A shape mismatch error occurs when using the atan2 function with broadcasted inputs
@trickiwoo 
I was able to replicate the issue in Colab using TF v2.12. Please find the gists [here](https://colab.research.google.com/gist/tiruk007/fdc546be405bbbdd29c0f220e1cd6026/untitled164.ipynb) for reference. It seems like we have to dig more into this issue, we will update soon here.

Thank you ! There seems to problem with `atan2` function with broadcastable shapes under Gradient Tape.When target is `atan2` function then `tape.jacobian` expecting both target and sources to be of same shape. With both same shape there is no error and if shape changes then there is compatibility error. `tape.gradient `works fine for both cases.

However if target is some other function like `tf.nn.sigmoid()` then with broadcastable shapes `GradientTape().jacobian` works fine without error.

All of my observations replicated in the attached [gist](https://colab.research.google.com/gist/SuryanarayanaY/44d64dbe14affc55ff1d170ba0836cb0/60085.ipynb).

This seems to be valid bug for me. 

@trickiwoo , do you have any Idea/plan to fix this ?
 @trickiwoo, The error you are encountering is due to the mismatch in the shape of the gradient. In this case, since you want to compute the Jacobian of value2 with respect to b, you need to reshape the tensors a and b to have compatible shapes. 
Do this below 

import tensorflow as tf
import numpy as np

a = tf.ones([1, 1, 3, 3])
b = tf.ones([1, 1, 3, 3])  # Reshape b to have the same shape as a

def atan2(a, b):
    a_b = tf.math.atan2(a, b)
    return a_b

value = atan2(a, b)
print(value.shape)

with tf.GradientTape() as tape:
    tape.watch(b)
    value2 = atan2(a, b)

gradient = tape.jacobian(value2, b)
print(gradient) . 

Expected output is 

(1, 1, 3, 3)
tf.Tensor(
[[[[[[[[-0.5 -0.  -0. ]
       [-0.  -0.  -0. ]
       [-0.  -0.  -0. ]]]]



    [[[[-0.  -0.5 -0. ]
       [-0.  -0.  -0. ]
       [-0.  -0.  -0. ]]]]



    [[[[-0.  -0.  -0.5]
       [-0.  -0.  -0. ]
       [-0.  -0.  -0. ]]]]]




   [[[[[-0.  -0.  -0. ]
       [-0.5 -0.  -0. ]
       [-0.  -0.  -0. ]]]]



    [[[[-0.  -0.  -0. ]
       [-0.  -0.5 -0. ]
       [-0.  -0.  -0. ]]]]



    [[[[-0.  -0.  -0. ]
       [-0.  -0.  -0.5]
       [-0.  -0.  -0. ]]]]]




   [[[[[-0.  -0.  -0. ]
       [-0.  -0.  -0. ]
       [-0.5 -0.  -0. ]]]]



    [[[[-0.  -0.  -0. ]
       [-0.  -0.  -0. ]
       [-0.  -0.5 -0. ]]]]



    [[[[-0.  -0.  -0. ]
       [-0.  -0.  -0. ]
       [-0.  -0.  -0.5]]]]]]]], shape=(1, 1, 3, 3, 1, 1, 3, 3), dtype=float32) Are you satisfied with the resolution of your issue?
<a href="https://docs.google.com/forms/d/e/1FAIpQLSfaP12TRhd9xSxjXZjcZFNXPGk4kc1-qMdv3gc6bEP90vY1ew/viewform?entry.85265664=Yes&entry.2137816233=https://github.com/tensorflow/tensorflow/issues/60085">Yes</a>
<a href="https://docs.google.com/forms/d/e/1FAIpQLSfaP12TRhd9xSxjXZjcZFNXPGk4kc1-qMdv3gc6bEP90vY1ew/viewform?entry.85265664=No&entry.2137816233=https://github.com/tensorflow/tensorflow/issues/60085">No</a>
 @trickiwoo ,

I have verified the issue with nightly(2.14.0.dev20230516) and the issue is resolved with above commit. Please refer to attached [gist](https://colab.research.google.com/gist/SuryanarayanaY/9c550b6120e21d8cf8f22405a78e4600/60085_nightly-2-14.ipynb). don't i get an accolade for my input @SuryanarayanaY  i resolved the issue earlier
<details><summary>Click to expand!</summary> 
 
 ### Issue Type

Bug

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

Yes

### Source

source

### Tensorflow Version

2.11

### Custom Code

Yes

### OS Platform and Distribution

_No response_

### Mobile device

_No response_

### Python version

_No response_

### Bazel version

_No response_

### GCC/Compiler version

_No response_

### CUDA/cuDNN version

_No response_

### GPU model and memory

_No response_

### Current Behaviour?

```shell
A shape mismatch error can occur when using the atan2 function with broadcasted inputs. This is because the function broadcasts b, to match the shape of a. However, this broadcasting can introduce errors in the gradient computation. Specifically, in this case, the shape of 'b' was broadcasted to [1, 1, 3, 3] according to the output of the atan2 function, but it remains the same shape as the gradient source. To ensure consistent behavior between the forward and backward passes, it would be desirable to avoid such errors.
```


### Standalone code to reproduce the issue

```shell
import tensorflow as tf
import numpy as np

a = tf.ones([1, 1, 3, 3])
b = tf.ones([3, 3])

def atan2(a, b):
    a_b = tf.math.atan2(a, b)
    return a_b

value = atan2(a, b)
print(value.shape)
with tf.GradientTape() as tape:
    tape.watch(b)
    value2 = atan2(a, b)

gradient = tape.jacobian(value2, b)
print(gradient)
```


### Relevant log output

```shell
(1, 1, 3, 3)
ValueError: Tensor's shape (1, 1, 3, 3, 1, 1, 3, 3) is not compatible with supplied shape (1, 1, 3, 3, 3, 3).
```
</details>