I am using Tensorflow's tf.nn.ctc_beam_search_decoder()
to decode the output of a RNN doing some many-to-many mapping (i.e., multiple softmax outputs for each network cell).
A simplified version of the network's output and the Beam search decoder is:
import numpy as np
import tensorflow as tf
batch_size = 4
sequence_max_len = 5
num_classes = 3
y_pred = tf.placeholder(tf.float32, shape=(batch_size, sequence_max_len, num_classes))
y_pred_transposed = tf.transpose(y_pred,
perm=[1, 0, 2]) # TF expects dimensions [max_time, batch_size, num_classes]
logits = tf.log(y_pred_transposed)
sequence_lengths = tf.to_int32(tf.fill([batch_size], sequence_max_len))
decoded, log_probabilities = tf.nn.ctc_beam_search_decoder(logits,
sequence_length=sequence_lengths,
beam_width=3,
merge_repeated=False, top_paths=1)
decoded = decoded[0]
decoded_paths = tf.sparse_tensor_to_dense(decoded) # Shape: [batch_size, max_sequence_len]
with tf.Session() as session:
tf.global_variables_initializer().run()
softmax_outputs = np.array([[[0.1, 0.1, 0.8], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1]],
[[0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]],
[[0.1, 0.7, 0.2], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]],
[[0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]]])
decoded_paths = session.run(decoded_paths, feed_dict = {y_pred: softmax_outputs})
print(decoded_paths)
The output in this case is:
[[0]
[1]
[1]
[1]]
My understanding is that the output tensor should be of dimensions [batch_size, max_sequence_len]
, with each row containing the indices of the relevant classes in the found path.
In this case I would expect the output to be similar to:
[[2, 0, 0, 0, 0],
[2, 2, 2, 2, 2],
[1, 2, 2, 2, 2],
[2, 2, 2, 2, 2]]
What am I not understanding about how ctc_beam_search_decoder
works?
As indicated in tf.nn.ctc_beam_search_decoder documentation, the shape of the output is not [batch_size, max_sequence_len]
. Instead, it is
[batch_size, max_decoded_length[j]]
(with j=0
in your case).
Based on the beginning of section 2 of this paper (which is cited in the github repository), max_decoded_length[0]
is bounded from above by max_sequence_len
, but they are not necessarily equal. The relevant citation is:
Let S be a set of training examples drawn from a fixed distribution D_{XxZ}. The input space X = (R^m) is the set of all sequences of m dimensional real valued vectors. The target space Z = L* is the set of all sequences over the (finite) alphabet L of labels. In general, we refer to elements of L* as label sequences or labellings. Each example in S consists of a pair of sequences (x, z). The target sequence z = (z1, z2, ..., zU) is at most as long as the input sequence x = (x1, x2, ..., xT ), i.e. U<=T. Since the input and target sequences are not generally the same length, there is no a priori way of aligning them.
In fact, max_decoded_length[0]
depends on the specific matrix softmax_outputs
. In particular, two such matrices with exactly the same dimensions can result in different max_decoded_length[0]
.
For example, if you replace the row
softmax_outputs = np.array([[[0.1, 0.1, 0.8], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1], [0.8, 0.1, 0.1]],
[[0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]],
[[0.1, 0.7, 0.2], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]],
[[0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7], [0.1, 0.2, 0.7]]])
with the rows
np.random.seed(7)
r=np.random.randint(0,100,size=(4,5,3))
softmax_outputs=r/np.sum(r,2).reshape(4,5,1)
you'll get the output
[[1 0 1]
[1 0 1]
[1 0 0]
[1 0 0]]
(in the above examples, softmax_outputs
consists of logits and it is exactly of the same dimensions as the matrix you provided).
On the other hand, changing the seed to np.random.seed(50)
gives the output
[[1 0]
[1 0]
[1 0]
[0 1]]
P.S.
Regarding the last part of your question:
In this case I would expect the output to be similar to:
[[2, 0, 0, 0, 0], [2, 2, 2, 2, 2], [1, 2, 2, 2, 2], [2, 2, 2, 2, 2]]
Note that, based on the documentation, num_classes
actually represents num_labels + 1
. Specifically:
The inputs Tensor's innermost dimension size,
num_classes
, representsnum_labels + 1
classes, wherenum_labels
is the number of true labels, and the largest value (num_classes - 1
) is reserved for the blank label.For example, for a vocabulary containing 3 labels [a, b, c],
num_classes = 4
and the labels indexing is {a: 0, b: 1, c: 2, blank: 3}.
So the true labels in your case are 0 and 1, and 2 is reserved for the blank label. The blank label represents the situation of observing no label (section 3.1 here):
A CTC network has a softmax output layer (Bridle, 1990) with one more unit than there are labels in L. The activations of the first |L| units are interpreted as the probabilities of observing the corresponding labels at particular times. The activation of the extra unit is the probability of observing a ‘blank’, or no label. Together, these outputs define the probabilities of all possible ways of aligning all possible label sequences with the input sequence.