Graph/memory corruption involving custom_gradient of functions involving pow
FWIW, this can be mitigated in client code with:
```diff
- unsigned_root = p**third
+ degenerate_p, p = _safe_denom(p)
+ unsigned_root = tf.where(degenerate_p, tf.constant(0., p.dtype), tf.exp(third*tf.math.log(p)))
```
(where `_safe_denom` is
```python
def _safe_denom(d: tf.Tensor) -> Tuple[tf.Tensor, tf.Tensor]:
    flag_degenerate = (d == tf.cast(0, dtype=d.dtype))
    return flag_degenerate, tf.where(flag_degenerate, tf.cast(1, dtype=d.dtype), d)
```
)
which is one reason to believe that the numerical issues in the linked TFJS issue are relevant to whatever triggers the corruption here. Hi @elfprince13 ,

Thanks for reaching us. I have replicated the behaviour and attached [gist](https://colab.research.google.com/gist/SuryanarayanaY/080f4f586f8c956ebc9f63cde5feee4c/60468.ipynb) for reference.

I observed the behaviour is changing due to the changes in setting to `tf.config.run_functions_eagerly()`. 

I am not sure of reason why you are changing the setting from tf.config.run_functions_eagerly(True) to `tf.config.run_functions_eagerly(False)` and vice versa. 

My observation is that if I set `tf.config.run_functions_eagerly(False)` then only the inconsistency observed.Same can be observed in attached gist.

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. Yes - the issue only occurs in graph execution mode and not in eager mode.
The example code shows that changing any one of the contributing factors I
highlighted fails to trigger the bug.--
~Thomas
 Hi I'm just checking if there's any projected timeline on this. Hi just following up again--
~Thomas

<details><summary>Click to expand!</summary> 
 
 ### Issue Type

Bug

### Have you reproduced the bug with TF nightly?

Yes

### Source

binary

### Tensorflow Version

2.9.1, 2.11, presumably more

### Custom Code

Yes

### OS Platform and Distribution

Linux Ubuntu 18.04, 20.04

### Mobile device

_No response_

### Python version

3.8

### Bazel version

_No response_

### GCC/Compiler version

_No response_

### CUDA/cuDNN version

_No response_

### GPU model and memory

_No response_

### Current Behaviour?

I have implemented `custom_gradient`s for `tf.function`s that smooth various Nth roots to avoid the singularity at `x=0`. I expect the value computed by the custom gradient to be used whenever that function is differentiated, and not substituted for any other value.

**HOWEVER** when the following conditions hold:
- input is a complex dtype
- the `GradientTape` is persistent
- the `tf.function` being differentiated invokes `tf.pow` directly (or indirectly through `**` operator)
- the argument is `0`

Then the custom gradient is invoked and the proper value is computed, but then discarded somewhere between returning from my custom gradient and returning from the gradient tape's internal computation.

Note: this problem does not appear when wrapping `sqrt()` as that has its own gradient implementation that presumably avoids `pow()`.

This seems likely related to numerical issues highlighted in tensorflow/tfjs#346, PLUS, some kind of graph/memory corruption, although why/how that would be conditional on the argument is beyond me.

### Standalone code to reproduce the issue

```shell
import tensorflow as tf


@tf.function
@tf.custom_gradient
def cbrt(p):
  third = 1. / 3.
  real_part_nonnegative = tf.math.real(p) >= 0
  signs = tf.cast(tf.where(real_part_nonnegative, 1.0, -1.0), p.dtype)
  p = signs * p
  unsigned_root = p ** third

  @tf.function
  def grad(upstream):
    unsigned_root_plus_eps = unsigned_root + 1e-4
    denom = 3 * unsigned_root_plus_eps * unsigned_root_plus_eps + 1e-4
    droot_dp = (1. / denom)
    grad_root = droot_dp * upstream
    tf.print("custom gradient:", tf.math.real(grad_root), tf.math.imag(grad_root))
    return grad_root

  root = signs * unsigned_root
  return root, grad
  

if __name__ == "__main__":
  tf.config.run_functions_eagerly(True)
  x = tf.Variable([-1e-2, -1e-10, 0, 1e-10, 1e-2], dtype=tf.complex64)
  with tf.GradientTape(persistent=True) as tape:
    cbrt_x = cbrt(x)
  gradients = tape.gradient(cbrt_x, x)
  tf.print("all good:", tf.math.real(gradients), tf.math.imag(gradients))

  tf.config.run_functions_eagerly(False)
  with tf.GradientTape() as tape:
    cbrt_x = cbrt(x)
  gradients = tape.gradient(cbrt_x, x)
  tf.print("all good:", tf.math.real(gradients), tf.math.imag(gradients))

  @tf.function
  def now_again_in_graph_mode(y):
    with tf.GradientTape(persistent=True) as tape:
      cbrt_y = cbrt(y)
    return tape.gradient(cbrt_y, y)
  gradients = now_again_in_graph_mode(x)
  tf.print("chaos reigns:", tf.math.real(gradients), tf.math.imag(gradients))
```


### Relevant log output

```shell
custom gradient: [7.16964388 9905.4209 9997.00098 9905.4209 7.16964388] [0 0 0 0 0]
all good: [7.16964388 9905.4209 9997.00098 9905.4209 7.16964388] [0 0 0 0 0]
custom gradient: [7.16964388 9905.4209 9997.00098 9905.4209 7.16964388] [0 0 0 0 0]
all good: [7.16964388 9905.4209 9997.00098 9905.4209 7.16964388] [0 0 0 0 0]
custom gradient: [7.16964388 9905.4209 9997.00098 9905.4209 7.16964388] [0 0 0 0 0]
chaos reigns: [7.16964388 9905.4209 -nan 9905.4209 7.16964388] [0 0 -nan 0 0]
```
</details>