# An implementation of sequence to sequence learning for performing addition

Input: "535+61"
Output: "596"
Padding is handled by using a repeated sentinel character (space)

Input may optionally be reversed, shown to increase performance in many tasks in:
"Learning to Execute"
http://arxiv.org/abs/1410.4615
and
"Sequence to Sequence Learning with Neural Networks"
http://papers.nips.cc/paper/5346-sequence-to-sequence-learning-with-neural-networks.pdf
Theoretically it introduces shorter term dependencies between source and target.

Two digits reversed:
+ One layer LSTM (128 HN), 5k training examples = 99% train/test accuracy in 55 epochs

Three digits reversed:
+ One layer LSTM (128 HN), 50k training examples = 99% train/test accuracy in 100 epochs

Four digits reversed:
+ One layer LSTM (128 HN), 400k training examples = 99% train/test accuracy in 20 epochs

Five digits reversed:
+ One layer LSTM (128 HN), 550k training examples = 99% train/test accuracy in 30 epochs


```python
from __future__ import print_function
from keras.models import Sequential
from keras import layers
import numpy as np
from six.moves import range


class CharacterTable(object):
    """Given a set of characters:
    + Encode them to a one-hot integer representation
    + Decode the one-hot or integer representation to their character output
    + Decode a vector of probabilities to their character output
    """
    def __init__(self, chars):
        """Initialize character table.

        # Arguments
            chars: Characters that can appear in the input.
        """
        self.chars = sorted(set(chars))
        self.char_indices = dict((c, i) for i, c in enumerate(self.chars))
        self.indices_char = dict((i, c) for i, c in enumerate(self.chars))

    def encode(self, C, num_rows):
        """One-hot encode given string C.

        # Arguments
            C: string, to be encoded.
            num_rows: Number of rows in the returned one-hot encoding. This is
                used to keep the # of rows for each data the same.
        """
        x = np.zeros((num_rows, len(self.chars)))
        for i, c in enumerate(C):
            x[i, self.char_indices[c]] = 1
        return x

    def decode(self, x, calc_argmax=True):
        """Decode the given vector or 2D array to their character output.

        # Arguments
            x: A vector or a 2D array of probabilities or one-hot representations;
                or a vector of character indices (used with `calc_argmax=False`).
            calc_argmax: Whether to find the character index with maximum
                probability, defaults to `True`.
        """
        if calc_argmax:
            x = x.argmax(axis=-1)
        return ''.join(self.indices_char[x] for x in x)


class colors:
    ok = '\033[92m'
    fail = '\033[91m'
    close = '\033[0m'

# Parameters for the model and dataset.
TRAINING_SIZE = 50000
DIGITS = 3
REVERSE = True

# Maximum length of input is 'int + int' (e.g., '345+678'). Maximum length of
# int is DIGITS.
MAXLEN = DIGITS + 1 + DIGITS

# All the numbers, plus sign and space for padding.
chars = '0123456789+ '
ctable = CharacterTable(chars)

questions = []
expected = []
seen = set()
print('Generating data...')
while len(questions) < TRAINING_SIZE:
    f = lambda: int(''.join(np.random.choice(list('0123456789'))
                    for i in range(np.random.randint(1, DIGITS + 1))))
    a, b = f(), f()
    # Skip any addition questions we've already seen
    # Also skip any such that x+Y == Y+x (hence the sorting).
    key = tuple(sorted((a, b)))
    if key in seen:
        continue
    seen.add(key)
    # Pad the data with spaces such that it is always MAXLEN.
    q = '{}+{}'.format(a, b)
    query = q + ' ' * (MAXLEN - len(q))
    ans = str(a + b)
    # Answers can be of maximum size DIGITS + 1.
    ans += ' ' * (DIGITS + 1 - len(ans))
    if REVERSE:
        # Reverse the query, e.g., '12+345  ' becomes '  543+21'. (Note the
        # space used for padding.)
        query = query[::-1]
    questions.append(query)
    expected.append(ans)
print('Total addition questions:', len(questions))

print('Vectorization...')
x = np.zeros((len(questions), MAXLEN, len(chars)), dtype=np.bool)
y = np.zeros((len(questions), DIGITS + 1, len(chars)), dtype=np.bool)
for i, sentence in enumerate(questions):
    x[i] = ctable.encode(sentence, MAXLEN)
for i, sentence in enumerate(expected):
    y[i] = ctable.encode(sentence, DIGITS + 1)

# Shuffle (x, y) in unison as the later parts of x will almost all be larger
# digits.
indices = np.arange(len(y))
np.random.shuffle(indices)
x = x[indices]
y = y[indices]

# Explicitly set apart 10% for validation data that we never train over.
split_at = len(x) - len(x) // 10
(x_train, x_val) = x[:split_at], x[split_at:]
(y_train, y_val) = y[:split_at], y[split_at:]

print('Training Data:')
print(x_train.shape)
print(y_train.shape)

print('Validation Data:')
print(x_val.shape)
print(y_val.shape)

# Try replacing GRU, or SimpleRNN.
RNN = layers.LSTM
HIDDEN_SIZE = 128
BATCH_SIZE = 128
LAYERS = 1

print('Build model...')
model = Sequential()
# "Encode" the input sequence using an RNN, producing an output of HIDDEN_SIZE.
# Note: In a situation where your input sequences have a variable length,
# use input_shape=(None, num_feature).
model.add(RNN(HIDDEN_SIZE, input_shape=(MAXLEN, len(chars))))
# As the decoder RNN's input, repeatedly provide with the last output of
# RNN for each time step. Repeat 'DIGITS + 1' times as that's the maximum
# length of output, e.g., when DIGITS=3, max output is 999+999=1998.
model.add(layers.RepeatVector(DIGITS + 1))
# The decoder RNN could be multiple layers stacked or a single layer.
for _ in range(LAYERS):
    # By setting return_sequences to True, return not only the last output but
    # all the outputs so far in the form of (num_samples, timesteps,
    # output_dim). This is necessary as TimeDistributed in the below expects
    # the first dimension to be the timesteps.
    model.add(RNN(HIDDEN_SIZE, return_sequences=True))

# Apply a dense layer to the every temporal slice of an input. For each of step
# of the output sequence, decide which character should be chosen.
model.add(layers.TimeDistributed(layers.Dense(len(chars), activation='softmax')))
model.compile(loss='categorical_crossentropy',
              optimizer='adam',
              metrics=['accuracy'])
model.summary()

# Train the model each generation and show predictions against the validation
# dataset.
for iteration in range(1, 200):
    print()
    print('-' * 50)
    print('Iteration', iteration)
    model.fit(x_train, y_train,
              batch_size=BATCH_SIZE,
              epochs=1,
              validation_data=(x_val, y_val))
    # Select 10 samples from the validation set at random so we can visualize
    # errors.
    for i in range(10):
        ind = np.random.randint(0, len(x_val))
        rowx, rowy = x_val[np.array([ind])], y_val[np.array([ind])]
        preds = model.predict_classes(rowx, verbose=0)
        q = ctable.decode(rowx[0])
        correct = ctable.decode(rowy[0])
        guess = ctable.decode(preds[0], calc_argmax=False)
        print('Q', q[::-1] if REVERSE else q, end=' ')
        print('T', correct, end=' ')
        if correct == guess:
            print(colors.ok + '☑' + colors.close, end=' ')
        else:
            print(colors.fail + '☒' + colors.close, end=' ')
        print(guess)
```