I have been doing a project on image matching, so I need to find correspondences between 2 images. To get descriptors, I will need a interpolate function. However, when I read about a equivalent function which is done in Tensorflow, I still don’t get how to implement tf.gather_nd(parmas, indices, barch_dims) in Pytorch. Especially when there is a argument: batch_dims. I have gone through stackoverflow and there is no perfect equivalence yet.
The referred interpolate function in Tensorflow is below and I have been trying to implement this in Pytorch Arguments' information is below:
inputs is a dense feature map[i] from a for loop of batch size, which means it is 3D[H, W, C](in pytorch is [C, H, W])
pos is a set of random point coordinate shapes like [[i, j], [i, j],...,[i, j]], so it is 2D when it goes in interpolate function(in pytorch is [[i,i,...,i], [j,j,...,j]])
and it then expands both of their dimensions when they get into this function
I just want a perfect implement of tf.gather_nd with argument batch_dims. Thank you!
And here's a simple example of using it:
pos = tf.ones((12, 2)) ## stands for a set of coordinates [[i, i,…, i], [j, j,…, j]]
inputs = tf.ones((4, 4, 128)) ## stands for [H, W, C] of dense feature map
outputs = interpolate(pos, inputs, batched=False)
print(outputs.get_shape()) # We get (12, 128) here
interpolate function (tf version):
def interpolate(pos, inputs, nd=True):
pos = tf.expand_dims(pos, 0)
inputs = tf.expand_dims(inputs, 0)
h = tf.shape(inputs)[1]
w = tf.shape(inputs)[2]
i = pos[:, :, 0]
j = pos[:, :, 1]
i_top_left = tf.clip_by_value(tf.cast(tf.math.floor(i), tf.int32), 0, h - 1)
j_top_left = tf.clip_by_value(tf.cast(tf.math.floor(j), tf.int32), 0, w - 1)
i_top_right = tf.clip_by_value(tf.cast(tf.math.floor(i), tf.int32), 0, h - 1)
j_top_right = tf.clip_by_value(tf.cast(tf.math.ceil(j), tf.int32), 0, w - 1)
i_bottom_left = tf.clip_by_value(tf.cast(tf.math.ceil(i), tf.int32), 0, h - 1)
j_bottom_left = tf.clip_by_value(tf.cast(tf.math.floor(j), tf.int32), 0, w - 1)
i_bottom_right = tf.clip_by_value(tf.cast(tf.math.ceil(i), tf.int32), 0, h - 1)
j_bottom_right = tf.clip_by_value(tf.cast(tf.math.ceil(j), tf.int32), 0, w - 1)
dist_i_top_left = i - tf.cast(i_top_left, tf.float32)
dist_j_top_left = j - tf.cast(j_top_left, tf.float32)
w_top_left = (1 - dist_i_top_left) * (1 - dist_j_top_left)
w_top_right = (1 - dist_i_top_left) * dist_j_top_left
w_bottom_left = dist_i_top_left * (1 - dist_j_top_left)
w_bottom_right = dist_i_top_left * dist_j_top_left
if nd:
w_top_left = w_top_left[..., None]
w_top_right = w_top_right[..., None]
w_bottom_left = w_bottom_left[..., None]
w_bottom_right = w_bottom_right[..., None]
interpolated_val = (
w_top_left * tf.gather_nd(inputs, tf.stack([i_top_left, j_top_left], axis=-1), batch_dims=1) +
w_top_right * tf.gather_nd(inputs, tf.stack([i_top_right, j_top_right], axis=-1), batch_dims=1) +
w_bottom_left * tf.gather_nd(inputs, tf.stack([i_bottom_left, j_bottom_left], axis=-1), batch_dims=1) +
w_bottom_right * tf.gather_nd(inputs, tf.stack([i_bottom_right, j_bottom_right], axis=-1), batch_dims=1)
)
interpolated_val = tf.squeeze(interpolated_val, axis=0)
return interpolated_val
As far as I'm aware there is no directly equivalent of tf.gather_nd in PyTorch and implementing a generic version with batch_dims is not that simple. However, you likely don't need a generic version, and given the context of your interpolate function, a version for [C, H, W] would suffice.
At the beginning of interpolate you add a singular dimension to the front, which is the batch dimension. Setting batch_dims=1 in tf.gather_nd means there is one batch dimension at the beginning, therefore it applies it per batch, i.e. it indexes inputs[0] with pos[0] etc. There is no benefit of adding a singular batch dimension, because you could have just used the direct computation.
# Adding singular batch dimension
# Shape: [1, num_pos, 2]
pos = tf.expand_dims(pos, 0)
# Shape: [1, H, W, C]
inputs = tf.expand_dims(inputs, 0)
batched_result = tf.gather_nd(inputs, pos, batch_dims=1)
single_result = tf.gater_nd(inputs[0], pos[0])
# The first element in the batched result is the same as the single result
# Hence there is no benefit to adding a singular batch dimension.
tf.reduce_all(batched_result[0] == single_result) # => True
Single version
In PyTorch the implementation for [H, W, C] can be done with Python's indexing. While PyTorch usually uses [C, H, W] for images, it's only a matter of what dimension to index, but let's keep them the same as in TensorFlow for the sake of comparison. If you were to index them manually, you would do it as such: inputs[pos_h[0], pos_w[0]], inputs[pos_h[1], pos_w[1]] and so on. PyTorch allows you to do that automatically by providing the indices as lists: inputs[pos_h, pos_w], where pos_h and pos_w have the same length. All you need to do is split your pos into two separate tensors, one for the indices along the height dimension and the other along the width dimension, which you also did in the TensorFlow version.
inputs = torch.randn(4, 4, 128)
# Random positions 0-3, shape: [12, 2]
pos = torch.randint(4, (12, 2))
# Positions split by dimension
pos_h = pos[:, 0]
pos_w = pos[:, 1]
# Index the inputs with the indices per dimension
gathered = inputs[pos_h, pos_w]
# Verify that it's identical to TensorFlow's output
inputs_tf = tf.convert_to_tensor(inputs.numpy())
pos_tf = tf.convert_to_tensor(pos.numpy())
gathered_tf = tf.gather_nd(inputs_tf, pos_tf)
gathered_tf = torch.from_numpy(gathered_tf.numpy())
torch.equal(gathered_tf, gathered) # => True
If you want to apply it to a tensor of size [C, H, W] instead, you only need to change the dimensions you want to index:
# For [H, W, C]
gathered = inputs[pos_h, pos_w]
# For [C, H, W]
gathered = inputs[:, pos_h, pos_w]
Batched version
Making it a batched batched version (for [N, H, W, C] or [N, C, H, W]) is not that difficult, and using that is more appropriate, since you're dealing with batches anyway. The only tricky part is that each element in the batch should only be applied to the corresponding batch. For this the batch dimensions needs to be enumerated, which can be done with torch.arange. The batch enumeration is just the list with the batch indices, which will be combined with the pos_h and pos_w indices, resulting in inputs[0, pos_h[0, 0], pos_h[0, 0]], inputs[0, pos_h[0, 1], pos_h[0, 1]] ... inputs[1, pos_h[1, 0], pos_h[1, 0]] etc.
batch_size = 3
inputs = torch.randn(batch_size, 4, 4, 128)
# Random positions 0-3, different for each batch, shape: [3, 12, 2]
pos = torch.randint(4, (batch_size, 12, 2))
# Positions split by dimension
pos_h = pos[:, :, 0]
pos_w = pos[:, :, 1]
batch_enumeration = torch.arange(batch_size) # => [0, 1, 2]
# pos_h and pos_w have shape [3, 12], so the batch enumeration needs to be
# repeated 12 times per batch.
# Unsqueeze to get shape [3, 1], now the 1 could be repeated to 12, but
# broadcasting will do that automatically.
batch_enumeration = batch_enumeration.unsqueeze(1)
# Index the inputs with the indices per dimension
gathered = inputs[batch_enumeration, pos_h, pos_w]
# Again, verify that it's identical to TensorFlow's output
inputs_tf = tf.convert_to_tensor(inputs.numpy())
pos_tf = tf.convert_to_tensor(pos.numpy())
# This time with batch_dims=1
gathered_tf = tf.gather_nd(inputs_tf, pos_tf, batch_dims=1)
gathered_tf = torch.from_numpy(gathered_tf.numpy())
torch.equal(gathered_tf, gathered) # => True
Again, for [N, C, H, W], only the dimensions that are indexed need to be changed:
# For [N, H, W, C]
gathered = inputs[batch_enumeration, pos_h, pos_w]
# For [N, C, H, W]
gathered = inputs[batch_enumeration, :, pos_h, pos_w]
Just a little side note on the interpolate implementation, rounding the positions (floor and ceil respectively) doesn't make sense, because indices must be integers, so it has no effect, as long as your positions are actual indices. That also results in i_top_left and i_bottom_left being the same value, but even if they are to be rounded differently, they are always 1 position apart. Furthermore, i_top_left and i_top_right are literally the same. I don't think that this function produces a meaningful output. I don't know what you're trying to achieve, but if you're looking for image interpolation you could have a look at torch.nn.functional.interpolate.
This is just an extension of Michael Jungo's batched version answer when pos is 2D array instead of 1D array (excluding batch dimension).
bs = 2
H = 4
W = 6
C = 3
inputs = torch.randn(bs, H, W, C)
pos_h = torch.randint(H, (bs, H, W))
pos_w = torch.randint(W, (bs, H, W))
batch_enumeration = torch.arange(bs)
batch_enumeration = batch_enumeration.unsqueeze(1).unsqueeze(2)
inputs.shape
Out[34]: torch.Size([2, 4, 6, 3])
pos_h.shape
Out[35]: torch.Size([2, 4, 6])
pos_w.shape
Out[36]: torch.Size([2, 4, 6])
batch_enumeration.shape
Out[37]: torch.Size([2, 1, 1])
gathered = inputs[batch_enumeration, pos_h, pos_w]
For channel first, we also need to enumerate channels
inputs = torch.randn(bs, C, H, W)
pos_h = torch.randint(H, (bs, 1, H, W))
pos_w = torch.randint(W, (bs, 1, H, W))
batch_enumeration = torch.arange(bs)
batch_enumeration = batch_enumeration.unsqueeze(1).unsqueeze(2).unsqueeze(3)
channel_enumeration = torch.arange(C)
channel_enumeration = channel_enumeration.unsqueeze(0).unsqueeze(2).unsqueeze(3)
inputs.shape
Out[49]: torch.Size([2, 3, 4, 6])
pos_h.shape
Out[50]: torch.Size([2, 1, 4, 6])
pos_w.shape
Out[51]: torch.Size([2, 1, 4, 6])
batch_enumeration.shape
Out[52]: torch.Size([2, 1, 1, 1])
channel_enumeration.shape
Out[57]: torch.Size([1, 3, 1, 1])
gathered = inputs[batch_enumeration, channel_enumeration, pos_h, pos_w]
gathered.shape
Out[59]: torch.Size([2, 3, 4, 6])
Let's verify
inputs_np = inputs.numpy()
pos_h_np = pos_h.numpy()
pos_w_np = pos_w.numpy()
gathered_np = gathered.numpy()
pos_h_np[0,0,0,0]
Out[68]: 0
pos_w_np[0,0,0,0]
Out[69]: 3
inputs_np[0,:,0,3]
Out[71]: array([ 0.79122806, -2.190181 , -0.16741803], dtype=float32)
gathered_np[0,:,0,0]
Out[72]: array([ 0.79122806, -2.190181 , -0.16741803], dtype=float32)
pos_h_np[1,0,3,4]
Out[73]: 1
pos_w_np[1,0,3,4]
Out[74]: 2
inputs_np[1,:,1,2]
Out[75]: array([ 0.9282498 , -0.34945545, 0.9136222 ], dtype=float32)
gathered_np[1,:,3,4]
Out[77]: array([ 0.9282498 , -0.34945545, 0.9136222 ], dtype=float32)
I improved the answer from Michael Jungo's implementation. Now it supports arbitrary leading batch dimensions.
def gather_nd_torch(params, indices, batch_dim=1):
""" A PyTorch porting of tensorflow.gather_nd
This implementation can handle leading batch dimensions in params, see below for detailed explanation.
The majority of this implementation is from Michael Jungo # https://stackoverflow.com/a/61810047/6670143
I just ported it compatible to leading batch dimension.
Args:
params: a tensor of dimension [b1, ..., bn, g1, ..., gm, c].
indices: a tensor of dimension [b1, ..., bn, x, m]
batch_dim: indicate how many batch dimension you have, in the above example, batch_dim = n.
Returns:
gathered: a tensor of dimension [b1, ..., bn, x, c].
Example:
>>> batch_size = 5
>>> inputs = torch.randn(batch_size, batch_size, batch_size, 4, 4, 4, 32)
>>> pos = torch.randint(4, (batch_size, batch_size, batch_size, 12, 3))
>>> gathered = gather_nd_torch(inputs, pos, batch_dim=3)
>>> gathered.shape
torch.Size([5, 5, 5, 12, 32])
>>> inputs_tf = tf.convert_to_tensor(inputs.numpy())
>>> pos_tf = tf.convert_to_tensor(pos.numpy())
>>> gathered_tf = tf.gather_nd(inputs_tf, pos_tf, batch_dims=3)
>>> gathered_tf.shape
TensorShape([5, 5, 5, 12, 32])
>>> gathered_tf = torch.from_numpy(gathered_tf.numpy())
>>> torch.equal(gathered_tf, gathered)
True
"""
batch_dims = params.size()[:batch_dim] # [b1, ..., bn]
batch_size = np.cumprod(list(batch_dims))[-1] # b1 * ... * bn
c_dim = params.size()[-1] # c
grid_dims = params.size()[batch_dim:-1] # [g1, ..., gm]
n_indices = indices.size(-2) # x
n_pos = indices.size(-1) # m
# reshape leadning batch dims to a single batch dim
params = params.reshape(batch_size, *grid_dims, c_dim)
indices = indices.reshape(batch_size, n_indices, n_pos)
# build gather indices
# gather for each of the data point in this "batch"
batch_enumeration = torch.arange(batch_size).unsqueeze(1)
gather_dims = [indices[:, :, i] for i in range(len(grid_dims))]
gather_dims.insert(0, batch_enumeration)
gathered = params[gather_dims]
# reshape back to the shape with leading batch dims
gathered = gathered.reshape(*batch_dims, n_indices, c_dim)
return gathered
I have also made a demo Colab notebook, you can check it here. This implementation is way faster than TF's original implementation according to my poor speed test on Colab server with a GPU instance.
From the accepted answer in this question,
given the following
input and kernel matrices, the output of tf.nn.conv2d is
[[14 6]
[6 12]]
which makes sense. However, when I make the input and kernel matrices have 3-channels each (by repeating each original matrix), and run the same code:
# the previous input
i_grey = np.array([
[4, 3, 1, 0],
[2, 1, 0, 1],
[1, 2, 4, 1],
[3, 1, 0, 2]
])
# copy to 3-dimensions
i_rgb = np.repeat( np.expand_dims(i_grey, axis=0), 3, axis=0 )
# convert to tensor
i_rgb = tf.constant(i_rgb, dtype=tf.float32)
# make kernel depth match input; same process as input
k = np.array([
[1, 0, 1],
[2, 1, 0],
[0, 0, 1]
])
k_rgb = np.repeat( np.expand_dims(k, axis=0), 3, axis=0 )
# convert to tensor
k_rgb = tf.constant(k_rgb, dtype=tf.float32)
here's what my input and kernel matrices look like at this point
# reshape input to format: [batch, in_height, in_width, in_channels]
image_rgb = tf.reshape(i_rgb, [1, 4, 4, 3])
# reshape kernel to format: [filter_height, filter_width, in_channels, out_channels]
kernel_rgb = tf.reshape(k_rgb, [3, 3, 3, 1])
conv_rgb = tf.squeeze( tf.nn.conv2d(image_rgb, kernel_rgb, [1,1,1,1], "VALID") )
with tf.Session() as sess:
conv_result = sess.run(conv_rgb)
print(conv_result)
I get the final output:
[[35. 15.]
[35. 26.]]
But I was expecting the original output*3:
[[42. 18.]
[18. 36.]]
because from my understanding, each channel of the kernel is convolved with each channel of the input, and the resultant matrices are summed to get the final output.
Am I missing something from this process or the tensorflow implementation?
Reshape is a tricky function. It will produce you the shape you want, but can easily ground things together. In cases like yours, one should avoid using reshape by all means.
In that particular case instead, it is better to duplicate the arrays along the new axis. When using [batch, in_height, in_width, in_channels] channels is the last dimension and it should be used in repeat() function. Next code should better reflect the logic behind it:
i_grey = np.expand_dims(i_grey, axis=0) # add batch dim
i_grey = np.expand_dims(i_grey, axis=3) # add channel dim
i_rgb = np.repeat(i_grey, 3, axis=3 ) # duplicate along channels dim
And likewise with filters:
k = np.expand_dims(k, axis=2) # input channels dim
k = np.expand_dims(k, axis=3) # output channels dim
k_rgb = np.repeat(k, 3, axis=2) # duplicate along the input channels dim
I'm trying to build a neural network where the labels and the number of labels change on input. For example, I could have a final layer of 10 units that represent the logit of their class, but sometimes I will only need units [1,3,4] to calculate cross entropy, some of the units [3,4,5,7] etc.
I tried using different combinations of map_fn, gather, py_fn and while_loop but no one seems to be in my case. Another way might be to list all types of label combinations (I call them network heads) and find some conditional constructs that allow me to choose one based on the value of a placeholder. But I'm not sure how to implement it.
For example:
x = tf.placeholder(dtype=tf.float32, shape=[None,3])
y = tf.placeholder(dtype=tf.int32, shape=[None, 3])
... to_do ...
with tf.Session() as sess:
sess.run(to_do, feed_dict={x: [[1, 3, 4], [3, 7, 8]], y: [[1, 0, 0], [0, 1, 1]]})
Here I need something that return [[1],[7,8]].
Oh no matter. There was a very easy way to get the probabilites I needed for cross-entropy.
x = tf.placeholder(dtype=tf.float32, shape=[None,3])
y = tf.placeholder(dtype=tf.int32, shape=[None, 3])
probabilities = tf.where(tf.equal(y,1), tf.exp(x), tf.zeros_like(x))
normalizing_sum = tf.reduce_sum(probabilities, 1, keep_dims=True)
probabilities/=normalizing_sum
with tf.Session() as sess:
res = sess.run(probabilities, feed_dict={x: [[1, 3, 4], [3, 7, 8]], y: [[1, 0, 0], [0, 1, 1]]})
Consider the following code:
x = tf.placeholder("float", shape=[42, 4])
y = tf.zeros([42, 4], "float")
xy_stacked = tf.concat(1, [x, y])
print(x.get_shape())
print(y.get_shape())
print(xy_stacked.get_shape())
This will produce the following output, as expected:
TensorShape([Dimension(42), Dimension(4)])
TensorShape([Dimension(42), Dimension(4)])
TensorShape([Dimension(42), Dimension(8)])
However, what if the placeholder has a dynamic dimension that is determined at run-time by the value passed to feed_dict=, as placeholders often do:
x = tf.placeholder("float", shape=[None, 4])
y = tf.zeros([None, 4], "float")
xy_stacked = tf.concat(1, [x, y])
This will produce an error for tf.zeros([None, 4], "float"). Apparently Dimension(None) is not allowed for tf.zeros:
TypeError Traceback (most recent call last)
<ipython-input-24-277eca38a392> in <module>()
2
3 x = tf.placeholder("float", shape=[None, 4])
----> 4 y = tf.zeros([None, 4], "float")
5 xy_stacked = tf.concat(1, [x, y])
6
[...]
/usr/local/lib/python3.4/dist-packages/numpy/core/_methods.py in _prod(a, axis, dtype, out, keepdims)
33
34 def _prod(a, axis=None, dtype=None, out=None, keepdims=False):
---> 35 return umr_prod(a, axis, dtype, out, keepdims)
36
37 def _any(a, axis=None, dtype=None, out=None, keepdims=False):
TypeError: unsupported operand type(s) for *: 'NoneType' and 'int'
I have figured out that it does not produce an error if I set the first dimension of my zeros tensor to non-None, such as 1:
x = tf.placeholder("float", shape=[None, 4])
y = tf.zeros([1, 4], "float")
xy_stacked = tf.concat(1, [x, y])
but then the resulting xy_stacked tensor is truncated to this size:
TensorShape([Dimension(None), Dimension(4)])
TensorShape([Dimension(1), Dimension(4)])
TensorShape([Dimension(1), Dimension(8)])
How can I pad the placeholder tensor with zeros so I get a tensor of shape TensorShape([Dimension(None), Dimension(8)]) in this example?
The only "solutions" I found so far is either something like the following:
x = tf.placeholder("float", shape=[None, 4])
y = 0 * x
xy_stacked = tf.concat(1, [x, y])
Or simply declaring y as a placeholder and always passing a zero array of the right size.
But neither looks like a clean solution to the problem and hacks like that get out of hand quickly in an application more complex than this simple example..
I'm using tensorflow-0.6.0-py3.
The recommended way to make a zero tensor with the same shape as another tensor is to use the tf.zeros_like() op:
x = tf.placeholder(tf.float32, shape=[None, 4])
y = tf.zeros_like(x)
The resulting tensor y appears to have the shape [None, None] according to Tensor.get_shape(), but at runtime it will expand to the same shape as x:
print y.get_shape()
# ==> TensorShape([Dimension(None), Dimension(None)])
sess = tf.Session()
y_result = sess.run(y, feed_dict={x: np.random.rand(4, 4)})
print y_result.shape
# ==> (4, 4)
The [None, None] static shape is returned because shape inference hasn't been specialized for tf.zeros_like(). I've filed a GitHub issue for that and it should be fixed soon.
EDIT: In your comment, you asked how to deal with the case where the zero tensor had a shape based on, but different from the original tensor. This is also possible, using tf.shape() and tf.stack() to build the dimensions, and tf.fill() to produce the zero tensor:
x = tf.placeholder(tf.float32, shape=[None, 4])
# Use tf.shape() to get the runtime size of `x` in the 0th dimension.
zeros_dims = tf.stack([tf.shape(x)[0], 7])
y = tf.fill(zeros_dims, 0.0)
sess = tf.Session()
y_result = sess.run(y, feed_dict={x: np.random.rand(4, 4)})
print y_result.shape
# ==> (4, 7)