I need some clarification on how Tensorflow treats the shape of its tensors. This is taken from the MNIST example:
I define a placeholder that will at some later point be fed with some of my training data:
x = tf.placeholder(tf.float32, shape=[None, 784])
During runtime I feed it in batches of 100, so its shape during runtime is (100, 784). I also define weights and biases:
W = tf.Variable(tf.zeros([784,10]))
b = tf.Variable(tf.zeros([10]))
Wis of shape (784, 10) and bis of shape (10). Now I compute
y = tf.matmul(x,W) + b
And this is where I am stuck. The matrix product of x and W is of shape (None, 10) or (100, 10) during runtime. However I can without error add vector b to it. This confuses me. How can this work? And is there some better documentation for this?
The + operator in tf.matmul(x, W) + b is actually shorthand for tf.add(tf.matmul(x, W), b) (operator overloading).
The documentation for tf.add mentions that it supports broadcasting, which means that when you add a tensor with shape (10) to a tensor with shape (100, 10), it's the equivalent of adding the (10) tensor to each row of the (100, 10) tensor.
Hope that helps
Related
My codes are as follow:
v = tf.Variable(initial_value=v, trainable=True)
v.shape is (1, 768)
In the model:
inputs_sents = keras.Input(shape=(50,3))
inputs_events = keras.Input(shape=(50,768))
x_1 = tf.matmul(v,tf.transpose(inputs_events))
x_2 = tf.matmul(x_1,inputs_sents)
But I got an error,
ValueError: Dimensions must be equal, but are 768 and 50 for
'{{node BatchMatMulV2_3}} =
BatchMatMulV2[T=DT_FLOAT,
adj_x=false,
adj_y=false](BatchMatMulV2_3/ReadVariableOp,
Transpose_3)' with input shapes: [1,768], [768,50,?]
I think it takes consideration of the batch? But how shall I deal with this?
v is a trainable vector (or 2d array with first dimension being 1), I want it to be trained in the training process.
PS: This is the result I got using the codes provided by the first answer, I think it is incorrect cause keras already takes consideration of the first batch dimension.
Plus, from the keras documentation,
shape: A shape tuple (integers), not including the batch size. For instance, shape=(32,) indicates that the expected input will be batches of 32-dimensional vectors. Elements of this tuple can be None; 'None' elements represent dimensions where the shape is not known.
https://keras.io/api/layers/core_layers/input/
Should I rewrite my codes without keras?
The shape of a batch is denoted by None:
import numpy as np
inputs_sents = keras.Input(shape=(None,1,3))
inputs_events = keras.Input(shape=(None,1,768))
v = np.ones(shape=(1,768), dtype=np.float32)
v = tf.Variable(initial_value=v, trainable=True)
x_1 = tf.matmul(v,tf.transpose(inputs_events))
x_2 = tf.matmul(x_1,inputs_sents)
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])
im following MNIST Softmax tutorials https://www.tensorflow.org/tutorials/mnist/beginners/
Followed by the document, the model should be
y = tf.nn.softmax(tf.matmul(x, W) + b)
but in the sample source code, as u can see
# Create the model
x = tf.placeholder(tf.float32, [None, 784])
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))
y = tf.matmul(x, W) + b
softmax is not used. I think it needs to be changed
y = tf.nn.softmax(tf.matmul(x, W) + b)
I assume that, in the testing function it uses argmax so the it doesn't needs to be normalized to 0~1.0 value. But it can bring some confusion to developers.
as idea on this?
Softmax is used, row 57:
# So here we use tf.nn.softmax_cross_entropy_with_logits on the raw
# outputs of 'y', and then average across the batch.
cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(y, y_))
See softmax_cross_entropy_with_logits for more details.
I started to play with TensorFlow two days ago and I'm wondering if there is the triplet and the contrastive losses implemented.
I've been looking at the documentation, but I haven't found any example or description about these things.
Update (2018/03/19): I wrote a blog post detailing how to implement triplet loss in TensorFlow.
You need to implement yourself the contrastive loss or the triplet loss, but once you know the pairs or triplets this is quite easy.
Contrastive Loss
Suppose you have as input the pairs of data and their label (positive or negative, i.e. same class or different class). For instance you have images as input of size 28x28x1:
left = tf.placeholder(tf.float32, [None, 28, 28, 1])
right = tf.placeholder(tf.float32, [None, 28, 28, 1])
label = tf.placeholder(tf.int32, [None, 1]). # 0 if same, 1 if different
margin = 0.2
left_output = model(left) # shape [None, 128]
right_output = model(right) # shape [None, 128]
d = tf.reduce_sum(tf.square(left_output - right_output), 1)
d_sqrt = tf.sqrt(d)
loss = label * tf.square(tf.maximum(0., margin - d_sqrt)) + (1 - label) * d
loss = 0.5 * tf.reduce_mean(loss)
Triplet Loss
Same as with contrastive loss, but with triplets (anchor, positive, negative). You don't need labels here.
anchor_output = ... # shape [None, 128]
positive_output = ... # shape [None, 128]
negative_output = ... # shape [None, 128]
d_pos = tf.reduce_sum(tf.square(anchor_output - positive_output), 1)
d_neg = tf.reduce_sum(tf.square(anchor_output - negative_output), 1)
loss = tf.maximum(0., margin + d_pos - d_neg)
loss = tf.reduce_mean(loss)
The real trouble when implementing triplet loss or contrastive loss in TensorFlow is how to sample the triplets or pairs. I will focus on generating triplets because it is harder than generating pairs.
The easiest way is to generate them outside of the Tensorflow graph, i.e. in python and feed them to the network through the placeholders. Basically you select images 3 at a time, with the first two from the same class and the third from another class. We then perform a feedforward on these triplets, and compute the triplet loss.
The issue here is that generating triplets is complicated. We want them to be valid triplets, triplets with a positive loss (otherwise the loss is 0 and the network doesn't learn).
To know whether a triplet is good or not you need to compute its loss, so you already make one feedforward through the network...
Clearly, implementing triplet loss in Tensorflow is hard, and there are ways to make it more efficient than sampling in python but explaining them would require a whole blog post !
Triplet loss with semihard negative mining is now implemented in tf.contrib, as follows:
triplet_semihard_loss(
labels,
embeddings,
margin=1.0
)
where:
Args:
labels: 1-D tf.int32 Tensor with shape [batch_size] of multiclass
integer labels.
embeddings: 2-D float Tensor of embedding vectors.Embeddings should
be l2 normalized.
margin: Float, margin term in theloss definition.
Returns:
triplet_loss: tf.float32 scalar.
For further information, check the link bellow:
https://www.tensorflow.org/versions/master/api_docs/python/tf/contrib/losses/metric_learning/triplet_semihard_loss
Tiago, I don't think you are using the same formula Olivier gave.
Here is the right code (not sure it will work though, just fixing the formula) :
def compute_euclidean_distance(x, y):
"""
Computes the euclidean distance between two tensorflow variables
"""
d = tf.reduce_sum(tf.square(tf.sub(x, y)),1)
return d
def compute_contrastive_loss(left_feature, right_feature, label, margin):
"""
Compute the contrastive loss as in
L = 0.5 * Y * D^2 + 0.5 * (Y-1) * {max(0, margin - D)}^2
**Parameters**
left_feature: First element of the pair
right_feature: Second element of the pair
label: Label of the pair (0 or 1)
margin: Contrastive margin
**Returns**
Return the loss operation
"""
label = tf.to_float(label)
one = tf.constant(1.0)
d = compute_euclidean_distance(left_feature, right_feature)
d_sqrt = tf.sqrt(compute_euclidean_distance(left_feature, right_feature))
first_part = tf.mul(one-label, d)# (Y-1)*(d)
max_part = tf.square(tf.maximum(margin-d_sqrt, 0))
second_part = tf.mul(label, max_part) # (Y) * max(margin - d, 0)
loss = 0.5 * tf.reduce_mean(first_part + second_part)
return loss
I have a problem with which I've been struggling. It is related to tf.matmul() and its absence of broadcasting.
I am aware of a similar issue on https://github.com/tensorflow/tensorflow/issues/216, but tf.batch_matmul() doesn't look like a solution for my case.
I need to encode my input data as a 4D tensor:
X = tf.placeholder(tf.float32, shape=(None, None, None, 100))
The first dimension is the size of a batch, the second the number of entries in the batch.
You can imagine each entry as a composition of a number of objects (third dimension). Finally, each object is described by a vector of 100 float values.
Note that I used None for the second and third dimensions because the actual sizes may change in each batch. However, for simplicity, let's shape the tensor with actual numbers:
X = tf.placeholder(tf.float32, shape=(5, 10, 4, 100))
These are the steps of my computation:
compute a function of each vector of 100 float values (e.g., linear function)
W = tf.Variable(tf.truncated_normal([100, 50], stddev=0.1))
Y = tf.matmul(X, W)
problem: no broadcasting for tf.matmul() and no success using tf.batch_matmul()
expected shape of Y: (5, 10, 4, 50)
applying average pooling for each entry of the batch (over the objects of each entry):
Y_avg = tf.reduce_mean(Y, 2)
expected shape of Y_avg: (5, 10, 50)
I expected that tf.matmul() would have supported broadcasting. Then I found tf.batch_matmul(), but still it looks like doesn't apply to my case (e.g., W needs to have 3 dimensions at least, not clear why).
BTW, above I used a simple linear function (the weights of which are stored in W). But in my model I have a deep network instead. So, the more general problem I have is automatically computing a function for each slice of a tensor. This is why I expected that tf.matmul() would have had a broadcasting behavior (if so, maybe tf.batch_matmul() wouldn't even be necessary).
Look forward to learning from you!
Alessio
You could achieve that by reshaping X to shape [n, d], where d is the dimensionality of one single "instance" of computation (100 in your example) and n is the number of those instances in your multi-dimensional object (5*10*4=200 in your example). After reshaping, you can use tf.matmul and then reshape back to the desired shape. The fact that the first three dimensions can vary makes that little tricky, but you can use tf.shape to determine the actual shapes during run time. Finally, you can perform the second step of your computation, which should be a simple tf.reduce_mean over the respective dimension. All in all, it would look like this:
X = tf.placeholder(tf.float32, shape=(None, None, None, 100))
W = tf.Variable(tf.truncated_normal([100, 50], stddev=0.1))
X_ = tf.reshape(X, [-1, 100])
Y_ = tf.matmul(X_, W)
X_shape = tf.gather(tf.shape(X), [0,1,2]) # Extract the first three dimensions
target_shape = tf.concat(0, [X_shape, [50]])
Y = tf.reshape(Y_, target_shape)
Y_avg = tf.reduce_mean(Y, 2)
As the renamed title of the GitHub issue you linked suggests, you should use tf.tensordot(). It enables contraction of axes pairs between two tensors, in line with Numpy's tensordot(). For your case:
X = tf.placeholder(tf.float32, shape=(5, 10, 4, 100))
W = tf.Variable(tf.truncated_normal([100, 50], stddev=0.1))
Y = tf.tensordot(X, W, [[3], [0]]) # gives shape=[5, 10, 4, 50]