My task is to transform a special formed dense matrix tensor into a sparse one. e.g. input matrix M as followed (dense positive integer sequence followed by 0 as padding in each row)
[[3 5 7 0]
[2 2 0 0]
[1 3 9 0]]
Additionally, given the non-padding length for each row, e.g. given by tensor L =
[3, 2, 3].
The desired output would be sparse tensor S.
SparseTensorValue(indices=array([[0, 0],[0, 1],[0, 2],[1, 0],[1, 1],[2, 0],[2, 1], [2, 2]]), values=array([3, 5, 7, 2, 2, 1, 3, 9], dtype=int32), shape=array([3, 4]))
This is useful in models where objects are described by variable-sized descriptors (S are then used in embedding_lookup_sparse to connect embeddings of descriptors.)
I am able to do it when number of M's row is known (by python loop and ops like slice and concat). However, M's row number here is determined by mini-batch size and could change (say in testing phase). Is there a good way to implement that? I am trying some control_flow_ops but haven't succeeded.
Thanks!!
Related
Summarize the problem
I am working with high dimensional tensors in pytorch and I need to index one tensor with the argmax values from another tensor. So I need to index tensor y of dim [3,4] with the results from the argmax of tensor xwith dim [3,4]. If tensors are:
import torch as T
# Tensor to get argmax from
# expected argmax: [2, 0, 1]
x = T.tensor([[1, 2, 8, 3],
[6, 3, 3, 5],
[2, 8, 1, 7]])
# Tensor to index with argmax from preivous
# expected tensor to retrieve [2, 4, 9]
y = T.tensor([[0, 1, 2, 3],
[4, 5, 6, 7],
[8, 9, 10, 11]])
# argmax
x_max, x_argmax = T.max(x, dim=1)
I would like an operation that given the argmax indexes of x, or x_argmax, retrieves the values in tensor y in the same indexes x_argmax indexes.
Describe what you’ve tried
This is what I have tried:
# What I have tried
print(y[x_argmax])
print(y[:, x_argmax])
print(y[..., x_argmax])
print(y[x_argmax.unsqueeze(1)])
I have been reading a lot about numpy indexing, basic indexing, advanced indexing and combined indexing. I have been trying to use combined indexing (since I want a slice in first dimension of the tensor and the indexes values on the second one). But I have not been able to come up with a solution for this use case.
You are looking for torch.gather:
idx = torch.argmax(x, dim=1, keepdim=true) # get argmax directly, w/o max
out = torch.gather(y, 1, idx)
Resulting with
tensor([[2],
[4],
[9]])
How about y[T.arange(3), x_argmax]?
That does the job for me...
Explanation: You take dimensional information away when you invoke T.max(x, dim=1), so this information needs to be restored explicitly.
tensorflow.reduce_sum(..) computes the sum of elements across dimensions of a tensor. it is Ok.
But one thing is not clear to me , what is the purpose of saying reduce in the function name ?
Is it related to map_reduce of parallel computation?
Let's say, it distributes the required computation to
different cores , and collect the result from the cores , finally delivers the sum of the collected results ?
Because you can compute the sum along a given dimension (and therefore reduce it). And no it has nothing to do with map-reduce.
Quoting the documentation string of the method:
Reduces input_tensor along the dimensions given in axis. Unless keepdims is true, the rank of the tensor is reduced by 1 for each entry in axis. If keepdims is true, the reduced dimensions are retained with length 1.
Example from the API:
x = tf.constant([[1, 1, 1], [1, 1, 1]])
tf.reduce_sum(x) # 6
tf.reduce_sum(x, 0) # [2, 2, 2]
tf.reduce_sum(x, 1) # [3, 3]
tf.reduce_sum(x, 1, keepdims=True) # [[3], [3]]
tf.reduce_sum(x, [0, 1]) # 6
Is their a way using tf functions to multiply certain columns of a 2D tensor by a scaler?
e.g. multiply the second and third column of a matrix by 2:
[[2,3,4,5],[4,3,4,3]] -> [[2,6,8,5],[4,6,8,3]]
Thanks for any help.
EDIT:
Thank you Psidom for the reply. Unfortunately I am not using a tf.Variable, so it seems I have to use tf.slice.
What I am trying to do is to multiply all components by 2 of a single-sided PSD, except for the DC component and the Nyquist frequency component, to conserve the total power when going from a double-sided spectrum to a single-sided spectrum.
This would correspond to: 2*PSD[:,1:-1] if it was a numpy array.
Here is my attempt with tf.assign and tf.slice:
x['PSD'] = tf.assign(tf.slice(x['PSD'], [0, 1], [tf.shape(x['PSD'])[0], tf.shape(x['PSD'])[1] - 2]),
tf.scalar_mul(2, tf.slice(x['PSD'], [0, 1], [tf.shape(x['PSD'])[0], tf.shape(x['PSD'])[1] - 2]))) # single-sided power spectral density.
However:
AttributeError: 'Tensor' object has no attribute 'assign'
If the tensor is a variable, you can do this by slicing the columns you want to update and then use tf.assign:
x = tf.Variable([[2,3,4,5],[4,3,4,3]])
x = tf.assign(x[:,1:3], x[:,1:3]*2) # update the second and third columns and assign
# the new tensor to x
with tf.Session() as sess:
tf.global_variables_initializer().run()
print(sess.run(x))
#[[2 6 8 5]
# [4 6 8 3]]
Ended up taking 3 different slices and concatenating them together, with the middle slice multiplied by 2. Probably not the most efficient way, but it works:
x['PSD'] = tf.concat([tf.slice(x['PSD'], [0, 0], [tf.shape(x['PSD'])[0], 1]),
tf.scalar_mul(2, tf.slice(x['PSD'], [0, 1], [tf.shape(x['PSD'])[0], tf.shape(x['PSD'])[1] - 2])),
tf.slice(x['PSD'], [0, tf.shape(x['PSD'])[1] - 1], [tf.shape(x['PSD'])[0], 1])], 1) # single-sided power spectral density.
I have two following tensors (note that they are both Tensorflow tensors which means they are still virtually symbolic at the time I construct the following slicing op before I launch a tf.Session()):
params: has shape (64,784, 256)
indices: has shape (64, 784)
and I want to construct an op that returns the following tensor:
output: has shape (64,784) where
output[i,j] = params_tensor[i,j, indices[i,j] ]
What is the most efficient way in Tensorflow to do so?
ps: I tried with tf.gather but couldn't make use of it to perform the operation I described above.
Many thanks.
-Bests
You can get exactly what you want using tf.gather_nd. The final expression is:
tf.gather_nd(params, tf.stack([tf.tile(tf.expand_dims(tf.range(tf.shape(indices)[0]), 1), [1, tf.shape(indices)[1]]), tf.transpose(tf.tile(tf.expand_dims(tf.range(tf.shape(indices)[1]), 1), [1, tf.shape(indices)[0]])), indices], 2))
This expression has the following explanation:
tf.gather_nd does what you expected and uses the indices to gather the output from the params
tf.stack combines three separate tensors, the last of which is the indices. The first two tensors specify the ordering of the first two dimensions (axis 0 and axis 1 of params/indices)
For the example provided, this ordering is simply 0, 1, 2, ..., 63 for axis 0, and 0, 1, 2, ... 783 for axis 1. These sequences are obtained with tf.range(tf.shape(indices)[0]) and tf.range(tf.shape(indices)[1]), respectively.
For the example provided, indices has shape (64, 784). The other two tensors from the last point above need to have this same shape in order to be combined with tf.stack
First, an additional dimension/axis is added to each of the two sequences using tf.expand_dims.
The use of tf.tile and tf.transpose can be shown by example: Assume the first two axes of params and index have shape (5,3). We want the first tensor to be:
[[0, 0, 0], [1, 1, 1], [2, 2, 2], [3, 3, 3], [4, 4, 4]]
We want the second tensor to be:
[[0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2], [0, 1, 2]]
These two tensors almost function like specifying the coordinates in a grid for the associated indices.
The final part of tf.stack combines the three tensors on a new third axis, so that the result has the same 3 axes as params.
Keep in mind if you have more or less axes than in the question, you need to modify the number of coordinate-specifying tensors in tf.stack accordingly.
What you want is like a custom reduction function. If you are keeping something like index of maximum value at indices then I would suggest using tf.reduce_max:
max_params = tf.reduce_max(params_tensor, reduction_indices=[2])
Otherwise, here is one way to get what you want (Tensor objects are not assignable so we create a 2d list of tensors and pack it using tf.pack):
import tensorflow as tf
import numpy as np
with tf.Graph().as_default():
params_tensor = tf.pack(np.random.randint(1,256, [5,5,10]).astype(np.int32))
indices = tf.pack(np.random.randint(1,10,[5,5]).astype(np.int32))
output = [ [None for j in range(params_tensor.get_shape()[1])] for i in range(params_tensor.get_shape()[0])]
for i in range(params_tensor.get_shape()[0]):
for j in range(params_tensor.get_shape()[1]):
output[i][j] = params_tensor[i,j,indices[i,j]]
output = tf.pack(output)
with tf.Session() as sess:
params_tensor,indices,output = sess.run([params_tensor,indices,output])
print params_tensor
print indices
print output
I know I'm late, but I recently had to do something similar, and was able to to do it using Ragged Tensors:
output = tf.gather(params, tf.RaggedTensor.from_tensor(indices), batch_dims=-1, axis=-1)
Hope it helps
I have a matrix:
Params =
[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
For each row I want to select some elements using column indices:
col_indices =
[[0 1]
[1 2]
[2 3]]
In Numpy, I can create row indices:
row_indices =
[[0 0]
[1 1]
[2 2]]
and do params[row_indices, col_indices]
In TenforFlow, I did this:
tf_params = tf.constant(params)
tf_col_indices = tf.constant(col_indices, dtype=tf.int32)
tf_row_indices = tf.constant(row_indices, dtype=tf.int32)
tf_params[row_indices, col_indices]
But there raised an error:
ValueError: Shape must be rank 1 but is rank 3
What does it mean? How should I do this kind of indexing properly?
Thanks!
Tensor rank (sometimes referred to as order or degree or n-dimension) is the number of dimensions of the tensor. For example, the following tensor (defined as a Python list) has a rank of 2:
t = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
A rank two tensor is what we typically think of as a matrix, a rank one tensor is a vector. For a rank two tensor you can access any element with the syntax t[i, j]. For a rank three tensor you would need to address an element with t[i, j, k]. See this for more details.
ValueError: Shape must be rank 1 but is rank 3 means you are trying to create a 3-tensor (cube of numbers) instead of a vector.
To see how you can declare tensor constants of different shape, you can see this.