We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Scattering 2D doesn't work when using 2^J == image size (TensorFlow backend)
Similar issues have been reported before (#284, #363) and also fixed (#412) for Torch backend. However, still not working in the tensorflow backend:

test:
```python 
import numpy as np
from kymatio.tensorflow import Scattering2D

scattering = Scattering2D(J=5, shape=(32, 32))
test_im = np.ones((1,1,32,32))
test = scattering.scattering(test_im)
```

Gives error:
```
      7 scattering = Scattering2D(J=5, shape=(32, 32))
      8 test_im = np.ones((1,1,32,32))
----> 9 test = scattering.scattering(test_im)

~/.local/lib/python3.9/site-packages/kymatio/scattering2d/frontend/tensorflow_frontend.py in scattering(self, input)
     48             input = tf.reshape(input, tf.concat(((-1,), signal_shape), 0))
     49 
---> 50             S = scattering2d(input, self.pad, self.unpad, self.backend, self.J, self.L, self.phi, self.psi,
     51                              self.max_order, self.out_type)
     52 

~/.local/lib/python3.9/site-packages/kymatio/scattering2d/core/scattering2d.py in scattering2d(x, pad, unpad, backend, J, L, phi, psi, max_order, out_type)
     13     out_S_0, out_S_1, out_S_2 = [], [], []
     14 
---> 15     U_r = pad(x)
     16 
     17     U_0_c = fft(U_r, 'C2C')

~/.local/lib/python3.9/site-packages/kymatio/scattering2d/backend/tensorflow_backend.py in __call__(self, x)
     27         paddings = [[0, 0]] * len(x.shape[:-2])
     28         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
---> 29         return tf.cast(tf.pad(x, paddings, mode="REFLECT"), tf.complex64)
     30 
     31 def unpad(in_):

~/.local/lib/python3.9/site-packages/tensorflow/python/util/traceback_utils.py in error_handler(*args, **kwargs)
    151     except Exception as e:
    152       filtered_tb = _process_traceback_frames(e.__traceback__)
--> 153       raise e.with_traceback(filtered_tb) from None
    154     finally:
    155       del filtered_tb

~/.local/lib/python3.9/site-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)
     56   try:
     57     ctx.ensure_initialized()
---> 58     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,
     59                                         inputs, attrs, num_outputs)
     60   except core._NotOkStatusException as e:

InvalidArgumentError: paddings must be less than the dimension size: 32, 32 not less than 32 [Op:MirrorPad]
```

(speculation) So possibly problems with the order of the padding being different in tensorflow from torch. 

Should also probably include some tests for these types of problems like the tests for implemented for Torch in #346 

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `kymatio/scattering2d/backend/tensorflow_backend.py`
Content:
```
1 import tensorflow as tf
2 
3 from ...backend.tensorflow_backend import TensorFlowBackend
4 
5 
6 class Pad(object):
7     def __init__(self, pad_size, input_size):
8         """
9             Padding which allows to simultaneously pad in a reflection fashion
10             and map to complex.
11             Parameters
12             ----------
13             pad_size : list of 4 integers
14                 size of padding to apply.
15             input_size : list of 2 integers
16                 size of the original signal
17         """
18         self.pad_size = pad_size
19 
20     def __call__(self, x):
21         paddings = [[0, 0]] * len(x.shape[:-2])
22         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
23         return tf.pad(x, paddings, mode="REFLECT")
24 
25 
26 class TensorFlowBackend2D(TensorFlowBackend):
27     Pad = Pad
28 
29     @staticmethod
30     def unpad(in_):
31         """
32             Slices the input tensor at indices between 1::-1
33             Parameters
34             ----------
35             in_ : tensor_like
36                 input tensor
37             Returns
38             -------
39             in_[..., 1:-1, 1:-1]
40         """
41         return in_[..., 1:-1, 1:-1]
42 
43 
44     @classmethod
45     def rfft(cls, x):
46         cls.real_check(x)
47         return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')
48 
49     @classmethod
50     def irfft(cls, x):
51         cls.complex_check(x)
52         return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))
53 
54 
55     @classmethod
56     def ifft(cls, x):
57         cls.complex_check(x)
58         return tf.signal.ifft2d(x, name='ifft2d')
59 
60     @classmethod
61     def subsample_fourier(cls, x, k):
62         """ Subsampling of a 2D image performed in the Fourier domain.
63 
64         Subsampling in the spatial domain amounts to periodization
65         in the Fourier domain, hence the formula.
66 
67         Parameters
68         ----------
69         x : tensor_like
70             input tensor with at least three dimensions.
71         k : int
72             integer such that x is subsampled by k along the spatial variables.
73 
74         Returns
75         -------
76         out : tensor_like
77             Tensor such that its Fourier transform is the Fourier
78             transform of a subsampled version of x, i.e. in
79             F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]
80 
81         """
82         cls.complex_check(x)
83 
84         y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))
85 
86         out = tf.reduce_mean(y, axis=(1, 3))
87         return out
88 
89 
90 backend = TensorFlowBackend2D
91
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/kymatio/scattering2d/backend/tensorflow_backend.py b/kymatio/scattering2d/backend/tensorflow_backend.py
--- a/kymatio/scattering2d/backend/tensorflow_backend.py
+++ b/kymatio/scattering2d/backend/tensorflow_backend.py
@@ -16,11 +16,34 @@
                 size of the original signal
         """
         self.pad_size = pad_size
+        self.input_size = input_size
 
     def __call__(self, x):
+        pad_size = list(self.pad_size)
+
+        # Clone to avoid passing on modifications.
+        new_pad_size = list(pad_size)
+
+        # This handles the case where the padding is equal to the image size.
+        if pad_size[0] == self.input_size[0]:
+            new_pad_size[0] -= 1
+            new_pad_size[1] -= 1
+        if pad_size[2] == self.input_size[1]:
+            new_pad_size[2] -= 1
+            new_pad_size[3] -= 1
+
         paddings = [[0, 0]] * len(x.shape[:-2])
-        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]
-        return tf.pad(x, paddings, mode="REFLECT")
+        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]
+
+        x_padded = tf.pad(x, paddings, mode="REFLECT")
+
+        # Again, special handling for when padding is the same as image size.
+        if pad_size[0] == self.input_size[0]:
+            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)
+        if pad_size[2] == self.input_size[1]:
+            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)
+
+        return x_padded
 
 
 class TensorFlowBackend2D(TensorFlowBackend):

{"golden_diff": "diff --git a/kymatio/scattering2d/backend/tensorflow_backend.py b/kymatio/scattering2d/backend/tensorflow_backend.py\n--- a/kymatio/scattering2d/backend/tensorflow_backend.py\n+++ b/kymatio/scattering2d/backend/tensorflow_backend.py\n@@ -16,11 +16,34 @@\n                 size of the original signal\n         \"\"\"\n         self.pad_size = pad_size\n+        self.input_size = input_size\n \n     def __call__(self, x):\n+        pad_size = list(self.pad_size)\n+\n+        # Clone to avoid passing on modifications.\n+        new_pad_size = list(pad_size)\n+\n+        # This handles the case where the padding is equal to the image size.\n+        if pad_size[0] == self.input_size[0]:\n+            new_pad_size[0] -= 1\n+            new_pad_size[1] -= 1\n+        if pad_size[2] == self.input_size[1]:\n+            new_pad_size[2] -= 1\n+            new_pad_size[3] -= 1\n+\n         paddings = [[0, 0]] * len(x.shape[:-2])\n-        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\n-        return tf.pad(x, paddings, mode=\"REFLECT\")\n+        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]\n+\n+        x_padded = tf.pad(x, paddings, mode=\"REFLECT\")\n+\n+        # Again, special handling for when padding is the same as image size.\n+        if pad_size[0] == self.input_size[0]:\n+            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)\n+        if pad_size[2] == self.input_size[1]:\n+            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)\n+\n+        return x_padded\n \n \n class TensorFlowBackend2D(TensorFlowBackend):\n", "issue": "Scattering 2D doesn't work when using 2^J == image size (TensorFlow backend)\nSimilar issues have been reported before (#284, #363) and also fixed (#412) for Torch backend. However, still not working in the tensorflow backend:\r\n\r\ntest:\r\n```python \r\nimport numpy as np\r\nfrom kymatio.tensorflow import Scattering2D\r\n\r\nscattering = Scattering2D(J=5, shape=(32, 32))\r\ntest_im = np.ones((1,1,32,32))\r\ntest = scattering.scattering(test_im)\r\n```\r\n\r\nGives error:\r\n```\r\n      7 scattering = Scattering2D(J=5, shape=(32, 32))\r\n      8 test_im = np.ones((1,1,32,32))\r\n----> 9 test = scattering.scattering(test_im)\r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/frontend/tensorflow_frontend.py in scattering(self, input)\r\n     48             input = tf.reshape(input, tf.concat(((-1,), signal_shape), 0))\r\n     49 \r\n---> 50             S = scattering2d(input, self.pad, self.unpad, self.backend, self.J, self.L, self.phi, self.psi,\r\n     51                              self.max_order, self.out_type)\r\n     52 \r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/core/scattering2d.py in scattering2d(x, pad, unpad, backend, J, L, phi, psi, max_order, out_type)\r\n     13     out_S_0, out_S_1, out_S_2 = [], [], []\r\n     14 \r\n---> 15     U_r = pad(x)\r\n     16 \r\n     17     U_0_c = fft(U_r, 'C2C')\r\n\r\n~/.local/lib/python3.9/site-packages/kymatio/scattering2d/backend/tensorflow_backend.py in __call__(self, x)\r\n     27         paddings = [[0, 0]] * len(x.shape[:-2])\r\n     28         paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\r\n---> 29         return tf.cast(tf.pad(x, paddings, mode=\"REFLECT\"), tf.complex64)\r\n     30 \r\n     31 def unpad(in_):\r\n\r\n~/.local/lib/python3.9/site-packages/tensorflow/python/util/traceback_utils.py in error_handler(*args, **kwargs)\r\n    151     except Exception as e:\r\n    152       filtered_tb = _process_traceback_frames(e.__traceback__)\r\n--> 153       raise e.with_traceback(filtered_tb) from None\r\n    154     finally:\r\n    155       del filtered_tb\r\n\r\n~/.local/lib/python3.9/site-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)\r\n     56   try:\r\n     57     ctx.ensure_initialized()\r\n---> 58     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,\r\n     59                                         inputs, attrs, num_outputs)\r\n     60   except core._NotOkStatusException as e:\r\n\r\nInvalidArgumentError: paddings must be less than the dimension size: 32, 32 not less than 32 [Op:MirrorPad]\r\n```\r\n\r\n(speculation) So possibly problems with the order of the padding being different in tensorflow from torch. \r\n\r\nShould also probably include some tests for these types of problems like the tests for implemented for Torch in #346 \n", "before_files": [{"content": "import tensorflow as tf\n\nfrom ...backend.tensorflow_backend import TensorFlowBackend\n\n\nclass Pad(object):\n    def __init__(self, pad_size, input_size):\n        \"\"\"\n            Padding which allows to simultaneously pad in a reflection fashion\n            and map to complex.\n            Parameters\n            ----------\n            pad_size : list of 4 integers\n                size of padding to apply.\n            input_size : list of 2 integers\n                size of the original signal\n        \"\"\"\n        self.pad_size = pad_size\n\n    def __call__(self, x):\n        paddings = [[0, 0]] * len(x.shape[:-2])\n        paddings += [[self.pad_size[0], self.pad_size[1]], [self.pad_size[2], self.pad_size[3]]]\n        return tf.pad(x, paddings, mode=\"REFLECT\")\n\n\nclass TensorFlowBackend2D(TensorFlowBackend):\n    Pad = Pad\n\n    @staticmethod\n    def unpad(in_):\n        \"\"\"\n            Slices the input tensor at indices between 1::-1\n            Parameters\n            ----------\n            in_ : tensor_like\n                input tensor\n            Returns\n            -------\n            in_[..., 1:-1, 1:-1]\n        \"\"\"\n        return in_[..., 1:-1, 1:-1]\n\n\n    @classmethod\n    def rfft(cls, x):\n        cls.real_check(x)\n        return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')\n\n    @classmethod\n    def irfft(cls, x):\n        cls.complex_check(x)\n        return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))\n\n\n    @classmethod\n    def ifft(cls, x):\n        cls.complex_check(x)\n        return tf.signal.ifft2d(x, name='ifft2d')\n\n    @classmethod\n    def subsample_fourier(cls, x, k):\n        \"\"\" Subsampling of a 2D image performed in the Fourier domain.\n\n        Subsampling in the spatial domain amounts to periodization\n        in the Fourier domain, hence the formula.\n\n        Parameters\n        ----------\n        x : tensor_like\n            input tensor with at least three dimensions.\n        k : int\n            integer such that x is subsampled by k along the spatial variables.\n\n        Returns\n        -------\n        out : tensor_like\n            Tensor such that its Fourier transform is the Fourier\n            transform of a subsampled version of x, i.e. in\n            F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]\n\n        \"\"\"\n        cls.complex_check(x)\n\n        y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))\n\n        out = tf.reduce_mean(y, axis=(1, 3))\n        return out\n\n\nbackend = TensorFlowBackend2D\n", "path": "kymatio/scattering2d/backend/tensorflow_backend.py"}], "after_files": [{"content": "import tensorflow as tf\n\nfrom ...backend.tensorflow_backend import TensorFlowBackend\n\n\nclass Pad(object):\n    def __init__(self, pad_size, input_size):\n        \"\"\"\n            Padding which allows to simultaneously pad in a reflection fashion\n            and map to complex.\n            Parameters\n            ----------\n            pad_size : list of 4 integers\n                size of padding to apply.\n            input_size : list of 2 integers\n                size of the original signal\n        \"\"\"\n        self.pad_size = pad_size\n        self.input_size = input_size\n\n    def __call__(self, x):\n        pad_size = list(self.pad_size)\n\n        # Clone to avoid passing on modifications.\n        new_pad_size = list(pad_size)\n\n        # This handles the case where the padding is equal to the image size.\n        if pad_size[0] == self.input_size[0]:\n            new_pad_size[0] -= 1\n            new_pad_size[1] -= 1\n        if pad_size[2] == self.input_size[1]:\n            new_pad_size[2] -= 1\n            new_pad_size[3] -= 1\n\n        paddings = [[0, 0]] * len(x.shape[:-2])\n        paddings += [[new_pad_size[0], new_pad_size[1]], [new_pad_size[2], new_pad_size[3]]]\n\n        x_padded = tf.pad(x, paddings, mode=\"REFLECT\")\n\n        # Again, special handling for when padding is the same as image size.\n        if pad_size[0] == self.input_size[0]:\n            x_padded = tf.concat([tf.expand_dims(x_padded[..., 1, :], axis=-2), x_padded, tf.expand_dims(x_padded[..., x_padded.shape[-2] -2, :], axis=-2)], axis=-2)\n        if pad_size[2] == self.input_size[1]:\n            x_padded = tf.concat([tf.expand_dims(x_padded[..., :, 1], axis=-1), x_padded, tf.expand_dims(x_padded[..., :,  x_padded.shape[-1]-2], axis=-1)], axis=-1)\n\n        return x_padded\n\n\nclass TensorFlowBackend2D(TensorFlowBackend):\n    Pad = Pad\n\n    @staticmethod\n    def unpad(in_):\n        \"\"\"\n            Slices the input tensor at indices between 1::-1\n            Parameters\n            ----------\n            in_ : tensor_like\n                input tensor\n            Returns\n            -------\n            in_[..., 1:-1, 1:-1]\n        \"\"\"\n        return in_[..., 1:-1, 1:-1]\n\n\n    @classmethod\n    def rfft(cls, x):\n        cls.real_check(x)\n        return tf.signal.fft2d(tf.cast(x, tf.complex64), name='rfft2d')\n\n    @classmethod\n    def irfft(cls, x):\n        cls.complex_check(x)\n        return tf.math.real(tf.signal.ifft2d(x, name='irfft2d'))\n\n\n    @classmethod\n    def ifft(cls, x):\n        cls.complex_check(x)\n        return tf.signal.ifft2d(x, name='ifft2d')\n\n    @classmethod\n    def subsample_fourier(cls, x, k):\n        \"\"\" Subsampling of a 2D image performed in the Fourier domain.\n\n        Subsampling in the spatial domain amounts to periodization\n        in the Fourier domain, hence the formula.\n\n        Parameters\n        ----------\n        x : tensor_like\n            input tensor with at least three dimensions.\n        k : int\n            integer such that x is subsampled by k along the spatial variables.\n\n        Returns\n        -------\n        out : tensor_like\n            Tensor such that its Fourier transform is the Fourier\n            transform of a subsampled version of x, i.e. in\n            F^{-1}(out)[u1, u2] = F^{-1}(x)[u1 * k, u2 * k]\n\n        \"\"\"\n        cls.complex_check(x)\n\n        y = tf.reshape(x, (-1, k, x.shape[1] // k, k, x.shape[2] // k))\n\n        out = tf.reduce_mean(y, axis=(1, 3))\n        return out\n\n\nbackend = TensorFlowBackend2D\n", "path": "kymatio/scattering2d/backend/tensorflow_backend.py"}]}