序列标注(sequence labelling)，输入序列每一帧预测一个类别。OCR(Optical Character Recognition 光学字符识别)。

MIT口语系统研究组Rob Kassel收集，斯坦福大学人工智能实验室Ben Taskar预处理OCR数据集(http://ai.stanford.edu/~btaskar/ocr/ )，包含大量单独手写小写字母，每个样本对应16X8像素二值图像。字线组合序列，序列对应单词。6800个，长度不超过14字母的单词。gzip压缩，内容用Tab分隔文本文件。Python csv模块直接读取。文件每行一个归一化字母属性，ID号、标签、像素值、下一字母ID号等。

下一字母ID值排序，按照正确顺序读取每个单词字母。收集字母，直到下一个ID对应字段未被设置为止。读取新序列。读取完目标字母及数据像素，用零图像填充序列对象，能纳入两个较大目标字母所有像素数据NumPy数组。

时间步之间共享softmax层。数据和目标数组包含序列，每个目标字母对应一个图像帧。RNN扩展，每个字母输出添加softmax分类器。分类器对每帧数据而非整个序列评估预测结果。计算序列长度。一个softmax层添加到所有帧：或者为所有帧添加几个不同分类器，或者令所有帧共享同一个分类器。共享分类器，权值在训练中被调整次数更多，训练单词每个字母。一个全连接层权值矩阵维数batch_sizein_sizeout_size。现需要在两个输入维度batch_size、sequence_steps更新权值矩阵。令输入(RNN输出活性值)扁平为形状batch_sizesequence_stepsin_size。权值矩阵变成较大的批数据。结果反扁平化(unflatten)。

代价函数，序列每一帧有预测目标对，在相应维度平均。依据张量长度(序列最大长度)归一化的tf.reduce_mean无法使用。需要按照实际序列长度归一化，手工调用tf.reduce_sum和除法运算均值。

损失函数，tf.argmax针对轴2非轴1,各帧填充，依据序列实际长度计算均值。tf.reduce_mean对批数据所有单词取均值。

TensorFlow自动导数计算，可使用序列分类相同优化运算，只需要代入新代价函数。对所有RNN梯度裁剪，防止训练发散，避免负面影响。

训练模型，get_sataset下载手写体图像，预处理，小写字母独热编码向量。随机打乱数据顺序，分偏划分训练集、测试集。

单词相邻字母存在依赖关系(或互信息)，RNN保存同一单词全部输入信息到隐含活性值。前几个字母分类，网络无大量输入推断额外信息，双向RNN(bidirectional RNN)克服缺陷。
两个RNN观测输入序列，一个按照通常顺序从左端读取单词，另一个按照相反顺序从右端读取单词。每个时间步得到两个输出活性值。送入共享softmax层前，拼接。分类器从每个字母获取完整单词信息。tf.modle.rnn.bidirectional_rnn已实现。

实现双向RNN。划分预测属性到两个函数，只关注较少内容。_shared_softmax函数，传入函数张量data推断输入尺寸。复用其他架构函数，相同扁平化技巧在所有时间步共享同一个softmax层。rnn.dynamic_rnn创建两个RNN。
序列反转，比实现新反向传递RNN运算容易。tf.reverse_sequence函数反转帧数据中sequence_lengths帧。数据流图节点有名称。scope参数是rnn_dynamic_cell变量scope名称，默认值RNN。两个参数不同RNN，需要不同域。
反转序列送入后向RNN，网络输出反转，和前向输出对齐。沿RNN神经元输出维度拼接两个张量，返回。双向RNN模型性能更优。

import gzip
import csv
import numpy as np

from helpers import download

class OcrDataset:

    URL = 'http://ai.stanford.edu/~btaskar/ocr/letter.data.gz'

    def __init__(self, cache_dir):
        path = download(type(self).URL, cache_dir)
        lines = self._read(path)
        data, target = self._parse(lines)
        self.data, self.target = self._pad(data, target)

    @staticmethod
    def _read(filepath):
        with gzip.open(filepath, 'rt') as file_:
            reader = csv.reader(file_, delimiter='\t')
            lines = list(reader)
            return lines

    @staticmethod
    def _parse(lines):
        lines = sorted(lines, key=lambda x: int(x[0]))
        data, target = [], []
        next_ = None
        for line in lines:
            if not next_:
                data.append([])
                target.append([])
            else:
                assert next_ == int(line[0])
            next_ = int(line[2]) if int(line[2]) > -1 else None
            pixels = np.array([int(x) for x in line[6:134]])
            pixels = pixels.reshape((16, 8))
            data[-1].append(pixels)
            target[-1].append(line[1])
        return data, target

    @staticmethod
    def _pad(data, target):
        max_length = max(len(x) for x in target)
        padding = np.zeros((16, 8))
        data = [x + ([padding] * (max_length - len(x))) for x in data]
        target = [x + ([''] * (max_length - len(x))) for x in target]
        return np.array(data), np.array(target)

import tensorflow as tf

from helpers import lazy_property

class SequenceLabellingModel:

    def __init__(self, data, target, params):
        self.data = data
        self.target = target
        self.params = params
        self.prediction
        self.cost
        self.error
        self.optimize

    @lazy_property
    def length(self):
        used = tf.sign(tf.reduce_max(tf.abs(self.data), reduction_indices=2))
        length = tf.reduce_sum(used, reduction_indices=1)
        length = tf.cast(length, tf.int32)
        return length

    @lazy_property
    def prediction(self):
        output, _ = tf.nn.dynamic_rnn(
            tf.nn.rnn_cell.GRUCell(self.params.rnn_hidden),
            self.data,
            dtype=tf.float32,
            sequence_length=self.length,
        )
        # Softmax layer.
        max_length = int(self.target.get_shape()[1])
        num_classes = int(self.target.get_shape()[2])
        weight = tf.Variable(tf.truncated_normal(
            [self.params.rnn_hidden, num_classes], stddev=0.01))
        bias = tf.Variable(tf.constant(0.1, shape=[num_classes]))
        # Flatten to apply same weights to all time steps.
        output = tf.reshape(output, [-1, self.params.rnn_hidden])
        prediction = tf.nn.softmax(tf.matmul(output, weight) + bias)
        prediction = tf.reshape(prediction, [-1, max_length, num_classes])
        return prediction

    @lazy_property
    def cost(self):
        # Compute cross entropy for each frame.
        cross_entropy = self.target * tf.log(self.prediction)
        cross_entropy = -tf.reduce_sum(cross_entropy, reduction_indices=2)
        mask = tf.sign(tf.reduce_max(tf.abs(self.target), reduction_indices=2))
        cross_entropy *= mask
        # Average over actual sequence lengths.
        cross_entropy = tf.reduce_sum(cross_entropy, reduction_indices=1)
        cross_entropy /= tf.cast(self.length, tf.float32)
        return tf.reduce_mean(cross_entropy)

    @lazy_property
    def error(self):
        mistakes = tf.not_equal(
            tf.argmax(self.target, 2), tf.argmax(self.prediction, 2))
        mistakes = tf.cast(mistakes, tf.float32)
        mask = tf.sign(tf.reduce_max(tf.abs(self.target), reduction_indices=2))
        mistakes *= mask
        # Average over actual sequence lengths.
        mistakes = tf.reduce_sum(mistakes, reduction_indices=1)
        mistakes /= tf.cast(self.length, tf.float32)
        return tf.reduce_mean(mistakes)

    @lazy_property
    def optimize(self):
        gradient = self.params.optimizer.compute_gradients(self.cost)
        try:
            limit = self.params.gradient_clipping
            gradient = [
                (tf.clip_by_value(g, -limit, limit), v)
                if g is not None else (None, v)
                for g, v in gradient]
        except AttributeError:
            print('No gradient clipping parameter specified.')
        optimize = self.params.optimizer.apply_gradients(gradient)
        return optimize

import random

import tensorflow as tf
import numpy as np

from helpers import AttrDict

from OcrDataset import OcrDataset
from SequenceLabellingModel import SequenceLabellingModel
from batched import batched

params = AttrDict(
    rnn_cell=tf.nn.rnn_cell.GRUCell,
    rnn_hidden=300,
    optimizer=tf.train.RMSPropOptimizer(0.002),
    gradient_clipping=5,
    batch_size=10,
    epochs=5,
    epoch_size=50
)

def get_dataset():
    dataset = OcrDataset('./ocr')
    # Flatten images into vectors.
    dataset.data = dataset.data.reshape(dataset.data.shape[:2] + (-1,))
    # One-hot encode targets.
    target = np.zeros(dataset.target.shape + (26,))
    for index, letter in np.ndenumerate(dataset.target):
        if letter:
            target[index][ord(letter) - ord('a')] = 1
    dataset.target = target
    # Shuffle order of examples.
    order = np.random.permutation(len(dataset.data))
    dataset.data = dataset.data[order]
    dataset.target = dataset.target[order]
    return dataset

# Split into training and test data.
dataset = get_dataset()
split = int(0.66 * len(dataset.data))
train_data, test_data = dataset.data[:split], dataset.data[split:]
train_target, test_target = dataset.target[:split], dataset.target[split:]

# Compute graph.
_, length, image_size = train_data.shape
num_classes = train_target.shape[2]
data = tf.placeholder(tf.float32, [None, length, image_size])
target = tf.placeholder(tf.float32, [None, length, num_classes])
model = SequenceLabellingModel(data, target, params)
batches = batched(train_data, train_target, params.batch_size)

sess = tf.Session()
sess.run(tf.initialize_all_variables())
for index, batch in enumerate(batches):
    batch_data = batch[0]
    batch_target = batch[1]
    epoch = batch[2]
    if epoch >= params.epochs:
        break
    feed = {data: batch_data, target: batch_target}
    error, _ = sess.run([model.error, model.optimize], feed)
    print('{}: {:3.6f}%'.format(index + 1, 100 * error))

test_feed = {data: test_data, target: test_target}
test_error, _ = sess.run([model.error, model.optimize], test_feed)
print('Test error: {:3.6f}%'.format(100 * error))

import tensorflow as tf

from helpers import lazy_property

class BidirectionalSequenceLabellingModel:

    def __init__(self, data, target, params):
        self.data = data
        self.target = target
        self.params = params
        self.prediction
        self.cost
        self.error
        self.optimize

    @lazy_property
    def length(self):
        used = tf.sign(tf.reduce_max(tf.abs(self.data), reduction_indices=2))
        length = tf.reduce_sum(used, reduction_indices=1)
        length = tf.cast(length, tf.int32)
        return length

    @lazy_property
    def prediction(self):
        output = self._bidirectional_rnn(self.data, self.length)
        num_classes = int(self.target.get_shape()[2])
        prediction = self._shared_softmax(output, num_classes)
        return prediction

    def _bidirectional_rnn(self, data, length):
        length_64 = tf.cast(length, tf.int64)
        forward, _ = tf.nn.dynamic_rnn(
            cell=self.params.rnn_cell(self.params.rnn_hidden),
            inputs=data,
            dtype=tf.float32,
            sequence_length=length,
            scope='rnn-forward')
        backward, _ = tf.nn.dynamic_rnn(
        cell=self.params.rnn_cell(self.params.rnn_hidden),
        inputs=tf.reverse_sequence(data, length_64, seq_dim=1),
        dtype=tf.float32,
        sequence_length=self.length,
        scope='rnn-backward')
        backward = tf.reverse_sequence(backward, length_64, seq_dim=1)
        output = tf.concat(2, [forward, backward])
        return output

    def _shared_softmax(self, data, out_size):
        max_length = int(data.get_shape()[1])
        in_size = int(data.get_shape()[2])
        weight = tf.Variable(tf.truncated_normal(
            [in_size, out_size], stddev=0.01))
        bias = tf.Variable(tf.constant(0.1, shape=[out_size]))
        # Flatten to apply same weights to all time steps.
        flat = tf.reshape(data, [-1, in_size])
        output = tf.nn.softmax(tf.matmul(flat, weight) + bias)
        output = tf.reshape(output, [-1, max_length, out_size])
        return output

    @lazy_property
    def cost(self):
        # Compute cross entropy for each frame.
        cross_entropy = self.target * tf.log(self.prediction)
        cross_entropy = -tf.reduce_sum(cross_entropy, reduction_indices=2)
        mask = tf.sign(tf.reduce_max(tf.abs(self.target), reduction_indices=2))
        cross_entropy *= mask
        # Average over actual sequence lengths.
        cross_entropy = tf.reduce_sum(cross_entropy, reduction_indices=1)
        cross_entropy /= tf.cast(self.length, tf.float32)
        return tf.reduce_mean(cross_entropy)

    @lazy_property
    def error(self):
        mistakes = tf.not_equal(
            tf.argmax(self.target, 2), tf.argmax(self.prediction, 2))
        mistakes = tf.cast(mistakes, tf.float32)
        mask = tf.sign(tf.reduce_max(tf.abs(self.target), reduction_indices=2))
        mistakes *= mask
        # Average over actual sequence lengths.
        mistakes = tf.reduce_sum(mistakes, reduction_indices=1)
        mistakes /= tf.cast(self.length, tf.float32)
        return tf.reduce_mean(mistakes)

    @lazy_property
    def optimize(self):
        gradient = self.params.optimizer.compute_gradients(self.cost)
        try:
            limit = self.params.gradient_clipping
            gradient = [
                (tf.clip_by_value(g, -limit, limit), v)
                if g is not None else (None, v)
                for g, v in gradient]
        except AttributeError:
            print('No gradient clipping parameter specified.')
        optimize = self.params.optimizer.apply_gradients(gradient)
        return optimize

参考资料：
《面向机器智能的TensorFlow实践》

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