dtype=float32)>, y3=9))
  input_signature: (
    B.Spec(y1=TensorSpec(shape=(7, 8), dtype=tf.float32, name=None), y2=TensorSpec(shape=(7, 8), dtype=tf.float32, name=None), y3=9)).
```

Mac:
```shell
tf.__version__: 2.13.0
Traceback (most recent call last):
  File "/tmp/a.py", line 31, in <module>
    c.f(b)
  File "/opt/homebrew/anaconda3/envs/ml/lib/python3.11/site-packages/tensorflow/python/util/traceback_utils.py", line 153, in error_handler
    raise e.with_traceback(filtered_tb) from None
  File "/opt/homebrew/anaconda3/envs/ml/lib/python3.11/site-packages/tensorflow/python/eager/polymorphic_function/atomic_function.py", line 181, in __call__
    raise ValueError(
ValueError: Signature specifies 4 arguments, got: 10.
```

Mac (tf_nightly-2.15.0.dev20230827-cp311-cp311-macosx_12_0_arm64):
```shell
tf.__version__: 2.15.0-dev20230827
Traceback (most recent call last):
  File "/tmp/a.py", line 33, in <module>
    c.f(b)
  File "/opt/homebrew/anaconda3/envs/ml/lib/python3.11/site-packages/tensorflow/python/util/traceback_utils.py", line 153, in error_handler
    raise e.with_traceback(filtered_tb) from None
  File "/opt/homebrew/anaconda3/envs/ml/lib/python3.11/site-packages/tensorflow/core/function/polymorphism/function_type.py", line 391, in unpack_inputs
    p.type_constraint._to_tensors(bound_parameters.arguments[p.name])  # pylint: disable=protected-access
    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
KeyError: 'y1'
```