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Image Captioning with RNNs

In this exercise you will implement a vanilla recurrent neural networks and use them it to train a model that can generate novel captions for images.





In [1]:



    


# As usual, a bit of setup

import time, os, json
import numpy as np
import matplotlib.pyplot as plt

from cs231n.gradient_check import eval_numerical_gradient, eval_numerical_gradient_array
from cs231n.rnn_layers import *
from cs231n.captioning_solver import CaptioningSolver
from cs231n.classifiers.rnn import CaptioningRNN
from cs231n.coco_utils import load_coco_data, sample_coco_minibatch, decode_captions
from cs231n.image_utils import image_from_url

%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'

# for auto-reloading external modules
# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython
%load_ext autoreload
%autoreload 2

def rel_error(x, y):
  """ returns relative error """
  return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))

Microsoft COCO

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.

To download the data, change to the cs231n/datasets directory and run the script get_coco_captioning.sh.

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 cs231n/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 cs231n/coco_utils.py. Run the following cell to do so:





In [2]:



    


# 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.iteritems():
  if type(v) == np.ndarray:
    print k, type(v), v.shape, v.dtype
  else:
    print k, type(v), len(v)



    


















    






idx_to_word <type 'list'> 1004
train_captions <type 'numpy.ndarray'> (400135L, 17L) int32
val_captions <type 'numpy.ndarray'> (195954L, 17L) int32
train_image_idxs <type 'numpy.ndarray'> (400135L,) int32
val_features <type 'numpy.ndarray'> (40504L, 512L) float32
val_image_idxs <type 'numpy.ndarray'> (195954L,) int32
train_features <type 'numpy.ndarray'> (82783L, 512L) float32
train_urls <type 'numpy.ndarray'> (82783L,) |S63
val_urls <type 'numpy.ndarray'> (40504L,) |S63
word_to_idx <type 'dict'> 1004

Look at the data

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 cs231n/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 viw images.





In [3]:



    


# 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()

Recurrent Neural Networks

As discussed in lecture, we will use recurrent neural network (RNN) language models for image captioning. The file cs231n/rnn_layers.py contains implementations of different layer types that are needed for recurrent neural networks, and the file cs231n/classifiers/rnn.py uses these layers to implement an image captioning model.

We will first implement different types of RNN layers in cs231n/rnn_layers.py.

Vanilla RNN: step forward

Open the file cs231n/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.





In [5]:



    


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)



    


















    






next_h error:  6.29242142647e-09

Vanilla RNN: step backward

In the file cs231n/rnn_layers.py implement the rnn_step_backward function. After doing so run the following to numerically gradient check your implementation. You should see errors less than 1e-8.





In [11]:



    


from cs231n.rnn_layers import rnn_step_forward, rnn_step_backward

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)



    


















    






dx error:  5.01771693416e-10
dprev_h error:  3.6188071417e-09
dWx error:  3.01964851896e-10
dWh error:  1.52742922965e-09
db error:  6.16193019179e-11

Vanilla RNN: forward

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 cs231n/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.





In [17]:



    


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)



    


















    






h error:  7.72846618019e-08

Vanilla RNN: backward

In the file cs231n/rnn_layers.py, implement the backward pass for a vanilla RNN in the function rnn_backward. This should run back-propagation over the entire sequence, calling into the rnn_step_backward function that you defined above.





In [35]:



    


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)



    


















    






dx error:  4.4634923583e-09
dh0 error:  1.84438738727e-09
dWx error:  2.45990890409e-08
dWh error:  1.67874546249e-09
db error:  4.20124203553e-10

Word embedding: forward

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 cs231n/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.





In [ ]:



    


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)

Word embedding: backward

Implement the backward pass for the word embedding function in the function word_embedding_backward. After doing so run the following to numerically gradient check your implementation. You should see errors less than 1e-11.





In [ ]:



    


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)

Temporal Affine layer

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. Because this is very similar to the affine layer that you implemented in assignment 2, we have provided this function for you in the temporal_affine_forward and temporal_affine_backward functions in the file cs231n/rnn_layers.py. Run the following to perform numeric gradient checking on the implementation.





In [ ]:



    


# 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)

Temporal Softmax loss

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 wrinke: 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.

Since this is very similar to the softmax loss function you implemented in assignment 1, we have implemented this loss function for you; look at the temporal_softmax_loss function in the file cs231n/rnn_layers.py.

Run the following cell to sanity check the loss and perform numeric gradient checking on the function.





In [ ]:



    


# Sanity check for temporal softmax loss
from cs231n.rnn_layers import temporal_softmax_loss

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)

RNN for image captioning

Now that you have implemented the necessary layers, you can combine them to build an image captioning model. Open the file cs231n/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.





In [ ]:



    


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.iteritems():
  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 1e-7 or less.





In [ ]:



    


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)

Overfit small data

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 cs231n/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 around 1.





In [ ]:



    


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()

Test-time sampling

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 cs231n/classifiers/rnn.py, implement the sample method for test-time sampling. After doing so, run the following to sample from your overfit 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.





In [ ]:



    


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()

Content source: dvirsamuel/MachineLearningCourses

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