Andrej Karpathy
613 linhas
18 KiB
Plaintext
613 linhas
18 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## RNN Language Model\n",
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"\n",
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"Below is a diagram of the RNN computation that we will implement below. We're plugging characters into the RNN with a 1-hot encoding and expecting it to predict the next character. In this example the training data is the string \"hello\", so there are 4 letters in the vocabulary: [h,e,l,o]."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"<img src=\"rnnlm.jpeg\">"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"np.random.seed(1337)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"data has 4573338 characters, 67 unique.\n"
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]
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}
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],
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"source": [
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"# data I/O\n",
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"# get shakespeare from http://cs.stanford.edu/people/karpathy/shakespeare.txt\n",
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"data = open('shakespeare.txt', 'r').read() # should be simple plain text file\n",
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"chars = list(set(data))\n",
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"data_size, vocab_size = len(data), len(chars)\n",
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"print 'data has %d characters, %d unique.' % (data_size, vocab_size)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"char_to_ix = { ch:i for i,ch in enumerate(chars) }\n",
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"ix_to_char = { i:ch for i,ch in enumerate(chars) }"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"41"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"char_to_ix['a']"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" thing when he was young,\n"
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]
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}
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],
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"source": [
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"# lets sample a batch of data\n",
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"seq_length = 25 # number of characters in the batch\n",
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"p = 220000 # point in the book to sample from\n",
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"print data[p:p+seq_length] # print a chunk of data"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[2, 61, 49, 48, 55, 46, 2, 62, 49, 44, 55, 2, 49, 44, 2, 62, 41, 58, 2, 64, 54, 60, 55, 46, 7]\n",
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"[61, 49, 48, 55, 46, 2, 62, 49, 44, 55, 2, 49, 44, 2, 62, 41, 58, 2, 64, 54, 60, 55, 46, 7, 0]\n"
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]
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}
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],
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"source": [
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"inputs = [char_to_ix[ch] for ch in data[p:p+seq_length]]\n",
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"targets = [char_to_ix[ch] for ch in data[p+1:p+seq_length+1]]\n",
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"print inputs\n",
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"print targets"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
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" 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
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" 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
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" 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
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]
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}
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],
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"source": [
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"# lets plug the first character into the RNN\n",
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"ix_input = inputs[0]\n",
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"ix_target = targets[0]\n",
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"# encode the input character with a 1-hot representation\n",
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"x = np.zeros((vocab_size,1))\n",
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"x[ix_input] = 1\n",
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"print x.ravel()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# create random starting parameters\n",
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"hidden_size = 10\n",
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"Wxh = np.random.randn(hidden_size, vocab_size)*0.01 # input to hidden\n",
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"Whh = np.random.randn(hidden_size, hidden_size)*0.01 # hidden to hidden\n",
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"Why = np.random.randn(vocab_size, hidden_size)*0.01 # hidden to output\n",
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"bh = np.zeros((hidden_size, 1)) # hidden bias\n",
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"by = np.zeros((vocab_size, 1)) # output bias"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[-0.00321813 0.00640499 0.00424507 0.00783602 -0.00428041 0.00900686\n",
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" -0.01618631 0.00071848 -0.01342806 -0.0048051 ]\n"
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]
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}
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],
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"source": [
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"# compute the hidden state\n",
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"h_prev = np.zeros((hidden_size, 1))\n",
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"h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h_prev + bh))\n",
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"print h.ravel()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 3.83078834e-05 3.73893809e-05 -1.07305639e-04 2.67774461e-04\n",
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" 1.19325035e-04 -3.37354220e-04 -3.34852820e-04 3.32538588e-04\n",
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" 3.18794726e-04 -1.03554566e-05 1.36845629e-04 -5.38710213e-04\n",
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" -4.57711660e-04 2.99868693e-04 1.68690516e-04 1.78520042e-04\n",
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" 2.36693532e-04 -7.03401501e-05 -7.16902773e-05 1.27203335e-04\n",
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" 8.04252112e-05 1.59279072e-04 2.17314448e-04 -2.72573982e-05\n",
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" -7.02211895e-04 -2.42104646e-05 5.30702842e-04 1.94948893e-04\n",
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" -9.90711082e-05 4.03627462e-04 -2.93323333e-04 3.93383233e-04\n",
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" -4.05743771e-04 -3.38345251e-04 -5.29097616e-05 -4.80911954e-05\n",
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" 1.33355225e-04 4.75679274e-04 6.58103198e-05 1.94801460e-04\n",
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" -2.20233399e-04 3.08235108e-04 -2.53968781e-05 1.44684905e-04\n",
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" -8.29930806e-05 5.83661343e-04 7.77516275e-05 2.55059906e-04\n",
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" 1.81287457e-04 2.64252428e-04 1.78958318e-04 -2.92440820e-04\n",
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" -3.40954240e-04 8.32849829e-05 -6.05381172e-05 3.07491179e-04\n",
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" 3.90229048e-04 -1.39828111e-04 2.11848605e-04 -5.79932785e-04\n",
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" 6.02578409e-05 -2.12493371e-04 2.07956569e-04 -2.84122452e-04\n",
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" -2.30967665e-04 3.80355416e-04 9.87418965e-05]\n"
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]
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}
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],
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"source": [
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"# compute the scores for next character\n",
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"y = np.dot(Why, h) + by\n",
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"print y.ravel()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 0.0149254 0.01492538 0.01492322 0.01492882 0.01492661 0.01491979\n",
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" 0.01491983 0.01492979 0.01492958 0.01492467 0.01492687 0.01491679\n",
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" 0.014918 0.0149293 0.01492734 0.01492749 0.01492836 0.01492378\n",
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" 0.01492376 0.01492672 0.01492603 0.0149272 0.01492807 0.01492442\n",
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" 0.01491435 0.01492446 0.01493275 0.01492774 0.01492335 0.01493085\n",
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" 0.01492045 0.0149307 0.01491877 0.01491978 0.01492404 0.01492411\n",
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" 0.01492682 0.01493193 0.01492581 0.01492773 0.01492154 0.01492943\n",
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" 0.01492445 0.01492699 0.01492359 0.01493354 0.01492599 0.01492863\n",
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" 0.01492753 0.01492877 0.0149275 0.01492046 0.01491974 0.01492607\n",
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" 0.01492392 0.01492942 0.01493065 0.01492274 0.01492799 0.01491617\n",
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" 0.01492572 0.01492165 0.01492793 0.01492059 0.01492138 0.0149305\n",
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" 0.0149263 ]\n",
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"probabilities sum to 1.0\n"
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]
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}
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],
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"source": [
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"# the scores are unnormalized log probabilities. compute the probabilities\n",
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"p = np.exp(y) / np.sum(np.exp(y))\n",
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"print p.ravel()\n",
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"print 'probabilities sum to ', p.sum()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"probability assigned to the correct next character is right now: 0.0149216543899\n"
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]
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}
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],
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"source": [
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"print 'probability assigned to the correct next character is right now: ', p[ix_target,0]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"the cross-entropy (softmax) loss is 4.20494180632\n"
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]
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}
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],
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"source": [
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"loss = -np.log(p[ix_target,0])\n",
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"print 'the cross-entropy (softmax) loss is ', loss"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[ 0.0149254 0.01492538 0.01492322 0.01492882 0.01492661 0.01491979\n",
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" 0.01491983 0.01492979 0.01492958 0.01492467 0.01492687 0.01491679\n",
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" 0.014918 0.0149293 0.01492734 0.01492749 0.01492836 0.01492378\n",
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" 0.01492376 0.01492672 0.01492603 0.0149272 0.01492807 0.01492442\n",
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" 0.01491435 0.01492446 0.01493275 0.01492774 0.01492335 0.01493085\n",
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" 0.01492045 0.0149307 0.01491877 0.01491978 0.01492404 0.01492411\n",
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" 0.01492682 0.01493193 0.01492581 0.01492773 0.01492154 0.01492943\n",
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" 0.01492445 0.01492699 0.01492359 0.01493354 0.01492599 0.01492863\n",
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" 0.01492753 0.01492877 0.0149275 0.01492046 0.01491974 0.01492607\n",
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" 0.01492392 0.01492942 0.01493065 0.01492274 0.01492799 0.01491617\n",
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" 0.01492572 -0.98507835 0.01492793 0.01492059 0.01492138 0.0149305\n",
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" 0.0149263 ]\n",
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"sum of dy is 1.45716771982e-16\n",
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"the gradient for the correct character (t) is: -0.98507834561\n",
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"the gradient for the character (a) is: 0.0149294265437\n"
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]
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}
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],
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"source": [
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"# compute the gradient on y\n",
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"dy = np.copy(p)\n",
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"dy[ix_target] -= 1\n",
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"print dy.ravel()\n",
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"print 'sum of dy is ', dy.sum()\n",
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"print 'the gradient for the correct character (%s) is: %s' % (ix_to_char[ix_target], dy[ix_target,0])\n",
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"print 'the gradient for the character (a) is: ', dy[char_to_ix['a'],0]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"the hidden vector activations were:\n",
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"[-0.00321813 0.00640499 0.00424507 0.00783602 -0.00428041 0.00900686\n",
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" -0.01618631 0.00071848 -0.01342806 -0.0048051 ]\n",
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"the gradients are:\n",
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"[-0.00983172 -0.01049054 0.00911112 -0.01110877 -0.00134586 0.00686193\n",
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" -0.01532285 0.0099507 -0.00530998 0.01267197]\n",
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"the gradients dWhy have size: (67, 10)\n",
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"a small sample is:\n",
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"[[ -4.80319012e-05 9.55970187e-05 6.33594305e-05 1.16955768e-04]\n",
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" [ -4.80318571e-05 9.55969309e-05 6.33593723e-05 1.16955661e-04]\n",
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" [ -4.80249076e-05 9.55830995e-05 6.33502052e-05 1.16938739e-04]\n",
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" [ -4.80429242e-05 9.56189576e-05 6.33739710e-05 1.16982609e-04]]\n"
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]
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}
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],
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"source": [
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"# we computed [y = np.dot(Why, h) + by]; Backpropagate to Why, h, and by\n",
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"dWhy = np.dot(dy, h.T)\n",
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"dh = np.dot(Why.T, dy)\n",
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"dby = np.copy(dy)\n",
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"print 'the hidden vector activations were:'\n",
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"print h.ravel()\n",
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"print 'the gradients are:'\n",
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"print dh.ravel()\n",
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"print 'the gradients dWhy have size: ', dWhy.shape\n",
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"print 'a small sample is:'\n",
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"print dWhy[:4,:4]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"small sample of Whh:\n",
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"[[-0.0028736 -0.00195895 0.00885911 -0.00349354]\n",
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" [-0.00773272 -0.00051873 0.00219991 -0.00234756]\n",
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" [ 0.01687054 -0.01221995 0.00125455 -0.00568523]\n",
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" [-0.00031645 0.00514377 0.01194564 0.0070584 ]]\n"
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]
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}
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],
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"source": [
|
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"# we computed [h = np.tanh(np.dot(Wxh, x) + np.dot(Whh, h_prev + bh))]; \n",
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"# Backprop into Wxh, x, Whh, h_prev, bh:\n",
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"dh_before_tanh = (1-h**2)*dh\n",
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"dbh = np.copy(dh_before_tanh)\n",
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"dWxh = np.dot(dh_before_tanh, x.T)\n",
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"dWhh = np.dot(dh_before_tanh, h.T)\n",
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"dh_prev = np.dot(Whh.T, dh_before_tanh)\n",
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"print 'small sample of Whh:'\n",
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"print Whh[:4,:4]"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
|
|
"source": [
|
|
"# we now have the gradients for all parameters! (Wxh, Whh, Why, bh, by)\n",
|
|
"# lets do a parameter update\n",
|
|
"learning_rate = 0.1\n",
|
|
"Wxh2 = Wxh - learning_rate * dWxh\n",
|
|
"Whh2 = Whh - learning_rate * dWhh\n",
|
|
"Why2 = Why - learning_rate * dWhy\n",
|
|
"bh2 = bh - learning_rate * dbh\n",
|
|
"by2 = by - learning_rate * dby"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 18,
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"probability assigned to the correct next character was: 0.0149216543899\n",
|
|
"probability assigned to the correct next character is now: 0.0164678301753\n",
|
|
"the cross-entropy (softmax) loss was 4.20494180632\n",
|
|
"the loss is now 4.10634648754\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# these parameters should be much better! lets try it out:\n",
|
|
"h2 = np.tanh(np.dot(Wxh2, x) + np.dot(Whh2, h_prev + bh2))\n",
|
|
"y2 = np.dot(Why2, h2) + by2\n",
|
|
"p2 = np.exp(y2) / np.sum(np.exp(y2))\n",
|
|
"print 'probability assigned to the correct next character was: ', p[ix_target,0]\n",
|
|
"print 'probability assigned to the correct next character is now: ', p2[ix_target,0]\n",
|
|
"loss2 = -np.log(p2[ix_target,0])\n",
|
|
"print 'the cross-entropy (softmax) loss was ', loss\n",
|
|
"print 'the loss is now ', loss2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 19,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# note: the probability for the correct character went up! (and the loss went down)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 20,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# putting it together with loops\n",
|
|
"def lossFun(inputs, targets, hprev):\n",
|
|
" \"\"\"\n",
|
|
" inputs,targets are both list of integers.\n",
|
|
" hprev is Hx1 array of initial hidden state\n",
|
|
" returns the loss, gradients on model parameters, and last hidden state\n",
|
|
" \"\"\"\n",
|
|
" xs, hs, ys, ps = {}, {}, {}, {}\n",
|
|
" hs[-1] = np.copy(hprev)\n",
|
|
" loss = 0\n",
|
|
" \n",
|
|
" # forward pass\n",
|
|
" for t in xrange(len(inputs)):\n",
|
|
" xs[t] = np.zeros((vocab_size,1)) # encode in 1-of-k representation\n",
|
|
" xs[t][inputs[t]] = 1\n",
|
|
" hs[t] = np.tanh(np.dot(Wxh, xs[t]) + np.dot(Whh, hs[t-1]) + bh) # hidden state\n",
|
|
" ys[t] = np.dot(Why, hs[t]) + by # unnormalized log probabilities for next chars\n",
|
|
" ps[t] = np.exp(ys[t]) / np.sum(np.exp(ys[t])) # probabilities for next chars\n",
|
|
" loss += -np.log(ps[t][targets[t],0]) # softmax (cross-entropy loss)\n",
|
|
" \n",
|
|
" # backward pass: compute gradients going backwards\n",
|
|
" dWxh, dWhh, dWhy = np.zeros_like(Wxh), np.zeros_like(Whh), np.zeros_like(Why)\n",
|
|
" dbh, dby = np.zeros_like(bh), np.zeros_like(by)\n",
|
|
" dhnext = np.zeros_like(hs[0])\n",
|
|
" for t in reversed(xrange(len(inputs))):\n",
|
|
" dy = np.copy(ps[t])\n",
|
|
" dy[targets[t]] -= 1 # backprop into y\n",
|
|
" dWhy += np.dot(dy, hs[t].T)\n",
|
|
" dby += dy\n",
|
|
" dh = np.dot(Why.T, dy) + dhnext # backprop into h\n",
|
|
" dhraw = (1 - hs[t] * hs[t]) * dh # backprop through tanh nonlinearity\n",
|
|
" dbh += dhraw\n",
|
|
" dWxh += np.dot(dhraw, xs[t].T)\n",
|
|
" dWhh += np.dot(dhraw, hs[t-1].T)\n",
|
|
" dhnext = np.dot(Whh.T, dhraw)\n",
|
|
" \n",
|
|
" # clip to mitigate exploding gradients\n",
|
|
" for dparam in [dWxh, dWhh, dWhy, dbh, dby]:\n",
|
|
" np.clip(dparam, -5, 5, out=dparam)\n",
|
|
" \n",
|
|
" return loss, dWxh, dWhh, dWhy, dbh, dby, hs[len(inputs)-1]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 21,
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"105.118896505\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"loss, dWxh, dWhh, dWhy, dbh, dby, hnew = lossFun(inputs, targets, h_prev)\n",
|
|
"print loss"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 22,
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# TODO: write the sampling code\n",
|
|
"def sample(h, seed_ix, n):\n",
|
|
" \"\"\" \n",
|
|
" sample a sequence of integers from the model \n",
|
|
" h is initial memory state, seed_ix is seed letter for first time step\n",
|
|
" n is the number of time steps to sample for\n",
|
|
" \"\"\"\n",
|
|
" x = np.zeros((vocab_size, 1))\n",
|
|
" x[seed_ix] = 1\n",
|
|
" ixes = [] # sampled indices\n",
|
|
" for t in xrange(n):\n",
|
|
" pass # TODO: run the RNN for one time step, sample from distribution\n",
|
|
" return ixes\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 23,
|
|
"metadata": {
|
|
"collapsed": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# TODO: write the optimization loop\n",
|
|
"# Loop over the dataset from beginning to end, sampling batches of characters seq_length long\n",
|
|
"# Call the loss function and get the gradients\n",
|
|
"# Perform a parameter update\n",
|
|
"# Sample some examples from the model"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 2",
|
|
"language": "python",
|
|
"name": "python2"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 2
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython2",
|
|
"version": "2.7.11"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 0
|
|
}
|