theano GRU rnn 亚当优化器

Question

技术资料：

操作系统：Mac OS X 10.9.5

IDE：Eclipse Mars.1 Release (4.5.1)，带有 PyDev 和 Anaconda 解释器（语法版本 3.4）

GPU：NVIDIA GeForce GT 650M

库：numpy、aeosa、Sphinx-1.3.1、Theano 0.7、nltk-3.1

我的背景：我对 theano 和 numpy 非常陌生，还没有参加过机器学习或离散数学方面的正式课程。

我目前使用的自然语言处理的循环神经网络取自这里：

https://github.com/dennybritz/rnn-tutorial-gru-lstm/blob/master/gru_theano.py

对该文件所做的唯一更改是将对theano.config.floatX 的引用替换为字符串'float32'。

我还使用存储库中包含的 utils.py 和 train.py 模块，只是做了一些小的改动。

我计划加入的亚当优化器代替示例存储库中实现的 sgd/rms 代码可在此处找到：https://gist.github.com/skaae/ae7225263ca8806868cb

在此转载（再次将.config.floatX 的引用替换为硬编码的'float32'）：

（theano 作为th，theano.shared 作为thsh，theano.tensor 作为T，numpy 作为np）

def adam(loss, all_params, learning_rate=0.001, b1=0.9, b2=0.999, e=1e-8, gamma=1-1e-8):
    """
    ADAM update rules
    Default values are taken from [Kingma2014]

    References:
    [Kingma2014] Kingma, Diederik, and Jimmy Ba.
    "Adam: A Method for Stochastic Optimization."
    arXiv preprint arXiv:1412.6980 (2014).
    http://arxiv.org/pdf/1412.6980v4.pdf
    """

    updates = []
    all_grads = th.grad(loss, all_params)
    alpha = learning_rate
    t = thsh(np.float32(1))
    b1_t = b1*gamma**(t-1)   #(Decay the first moment running average coefficient)

    for theta_previous, g in zip(all_params, all_grads):
        m_previous = thsh(np.zeros(theta_previous.get_value().shape.astype('float32')))
        v_previous = thsh(np.zeros(theta_previous.get_value().shape.astype('float32')))

        m = b1_t*m_previous + (1 - b1_t)*g  # (Update biased first moment estimate)
        v = b2*v_previous + (1 - b2)*g**2   # (Update biased second raw moment estimate)
        m_hat = m / (1-b1**t)               # (Compute bias-corrected first moment estimate)
        v_hat = v / (1-b2**t)               # (Compute bias-corrected second raw moment estimate)
        theta = theta_previous - (alpha * m_hat) / (T.sqrt(v_hat) + e) #(Update parameters)

        updates.append((m_previous, m))
        updates.append((v_previous, v))
        updates.append((theta_previous, theta) )
    updates.append((t, t + 1.))
    return updates

我的问题是这样的：

您将如何修改 GRUTheano 模块以使用上述 Adam 方法代替内置的 sgd/rmsprop 函数？

看起来关键的变化是 GRUTheano 的第 99-126 行：

    # SGD parameters
    learning_rate = T.scalar('learning_rate')
    decay = T.scalar('decay')

    # rmsprop cache updates
    mE = decay * self.mE + (1 - decay) * dE ** 2
    mU = decay * self.mU + (1 - decay) * dU ** 2
    mW = decay * self.mW + (1 - decay) * dW ** 2
    mV = decay * self.mV + (1 - decay) * dV ** 2
    mb = decay * self.mb + (1 - decay) * db ** 2
    mc = decay * self.mc + (1 - decay) * dc ** 2

    self.sgd_step = theano.function(
        [x, y, learning_rate, theano.Param(decay, default=0.9)],
        [], 
        updates=[(E, E - learning_rate * dE / T.sqrt(mE + 1e-6)),
                 (U, U - learning_rate * dU / T.sqrt(mU + 1e-6)),
                 (W, W - learning_rate * dW / T.sqrt(mW + 1e-6)),
                 (V, V - learning_rate * dV / T.sqrt(mV + 1e-6)),
                 (b, b - learning_rate * db / T.sqrt(mb + 1e-6)),
                 (c, c - learning_rate * dc / T.sqrt(mc + 1e-6)),
                 (self.mE, mE),
                 (self.mU, mU),
                 (self.mW, mW),
                 (self.mV, mV),
                 (self.mb, mb),
                 (self.mc, mc)
                ])

Answer 1

我没有测试过这段代码，但您唯一需要更改的是告诉 updates 使用 adam(..) 而不是已经提供的更新在这里，这样的事情应该可以工作（完整的代码看起来像这样（我们需要摆脱 rmsprop 的东西））：

import numpy as np
import theano as theano
import theano.tensor as T
from theano.gradient import grad_clip
import time
import operator

class GRUTheano(object):
    def __init__(self, word_dim, hidden_dim=128, bptt_truncate=-1):
        # Assign instance variables
        self.word_dim = word_dim
        self.hidden_dim = hidden_dim
        self.bptt_truncate = bptt_truncate
        # Initialize the network parameters
        E = np.random.uniform(-np.sqrt(1./word_dim), np.sqrt(1./word_dim), (hidden_dim, word_dim))
        U = np.random.uniform(-np.sqrt(1./hidden_dim), np.sqrt(1./hidden_dim), (6, hidden_dim, hidden_dim))
        W = np.random.uniform(-np.sqrt(1./hidden_dim), np.sqrt(1./hidden_dim), (6, hidden_dim, hidden_dim))
        V = np.random.uniform(-np.sqrt(1./hidden_dim), np.sqrt(1./hidden_dim), (word_dim, hidden_dim))
        b = np.zeros((6, hidden_dim))
        c = np.zeros(word_dim)
        # Theano: Created shared variables
        self.E = theano.shared(name='E', value=E.astype(theano.config.floatX))
        self.U = theano.shared(name='U', value=U.astype(theano.config.floatX))
        self.W = theano.shared(name='W', value=W.astype(theano.config.floatX))
        self.V = theano.shared(name='V', value=V.astype(theano.config.floatX))
        self.b = theano.shared(name='b', value=b.astype(theano.config.floatX))
        self.c = theano.shared(name='c', value=c.astype(theano.config.floatX))
        # We store the Theano graph here
        self.theano = {}
        self.__theano_build__()

    def __theano_build__(self):
        E, V, U, W, b, c = self.E, self.V, self.U, self.W, self.b, self.c

        x = T.ivector('x')
        y = T.ivector('y')

        def forward_prop_step(x_t, s_t1_prev, s_t2_prev):
            # This is how we calculated the hidden state in a simple RNN. No longer!
            # s_t = T.tanh(U[:,x_t] + W.dot(s_t1_prev))

            # Word embedding layer
            x_e = E[:,x_t]

            # GRU Layer 1
            z_t1 = T.nnet.hard_sigmoid(U[0].dot(x_e) + W[0].dot(s_t1_prev) + b[0])
            r_t1 = T.nnet.hard_sigmoid(U[1].dot(x_e) + W[1].dot(s_t1_prev) + b[1])
            c_t1 = T.tanh(U[2].dot(x_e) + W[2].dot(s_t1_prev * r_t1) + b[2])
            s_t1 = (T.ones_like(z_t1) - z_t1) * c_t1 + z_t1 * s_t1_prev

            # GRU Layer 2
            z_t2 = T.nnet.hard_sigmoid(U[3].dot(s_t1) + W[3].dot(s_t2_prev) + b[3])
            r_t2 = T.nnet.hard_sigmoid(U[4].dot(s_t1) + W[4].dot(s_t2_prev) + b[4])
            c_t2 = T.tanh(U[5].dot(s_t1) + W[5].dot(s_t2_prev * r_t2) + b[5])
            s_t2 = (T.ones_like(z_t2) - z_t2) * c_t2 + z_t2 * s_t2_prev

            # Final output calculation
            # Theano's softmax returns a matrix with one row, we only need the row
            o_t = T.nnet.softmax(V.dot(s_t2) + c)[0]

            return [o_t, s_t1, s_t2]

    [o, s, s2], updates = theano.scan(
        forward_prop_step,
        sequences=x,
        truncate_gradient=self.bptt_truncate,
        outputs_info=[None,
                      dict(initial=T.zeros(self.hidden_dim)),
                      dict(initial=T.zeros(self.hidden_dim))])

    prediction = T.argmax(o, axis=1)
    o_error = T.sum(T.nnet.categorical_crossentropy(o, y))

    # Total cost (could add regularization here)
    cost = o_error

    # Gradients
    dE = T.grad(cost, E)
    dU = T.grad(cost, U)
    dW = T.grad(cost, W)
    db = T.grad(cost, b)
    dV = T.grad(cost, V)
    dc = T.grad(cost, c)

    # Assign functions
    self.predict = theano.function([x], o)
    self.predict_class = theano.function([x], prediction)
    self.ce_error = theano.function([x, y], cost)
    self.bptt = theano.function([x, y], [dE, dU, dW, db, dV, dc])

    self.params = [self.E, self.U, self.W, self.V, self.b, self.c]

    updates=adam(cost, self.params)
    self.sgd_step = theano.function(
        inputs=[x, y],
        outputs=[],
        updates=updates
    )


def calculate_total_loss(self, X, Y):
    return np.sum([self.ce_error(x,y) for x,y in zip(X,Y)])


def calculate_loss(self, X, Y):
    # Divide calculate_loss by the number of words
    num_words = np.sum([len(y) for y in Y])
    return self.calculate_total_loss(X,Y)/float(num_words)


def adam(loss, all_params, learning_rate=0.001, b1=0.9, b2=0.999, e=1e-8,
     gamma=1-1e-8):
    """
    ADAM update rules
    Default values are taken from [Kingma2014]

    References:
    [Kingma2014] Kingma, Diederik, and Jimmy Ba.
    "Adam: A Method for Stochastic Optimization."
    arXiv preprint arXiv:1412.6980 (2014).
    http://arxiv.org/pdf/1412.6980v4.pdf

    """
    updates = []
    all_grads = theano.grad(loss, all_params)
    alpha = learning_rate
    t = theano.shared(np.float32(1))
    b1_t = b1*gamma**(t-1)   #(Decay the first moment running average coefficient)

    for theta_previous, g in zip(all_params, all_grads):
        m_previous =   theano.shared(np.zeros(theta_previous.get_value().shape,
                                        dtype=theano.config.floatX))
        v_previous = theano.shared(np.zeros(theta_previous.get_value().shape,
                                        dtype=theano.config.floatX))

        m = b1_t*m_previous + (1 - b1_t)*g                             # (Update biased first moment estimate)
        v = b2*v_previous + (1 - b2)*g**2                              # (Update biased second raw moment estimate)
        m_hat = m / (1-b1**t)                                          # (Compute bias-corrected first moment estimate)
        v_hat = v / (1-b2**t)                                          # (Compute bias-corrected second raw moment estimate)
        theta = theta_previous - (alpha * m_hat) / (T.sqrt(v_hat) + e) #(Update parameters)

        updates.append((m_previous, m))
        updates.append((v_previous, v))
        updates.append((theta_previous, theta) )
    updates.append((t, t + 1.))
    return updates