In [1]:
import os
os.chdir(os.getcwd() + '/..')
# Run some setup code for this notebook
import time, json
import numpy as np
import matplotlib.pyplot as plt
from utils.metrics_utils import rel_error
%matplotlib inline
plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
# Some more magic so that the notebook will reload external python modules;
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2
The COCO dataset we will be using is stored in HDF5 format. To load HDF5 files, we will need to install the h5py Python package. From the command line, run:
pip install h5py
If you receive a permissions error, you may need to run the command as root:
sudo pip install h5py
You can also run commands directly from the Jupyter notebook by prefixing the command with the "!" character:
In [2]:
!pip install h5py
For this exercise we will use the 2014 release of the Microsoft COCO dataset which has become the standard testbed for image captioning. The dataset consists of 80,000 training images and 40,000 validation images, each annotated with 5 captions written by workers on Amazon Mechanical Turk.
You should have already downloaded the data by changing to the datasets directory and running the script get_datasets_for_rnn.sh. If you haven't yet done so, run that script now. Warning: the COCO data download is ~1GB.
We have preprocessed the data and extracted features for you already. For all images we have extracted features from the fc7 layer of the VGG-16 network pretrained on ImageNet; these features are stored in the files train2014_vgg16_fc7.h5 and val2014_vgg16_fc7.h5 respectively. To cut down on processing time and memory requirements, we have reduced the dimensionality of the features from 4096 to 512; these features can be found in the files train2014_vgg16_fc7_pca.h5 and val2014_vgg16_fc7_pca.h5.
The raw images take up a lot of space (nearly 20GB) so we have not included them in the download. However all images are taken from Flickr, and URLs of the training and validation images are stored in the files train2014_urls.txt and val2014_urls.txt respectively. This allows you to download images on the fly for visualization. Since images are downloaded on-the-fly, you must be connected to the internet to view images.
Dealing with strings is inefficient, so we will work with an encoded version of the captions. Each word is assigned an integer ID, allowing us to represent a caption by a sequence of integers. The mapping between integer IDs and words is in the file coco2014_vocab.json, and you can use the function decode_captions from the file utils/coco_utils.py to convert numpy arrays of integer IDs back into strings.
There are a couple special tokens that we add to the vocabulary. We prepend a special <START> token and append an <END> token to the beginning and end of each caption respectively. Rare words are replaced with a special <UNK> token (for "unknown"). In addition, since we want to train with minibatches containing captions of different lengths, we pad short captions with a special <NULL> token after the <END> token and don't compute loss or gradient for <NULL> tokens. Since they are a bit of a pain, we have taken care of all implementation details around special tokens for you.
You can load all of the MS-COCO data (captions, features, URLs, and vocabulary) using the load_coco_data function from the file utils/coco_utils.py. Run the following cell to do so:
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from utils.coco_utils import load_coco_data
# Load COCO data from disk; this returns a dictionary
# We'll work with dimensionality-reduced features for this notebook, but feel
# free to experiment with the original features by changing the flag below.
data = load_coco_data(pca_features=True)
# Print out all the keys and values from the data dictionary
for k, v in data.items():
if type(v) == np.ndarray:
print(k, type(v), v.shape, v.dtype)
else:
print(k, type(v), len(v))
It is always a good idea to look at examples from the dataset before working with it.
You can use the sample_coco_minibatch function from the file utils/coco_utils.py to sample minibatches of data from the data structure returned from load_coco_data. Run the following to sample a small minibatch of training data and show the images and their captions. Running it multiple times and looking at the results helps you to get a sense of the dataset.
Note that we decode the captions using the decode_captions function and that we download the images on-the-fly using their Flickr URL, so you must be connected to the internet to view images.
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from utils.coco_utils import sample_coco_minibatch, decode_captions
from utils.image_utils import image_from_url
# Sample a minibatch and show the images and captions
batch_size = 3
captions, features, urls = sample_coco_minibatch(data, batch_size=batch_size)
for i, (caption, url) in enumerate(zip(captions, urls)):
plt.imshow(image_from_url(url))
plt.axis('off')
caption_str = decode_captions(caption, data['idx_to_word'])
plt.title(caption_str)
plt.show()
As discussed in lecture, we will use recurrent neural network (RNN) language models for image captioning. The file layers/rnn_layers.py contains implementations of different layer types that are needed for recurrent neural networks, and the file classifiers/rnn.py uses these layers to implement an image captioning model.
We will first implement different types of RNN layers in layers/rnn_layers.py.
Open the file layers/rnn_layers.py. This file implements the forward and backward passes for different types of layers that are commonly used in recurrent neural networks.
First implement the function rnn_step_forward which implements the forward pass for a single timestep of a vanilla recurrent neural network. After doing so run the following to check your implementation. You should see errors less than 1e-8.
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from layers.rnn_layers import rnn_step_forward
N, D, H = 3, 10, 4
x = np.linspace(-0.4, 0.7, num=N*D).reshape(N, D)
prev_h = np.linspace(-0.2, 0.5, num=N*H).reshape(N, H)
Wx = np.linspace(-0.1, 0.9, num=D*H).reshape(D, H)
Wh = np.linspace(-0.3, 0.7, num=H*H).reshape(H, H)
b = np.linspace(-0.2, 0.4, num=H)
next_h, _ = rnn_step_forward(x, prev_h, Wx, Wh, b)
expected_next_h = np.asarray([
[-0.58172089, -0.50182032, -0.41232771, -0.31410098],
[ 0.66854692, 0.79562378, 0.87755553, 0.92795967],
[ 0.97934501, 0.99144213, 0.99646691, 0.99854353]])
print('next_h error: ', rel_error(expected_next_h, next_h))
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from layers.rnn_layers import rnn_step_backward
from utils.gradient_check import eval_numerical_gradient_array
np.random.seed(231)
N, D, H = 4, 5, 6
x = np.random.randn(N, D)
h = np.random.randn(N, H)
Wx = np.random.randn(D, H)
Wh = np.random.randn(H, H)
b = np.random.randn(H)
out, cache = rnn_step_forward(x, h, Wx, Wh, b)
dnext_h = np.random.randn(*out.shape)
fx = lambda x: rnn_step_forward(x, h, Wx, Wh, b)[0]
fh = lambda prev_h: rnn_step_forward(x, h, Wx, Wh, b)[0]
fWx = lambda Wx: rnn_step_forward(x, h, Wx, Wh, b)[0]
fWh = lambda Wh: rnn_step_forward(x, h, Wx, Wh, b)[0]
fb = lambda b: rnn_step_forward(x, h, Wx, Wh, b)[0]
dx_num = eval_numerical_gradient_array(fx, x, dnext_h)
dprev_h_num = eval_numerical_gradient_array(fh, h, dnext_h)
dWx_num = eval_numerical_gradient_array(fWx, Wx, dnext_h)
dWh_num = eval_numerical_gradient_array(fWh, Wh, dnext_h)
db_num = eval_numerical_gradient_array(fb, b, dnext_h)
dx, dprev_h, dWx, dWh, db = rnn_step_backward(dnext_h, cache)
print('dx error: ', rel_error(dx_num, dx))
print('dprev_h error: ', rel_error(dprev_h_num, dprev_h))
print('dWx error: ', rel_error(dWx_num, dWx))
print('dWh error: ', rel_error(dWh_num, dWh))
print('db error: ', rel_error(db_num, db))
Now that you have implemented the forward and backward passes for a single timestep of a vanilla RNN, you will combine these pieces to implement a RNN that process an entire sequence of data.
In the file layers/rnn_layers.py, implement the function rnn_forward. This should be implemented using the rnn_step_forward function that you defined above. After doing so run the following to check your implementation. You should see errors less than 1e-7.
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from layers.rnn_layers import rnn_forward
N, T, D, H = 2, 3, 4, 5
x = np.linspace(-0.1, 0.3, num=N*T*D).reshape(N, T, D)
h0 = np.linspace(-0.3, 0.1, num=N*H).reshape(N, H)
Wx = np.linspace(-0.2, 0.4, num=D*H).reshape(D, H)
Wh = np.linspace(-0.4, 0.1, num=H*H).reshape(H, H)
b = np.linspace(-0.7, 0.1, num=H)
h, _ = rnn_forward(x, h0, Wx, Wh, b)
expected_h = np.asarray([
[
[-0.42070749, -0.27279261, -0.11074945, 0.05740409, 0.22236251],
[-0.39525808, -0.22554661, -0.0409454, 0.14649412, 0.32397316],
[-0.42305111, -0.24223728, -0.04287027, 0.15997045, 0.35014525],
],
[
[-0.55857474, -0.39065825, -0.19198182, 0.02378408, 0.23735671],
[-0.27150199, -0.07088804, 0.13562939, 0.33099728, 0.50158768],
[-0.51014825, -0.30524429, -0.06755202, 0.17806392, 0.40333043]]])
print('h error: ', rel_error(expected_h, h))
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from layers.rnn_layers import rnn_backward
np.random.seed(231)
N, D, T, H = 2, 3, 10, 5
x = np.random.randn(N, T, D)
h0 = np.random.randn(N, H)
Wx = np.random.randn(D, H)
Wh = np.random.randn(H, H)
b = np.random.randn(H)
out, cache = rnn_forward(x, h0, Wx, Wh, b)
dout = np.random.randn(*out.shape)
dx, dh0, dWx, dWh, db = rnn_backward(dout, cache)
fx = lambda x: rnn_forward(x, h0, Wx, Wh, b)[0]
fh0 = lambda h0: rnn_forward(x, h0, Wx, Wh, b)[0]
fWx = lambda Wx: rnn_forward(x, h0, Wx, Wh, b)[0]
fWh = lambda Wh: rnn_forward(x, h0, Wx, Wh, b)[0]
fb = lambda b: rnn_forward(x, h0, Wx, Wh, b)[0]
dx_num = eval_numerical_gradient_array(fx, x, dout)
dh0_num = eval_numerical_gradient_array(fh0, h0, dout)
dWx_num = eval_numerical_gradient_array(fWx, Wx, dout)
dWh_num = eval_numerical_gradient_array(fWh, Wh, dout)
db_num = eval_numerical_gradient_array(fb, b, dout)
print('dx error: ', rel_error(dx_num, dx))
print('dh0 error: ', rel_error(dh0_num, dh0))
print('dWx error: ', rel_error(dWx_num, dWx))
print('dWh error: ', rel_error(dWh_num, dWh))
print('db error: ', rel_error(db_num, db))
In deep learning systems, we commonly represent words using vectors. Each word of the vocabulary will be associated with a vector, and these vectors will be learned jointly with the rest of the system.
In the file layers/rnn_layers.py, implement the function word_embedding_forward to convert words (represented by integers) into vectors. Run the following to check your implementation. You should see error around 1e-8.
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from layers.rnn_layers import word_embedding_forward
N, T, V, D = 2, 4, 5, 3
x = np.asarray([[0, 3, 1, 2], [2, 1, 0, 3]])
W = np.linspace(0, 1, num=V*D).reshape(V, D)
out, _ = word_embedding_forward(x, W)
expected_out = np.asarray([
[[ 0., 0.07142857, 0.14285714],
[ 0.64285714, 0.71428571, 0.78571429],
[ 0.21428571, 0.28571429, 0.35714286],
[ 0.42857143, 0.5, 0.57142857]],
[[ 0.42857143, 0.5, 0.57142857],
[ 0.21428571, 0.28571429, 0.35714286],
[ 0., 0.07142857, 0.14285714],
[ 0.64285714, 0.71428571, 0.78571429]]])
print('out error: ', rel_error(expected_out, out))
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from layers.rnn_layers import word_embedding_backward
np.random.seed(231)
N, T, V, D = 50, 3, 5, 6
x = np.random.randint(V, size=(N, T))
W = np.random.randn(V, D)
out, cache = word_embedding_forward(x, W)
dout = np.random.randn(*out.shape)
dW = word_embedding_backward(dout, cache)
f = lambda W: word_embedding_forward(x, W)[0]
dW_num = eval_numerical_gradient_array(f, W, dout)
print('dW error: ', rel_error(dW, dW_num))
At every timestep we use an affine function to transform the RNN hidden vector at that timestep into scores for each word in the vocabulary. See the temporal_affine_forward and temporal_affine_backward functions in the file layers/rnn_layers.py. Run the following to perform numeric gradient checking on the implementation. You should see errors less than 1e-9.
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from layers.rnn_layers import temporal_affine_forward, temporal_affine_backward
np.random.seed(231)
# Gradient check for temporal affine layer
N, T, D, M = 2, 3, 4, 5
x = np.random.randn(N, T, D)
w = np.random.randn(D, M)
b = np.random.randn(M)
out, cache = temporal_affine_forward(x, w, b)
dout = np.random.randn(*out.shape)
fx = lambda x: temporal_affine_forward(x, w, b)[0]
fw = lambda w: temporal_affine_forward(x, w, b)[0]
fb = lambda b: temporal_affine_forward(x, w, b)[0]
dx_num = eval_numerical_gradient_array(fx, x, dout)
dw_num = eval_numerical_gradient_array(fw, w, dout)
db_num = eval_numerical_gradient_array(fb, b, dout)
dx, dw, db = temporal_affine_backward(dout, cache)
print('dx error: ', rel_error(dx_num, dx))
print('dw error: ', rel_error(dw_num, dw))
print('db error: ', rel_error(db_num, db))
In an RNN language model, at every timestep we produce a score for each word in the vocabulary. We know the ground-truth word at each timestep, so we use a softmax loss function to compute loss and gradient at each timestep. We sum the losses over time and average them over the minibatch.
However there is one wrinkle: since we operate over minibatches and different captions may have different lengths, we append <NULL> tokens to the end of each caption so they all have the same length. We don't want these <NULL> tokens to count toward the loss or gradient, so in addition to scores and ground-truth labels our loss function also accepts a mask array that tells it which elements of the scores count towards the loss.
Look at the temporal_softmax_loss function in the file layers/rnn_layers.py.
Run the following cell to sanity check the loss and perform numeric gradient checking on the function. You should see an error for dx less than 1e-7.
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# Sanity check for temporal softmax loss
from layers.rnn_layers import temporal_softmax_loss
from utils.gradient_check import eval_numerical_gradient
N, T, V = 100, 1, 10
def check_loss(N, T, V, p):
x = 0.001 * np.random.randn(N, T, V)
y = np.random.randint(V, size=(N, T))
mask = np.random.rand(N, T) <= p
print(temporal_softmax_loss(x, y, mask)[0])
check_loss(100, 1, 10, 1.0) # Should be about 2.3
check_loss(100, 10, 10, 1.0) # Should be about 23
check_loss(5000, 10, 10, 0.1) # Should be about 2.3
# Gradient check for temporal softmax loss
N, T, V = 7, 8, 9
x = np.random.randn(N, T, V)
y = np.random.randint(V, size=(N, T))
mask = (np.random.rand(N, T) > 0.5)
loss, dx = temporal_softmax_loss(x, y, mask, verbose=False)
dx_num = eval_numerical_gradient(lambda x: temporal_softmax_loss(x, y, mask)[0], x, verbose=False)
print('dx error: ', rel_error(dx, dx_num))
Now that you have implemented the necessary layers, you can combine them to build an image captioning model. Open the file classifiers/rnn.py and look at the CaptioningRNN class.
Implement the forward and backward pass of the model in the loss function. For now you only need to implement the case where cell_type='rnn' for vanialla RNNs; you will implement the LSTM case later. After doing so, run the following to check your forward pass using a small test case; you should see error less than 1e-10.
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from classifiers.rnn import CaptioningRNN
N, D, W, H = 10, 20, 30, 40
word_to_idx = {'<NULL>': 0, 'cat': 2, 'dog': 3}
V = len(word_to_idx)
T = 13
model = CaptioningRNN(word_to_idx,
input_dim=D,
wordvec_dim=W,
hidden_dim=H,
cell_type='rnn',
dtype=np.float64)
# Set all model parameters to fixed values
for k, v in model.params.items():
model.params[k] = np.linspace(-1.4, 1.3, num=v.size).reshape(*v.shape)
features = np.linspace(-1.5, 0.3, num=(N * D)).reshape(N, D)
captions = (np.arange(N * T) % V).reshape(N, T)
loss, grads = model.loss(features, captions)
expected_loss = 9.83235591003
print('loss: ', loss)
print('expected loss: ', expected_loss)
print('difference: ', abs(loss - expected_loss))
Run the following cell to perform numeric gradient checking on the CaptioningRNN class; you should errors around 5e-6 or less.
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np.random.seed(231)
batch_size = 2
timesteps = 3
input_dim = 4
wordvec_dim = 5
hidden_dim = 6
word_to_idx = {'<NULL>': 0, 'cat': 2, 'dog': 3}
vocab_size = len(word_to_idx)
captions = np.random.randint(vocab_size, size=(batch_size, timesteps))
features = np.random.randn(batch_size, input_dim)
model = CaptioningRNN(word_to_idx,
input_dim=input_dim,
wordvec_dim=wordvec_dim,
hidden_dim=hidden_dim,
cell_type='rnn',
dtype=np.float64,
)
loss, grads = model.loss(features, captions)
for param_name in sorted(grads):
f = lambda _: model.loss(features, captions)[0]
param_grad_num = eval_numerical_gradient(f, model.params[param_name], verbose=False, h=1e-6)
e = rel_error(param_grad_num, grads[param_name])
print('%s relative error: %e' % (param_name, e))
Similar to the Solver class that we used to train image classification models on the previous assignment, on this assignment we use a CaptioningSolver class to train image captioning models. Open the file base/captioning_solver.py and read through the CaptioningSolver class; it should look very familiar.
Once you have familiarized yourself with the API, run the following to make sure your model overfit a small sample of 100 training examples. You should see losses of less than 0.1.
In [15]:
from base.captioning_solver import CaptioningSolver
np.random.seed(231)
small_data = load_coco_data(max_train=50)
small_rnn_model = CaptioningRNN(
cell_type='rnn',
word_to_idx=data['word_to_idx'],
input_dim=data['train_features'].shape[1],
hidden_dim=512,
wordvec_dim=256,
)
small_rnn_solver = CaptioningSolver(small_rnn_model, small_data,
update_rule='adam',
num_epochs=50,
batch_size=25,
optim_config={
'learning_rate': 5e-3,
},
lr_decay=0.95,
verbose=True, print_every=10,
)
small_rnn_solver.train()
# Plot the training losses
plt.plot(small_rnn_solver.loss_history)
plt.xlabel('Iteration')
plt.ylabel('Loss')
plt.title('Training loss history')
plt.show()
Unlike classification models, image captioning models behave very differently at training time and at test time. At training time, we have access to the ground-truth caption, so we feed ground-truth words as input to the RNN at each timestep. At test time, we sample from the distribution over the vocabulary at each timestep, and feed the sample as input to the RNN at the next timestep.
In the file classifiers/rnn.py, implement the sample method for test-time sampling. After doing so, run the following to sample from your overfitted model on both training and validation data. The samples on training data should be very good; the samples on validation data probably won't make sense.
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for split in ['train', 'val']:
minibatch = sample_coco_minibatch(small_data, split=split, batch_size=2)
gt_captions, features, urls = minibatch
gt_captions = decode_captions(gt_captions, data['idx_to_word'])
sample_captions = small_rnn_model.sample(features)
sample_captions = decode_captions(sample_captions, data['idx_to_word'])
for gt_caption, sample_caption, url in zip(gt_captions, sample_captions, urls):
plt.imshow(image_from_url(url))
plt.title('%s\n%s\nGT:%s' % (split, sample_caption, gt_caption))
plt.axis('off')
plt.show()
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