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2705 lines
200 KiB
2705 lines
200 KiB
3 years ago
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{
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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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"# 7.4 动量法"
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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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"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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"1.0.0\n"
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]
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}
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],
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"source": [
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"%matplotlib inline\n",
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"import sys\n",
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|
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"sys.path.append(\"..\") \n",
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"import d2lzh_pytorch as d2l\n",
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|
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"import torch\n",
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"\n",
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"eta = 0.4\n",
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|
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"print(torch.__version__)"
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]
|
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},
|
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{
|
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|
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"cell_type": "markdown",
|
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|
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"metadata": {},
|
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"source": [
|
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|
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"## 7.4.1 梯度下降的问题"
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]
|
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},
|
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{
|
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|
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"cell_type": "code",
|
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|
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"execution_count": 2,
|
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|
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"metadata": {},
|
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"outputs": [
|
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|
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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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|
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"epoch 20, x1 -0.943467, x2 -0.000073\n"
|
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|
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]
|
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|
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},
|
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|
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{
|
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|
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"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEIRFz2knHF2Do9z81Z1
|
||
|
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"text/plain": [
|
||
|
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"<matplotlib.figure.Figure at 0x1110a18d0>"
|
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|
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]
|
||
|
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},
|
||
|
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"metadata": {},
|
||
|
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"output_type": "display_data"
|
||
|
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}
|
||
|
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],
|
||
|
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"source": [
|
||
|
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"def f_2d(x1, x2):\n",
|
||
|
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" return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
|
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"\n",
|
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|
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"def gd_2d(x1, x2, s1, s2):\n",
|
||
|
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" return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)\n",
|
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"\n",
|
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|
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"d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
|
||
|
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]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
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"metadata": {},
|
||
|
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"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"epoch 20, x1 -0.387814, x2 -1673.365109\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEKCAYAAADenhiQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsM7d1wOY2bXAicCfa71
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x1111691d0>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"eta = 0.6\n",
|
||
|
|
"d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## 7.4.2 动量法"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"epoch 20, x1 -0.062843, x2 0.001202\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngaz8KDzxLdXq0MIxfLY
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x11dec3c88>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"def momentum_2d(x1, x2, v1, v2):\n",
|
||
|
|
" v1 = gamma * v1 + eta * 0.2 * x1\n",
|
||
|
|
" v2 = gamma * v2 + eta * 4 * x2\n",
|
||
|
|
" return x1 - v1, x2 - v2, v1, v2\n",
|
||
|
|
"\n",
|
||
|
|
"eta, gamma = 0.4, 0.5\n",
|
||
|
|
"d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"epoch 20, x1 0.007188, x2 0.002553\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDMuKnnCcHYd72H64mx2
|
||
|
|
"text/plain": [
|
||
|
|
"<matplotlib.figure.Figure at 0x11de85ac8>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"eta = 0.6\n",
|
||
|
|
"d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## 7.4.3 从零开始实现"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": true
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"features, labels = d2l.get_data_ch7()\n",
|
||
|
|
"\n",
|
||
|
|
"def init_momentum_states():\n",
|
||
|
|
" v_w = torch.zeros((features.shape[1], 1), dtype=torch.float32)\n",
|
||
|
|
" v_b = torch.zeros(1, dtype=torch.float32)\n",
|
||
|
|
" return (v_w, v_b)\n",
|
||
|
|
"\n",
|
||
|
|
"def sgd_momentum(params, states, hyperparams):\n",
|
||
|
|
" for p, v in zip(params, states):\n",
|
||
|
|
" v.data = hyperparams['momentum'] * v.data + hyperparams['lr'] * p.grad.data\n",
|
||
|
|
" p.data -= v.data"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 7,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"loss: 0.247369, 0.040711 sec per epoch\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
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" {'lr': 0.004, 'momentum': 0.9}, features, labels)"
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