Keras has a preprocessing util to pad sequences, but it assumes that the sequences are integer numbers.
My sequences are vectors (my own embeddings, I do not want to use Keras embeddings), is there any way in which I can pad them to use in a LSTM?
Sequences can be made equal in Python, but the padding methods in Keras provide additional metainformation for layers like LSTM to consider for masking.
this is a possibility to pad an array of float of different length with zeros
to mask the zeros you can use the masking layer (otherwise remove it)
I initialize your embeddings in a list because numpy can't handle array of different lenght. in the example, I use 4 samples of different lengths. the relative embeddings are stored in this list list([1,300],[2,300],[3,300],[4,300])
# recreate your embed
emb = []
for i in range(1,5):
emb.append(np.random.uniform(0,1, (i,300)))
# custom padding function
def pad(x, max_len):
new_x = np.zeros((max_len,x.shape[-1]))
new_x[:len(x),:] = x # post padding
return new_x
# pad own embeddings
emb = np.stack(list(map(lambda x: pad(x, max_len=100), emb)))
emb_model = tf.keras.Sequential()
emb_model.add(tf.keras.layers.Masking(mask_value=0., input_shape=(100, 300)))
emb_model.add(tf.keras.layers.LSTM(32))
emb_model(emb)
I am trying to replace Word2Vec word embeddings by sentence embeddings by BERT in a siamese LSTM network (https://github.com/eliorc/Medium/blob/master/MaLSTM.ipynb). However my BERT embeddings are (1,768) shaped matrix and not tensors that can be fed to a keras layer. I wanted to know if it would be possible to convert it.
I have found a way to replace word embeddings by Universal sentence embeddings (http://hunterheidenreich.com/blog/google-universal-sentence-encoder-in-keras/) I tried to modify the code of the LSTM to use BERT sentence embeddings from the following service (https://github.com/hanxiao/bert-as-service#what-is-it).
# Model variables for LSTM
n_hidden = 50
gradient_clipping_norm = 1.25
batch_size = 64
n_epoch = 25
def BERTEmbedding(x):
#x is an input tensor
encoded= bc.encode(tf.squeeze(tf.cast(x, tf.string)))
return encoded
def exponent_neg_manhattan_distance(left, right):
''' Helper function for the similarity estimate of the LSTMs outputs'''
return K.exp(-K.sum(K.abs(left-right), axis=1, keepdims=True))
left_input_text = Input(shape=(1,), dtype=tf.string)
right_input_text = Input(shape=(1,), dtype=tf.string)
encoded_left = Lambda(BERTEmbedding, output_shape=(768, ))(left_input_text)
encoded_right = Lambda(BERTEmbedding, output_shape=(768, ))(right_input_text)
# Since this is a siamese network, both sides share the same LSTM
shared_lstm = LSTM(n_hidden)
left_output = shared_lstm(encoded_left)
right_output = shared_lstm(encoded_right)
I am getting the following error message TypeError: "Tensor("lambda_3/Squeeze:0", dtype=string)" must be , but received class 'tensorflow.python.framework.ops.Tensor'
LSTM takes three dimensional input [ Batch_size, sequence_length, feature_dim ]
From bert you can get two types of embeddings :
Token representation for each sequence
'CLS' token representation [ where 'CLS' represent 'CLASSIFICATION ]
If you take Token 'CLS' representation, it would be [1,768] but if
you take all sequence output it will be [ len of sequence, 768 ]
Now if you train the model in batch, it will become
[ Batch_size,len_of_sentence, 768] that's what LSTM encoder takes.
An alternative way, You can add one extra dim [batch_size, 768, 1]
and feed it to LSTM.
Adding extra dim in sequence length doesn't make sense because LSTM
unfold according to the len of sequence.
I'm currently trying to implement a Recurrent Neural Network in Keras. The data consists of a collection of 45.000 whereby each entry is a collection (of variable length) of MFCC vectors with each 13 coefficients:
spoken = numpy.load('spoken.npy')
print(spoken[0]) # Gives:
example_row = [
[
5.67170000e-01 -1.79430000e-01 -7.27360000e+00 -9.59300000e-02
-9.30140000e-02 -1.62960000e-01 4.11620000e-01 3.00590000e-01
6.86360000e-02 1.07130000e+00 1.07090000e-01 5.00890000e-01
7.51750000e-01],
[.....]
]
print(spoken.shape) # Gives: (45000,0)
print(spoken[0].shape) # Gives (N, 13) --> N amount of MFCC vectors
I'm struggling to understand how I need to reshape this Numpy array in order to feed it to the SimpleRNN of Keras:
model = Sequential()
model_spoken.add(SimpleRNN(units=10, activation='relu', input_shape=?))
.....
Therefore, my question is how do I need to reshape a collection of variable length MFCC vectors so that I can feed it to the SimpleRNN object of Keras?
It was actually quite simple since Keras has built in function for reformatting the array and padding zeros to get a static length:
spoken_train = pad_sequences(spoken_train, maxlen=100)
See github issue
So, I'm using Michael Nielson's machine learning book as a reference for my code (it is basically identical): http://neuralnetworksanddeeplearning.com/chap1.html
The code in question:
def backpropagate(self, image, image_value) :
# declare two new numpy arrays for the updated weights & biases
new_biases = [np.zeros(bias.shape) for bias in self.biases]
new_weights = [np.zeros(weight_matrix.shape) for weight_matrix in self.weights]
# -------- feed forward --------
# store all the activations in a list
activations = [image]
# declare empty list that will contain all the z vectors
zs = []
for bias, weight in zip(self.biases, self.weights) :
print(bias.shape)
print(weight.shape)
print(image.shape)
z = np.dot(weight, image) + bias
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# -------- backward pass --------
# transpose() returns the numpy array with the rows as columns and columns as rows
delta = self.cost_derivative(activations[-1], image_value) * sigmoid_prime(zs[-1])
new_biases[-1] = delta
new_weights[-1] = np.dot(delta, activations[-2].transpose())
# l = 1 means the last layer of neurons, l = 2 is the second-last, etc.
# this takes advantage of Python's ability to use negative indices in lists
for l in range(2, self.num_layers) :
z = zs[-1]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
new_biases[-l] = delta
new_weights[-l] = np.dot(delta, activations[-l-1].transpose())
return (new_biases, new_weights)
My algorithm can only get to the first round backpropagation before this error occurs:
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 97, in stochastic_gradient_descent
self.update_mini_batch(mini_batch, learning_rate)
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 117, in update_mini_batch
delta_biases, delta_weights = self.backpropagate(image, image_value)
File "D:/Programming/Python/DPUDS/DPUDS_Projects/Fall_2017/MNIST/network.py", line 160, in backpropagate
z = np.dot(weight, activation) + bias
ValueError: shapes (30,50000) and (784,1) not aligned: 50000 (dim 1) != 784 (dim 0)
I get why it's an error. The number of columns in weights doesn't match the number of rows in the pixel image, so I can't do matrix multiplication. Here's where I'm confused -- there are 30 neurons used in the backpropagation, each with 50,000 images being evaluated. My understanding is that each of the 50,000 should have 784 weights attached, one for each pixel. But when I modify the code accordingly:
count = 0
for bias, weight in zip(self.biases, self.weights) :
print(bias.shape)
print(weight[count].shape)
print(image.shape)
z = np.dot(weight[count], image) + bias
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
count += 1
I still get a similar error:
ValueError: shapes (50000,) and (784,1) not aligned: 50000 (dim 0) != 784 (dim 0)
I'm just really confuzzled by all the linear algebra involved and I think I'm just missing something about the structure of the weight matrix. Any help at all would be greatly appreciated.
It looks like the issue is in your changes to the original code.
I’be downloaded example from the link you provided and it works without any errors:
Here is full source code I used:
import cPickle
import gzip
import numpy as np
import random
def load_data():
"""Return the MNIST data as a tuple containing the training data,
the validation data, and the test data.
The ``training_data`` is returned as a tuple with two entries.
The first entry contains the actual training images. This is a
numpy ndarray with 50,000 entries. Each entry is, in turn, a
numpy ndarray with 784 values, representing the 28 * 28 = 784
pixels in a single MNIST image.
The second entry in the ``training_data`` tuple is a numpy ndarray
containing 50,000 entries. Those entries are just the digit
values (0...9) for the corresponding images contained in the first
entry of the tuple.
The ``validation_data`` and ``test_data`` are similar, except
each contains only 10,000 images.
This is a nice data format, but for use in neural networks it's
helpful to modify the format of the ``training_data`` a little.
That's done in the wrapper function ``load_data_wrapper()``, see
below.
"""
f = gzip.open('../data/mnist.pkl.gz', 'rb')
training_data, validation_data, test_data = cPickle.load(f)
f.close()
return (training_data, validation_data, test_data)
def load_data_wrapper():
"""Return a tuple containing ``(training_data, validation_data,
test_data)``. Based on ``load_data``, but the format is more
convenient for use in our implementation of neural networks.
In particular, ``training_data`` is a list containing 50,000
2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray
containing the input image. ``y`` is a 10-dimensional
numpy.ndarray representing the unit vector corresponding to the
correct digit for ``x``.
``validation_data`` and ``test_data`` are lists containing 10,000
2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional
numpy.ndarry containing the input image, and ``y`` is the
corresponding classification, i.e., the digit values (integers)
corresponding to ``x``.
Obviously, this means we're using slightly different formats for
the training data and the validation / test data. These formats
turn out to be the most convenient for use in our neural network
code."""
tr_d, va_d, te_d = load_data()
training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]
training_results = [vectorized_result(y) for y in tr_d[1]]
training_data = zip(training_inputs, training_results)
validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]
validation_data = zip(validation_inputs, va_d[1])
test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]
test_data = zip(test_inputs, te_d[1])
return (training_data, validation_data, test_data)
def vectorized_result(j):
"""Return a 10-dimensional unit vector with a 1.0 in the jth
position and zeroes elsewhere. This is used to convert a digit
(0...9) into a corresponding desired output from the neural
network."""
e = np.zeros((10, 1))
e[j] = 1.0
return e
class Network(object):
def __init__(self, sizes):
"""The list ``sizes`` contains the number of neurons in the
respective layers of the network. For example, if the list
was [2, 3, 1] then it would be a three-layer network, with the
first layer containing 2 neurons, the second layer 3 neurons,
and the third layer 1 neuron. The biases and weights for the
network are initialized randomly, using a Gaussian
distribution with mean 0, and variance 1. Note that the first
layer is assumed to be an input layer, and by convention we
won't set any biases for those neurons, since biases are only
ever used in computing the outputs from later layers."""
self.num_layers = len(sizes)
self.sizes = sizes
self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
self.weights = [np.random.randn(y, x)
for x, y in zip(sizes[:-1], sizes[1:])]
def feedforward(self, a):
"""Return the output of the network if ``a`` is input."""
for b, w in zip(self.biases, self.weights):
a = sigmoid(np.dot(w, a)+b)
return a
def SGD(self, training_data, epochs, mini_batch_size, eta,
test_data=None):
"""Train the neural network using mini-batch stochastic
gradient descent. The ``training_data`` is a list of tuples
``(x, y)`` representing the training inputs and the desired
outputs. The other non-optional parameters are
self-explanatory. If ``test_data`` is provided then the
network will be evaluated against the test data after each
epoch, and partial progress printed out. This is useful for
tracking progress, but slows things down substantially."""
if test_data: n_test = len(test_data)
n = len(training_data)
for j in xrange(epochs):
random.shuffle(training_data)
mini_batches = [
training_data[k:k+mini_batch_size]
for k in xrange(0, n, mini_batch_size)]
for mini_batch in mini_batches:
self.update_mini_batch(mini_batch, eta)
if test_data:
print "Epoch {0}: {1} / {2}".format(
j, self.evaluate(test_data), n_test)
else:
print "Epoch {0} complete".format(j)
def update_mini_batch(self, mini_batch, eta):
"""Update the network's weights and biases by applying
gradient descent using backpropagation to a single mini batch.
The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
is the learning rate."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
for x, y in mini_batch:
delta_nabla_b, delta_nabla_w = self.backprop(x, y)
nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
self.weights = [w-(eta/len(mini_batch))*nw
for w, nw in zip(self.weights, nabla_w)]
self.biases = [b-(eta/len(mini_batch))*nb
for b, nb in zip(self.biases, nabla_b)]
def backprop(self, x, y):
"""Return a tuple ``(nabla_b, nabla_w)`` representing the
gradient for the cost function C_x. ``nabla_b`` and
``nabla_w`` are layer-by-layer lists of numpy arrays, similar
to ``self.biases`` and ``self.weights``."""
nabla_b = [np.zeros(b.shape) for b in self.biases]
nabla_w = [np.zeros(w.shape) for w in self.weights]
# feedforward
activation = x
activations = [x] # list to store all the activations, layer by layer
zs = [] # list to store all the z vectors, layer by layer
for b, w in zip(self.biases, self.weights):
z = np.dot(w, activation)+b
zs.append(z)
activation = sigmoid(z)
activations.append(activation)
# backward pass
delta = self.cost_derivative(activations[-1], y) * \
sigmoid_prime(zs[-1])
nabla_b[-1] = delta
nabla_w[-1] = np.dot(delta, activations[-2].transpose())
# Note that the variable l in the loop below is used a little
# differently to the notation in Chapter 2 of the book. Here,
# l = 1 means the last layer of neurons, l = 2 is the
# second-last layer, and so on. It's a renumbering of the
# scheme in the book, used here to take advantage of the fact
# that Python can use negative indices in lists.
for l in xrange(2, self.num_layers):
z = zs[-l]
sp = sigmoid_prime(z)
delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
nabla_b[-l] = delta
nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
return (nabla_b, nabla_w)
def evaluate(self, test_data):
"""Return the number of test inputs for which the neural
network outputs the correct result. Note that the neural
network's output is assumed to be the index of whichever
neuron in the final layer has the highest activation."""
test_results = [(np.argmax(self.feedforward(x)), y)
for (x, y) in test_data]
return sum(int(x == y) for (x, y) in test_results)
def cost_derivative(self, output_activations, y):
"""Return the vector of partial derivatives \partial C_x /
\partial a for the output activations."""
return (output_activations-y)
#### Miscellaneous functions
def sigmoid(z):
"""The sigmoid function."""
return 1.0/(1.0+np.exp(-z))
def sigmoid_prime(z):
"""Derivative of the sigmoid function."""
return sigmoid(z)*(1-sigmoid(z))
training_data, validation_data, test_data = load_data_wrapper()
net = Network([784, 30, 10])
net.SGD(training_data, 30, 10, 3.0, test_data=test_data)
Additional info:
However, I would recommend using one of existing frameworks, for example - Keras to don't reinvent the wheel
Also, it was checked with python 3.6:
Kudos on digging into Nielsen's code. It's a great resource to develop thorough understanding of NN principles. Too many people leap ahead to Keras without knowing what goes on under the hood.
Each training example doesn't get its own weights. Each of the 784 features does. If each example got its own weights then each weight set would overfit to its corresponding training example. Also, if you later used your trained network to run inference on a single test example, what would it do with 50,000 sets of weights when presented with just one handwritten digit? Instead, each of the 30 neurons in your hidden layer learns a set of 784 weights, one for each pixel, that offers high predictive accuracy when generalized to any handwritten digit.
Import network.py and instantiate a Network class like this without modifying any code:
net = network.Network([784, 30, 10])
..which gives you a network with 784 input neurons, 30 hidden neurons and 10 output neurons. Your weight matrices will have dimensions [30, 784] and [10, 30], respectively. When you feed the network an input array of dimensions [784, 1] the matrix multiplication that gave you an error is valid because dim 1 of the weight matrix equals dim 0 of the input array (both 784).
Your problem is not implementation of backprop but rather setting up a network architecture appropriate for the shape of your input data. If memory serves Nielsen leaves backprop as a black box in chapter 1 and doesn't dive into it until chapter 2. Keep at it, and good luck!
I want to create a word embedding pretraining network which adds something on top of word2vec CBOW. Therefore, I'm trying to implement word2vec CBOW first. Since I'm very new to keras, I'm unable to figure out how to implement CBOW in it.
Initialization:
I have calculated the vocabulary and have the mapping of word to integers.
Input to the (yet to be implemented) network:
A list of 2*k + 1 integers (representing the central word and 2*k words in context)
Network Specification
A shared Embedding layer should take this list of integers and give their corresponding vector outputs. Further a mean of 2*k context vector is to be taken (I believe this can be done using add_node(layer, name, inputs=[2*k vectors], merge_mode='ave')).
It will be very helpful if anyone can share a small code-snippet of this.
P.S.: I was looking at word2veckeras, but couldn't follow its code because it also uses a gensim.
UPDATE 1:
I want to share the embedding layer in the network. The embedding layer should be able to take context words (2*k) and the current word as well. I can do this by taking all 2*k + 1 word indices in the input and write a custom lambda function which will do the needful. But, after that I also want to add negative sampling network for which I'll have to take embedding of more words and dot product with the context vector. Can someone provide with an example where Embedding layer is a shared node in the Graph() network
Graph() has been deprecated from keras
Any arbitrary network can be created by using keras functional API.
Following is the demo code which created a word2vec cbow model with negative sampling tested on randomized inputs
from keras import backend as K
import numpy as np
from keras.utils.np_utils import accuracy
from keras.models import Sequential, Model
from keras.layers import Input, Lambda, Dense, merge
from keras.layers.embeddings import Embedding
k = 3 # context windows size
context_size = 2*k
neg = 5 # number of negative samples
# generate weight matrix for embeddings
embedding = []
for i in range(10):
embedding.append(np.full(100, i))
embedding = np.array(embedding)
print embedding
# Creating CBOW model
word_index = Input(shape=(1,))
context = Input(shape=(context_size,))
negative_samples = Input(shape=(neg,))
shared_embedding_layer = Embedding(input_dim=10, output_dim=100, weights=[embedding])
word_embedding = shared_embedding_layer(word_index)
context_embeddings = shared_embedding_layer(context)
negative_words_embedding = shared_embedding_layer(negative_samples)
cbow = Lambda(lambda x: K.mean(x, axis=1), output_shape=(100,))(context_embeddings)
word_context_product = merge([word_embedding, cbow], mode='dot')
negative_context_product = merge([negative_words_embedding, cbow], mode='dot', concat_axis=-1)
model = Model(input=[word_index, context, negative_samples], output=[word_context_product, negative_context_product])
model.compile(optimizer='rmsprop', loss='mse', metrics=['accuracy'])
input_context = np.random.randint(10, size=(1, context_size))
input_word = np.random.randint(10, size=(1,))
input_negative = np.random.randint(10, size=(1, neg))
print "word, context, negative samples"
print input_word.shape, input_word
print input_context.shape, input_context
print input_negative.shape, input_negative
output_dot_product, output_negative_product = model.predict([input_word, input_context, input_negative])
print "word cbow dot product"
print output_dot_product.shape, output_dot_product
print "cbow negative dot product"
print output_negative_product.shape, output_negative_product
Hope it helps!
UPDATE 1:
I've completed the code and uploaded it here
You could try something like this. Here I've initialized the embedding matrix to a fixed value. For an input array of shape (1, 6) you'll get the output of shape (1, 100) where the 100 is the average of the 6 input embedding.
model = Sequential()
k = 3 # context windows size
context_size = 2*k
# generate weight matrix for embeddings
embedding = []
for i in range(10):
embedding.append(np.full(100, i))
embedding = np.array(embedding)
print embedding
model.add(Embedding(input_dim=10, output_dim=100, input_length=context_size, weights=[embedding]))
model.add(Lambda(lambda x: K.mean(x, axis=1), output_shape=(100,)))
model.compile('rmsprop', 'mse')
input_array = np.random.randint(10, size=(1, context_size))
print input_array.shape
output_array = model.predict(input_array)
print output_array.shape
print output_array[0]