I have an idea for a tensor operation that would not be difficult to implement via iteration, with batch size one. However I would like to parallelize it as much as possible.
I have two tensors with shape (n, 5) called X and Y. X is actually supposed to represent 5 one-dimensional tensors with shape (n, 1): (x_1, ..., x_n). Ditto for Y.
I would like to compute a tensor with shape (n, 25) where each column represents the output of the tensor operation f(x_i, y_j), where f is fixed for all 1 <= i, j <= 5. The operation f has output shape (n, 1), just like x_i and y_i.
I feel it is important to clarify that f is essentially a fully-connected layer from the concatenated [...x_i, ...y_i] tensor with shape (1, 10), to an output layer with shape (1,5).
Again, it is easy to see how to do this manually with iteration and slicing. However this is probably very slow. Performing this operation in batches, where the tensors X, Y now have shape (n, 5, batch_size) is also desirable, particularly for mini-batch gradient descent.
It is difficult to really articulate here why I desire to create this network; I feel it is suited for my domain of 'itemized tabular data' and cuts down significantly on the number of weights per operation, compared to a fully connected network.
Is this possible using tensorflow? Certainly not using just keras.
Below is an example in numpy per AloneTogether's request
import numpy as np
features = 16
batch_size = 256
X_batch = np.random.random((features, 5, batch_size))
Y_batch = np.random.random((features, 5, batch_size))
# one tensor operation to reduce weights in this custom 'layer'
f = np.random.random((features, 2 * features))
for b in range(batch_size):
X = X_batch[:, :, b]
Y = Y_batch[:, :, b]
for i in range(5):
x_i = X[:, i:i+1]
for j in range(5):
y_j = Y[:, j:j+1]
x_i_y_j = np.concatenate([x_i, y_j], axis=0)
# f(x_i, y_j)
# implemented by a fully-connected layer
f_i_j = np.matmul(f, x_i_y_j)
All operations you need (concatenation and matrix multiplication) can be batched.
Difficult part here is, that you want to concatenate features of all items in X with features of all items in Y (all combinations).
My recommended solution is to expand the dimensions of X to [batch, features, 5, 1], expand dimensions of Y to [batch, features, 1, 5]
Than tf.repeat() both tensors so their shapes become [batch, features, 5, 5].
Now you can concatenate X and Y. You will have a tensor of shape [batch, 2*features, 5, 5]. Observe that this way all combinations are built.
Next step is matrix multiplication. tf.matmul() can also do batch matrix multiplication, but I use here tf.einsum() because I want more control over which dimensions are considered as batch.
Full code:
import tensorflow as tf
import numpy as np
batch_size=3
features=6
items=5
x = np.random.uniform(size=[batch_size,features,items])
y = np.random.uniform(size=[batch_size,features,items])
f = np.random.uniform(size=[2*features,features])
x_reps= tf.repeat(x[:,:,:,tf.newaxis], items, axis=3)
y_reps= tf.repeat(y[:,:,tf.newaxis,:], items, axis=2)
xy_conc = tf.concat([x_reps,y_reps], axis=1)
f_i_j = tf.einsum("bfij, fg->bgij", xy_conc,f)
f_i_j = tf.reshape(f_i_j , [batch_size,features,items*items])
I would like to multiply a sparse tensor by a dense tensor but do so within a batch.
For example I have a sparse tensor with the corresponding dense shape of (20,65536,65536) where 20 is the batch size. I would like to multiply each (65536,65536) in the batch with the corresponding (65536x1) from a tensor shape (20,65536) which has a dense representation. tf.sparse_tensor_dense_matmul only accepts a rank 2 sparse tensor. Is there a way to perform this over a batch?
I would like to avoid converting the sparse matrix to a dense matrix if possible due to memory constraints.
Assuming that a is a sparse tensor with shape (20, 65536, 65536) and b a dense tensor with shape (20, 65536), you could perform the batch sparse-dense matrix multiplication as follows:
y_sparse = tf.sparse.reduce_sum_sparse(a * b[:, None, :], axis=-1)
This solution expands the second dimension of tensor b to enable implicit broadcasting. Then, the batch matrix multiplication takes place by performing a sparse-dense multiplication and a sparse sum along the last axis.
If b has got a third dimension so it is a batch of matrices, you can multiply their columns individually and concatenate them later:
multiplied_dims = []
for i in range (b.shape[-1]):
multiplied_dims.append(tf.expand_dims(tf.sparse.reduce_sum(a * b[:, :, i][:, None, :], axis=-1), -1))
result = tf.concat(multiplied_dims, -1)
The answer is simple - you reshape the sparse tensor first and then multiply it by the dense matrix. Something like this would work:
sparse_tensor_rank2 = tf.sparse_reshape(sparse_tensor, [-1, 65536])
I'm a total beginner to TensorFlow, now I have a 1-D tensor, its shape is [4, 1], I have 2 matrix
a=tf.placeholder(tf.float32,[4,2]);
b=tf.placeholder(tf.float32,[2])
when I multiple them: c=tf.mul(a,tf.expand_dims(b,1))
then I got a [4,1] matrix c. it is a 2-D tensor, but I want to change it to a 1-D tensor , means it's a vector and its shape is [4], not [4,1].
tf.shape shows that tf.shape[c]=[4 1],not [4]
Can anyone tell me how to do this? thanks very much.
I think you want tf.squeeze or tf.reshape.
a = tf.constant(1.0, shape=[4, 2])
b = tf.constant(1.0, shape=[2])
c = tf.matmul(a, tf.expand_dims(b,1))
c = tf.squeeze(c)
# This will also work:
# c = tf.reshape(c, [4])
You also want tf.matmul instead of tf.mul in your example if you want to do matrix multiplication instead of elementwise multiplication.
I ma trying to understand tf.rank function in tensorflow. From the documentation here, I understood that rank should return the number of distinct elements in the tensor.
Here x and weights are 2 distinct 2*2 tensors with 4 distinct elemnts in each of them. However, rank() function outputs are:
Tensor("Rank:0", shape=(), dtype=int32) Tensor("Rank_1:0", shape=(),
dtype=int32)
Also, for the tensor x, I used tf.constant() with dtype = float to convert ndarray into float32 tensor but the rank() still outputs as int32.
g = tf.Graph()
with g.as_default():
weights = tf.Variable(tf.truncated_normal([2,2]))
x = np.asarray([[1 , 2], [3 , 4]])
x = tf.constant(x, dtype = tf.float32)
y = tf.matmul(weights, x)
print (tf.rank(x), tf.rank(weights))
with tf.Session(graph = g) as s:
tf.initialize_all_variables().run()
print (s.run(weights), s.run(x))
print (s.run(y))
How should I interpret the output.
Firstly, tf.rank returns the dimension of a tensor, not the number of elements. For instance, the output from tf.rank called for the 2x2 matrix would be 2.
To print the rank of a tensor, create an appropriate node, e.g. rank = tf.rank(x) and then evaluate this node using a Session.run(), as you've done for weights and x. Execution of print (tf.rank(x), tf.rank(weights)) expectedly prints out description of tensors, as tf.rank(x), tf.rank(weights) are nodes of the graph, not the variables with defined values.
Tensorflow has a function called batch_matmul which multiplies higher dimensional tensors. But I'm having a hard time understanding how it works, perhaps partially because I'm having a hard time visualizing it.
What I want to do is multiply a matrix by each slice of a 3D tensor, but I don't quite understand what the shape of tensor a is. Is z the innermost dimension? Which of the following is correct?
I would most prefer the first to be correct -- it's most intuitive to me and easy to see in the .eval() output. But I suspect the second is correct.
Tensorflow says that batch_matmul performs:
out[..., :, :] = matrix(x[..., :, :]) * matrix(y[..., :, :])
What does that mean? What does that mean in the context of my example? What is being multiplied with with what? And why aren't I getting a 3D tensor the way I expected?
You can imagine it as doing a matmul over each training example in the batch.
For example, if you have two tensors with the following dimensions:
a.shape = [100, 2, 5]
b.shape = [100, 5, 2]
and you do a batch tf.matmul(a, b), your output will have the shape [100, 2, 2].
100 is your batch size, the other two dimensions are the dimensions of your data.
First of all tf.batch_matmul() was removed and no longer available. Now you suppose to use tf.matmul():
The inputs must be matrices (or tensors of rank > 2, representing
batches of matrices), with matching inner dimensions, possibly after
transposition.
So let's assume you have the following code:
import tensorflow as tf
batch_size, n, m, k = 10, 3, 5, 2
A = tf.Variable(tf.random_normal(shape=(batch_size, n, m)))
B = tf.Variable(tf.random_normal(shape=(batch_size, m, k)))
tf.matmul(A, B)
Now you will receive a tensor of the shape (batch_size, n, k). Here is what is going on here. Assume you have batch_size of matrices nxm and batch_size of matrices mxk. Now for each pair of them you calculate nxm X mxk which gives you an nxk matrix. You will have batch_size of them.
Notice that something like this is also valid:
A = tf.Variable(tf.random_normal(shape=(a, b, n, m)))
B = tf.Variable(tf.random_normal(shape=(a, b, m, k)))
tf.matmul(A, B)
and will give you a shape (a, b, n, k)
You can now do it using tf.einsum, starting from Tensorflow 0.11.0rc0.
For example,
M1 = tf.Variable(tf.random_normal([2,3,4]))
M2 = tf.Variable(tf.random_normal([5,4]))
N = tf.einsum('ijk,lk->ijl',M1,M2)
It multiplies the matrix M2 with every frame (3 frames) in every batch (2 batches) in M1.
The output is:
[array([[[ 0.80474716, -1.38590837, -0.3379252 , -1.24965811],
[ 2.57852983, 0.05492432, 0.23039417, -0.74263287],
[-2.42627382, 1.70774114, 1.19503212, 0.43006262]],
[[-1.04652011, -0.32753903, -1.26430523, 0.8810069 ],
[-0.48935518, 0.12831448, -1.30816901, -0.01271309],
[ 2.33260512, -1.22395933, -0.92082584, 0.48991606]]], dtype=float32),
array([[ 1.71076882, 0.79229093, -0.58058828, -0.23246667],
[ 0.20446332, 1.30742455, -0.07969904, 0.9247328 ],
[-0.32047141, 0.66072595, -1.12330854, 0.80426538],
[-0.02781649, -0.29672042, 2.17819595, -0.73862702],
[-0.99663496, 1.3840003 , -1.39621222, 0.77119476]], dtype=float32),
array([[[ 0.76539308, 2.77609682, -1.79906654, 0.57580602, -3.21205115],
[ 4.49365759, -0.10607499, -1.64613271, 0.96234947, -3.38823152],
[-3.59156275, 2.03910899, 0.90939498, 1.84612727, 3.44476724]],
[[-1.52062428, 0.27325237, 2.24773455, -3.27834225, 3.03435063],
[ 0.02695178, 0.16020992, 1.70085776, -2.8645196 , 2.48197317],
[ 3.44154787, -0.59687197, -0.12784094, -2.06931567, -2.35522676]]], dtype=float32)]
I have verified, the arithmetic is correct.
tf.tensordot should solve this problem. It supports batch operations, e.g., if you want to contract a 2D tensor with a 3D tensor, with the latter having a batch dimension.
If a is shape [n,m] b is shape [?,m,l], then
y = tf.tensordot(b, a, axes=[1, 1]) will produce a tensor of shape [?,n,l]
https://www.tensorflow.org/api_docs/python/tf/tensordot
It is simply like splitting on the first dimension respectively, multiply and concat them back. If you want to do 3D by 2D, you can reshape, multiply, and reshape it back. I.e. [100, 2, 5] -> [200, 5] -> [200, 2] -> [100, 2, 2]
The answer to this particular answer is using tf.scan function.
If a = [5,3,2] #dimension of 5 batch, with 3X2 mat in each batch
and b = [2,3] # a constant matrix to be multiplied with each sample
then let def fn(a,x):
return tf.matmul(x,b)
initializer = tf.Variable(tf.random_number(3,3))
h = tf.scan(fn,outputs,initializer)
this h will store all the outputs.