Training char_rnn by Andrej Karpathy on first chapter of Genesis

char_rnn_karpathy.py

"""
Minimal character-level Vanilla RNN model. Written by Andrej Karpathy (@karpathy)
BSD License
"""
from __future__ import print_function
import numpy as np

# data I/O
data = open('input.txt', 'r').read()  # should be simple plain text file
chars = list(set(data))
data_size, vocab_size = len(data), len(chars)
print('data has %d characters, %d unique.' % (data_size, vocab_size))
char_to_ix = {ch: i for i, ch in enumerate(chars)}
ix_to_char = {i: ch for i, ch in enumerate(chars)}

# hyperparameters
hidden_size = 100  # size of hidden layer of neurons
seq_length = 25  # number of steps to unroll the RNN for
learning_rate = 1e-1

# model parameters
Wxh = np.random.randn(hidden_size, vocab_size) * 0.01  # input to hidden
Whh = np.random.randn(hidden_size, hidden_size) * 0.01  # hidden to hidden
Why = np.random.randn(vocab_size, hidden_size) * 0.01  # hidden to output
bh = np.zeros((hidden_size, 1))  # hidden bias
by = np.zeros((vocab_size, 1))  # output bias


def lossFun(inputs, targets, hprev):
    """
    inputs,targets are both list of integers.
    hprev is Hx1 array of initial hidden state
    returns the loss, gradients on model parameters, and last hidden state
    """
    xs, hs, ys, ps = {}, {}, {}, {}
    hs[-1] = np.copy(hprev)
    loss = 0
    # forward pass
    for t in range(len(inputs)):
        xs[t] = np.zeros((vocab_size, 1))  # encode in 1-of-k representation
        xs[t][inputs[t]] = 1
        hs[t] = np.tanh(np.dot(Wxh, xs[t]) + np.dot(Whh,
                                                    hs[t - 1]) + bh)  # hidden state
        # unnormalized log probabilities for next chars
        ys[t] = np.dot(Why, hs[t]) + by
        # probabilities for next chars
        ps[t] = np.exp(ys[t]) / np.sum(np.exp(ys[t]))
        loss += -np.log(ps[t][targets[t], 0])  # softmax (cross-entropy loss) (negative log of cross entropy)
    # backward pass: compute gradients going backwards
    dWxh, dWhh, dWhy = np.zeros_like(
        Wxh), np.zeros_like(Whh), np.zeros_like(Why)
    dbh, dby = np.zeros_like(bh), np.zeros_like(by)
    dhnext = np.zeros_like(hs[0])
    for t in reversed(range(len(inputs))):
        dy = np.copy(ps[t])
        # backprop into y. see http://cs231n.github.io/neural-networks-case-study/#grad if confused here
        dy[targets[t]] -= 1
        dWhy += np.dot(dy, hs[t].T)
        dby += dy
        dh = np.dot(Why.T, dy) + dhnext  # backprop into h
        dhraw = (1 - hs[t] * hs[t]) * dh  # backprop through tanh nonlinearity
        dbh += dhraw
        dWxh += np.dot(dhraw, xs[t].T)
        dWhh += np.dot(dhraw, hs[t - 1].T)
        dhnext = np.dot(Whh.T, dhraw)
    for dparam in [dWxh, dWhh, dWhy, dbh, dby]:
        # clip to mitigate exploding gradients
        np.clip(dparam, -5, 5, out=dparam)
    return loss, dWxh, dWhh, dWhy, dbh, dby, hs[len(inputs) - 1]


def sample(h, seed_ix, n):
    """
    sample a sequence of integers from the model
    h is memory state, seed_ix is seed letter for first time step
    """
    x = np.zeros((vocab_size, 1))
    x[seed_ix] = 1 # one hot encoding
    ixes = []
    for t in range(n):
        h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h) + bh)
        y = np.dot(Why, h) + by
        p = np.exp(y) / np.sum(np.exp(y))
        # ix = np.random.choice(range(vocab_size), p=p.ravel())
        # How this step gives a validation of generating the next letter is not lucid
        # Instead using max of the softmax probablity would be more appropriate
        ix = p.argmax()
        x = np.zeros((vocab_size, 1))
        x[ix] = 1
        ixes.append(ix)
    return ixes


n, p = 0, 0
mWxh, mWhh, mWhy = np.zeros_like(Wxh), np.zeros_like(Whh), np.zeros_like(Why)
mbh, mby = np.zeros_like(bh), np.zeros_like(by)  # memory variables for Adagrad
smooth_loss = -np.log(1.0 / vocab_size) * seq_length  # loss at iteration 0

# MAIN LOOP

while n < 100000:
  # prepare inputs (we're sweeping from left to right in steps seq_length long)
    if p + seq_length + 1 >= len(data) or n == 0:
        hprev = np.zeros((hidden_size, 1))  # reset RNN memory
        p = 0  # go from start of data
    inputs = [char_to_ix[ch]
              for ch in data[p:p + seq_length]]  # input characters
    # output characters (shifted input by one position to right)
    targets = [char_to_ix[ch] for ch in data[p + 1:p + seq_length + 1]]

    # sample from the model now and then to identify the improvement
    if n % 100 == 0:
        sample_ix = sample(hprev, inputs[0], 200)
        txt = ''.join(ix_to_char[ix] for ix in sample_ix)
        print('----\n %s \n----' % (txt, ))

    # forward seq_length characters through the net and fetch gradient
    # hprev is the hidden state previous vector
    loss, dWxh, dWhh, dWhy, dbh, dby, hprev = lossFun(inputs, targets, hprev)
    smooth_loss = smooth_loss * 0.999 + loss * 0.001
    if n % 100 == 0:
        print('iter %d, loss: %f' % (n, smooth_loss))  # print progress
    # perform parameter update with Adagrad
    for param, dparam, mem in zip([Wxh, Whh, Why, bh, by],
                                  [dWxh, dWhh, dWhy, dbh, dby],
                                  [mWxh, mWhh, mWhy, mbh, mby]):
        mem += dparam * dparam
        param += -learning_rate * dparam / \
            np.sqrt(mem + 1e-8)  # adagrad update

    p += seq_length  # move data pointer
    n += 1  # iteration counter

  # gradient checking
from random import uniform


def gradCheck(inputs, target, hprev):
    global Wxh, Whh, Why, bh, by
    num_checks, delta = 10, 1e-5
    _, dWxh, dWhh, dWhy, dbh, dby, _ = lossFun(inputs, targets, hprev)
    for param, dparam, name in zip([Wxh, Whh, Why, bh, by], [dWxh, dWhh, dWhy, dbh, dby], ['Wxh', 'Whh', 'Why', 'bh', 'by']):
        s0 = dparam.shape
        s1 = param.shape
        assert (s0 == s1), "Error dims dont match: %s and %s." % (s0, s1)
        print(name)
        for i in range(num_checks):
            ri = int(uniform(0, param.size))
            # evaluate cost at [x + delta] and [x - delta]
            old_val = param.flat[ri]
            param.flat[ri] = old_val + delta
            cg0, _, _, _, _, _, _ = lossFun(inputs, targets, hprev)
            param.flat[ri] = old_val - delta
            cg1, _, _, _, _, _, _ = lossFun(inputs, targets, hprev)
            param.flat[ri] = old_val  # reset old value for this parameter
            # fetch both numerical and analytic gradient
            grad_analytic = dparam.flat[ri]
            grad_numerical = (cg0 - cg1) / (2 * delta)
            rel_error = abs(grad_analytic - grad_numerical) / \
                abs(grad_numerical + grad_analytic)
            print('%f, %f => %e ' % (grad_numerical, grad_analytic, rel_error))
            # rel_error should be on order of 1e-7 or less