Welcome to Dinosaurus Island! 65 million years ago, dinosaurs existed, and in this assignment they are back. You are in charge of a special task. Leading biology researchers are creating new breeds of dinosaurs and bringing them to life on earth, and your job is to give names to these dinosaurs. If a dinosaur does not like its name, it might go beserk, so choose wisely!

Luckily you have learned some deep learning and you will use it to save the day. Your assistant has collected a list of all the dinosaur names they could find, and compiled them into this dataset. (Feel free to take a look by clicking the previous link.) To create new dinosaur names, you will build a character level language model to generate new names. Your algorithm will learn the different name patterns, and randomly generate new names. Hopefully this algorithm will keep you and your team safe from the dinosaurs' wrath!
By completing this assignment you will learn:
We will begin by loading in some functions that we have provided for you in rnn_utils
. Specifically, you have access to functions such as rnn_forward
and rnn_backward
which are equivalent to those you've implemented in the previous assignment.
In [1]:
import numpy as np
from utils import *
import random
In [2]:
data = open('dinos.txt', 'r').read()
data= data.lower()
chars = list(set(data))
data_size, vocab_size = len(data), len(chars)
print('There are %d total characters and %d unique characters in your data.' % (data_size, vocab_size))
The characters are az (26 characters) plus the "\n" (or newline character), which in this assignment plays a role similar to the <EOS>
(or "End of sentence") token we had discussed in lecture, only here it indicates the end of the dinosaur name rather than the end of a sentence. In the cell below, we create a python dictionary (i.e., a hash table) to map each character to an index from 026. We also create a second python dictionary that maps each index back to the corresponding character character. This will help you figure out what index corresponds to what character in the probability distribution output of the softmax layer. Below, char_to_ix
and ix_to_char
are the python dictionaries.
In [3]:
char_to_ix = { ch:i for i,ch in enumerate(sorted(chars)) }
ix_to_char = { i:ch for i,ch in enumerate(sorted(chars)) }
print(ix_to_char)
Your model will have the following structure:
At each timestep, the RNN tries to predict what is the next character given the previous characters. The dataset $X = (x^{\langle 1 \rangle}, x^{\langle 2 \rangle}, ..., x^{\langle T_x \rangle})$ is a list of characters in the training set, while $Y = (y^{\langle 1 \rangle}, y^{\langle 2 \rangle}, ..., y^{\langle T_x \rangle})$ is such that at every timestep $t$, we have $y^{\langle t \rangle} = x^{\langle t+1 \rangle}$.
In this section you will implement the clip
function that you will call inside of your optimization loop. Recall that your overall loop structure usually consists of a forward pass, a cost computation, a backward pass, and a parameter update. Before updating the parameters, you will perform gradient clipping when needed to make sure that your gradients are not "exploding," meaning taking on overly large values.
In the exercise below, you will implement a function clip
that takes in a dictionary of gradients and returns a clipped version of gradients if needed. There are different ways to clip gradients; we will use a simple elementwise clipping procedure, in which every element of the gradient vector is clipped to lie between some range [N, N]. More generally, you will provide a maxValue
(say 10). In this example, if any component of the gradient vector is greater than 10, it would be set to 10; and if any component of the gradient vector is less than 10, it would be set to 10. If it is between 10 and 10, it is left alone.
Exercise: Implement the function below to return the clipped gradients of your dictionary gradients
. Your function takes in a maximum threshold and returns the clipped versions of your gradients. You can check out this hint for examples of how to clip in numpy. You will need to use the argument out = ...
.
In [4]:
### GRADED FUNCTION: clip
def clip(gradients, maxValue):
'''
Clips the gradients' values between minimum and maximum.
Arguments:
gradients  a dictionary containing the gradients "dWaa", "dWax", "dWya", "db", "dby"
maxValue  everything above this number is set to this number, and everything less than maxValue is set to maxValue
Returns:
gradients  a dictionary with the clipped gradients.
'''
dWaa, dWax, dWya, db, dby = gradients['dWaa'], gradients['dWax'], gradients['dWya'], gradients['db'], gradients['dby']
### START CODE HERE ###
# clip to mitigate exploding gradients, loop over [dWax, dWaa, dWya, db, dby]. (≈2 lines)
#for gradient in [dWax, dWaa, dWya, db, dby]: # not a good way to go
### END CODE HERE ###
gradients = {"dWaa": dWaa, "dWax": dWax, "dWya": dWya, "db": db, "dby": dby}
for k, v in gradients.items():
gradients[k] = np.clip(v, a_min=maxValue, a_max=maxValue)
return gradients
In [5]:
np.random.seed(3)
dWax = np.random.randn(5,3)*10
dWaa = np.random.randn(5,5)*10
dWya = np.random.randn(2,5)*10
db = np.random.randn(5,1)*10
dby = np.random.randn(2,1)*10
gradients = {"dWax": dWax, "dWaa": dWaa, "dWya": dWya, "db": db, "dby": dby}
gradients = clip(gradients, 10)
print("gradients[\"dWaa\"][1][2] =", gradients["dWaa"][1][2])
print("gradients[\"dWax\"][3][1] =", gradients["dWax"][3][1])
print("gradients[\"dWya\"][1][2] =", gradients["dWya"][1][2])
print("gradients[\"db\"][4] =", gradients["db"][4])
print("gradients[\"dby\"][1] =", gradients["dby"][1])
Expected output:
**gradients["dWaa"][1][2] **  10.0 
**gradients["dWax"][3][1]**  10.0 
**gradients["dWya"][1][2]**  0.29713815361 
**gradients["db"][4]**  [ 10.] 
**gradients["dby"][1]**  [ 8.45833407] 
Now assume that your model is trained. You would like to generate new text (characters). The process of generation is explained in the picture below:
Exercise: Implement the sample
function below to sample characters. You need to carry out 4 steps:
Step 1: Pass the network the first "dummy" input $x^{\langle 1 \rangle} = \vec{0}$ (the vector of zeros). This is the default input before we've generated any characters. We also set $a^{\langle 0 \rangle} = \vec{0}$
Step 2: Run one step of forward propagation to get $a^{\langle 1 \rangle}$ and $\hat{y}^{\langle 1 \rangle}$. Here are the equations:
Note that $\hat{y}^{\langle t+1 \rangle }$ is a (softmax) probability vector (its entries are between 0 and 1 and sum to 1). $\hat{y}^{\langle t+1 \rangle}_i$ represents the probability that the character indexed by "i" is the next character. We have provided a softmax()
function that you can use.
np.random.choice
.Here is an example of how to use np.random.choice()
:
np.random.seed(0)
p = np.array([0.1, 0.0, 0.7, 0.2])
index = np.random.choice([0, 1, 2, 3], p = p.ravel())
This means that you will pick the index
according to the distribution:
$P(index = 0) = 0.1, P(index = 1) = 0.0, P(index = 2) = 0.7, P(index = 3) = 0.2$.
sample()
is to overwrite the variable x
, which currently stores $x^{\langle t \rangle }$, with the value of $x^{\langle t + 1 \rangle }$. You will represent $x^{\langle t + 1 \rangle }$ by creating a onehot vector corresponding to the character you've chosen as your prediction. You will then forward propagate $x^{\langle t + 1 \rangle }$ in Step 1 and keep repeating the process until you get a "\n" character, indicating you've reached the end of the dinosaur name.
In [6]:
# GRADED FUNCTION: sample
def sample(parameters, char_to_ix, seed):
"""
Sample a sequence of characters according to a sequence of probability distributions output of the RNN
Arguments:
parameters  python dictionary containing the parameters Waa, Wax, Wya, by, and b.
char_to_ix  python dictionary mapping each character to an index.
seed  used for grading purposes. Do not worry about it.
Returns:
indices  a list of length n containing the indices of the sampled characters.
"""
# Retrieve parameters and relevant shapes from "parameters" dictionary
Waa, Wax, Wya, by, b = parameters['Waa'], parameters['Wax'], parameters['Wya'], parameters['by'], parameters['b']
vocab_size = by.shape[0]
n_a = Waa.shape[1]
### START CODE HERE ###
# Step 1: Create the onehot vector x for the first character (initializing the sequence generation). (≈1 line)
x = np.zeros((vocab_size, 1))
# Step 1': Initialize a_prev as zeros (≈1 line)
a_prev = np.zeros((n_a, 1))
# Create an empty list of indices, this is the list which will contain the list of indices of the characters to generate (≈1 line)
indices = []
# Idx is a flag to detect a newline character, we initialize it to 1
idx = 1
# Loop over timesteps t. At each timestep, sample a character from a probability distribution and append
# its index to "indices". We'll stop if we reach 50 characters (which should be very unlikely with a well
# trained model), which helps debugging and prevents entering an infinite loop.
counter = 0
newline_character = char_to_ix['\n']
while (idx != newline_character and counter != 50):
# Step 2: Forward propagate x using the equations (1), (2) and (3)
a = np.tanh(np.dot(Wax, x) + np.dot(Waa, a_prev) + b)
z = np.dot(Wya, a) + by
y = softmax(z)
# for grading purposes
np.random.seed(counter+seed)
# Step 3: Sample the index of a character within the vocabulary from the probability distribution y
idx = np.random.choice(range(vocab_size), p=y.ravel())
# Append the index to "indices"
indices.append(idx)
# Step 4: Overwrite the input character as the one corresponding to the sampled index.
x = np.zeros((vocab_size, 1))
x[idx] = 1
# Update "a_prev" to be "a"
a_prev = a
# for grading purposes
seed += 1
counter +=1
### END CODE HERE ###
if (counter == 50):
indices.append(char_to_ix['\n'])
return indices
In [7]:
np.random.seed(2)
_, n_a = 20, 100
Wax, Waa, Wya = np.random.randn(n_a, vocab_size), np.random.randn(n_a, n_a), np.random.randn(vocab_size, n_a)
b, by = np.random.randn(n_a, 1), np.random.randn(vocab_size, 1)
parameters = {"Wax": Wax, "Waa": Waa, "Wya": Wya, "b": b, "by": by}
indices = sample(parameters, char_to_ix, 0)
print("Sampling:")
print("list of sampled indices:", indices)
print("list of sampled characters:", [ix_to_char[i] for i in indices])
Expected output:
**list of sampled indices:** 
[12, 17, 24, 14, 13, 9, 10, 22, 24, 6, 13, 11, 12, 6, 21, 15, 21, 14, 3, 2, 1, 21, 18, 24, 7, 25, 6, 25, 18, 10, 16, 2, 3, 8, 15, 12, 11, 7, 1, 12, 10, 2, 7, 7, 11, 5, 6, 12, 25, 0, 0] 
**list of sampled characters:** 
['l', 'q', 'x', 'n', 'm', 'i', 'j', 'v', 'x', 'f', 'm', 'k', 'l', 'f', 'u', 'o', 'u', 'n', 'c', 'b', 'a', 'u', 'r', 'x', 'g', 'y', 'f', 'y', 'r', 'j', 'p', 'b', 'c', 'h', 'o', 'l', 'k', 'g', 'a', 'l', 'j', 'b', 'g', 'g', 'k', 'e', 'f', 'l', 'y', '\n', '\n'] 
It is time to build the characterlevel language model for text generation.
In this section you will implement a function performing one step of stochastic gradient descent (with clipped gradients). You will go through the training examples one at a time, so the optimization algorithm will be stochastic gradient descent. As a reminder, here are the steps of a common optimization loop for an RNN:
Exercise: Implement this optimization process (one step of stochastic gradient descent).
We provide you with the following functions:
def rnn_forward(X, Y, a_prev, parameters):
""" Performs the forward propagation through the RNN and computes the crossentropy loss.
It returns the loss' value as well as a "cache" storing values to be used in the backpropagation."""
....
return loss, cache
def rnn_backward(X, Y, parameters, cache):
""" Performs the backward propagation through time to compute the gradients of the loss with respect
to the parameters. It returns also all the hidden states."""
...
return gradients, a
def update_parameters(parameters, gradients, learning_rate):
""" Updates parameters using the Gradient Descent Update Rule."""
...
return parameters
In [10]:
# GRADED FUNCTION: optimize
def optimize(X, Y, a_prev, parameters, learning_rate = 0.01):
"""
Execute one step of the optimization to train the model.
Arguments:
X  list of integers, where each integer is a number that maps to a character in the vocabulary.
Y  list of integers, exactly the same as X but shifted one index to the left.
a_prev  previous hidden state.
parameters  python dictionary containing:
Wax  Weight matrix multiplying the input, numpy array of shape (n_a, n_x)
Waa  Weight matrix multiplying the hidden state, numpy array of shape (n_a, n_a)
Wya  Weight matrix relating the hiddenstate to the output, numpy array of shape (n_y, n_a)
b  Bias, numpy array of shape (n_a, 1)
by  Bias relating the hiddenstate to the output, numpy array of shape (n_y, 1)
learning_rate  learning rate for the model.
Returns:
loss  value of the loss function (crossentropy)
gradients  python dictionary containing:
dWax  Gradients of inputtohidden weights, of shape (n_a, n_x)
dWaa  Gradients of hiddentohidden weights, of shape (n_a, n_a)
dWya  Gradients of hiddentooutput weights, of shape (n_y, n_a)
db  Gradients of bias vector, of shape (n_a, 1)
dby  Gradients of output bias vector, of shape (n_y, 1)
a[len(X)1]  the last hidden state, of shape (n_a, 1)
"""
### START CODE HERE ###
# Forward propagate through time (≈1 line)
loss, cache = rnn_forward(X, Y, a_prev, parameters)
# Backpropagate through time (≈1 line)
gradients, a = rnn_backward(X, Y, parameters, cache)
# Clip your gradients between 5 (min) and 5 (max) (≈1 line)
gradients = clip(gradients, 5)
# Update parameters (≈1 line)
parameters.update({k: v  learning_rate * gradients["d" + k] for k, v in parameters.items()})
### END CODE HERE ###
return loss, gradients, a[len(X)1]
In [11]:
np.random.seed(1)
vocab_size, n_a = 27, 100
a_prev = np.random.randn(n_a, 1)
Wax, Waa, Wya = np.random.randn(n_a, vocab_size), np.random.randn(n_a, n_a), np.random.randn(vocab_size, n_a)
b, by = np.random.randn(n_a, 1), np.random.randn(vocab_size, 1)
parameters = {"Wax": Wax, "Waa": Waa, "Wya": Wya, "b": b, "by": by}
X = [12,3,5,11,22,3]
Y = [4,14,11,22,25, 26]
loss, gradients, a_last = optimize(X, Y, a_prev, parameters, learning_rate = 0.01)
print("Loss =", loss)
print("gradients[\"dWaa\"][1][2] =", gradients["dWaa"][1][2])
print("np.argmax(gradients[\"dWax\"]) =", np.argmax(gradients["dWax"]))
print("gradients[\"dWya\"][1][2] =", gradients["dWya"][1][2])
print("gradients[\"db\"][4] =", gradients["db"][4])
print("gradients[\"dby\"][1] =", gradients["dby"][1])
print("a_last[4] =", a_last[4])
Expected output:
**Loss **  126.503975722 
**gradients["dWaa"][1][2]**  0.194709315347 
**np.argmax(gradients["dWax"])**  93 
**gradients["dWya"][1][2]**  0.007773876032 
**gradients["db"][4]**  [0.06809825] 
**gradients["dby"][1]**  [ 0.01538192] 
**a_last[4]**  [1.] 
Given the dataset of dinosaur names, we use each line of the dataset (one name) as one training example. Every 100 steps of stochastic gradient descent, you will sample 10 randomly chosen names to see how the algorithm is doing. Remember to shuffle the dataset, so that stochastic gradient descent visits the examples in random order.
Exercise: Follow the instructions and implement model()
. When examples[index]
contains one dinosaur name (string), to create an example (X, Y), you can use this:
index = j % len(examples)
X = [None] + [char_to_ix[ch] for ch in examples[index]]
Y = X[1:] + [char_to_ix["\n"]]
Note that we use: index= j % len(examples)
, where j = 1....num_iterations
, to make sure that examples[index]
is always a valid statement (index
is smaller than len(examples)
).
The first entry of X
being None
will be interpreted by rnn_forward()
as setting $x^{\langle 0 \rangle} = \vec{0}$. Further, this ensures that Y
is equal to X
but shifted one step to the left, and with an additional "\n" appended to signify the end of the dinosaur name.
In [12]:
# GRADED FUNCTION: model
def model(data, ix_to_char, char_to_ix, num_iterations = 35000, n_a = 50, dino_names = 7, vocab_size = 27):
"""
Trains the model and generates dinosaur names.
Arguments:
data  text corpus
ix_to_char  dictionary that maps the index to a character
char_to_ix  dictionary that maps a character to an index
num_iterations  number of iterations to train the model for
n_a  number of units of the RNN cell
dino_names  number of dinosaur names you want to sample at each iteration.
vocab_size  number of unique characters found in the text, size of the vocabulary
Returns:
parameters  learned parameters
"""
# Retrieve n_x and n_y from vocab_size
n_x, n_y = vocab_size, vocab_size
# Initialize parameters
parameters = initialize_parameters(n_a, n_x, n_y)
# Initialize loss (this is required because we want to smooth our loss, don't worry about it)
loss = get_initial_loss(vocab_size, dino_names)
# Build list of all dinosaur names (training examples).
with open("dinos.txt") as f:
examples = f.readlines()
examples = [x.lower().strip() for x in examples]
# Shuffle list of all dinosaur names
np.random.seed(0)
np.random.shuffle(examples)
# Initialize the hidden state of your LSTM
a_prev = np.zeros((n_a, 1))
# Optimization loop
for j in range(num_iterations):
### START CODE HERE ###
# Use the hint above to define one training example (X,Y) (≈ 2 lines)
index = j % len(examples)
X = [None] + [char_to_ix[ch] for ch in examples[index]]
Y = X[1:] + [char_to_ix["\n"]]
# Perform one optimization step: Forwardprop > Backwardprop > Clip > Update parameters
# Choose a learning rate of 0.01
curr_loss, gradients, a_prev = optimize(X, Y, a_prev, parameters, learning_rate = 0.01)
### END CODE HERE ###
# Use a latency trick to keep the loss smooth. It happens here to accelerate the training.
loss = smooth(loss, curr_loss)
# Every 2000 Iteration, generate "n" characters thanks to sample() to check if the model is learning properly
if j % 2000 == 0:
print('Iteration: %d, Loss: %f' % (j, loss) + '\n')
# The number of dinosaur names to print
seed = 0
for name in range(dino_names):
# Sample indices and print them
sampled_indices = sample(parameters, char_to_ix, seed)
print_sample(sampled_indices, ix_to_char)
seed += 1 # To get the same result for grading purposed, increment the seed by one.
print('\n')
return parameters
Run the following cell, you should observe your model outputting randomlooking characters at the first iteration. After a few thousand iterations, your model should learn to generate reasonablelooking names.
In [13]:
parameters = model(data, ix_to_char, char_to_ix)
You can see that your algorithm has started to generate plausible dinosaur names towards the end of the training. At first, it was generating random characters, but towards the end you could see dinosaur names with cool endings. Feel free to run the algorithm even longer and play with hyperparameters to see if you can get even better results. Our implemetation generated some really cool names like maconucon
, marloralus
and macingsersaurus
. Your model hopefully also learned that dinosaur names tend to end in saurus
, don
, aura
, tor
, etc.
If your model generates some noncool names, don't blame the model entirelynot all actual dinosaur names sound cool. (For example, dromaeosauroides
is an actual dinosaur name and is in the training set.) But this model should give you a set of candidates from which you can pick the coolest!
This assignment had used a relatively small dataset, so that you could train an RNN quickly on a CPU. Training a model of the english language requires a much bigger dataset, and usually needs much more computation, and could run for many hours on GPUs. We ran our dinosaur name for quite some time, and so far our favoriate name is the great, undefeatable, and fierce: Mangosaurus!
The rest of this notebook is optional and is not graded, but we hope you'll do it anyway since it's quite fun and informative.
A similar (but more complicated) task is to generate Shakespeare poems. Instead of learning from a dataset of Dinosaur names you can use a collection of Shakespearian poems. Using LSTM cells, you can learn longer term dependencies that span many characters in the texte.g., where a character appearing somewhere a sequence can influence what should be a different character much much later in ths sequence. These long term dependencies were less important with dinosaur names, since the names were quite short.
We have implemented a Shakespeare poem generator with Keras. Run the following cell to load the required packages and models. This may take a few minutes.
In [14]:
from __future__ import print_function
from keras.callbacks import LambdaCallback
from keras.models import Model, load_model, Sequential
from keras.layers import Dense, Activation, Dropout, Input, Masking
from keras.layers import LSTM
from keras.utils.data_utils import get_file
from keras.preprocessing.sequence import pad_sequences
from shakespeare_utils import *
import sys
import io
To save you some time, we have already trained a model for ~1000 epochs on a collection of Shakespearian poems called "The Sonnets".
Let's train the model for one more epoch. When it finishes training for an epochthis will also take a few minutesyou can run generate_output
, which will prompt asking you for an input (<
40 characters). The poem will start with your sentence, and our RNNShakespeare will complete the rest of the poem for you! For example, try "Forsooth this maketh no sense " (don't enter the quotation marks). Depending on whether you include the space at the end, your results might also differtry it both ways, and try other inputs as well.
In [ ]:
print_callback = LambdaCallback(on_epoch_end=on_epoch_end)
model.fit(x, y, batch_size=128, epochs=1, callbacks=[print_callback])
In [ ]:
# Run this cell to try with different inputs without having to retrain the model
generate_output()
The RNNShakespeare model is very similar to the one you have built for dinosaur names. The only major differences are:
If you want to learn more, you can also check out the Keras Team's text generation implementation on GitHub: https://github.com/kerasteam/keras/blob/master/examples/lstm_text_generation.py.
Congratulations on finishing this notebook!
References:
In [ ]: