967 lines
37 KiB
Plaintext
967 lines
37 KiB
Plaintext
{
|
||
"cells": [
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9122670f",
|
||
"metadata": {
|
||
"origin_pos": 0
|
||
},
|
||
"source": [
|
||
"# 注意力提示\n",
|
||
":label:`sec_attention-cues`\n",
|
||
"\n",
|
||
"感谢读者对本书的关注,因为读者的注意力是一种稀缺的资源:\n",
|
||
"此刻读者正在阅读本书(而忽略了其他的书),\n",
|
||
"因此读者的注意力是用机会成本(与金钱类似)来支付的。\n",
|
||
"为了确保读者现在投入的注意力是值得的,\n",
|
||
"作者们尽全力(全部的注意力)创作一本好书。\n",
|
||
"\n",
|
||
"自经济学研究稀缺资源分配以来,人们正处在“注意力经济”时代,\n",
|
||
"即人类的注意力被视为可以交换的、有限的、有价值的且稀缺的商品。\n",
|
||
"许多商业模式也被开发出来去利用这一点:\n",
|
||
"在音乐或视频流媒体服务上,人们要么消耗注意力在广告上,要么付钱来隐藏广告;\n",
|
||
"为了在网络游戏世界的成长,人们要么消耗注意力在游戏战斗中,\n",
|
||
"从而帮助吸引新的玩家,要么付钱立即变得强大。\n",
|
||
"总之,注意力不是免费的。\n",
|
||
"\n",
|
||
"注意力是稀缺的,而环境中的干扰注意力的信息却并不少。\n",
|
||
"比如人类的视觉神经系统大约每秒收到$10^8$位的信息,\n",
|
||
"这远远超过了大脑能够完全处理的水平。\n",
|
||
"幸运的是,人类的祖先已经从经验(也称为数据)中认识到\n",
|
||
"“并非感官的所有输入都是一样的”。\n",
|
||
"在整个人类历史中,这种只将注意力引向感兴趣的一小部分信息的能力,\n",
|
||
"使人类的大脑能够更明智地分配资源来生存、成长和社交,\n",
|
||
"例如发现天敌、找寻食物和伴侣。\n",
|
||
"\n",
|
||
"## 生物学中的注意力提示\n",
|
||
"\n",
|
||
"注意力是如何应用于视觉世界中的呢?\n",
|
||
"这要从当今十分普及的*双组件*(two-component)的框架开始讲起:\n",
|
||
"这个框架的出现可以追溯到19世纪90年代的威廉·詹姆斯,\n",
|
||
"他被认为是“美国心理学之父” :cite:`James.2007`。\n",
|
||
"在这个框架中,受试者基于*非自主性提示*和*自主性提示*\n",
|
||
"有选择地引导注意力的焦点。\n",
|
||
"\n",
|
||
"非自主性提示是基于环境中物体的突出性和易见性。\n",
|
||
"想象一下,假如我们面前有五个物品:\n",
|
||
"一份报纸、一篇研究论文、一杯咖啡、一本笔记本和一本书,\n",
|
||
"就像 :numref:`fig_eye-coffee`。\n",
|
||
"所有纸制品都是黑白印刷的,但咖啡杯是红色的。\n",
|
||
"换句话说,这个咖啡杯在这种视觉环境中是突出和显眼的,\n",
|
||
"不由自主地引起人们的注意。\n",
|
||
"所以我们会把视力最敏锐的地方放到咖啡上,\n",
|
||
"如 :numref:`fig_eye-coffee`所示。\n",
|
||
"\n",
|
||
"\n",
|
||
":width:`400px`\n",
|
||
":label:`fig_eye-coffee`\n",
|
||
"\n",
|
||
"喝咖啡后,我们会变得兴奋并想读书,\n",
|
||
"所以转过头,重新聚焦眼睛,然后看看书,\n",
|
||
"就像 :numref:`fig_eye-book`中描述那样。\n",
|
||
"与 :numref:`fig_eye-coffee`中由于突出性导致的选择不同,\n",
|
||
"此时选择书是受到了认知和意识的控制,\n",
|
||
"因此注意力在基于自主性提示去辅助选择时将更为谨慎。\n",
|
||
"受试者的主观意愿推动,选择的力量也就更强大。\n",
|
||
"\n",
|
||
"\n",
|
||
":width:`400px`\n",
|
||
":label:`fig_eye-book`\n",
|
||
"\n",
|
||
"## 查询、键和值\n",
|
||
"\n",
|
||
"自主性的与非自主性的注意力提示解释了人类的注意力的方式,\n",
|
||
"下面来看看如何通过这两种注意力提示,\n",
|
||
"用神经网络来设计注意力机制的框架,\n",
|
||
"\n",
|
||
"首先,考虑一个相对简单的状况,\n",
|
||
"即只使用非自主性提示。\n",
|
||
"要想将选择偏向于感官输入,\n",
|
||
"则可以简单地使用参数化的全连接层,\n",
|
||
"甚至是非参数化的最大汇聚层或平均汇聚层。\n",
|
||
"\n",
|
||
"因此,“是否包含自主性提示”将注意力机制与全连接层或汇聚层区别开来。\n",
|
||
"在注意力机制的背景下,自主性提示被称为*查询*(query)。\n",
|
||
"给定任何查询,注意力机制通过*注意力汇聚*(attention pooling)\n",
|
||
"将选择引导至*感官输入*(sensory inputs,例如中间特征表示)。\n",
|
||
"在注意力机制中,这些感官输入被称为*值*(value)。\n",
|
||
"更通俗的解释,每个值都与一个*键*(key)配对,\n",
|
||
"这可以想象为感官输入的非自主提示。\n",
|
||
"如 :numref:`fig_qkv`所示,可以通过设计注意力汇聚的方式,\n",
|
||
"便于给定的查询(自主性提示)与键(非自主性提示)进行匹配,\n",
|
||
"这将引导得出最匹配的值(感官输入)。\n",
|
||
"\n",
|
||
"\n",
|
||
":label:`fig_qkv`\n",
|
||
"\n",
|
||
"鉴于上面所提框架在 :numref:`fig_qkv`中的主导地位,\n",
|
||
"因此这个框架下的模型将成为本章的中心。\n",
|
||
"然而,注意力机制的设计有许多替代方案。\n",
|
||
"例如可以设计一个不可微的注意力模型,\n",
|
||
"该模型可以使用强化学习方法 :cite:`Mnih.Heess.Graves.ea.2014`进行训练。\n",
|
||
"\n",
|
||
"## 注意力的可视化\n",
|
||
"\n",
|
||
"平均汇聚层可以被视为输入的加权平均值,\n",
|
||
"其中各输入的权重是一样的。\n",
|
||
"实际上,注意力汇聚得到的是加权平均的总和值,\n",
|
||
"其中权重是在给定的查询和不同的键之间计算得出的。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 1,
|
||
"id": "58a7898f",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:03:03.521946Z",
|
||
"iopub.status.busy": "2023-08-18T07:03:03.521507Z",
|
||
"iopub.status.idle": "2023-08-18T07:03:05.621623Z",
|
||
"shell.execute_reply": "2023-08-18T07:03:05.620583Z"
|
||
},
|
||
"origin_pos": 2,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"import torch\n",
|
||
"from d2l import torch as d2l"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6e9e92fc",
|
||
"metadata": {
|
||
"origin_pos": 5
|
||
},
|
||
"source": [
|
||
"为了可视化注意力权重,需要定义一个`show_heatmaps`函数。\n",
|
||
"其输入`matrices`的形状是\n",
|
||
"(要显示的行数,要显示的列数,查询的数目,键的数目)。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "3c30d535",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:03:05.627152Z",
|
||
"iopub.status.busy": "2023-08-18T07:03:05.626530Z",
|
||
"iopub.status.idle": "2023-08-18T07:03:05.634951Z",
|
||
"shell.execute_reply": "2023-08-18T07:03:05.633763Z"
|
||
},
|
||
"origin_pos": 6,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"#@save\n",
|
||
"def show_heatmaps(matrices, xlabel, ylabel, titles=None, figsize=(2.5, 2.5),\n",
|
||
" cmap='Reds'):\n",
|
||
" \"\"\"显示矩阵热图\"\"\"\n",
|
||
" d2l.use_svg_display()\n",
|
||
" num_rows, num_cols = matrices.shape[0], matrices.shape[1]\n",
|
||
" fig, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize,\n",
|
||
" sharex=True, sharey=True, squeeze=False)\n",
|
||
" for i, (row_axes, row_matrices) in enumerate(zip(axes, matrices)):\n",
|
||
" for j, (ax, matrix) in enumerate(zip(row_axes, row_matrices)):\n",
|
||
" pcm = ax.imshow(matrix.detach().numpy(), cmap=cmap)\n",
|
||
" if i == num_rows - 1:\n",
|
||
" ax.set_xlabel(xlabel)\n",
|
||
" if j == 0:\n",
|
||
" ax.set_ylabel(ylabel)\n",
|
||
" if titles:\n",
|
||
" ax.set_title(titles[j])\n",
|
||
" fig.colorbar(pcm, ax=axes, shrink=0.6);"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f48978d9",
|
||
"metadata": {
|
||
"origin_pos": 7
|
||
},
|
||
"source": [
|
||
"下面使用一个简单的例子进行演示。\n",
|
||
"在本例子中,仅当查询和键相同时,注意力权重为1,否则为0。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "bbabe8f3",
|
||
"metadata": {
|
||
"execution": {
|
||
"iopub.execute_input": "2023-08-18T07:03:05.640096Z",
|
||
"iopub.status.busy": "2023-08-18T07:03:05.639355Z",
|
||
"iopub.status.idle": "2023-08-18T07:03:05.886353Z",
|
||
"shell.execute_reply": "2023-08-18T07:03:05.885235Z"
|
||
},
|
||
"origin_pos": 8,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/svg+xml": [
|
||
"<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
|
||
"<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
|
||
" \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
|
||
"<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"193.35825pt\" height=\"156.35625pt\" viewBox=\"0 0 193.35825 156.35625\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
|
||
" <metadata>\n",
|
||
" <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
|
||
" <cc:Work>\n",
|
||
" <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
|
||
" <dc:date>2023-08-18T07:03:05.823629</dc:date>\n",
|
||
" <dc:format>image/svg+xml</dc:format>\n",
|
||
" <dc:creator>\n",
|
||
" <cc:Agent>\n",
|
||
" <dc:title>Matplotlib v3.5.1, https://matplotlib.org/</dc:title>\n",
|
||
" </cc:Agent>\n",
|
||
" </dc:creator>\n",
|
||
" </cc:Work>\n",
|
||
" </rdf:RDF>\n",
|
||
" </metadata>\n",
|
||
" <defs>\n",
|
||
" <style type=\"text/css\">*{stroke-linejoin: round; stroke-linecap: butt}</style>\n",
|
||
" </defs>\n",
|
||
" <g id=\"figure_1\">\n",
|
||
" <g id=\"patch_1\">\n",
|
||
" <path d=\"M -0 156.35625 \n",
|
||
"L 193.35825 156.35625 \n",
|
||
"L 193.35825 0 \n",
|
||
"L -0 0 \n",
|
||
"L -0 156.35625 \n",
|
||
"z\n",
|
||
"\" style=\"fill: none\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"axes_1\">\n",
|
||
" <g id=\"patch_2\">\n",
|
||
" <path d=\"M 34.240625 118.8 \n",
|
||
"L 145.840625 118.8 \n",
|
||
"L 145.840625 7.2 \n",
|
||
"L 34.240625 7.2 \n",
|
||
"z\n",
|
||
"\" style=\"fill: #ffffff\"/>\n",
|
||
" </g>\n",
|
||
" <g clip-path=\"url(#p3a36c213e6)\">\n",
|
||
" <image xlink:href=\"data:image/png;base64,\n",
|
||
"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\" id=\"image8a96b358df\" transform=\"scale(1 -1)translate(0 -112)\" x=\"34.240625\" y=\"-6.8\" width=\"112\" height=\"112\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"matplotlib.axis_1\">\n",
|
||
" <g id=\"xtick_1\">\n",
|
||
" <g id=\"line2d_1\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"mdcf2e5a8c4\" d=\"M 0 0 \n",
|
||
"L 0 3.5 \n",
|
||
"\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </defs>\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#mdcf2e5a8c4\" x=\"39.820625\" y=\"118.8\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_1\">\n",
|
||
" <!-- 0 -->\n",
|
||
" <g transform=\"translate(36.639375 133.398438)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-30\" d=\"M 2034 4250 \n",
|
||
"Q 1547 4250 1301 3770 \n",
|
||
"Q 1056 3291 1056 2328 \n",
|
||
"Q 1056 1369 1301 889 \n",
|
||
"Q 1547 409 2034 409 \n",
|
||
"Q 2525 409 2770 889 \n",
|
||
"Q 3016 1369 3016 2328 \n",
|
||
"Q 3016 3291 2770 3770 \n",
|
||
"Q 2525 4250 2034 4250 \n",
|
||
"z\n",
|
||
"M 2034 4750 \n",
|
||
"Q 2819 4750 3233 4129 \n",
|
||
"Q 3647 3509 3647 2328 \n",
|
||
"Q 3647 1150 3233 529 \n",
|
||
"Q 2819 -91 2034 -91 \n",
|
||
"Q 1250 -91 836 529 \n",
|
||
"Q 422 1150 422 2328 \n",
|
||
"Q 422 3509 836 4129 \n",
|
||
"Q 1250 4750 2034 4750 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"xtick_2\">\n",
|
||
" <g id=\"line2d_2\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#mdcf2e5a8c4\" x=\"95.620625\" y=\"118.8\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_2\">\n",
|
||
" <!-- 5 -->\n",
|
||
" <g transform=\"translate(92.439375 133.398438)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-35\" d=\"M 691 4666 \n",
|
||
"L 3169 4666 \n",
|
||
"L 3169 4134 \n",
|
||
"L 1269 4134 \n",
|
||
"L 1269 2991 \n",
|
||
"Q 1406 3038 1543 3061 \n",
|
||
"Q 1681 3084 1819 3084 \n",
|
||
"Q 2600 3084 3056 2656 \n",
|
||
"Q 3513 2228 3513 1497 \n",
|
||
"Q 3513 744 3044 326 \n",
|
||
"Q 2575 -91 1722 -91 \n",
|
||
"Q 1428 -91 1123 -41 \n",
|
||
"Q 819 9 494 109 \n",
|
||
"L 494 744 \n",
|
||
"Q 775 591 1075 516 \n",
|
||
"Q 1375 441 1709 441 \n",
|
||
"Q 2250 441 2565 725 \n",
|
||
"Q 2881 1009 2881 1497 \n",
|
||
"Q 2881 1984 2565 2268 \n",
|
||
"Q 2250 2553 1709 2553 \n",
|
||
"Q 1456 2553 1204 2497 \n",
|
||
"Q 953 2441 691 2322 \n",
|
||
"L 691 4666 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-35\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_3\">\n",
|
||
" <!-- Keys -->\n",
|
||
" <g transform=\"translate(78.371094 147.076563)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-4b\" d=\"M 628 4666 \n",
|
||
"L 1259 4666 \n",
|
||
"L 1259 2694 \n",
|
||
"L 3353 4666 \n",
|
||
"L 4166 4666 \n",
|
||
"L 1850 2491 \n",
|
||
"L 4331 0 \n",
|
||
"L 3500 0 \n",
|
||
"L 1259 2247 \n",
|
||
"L 1259 0 \n",
|
||
"L 628 0 \n",
|
||
"L 628 4666 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-65\" d=\"M 3597 1894 \n",
|
||
"L 3597 1613 \n",
|
||
"L 953 1613 \n",
|
||
"Q 991 1019 1311 708 \n",
|
||
"Q 1631 397 2203 397 \n",
|
||
"Q 2534 397 2845 478 \n",
|
||
"Q 3156 559 3463 722 \n",
|
||
"L 3463 178 \n",
|
||
"Q 3153 47 2828 -22 \n",
|
||
"Q 2503 -91 2169 -91 \n",
|
||
"Q 1331 -91 842 396 \n",
|
||
"Q 353 884 353 1716 \n",
|
||
"Q 353 2575 817 3079 \n",
|
||
"Q 1281 3584 2069 3584 \n",
|
||
"Q 2775 3584 3186 3129 \n",
|
||
"Q 3597 2675 3597 1894 \n",
|
||
"z\n",
|
||
"M 3022 2063 \n",
|
||
"Q 3016 2534 2758 2815 \n",
|
||
"Q 2500 3097 2075 3097 \n",
|
||
"Q 1594 3097 1305 2825 \n",
|
||
"Q 1016 2553 972 2059 \n",
|
||
"L 3022 2063 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-79\" d=\"M 2059 -325 \n",
|
||
"Q 1816 -950 1584 -1140 \n",
|
||
"Q 1353 -1331 966 -1331 \n",
|
||
"L 506 -1331 \n",
|
||
"L 506 -850 \n",
|
||
"L 844 -850 \n",
|
||
"Q 1081 -850 1212 -737 \n",
|
||
"Q 1344 -625 1503 -206 \n",
|
||
"L 1606 56 \n",
|
||
"L 191 3500 \n",
|
||
"L 800 3500 \n",
|
||
"L 1894 763 \n",
|
||
"L 2988 3500 \n",
|
||
"L 3597 3500 \n",
|
||
"L 2059 -325 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-73\" d=\"M 2834 3397 \n",
|
||
"L 2834 2853 \n",
|
||
"Q 2591 2978 2328 3040 \n",
|
||
"Q 2066 3103 1784 3103 \n",
|
||
"Q 1356 3103 1142 2972 \n",
|
||
"Q 928 2841 928 2578 \n",
|
||
"Q 928 2378 1081 2264 \n",
|
||
"Q 1234 2150 1697 2047 \n",
|
||
"L 1894 2003 \n",
|
||
"Q 2506 1872 2764 1633 \n",
|
||
"Q 3022 1394 3022 966 \n",
|
||
"Q 3022 478 2636 193 \n",
|
||
"Q 2250 -91 1575 -91 \n",
|
||
"Q 1294 -91 989 -36 \n",
|
||
"Q 684 19 347 128 \n",
|
||
"L 347 722 \n",
|
||
"Q 666 556 975 473 \n",
|
||
"Q 1284 391 1588 391 \n",
|
||
"Q 1994 391 2212 530 \n",
|
||
"Q 2431 669 2431 922 \n",
|
||
"Q 2431 1156 2273 1281 \n",
|
||
"Q 2116 1406 1581 1522 \n",
|
||
"L 1381 1569 \n",
|
||
"Q 847 1681 609 1914 \n",
|
||
"Q 372 2147 372 2553 \n",
|
||
"Q 372 3047 722 3315 \n",
|
||
"Q 1072 3584 1716 3584 \n",
|
||
"Q 2034 3584 2315 3537 \n",
|
||
"Q 2597 3491 2834 3397 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-4b\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-65\" x=\"60.576172\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-79\" x=\"122.099609\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-73\" x=\"181.279297\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"matplotlib.axis_2\">\n",
|
||
" <g id=\"ytick_1\">\n",
|
||
" <g id=\"line2d_3\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"m473666877a\" d=\"M 0 0 \n",
|
||
"L -3.5 0 \n",
|
||
"\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </defs>\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m473666877a\" x=\"34.240625\" y=\"12.78\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_4\">\n",
|
||
" <!-- 0 -->\n",
|
||
" <g transform=\"translate(20.878125 16.579219)scale(0.1 -0.1)\">\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_2\">\n",
|
||
" <g id=\"line2d_4\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m473666877a\" x=\"34.240625\" y=\"35.1\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_5\">\n",
|
||
" <!-- 2 -->\n",
|
||
" <g transform=\"translate(20.878125 38.899219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-32\" d=\"M 1228 531 \n",
|
||
"L 3431 531 \n",
|
||
"L 3431 0 \n",
|
||
"L 469 0 \n",
|
||
"L 469 531 \n",
|
||
"Q 828 903 1448 1529 \n",
|
||
"Q 2069 2156 2228 2338 \n",
|
||
"Q 2531 2678 2651 2914 \n",
|
||
"Q 2772 3150 2772 3378 \n",
|
||
"Q 2772 3750 2511 3984 \n",
|
||
"Q 2250 4219 1831 4219 \n",
|
||
"Q 1534 4219 1204 4116 \n",
|
||
"Q 875 4013 500 3803 \n",
|
||
"L 500 4441 \n",
|
||
"Q 881 4594 1212 4672 \n",
|
||
"Q 1544 4750 1819 4750 \n",
|
||
"Q 2544 4750 2975 4387 \n",
|
||
"Q 3406 4025 3406 3419 \n",
|
||
"Q 3406 3131 3298 2873 \n",
|
||
"Q 3191 2616 2906 2266 \n",
|
||
"Q 2828 2175 2409 1742 \n",
|
||
"Q 1991 1309 1228 531 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-32\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_3\">\n",
|
||
" <g id=\"line2d_5\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m473666877a\" x=\"34.240625\" y=\"57.42\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_6\">\n",
|
||
" <!-- 4 -->\n",
|
||
" <g transform=\"translate(20.878125 61.219219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-34\" d=\"M 2419 4116 \n",
|
||
"L 825 1625 \n",
|
||
"L 2419 1625 \n",
|
||
"L 2419 4116 \n",
|
||
"z\n",
|
||
"M 2253 4666 \n",
|
||
"L 3047 4666 \n",
|
||
"L 3047 1625 \n",
|
||
"L 3713 1625 \n",
|
||
"L 3713 1100 \n",
|
||
"L 3047 1100 \n",
|
||
"L 3047 0 \n",
|
||
"L 2419 0 \n",
|
||
"L 2419 1100 \n",
|
||
"L 313 1100 \n",
|
||
"L 313 1709 \n",
|
||
"L 2253 4666 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-34\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_4\">\n",
|
||
" <g id=\"line2d_6\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m473666877a\" x=\"34.240625\" y=\"79.74\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_7\">\n",
|
||
" <!-- 6 -->\n",
|
||
" <g transform=\"translate(20.878125 83.539219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-36\" d=\"M 2113 2584 \n",
|
||
"Q 1688 2584 1439 2293 \n",
|
||
"Q 1191 2003 1191 1497 \n",
|
||
"Q 1191 994 1439 701 \n",
|
||
"Q 1688 409 2113 409 \n",
|
||
"Q 2538 409 2786 701 \n",
|
||
"Q 3034 994 3034 1497 \n",
|
||
"Q 3034 2003 2786 2293 \n",
|
||
"Q 2538 2584 2113 2584 \n",
|
||
"z\n",
|
||
"M 3366 4563 \n",
|
||
"L 3366 3988 \n",
|
||
"Q 3128 4100 2886 4159 \n",
|
||
"Q 2644 4219 2406 4219 \n",
|
||
"Q 1781 4219 1451 3797 \n",
|
||
"Q 1122 3375 1075 2522 \n",
|
||
"Q 1259 2794 1537 2939 \n",
|
||
"Q 1816 3084 2150 3084 \n",
|
||
"Q 2853 3084 3261 2657 \n",
|
||
"Q 3669 2231 3669 1497 \n",
|
||
"Q 3669 778 3244 343 \n",
|
||
"Q 2819 -91 2113 -91 \n",
|
||
"Q 1303 -91 875 529 \n",
|
||
"Q 447 1150 447 2328 \n",
|
||
"Q 447 3434 972 4092 \n",
|
||
"Q 1497 4750 2381 4750 \n",
|
||
"Q 2619 4750 2861 4703 \n",
|
||
"Q 3103 4656 3366 4563 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-36\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_5\">\n",
|
||
" <g id=\"line2d_7\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m473666877a\" x=\"34.240625\" y=\"102.06\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_8\">\n",
|
||
" <!-- 8 -->\n",
|
||
" <g transform=\"translate(20.878125 105.859219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-38\" d=\"M 2034 2216 \n",
|
||
"Q 1584 2216 1326 1975 \n",
|
||
"Q 1069 1734 1069 1313 \n",
|
||
"Q 1069 891 1326 650 \n",
|
||
"Q 1584 409 2034 409 \n",
|
||
"Q 2484 409 2743 651 \n",
|
||
"Q 3003 894 3003 1313 \n",
|
||
"Q 3003 1734 2745 1975 \n",
|
||
"Q 2488 2216 2034 2216 \n",
|
||
"z\n",
|
||
"M 1403 2484 \n",
|
||
"Q 997 2584 770 2862 \n",
|
||
"Q 544 3141 544 3541 \n",
|
||
"Q 544 4100 942 4425 \n",
|
||
"Q 1341 4750 2034 4750 \n",
|
||
"Q 2731 4750 3128 4425 \n",
|
||
"Q 3525 4100 3525 3541 \n",
|
||
"Q 3525 3141 3298 2862 \n",
|
||
"Q 3072 2584 2669 2484 \n",
|
||
"Q 3125 2378 3379 2068 \n",
|
||
"Q 3634 1759 3634 1313 \n",
|
||
"Q 3634 634 3220 271 \n",
|
||
"Q 2806 -91 2034 -91 \n",
|
||
"Q 1263 -91 848 271 \n",
|
||
"Q 434 634 434 1313 \n",
|
||
"Q 434 1759 690 2068 \n",
|
||
"Q 947 2378 1403 2484 \n",
|
||
"z\n",
|
||
"M 1172 3481 \n",
|
||
"Q 1172 3119 1398 2916 \n",
|
||
"Q 1625 2713 2034 2713 \n",
|
||
"Q 2441 2713 2670 2916 \n",
|
||
"Q 2900 3119 2900 3481 \n",
|
||
"Q 2900 3844 2670 4047 \n",
|
||
"Q 2441 4250 2034 4250 \n",
|
||
"Q 1625 4250 1398 4047 \n",
|
||
"Q 1172 3844 1172 3481 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-38\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_9\">\n",
|
||
" <!-- Queries -->\n",
|
||
" <g transform=\"translate(14.798437 82.307031)rotate(-90)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-51\" d=\"M 2522 4238 \n",
|
||
"Q 1834 4238 1429 3725 \n",
|
||
"Q 1025 3213 1025 2328 \n",
|
||
"Q 1025 1447 1429 934 \n",
|
||
"Q 1834 422 2522 422 \n",
|
||
"Q 3209 422 3611 934 \n",
|
||
"Q 4013 1447 4013 2328 \n",
|
||
"Q 4013 3213 3611 3725 \n",
|
||
"Q 3209 4238 2522 4238 \n",
|
||
"z\n",
|
||
"M 3406 84 \n",
|
||
"L 4238 -825 \n",
|
||
"L 3475 -825 \n",
|
||
"L 2784 -78 \n",
|
||
"Q 2681 -84 2626 -87 \n",
|
||
"Q 2572 -91 2522 -91 \n",
|
||
"Q 1538 -91 948 567 \n",
|
||
"Q 359 1225 359 2328 \n",
|
||
"Q 359 3434 948 4092 \n",
|
||
"Q 1538 4750 2522 4750 \n",
|
||
"Q 3503 4750 4090 4092 \n",
|
||
"Q 4678 3434 4678 2328 \n",
|
||
"Q 4678 1516 4351 937 \n",
|
||
"Q 4025 359 3406 84 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-75\" d=\"M 544 1381 \n",
|
||
"L 544 3500 \n",
|
||
"L 1119 3500 \n",
|
||
"L 1119 1403 \n",
|
||
"Q 1119 906 1312 657 \n",
|
||
"Q 1506 409 1894 409 \n",
|
||
"Q 2359 409 2629 706 \n",
|
||
"Q 2900 1003 2900 1516 \n",
|
||
"L 2900 3500 \n",
|
||
"L 3475 3500 \n",
|
||
"L 3475 0 \n",
|
||
"L 2900 0 \n",
|
||
"L 2900 538 \n",
|
||
"Q 2691 219 2414 64 \n",
|
||
"Q 2138 -91 1772 -91 \n",
|
||
"Q 1169 -91 856 284 \n",
|
||
"Q 544 659 544 1381 \n",
|
||
"z\n",
|
||
"M 1991 3584 \n",
|
||
"L 1991 3584 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-72\" d=\"M 2631 2963 \n",
|
||
"Q 2534 3019 2420 3045 \n",
|
||
"Q 2306 3072 2169 3072 \n",
|
||
"Q 1681 3072 1420 2755 \n",
|
||
"Q 1159 2438 1159 1844 \n",
|
||
"L 1159 0 \n",
|
||
"L 581 0 \n",
|
||
"L 581 3500 \n",
|
||
"L 1159 3500 \n",
|
||
"L 1159 2956 \n",
|
||
"Q 1341 3275 1631 3429 \n",
|
||
"Q 1922 3584 2338 3584 \n",
|
||
"Q 2397 3584 2469 3576 \n",
|
||
"Q 2541 3569 2628 3553 \n",
|
||
"L 2631 2963 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" <path id=\"DejaVuSans-69\" d=\"M 603 3500 \n",
|
||
"L 1178 3500 \n",
|
||
"L 1178 0 \n",
|
||
"L 603 0 \n",
|
||
"L 603 3500 \n",
|
||
"z\n",
|
||
"M 603 4863 \n",
|
||
"L 1178 4863 \n",
|
||
"L 1178 4134 \n",
|
||
"L 603 4134 \n",
|
||
"L 603 4863 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-51\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-75\" x=\"78.710938\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-65\" x=\"142.089844\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-72\" x=\"203.613281\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-69\" x=\"244.726562\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-65\" x=\"272.509766\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-73\" x=\"334.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"patch_3\">\n",
|
||
" <path d=\"M 34.240625 118.8 \n",
|
||
"L 34.240625 7.2 \n",
|
||
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"patch_4\">\n",
|
||
" <path d=\"M 145.840625 118.8 \n",
|
||
"L 145.840625 7.2 \n",
|
||
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"patch_5\">\n",
|
||
" <path d=\"M 34.240625 118.8 \n",
|
||
"L 145.840625 118.8 \n",
|
||
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"patch_6\">\n",
|
||
" <path d=\"M 34.240625 7.2 \n",
|
||
"L 145.840625 7.2 \n",
|
||
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"axes_2\">\n",
|
||
" <g id=\"patch_7\">\n",
|
||
" <path d=\"M 152.815625 103.77 \n",
|
||
"L 156.892625 103.77 \n",
|
||
"L 156.892625 22.23 \n",
|
||
"L 152.815625 22.23 \n",
|
||
"z\n",
|
||
"\" style=\"fill: #ffffff\"/>\n",
|
||
" </g>\n",
|
||
" <g id=\"patch_8\">\n",
|
||
" <path clip-path=\"url(#p81ac4143b7)\" style=\"fill: #ffffff; stroke: #ffffff; stroke-width: 0.01; stroke-linejoin: miter\"/>\n",
|
||
" </g>\n",
|
||
" <image xlink:href=\"data:image/png;base64,\n",
|
||
"iVBORw0KGgoAAAANSUhEUgAAAAQAAABRCAYAAAD1sgc6AAAAnklEQVR4nJ2Suw7CQAwEjZT//1QqCnR+0XKzJxmSLqPx7krJo1/Ptq/nsgzbQRVBDqBH4wCkhTtkWDhqR8OSIHjii6H/Z2jtaLD2EDpm3DCkNvldftgB0GJIqM/TBfAfE+AAJcaSpZJRg1Fs0QyCjN5BRA0gkycEmTyRFhox7simsb/blSbGDWCDcdgB4MxwGu8CWAJ4shgqJ9IiBms/jwXJt9gA8G4AAAAASUVORK5CYII=\" id=\"image52587ed27e\" transform=\"scale(1 -1)translate(0 -81)\" x=\"153\" y=\"-22\" width=\"4\" height=\"81\"/>\n",
|
||
" <g id=\"matplotlib.axis_3\">\n",
|
||
" <g id=\"ytick_6\">\n",
|
||
" <g id=\"line2d_8\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"m4194a474b4\" d=\"M 0 0 \n",
|
||
"L 3.5 0 \n",
|
||
"\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </defs>\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m4194a474b4\" x=\"156.892625\" y=\"103.77\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_10\">\n",
|
||
" <!-- 0.00 -->\n",
|
||
" <g transform=\"translate(163.892625 107.569219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-2e\" d=\"M 684 794 \n",
|
||
"L 1344 794 \n",
|
||
"L 1344 0 \n",
|
||
"L 684 0 \n",
|
||
"L 684 794 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\" x=\"95.410156\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_7\">\n",
|
||
" <g id=\"line2d_9\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m4194a474b4\" x=\"156.892625\" y=\"83.385\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_11\">\n",
|
||
" <!-- 0.25 -->\n",
|
||
" <g transform=\"translate(163.892625 87.184219)scale(0.1 -0.1)\">\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-32\" x=\"95.410156\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-35\" x=\"159.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_8\">\n",
|
||
" <g id=\"line2d_10\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m4194a474b4\" x=\"156.892625\" y=\"63\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_12\">\n",
|
||
" <!-- 0.50 -->\n",
|
||
" <g transform=\"translate(163.892625 66.799219)scale(0.1 -0.1)\">\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-35\" x=\"95.410156\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_9\">\n",
|
||
" <g id=\"line2d_11\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m4194a474b4\" x=\"156.892625\" y=\"42.615\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_13\">\n",
|
||
" <!-- 0.75 -->\n",
|
||
" <g transform=\"translate(163.892625 46.414219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-37\" d=\"M 525 4666 \n",
|
||
"L 3525 4666 \n",
|
||
"L 3525 4397 \n",
|
||
"L 1831 0 \n",
|
||
"L 1172 0 \n",
|
||
"L 2766 4134 \n",
|
||
"L 525 4134 \n",
|
||
"L 525 4666 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-37\" x=\"95.410156\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-35\" x=\"159.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"ytick_10\">\n",
|
||
" <g id=\"line2d_12\">\n",
|
||
" <g>\n",
|
||
" <use xlink:href=\"#m4194a474b4\" x=\"156.892625\" y=\"22.23\" style=\"stroke: #000000; stroke-width: 0.8\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"text_14\">\n",
|
||
" <!-- 1.00 -->\n",
|
||
" <g transform=\"translate(163.892625 26.029219)scale(0.1 -0.1)\">\n",
|
||
" <defs>\n",
|
||
" <path id=\"DejaVuSans-31\" d=\"M 794 531 \n",
|
||
"L 1825 531 \n",
|
||
"L 1825 4091 \n",
|
||
"L 703 3866 \n",
|
||
"L 703 4441 \n",
|
||
"L 1819 4666 \n",
|
||
"L 2450 4666 \n",
|
||
"L 2450 531 \n",
|
||
"L 3481 531 \n",
|
||
"L 3481 0 \n",
|
||
"L 794 0 \n",
|
||
"L 794 531 \n",
|
||
"z\n",
|
||
"\" transform=\"scale(0.015625)\"/>\n",
|
||
" </defs>\n",
|
||
" <use xlink:href=\"#DejaVuSans-31\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-2e\" x=\"63.623047\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\" x=\"95.410156\"/>\n",
|
||
" <use xlink:href=\"#DejaVuSans-30\" x=\"159.033203\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <g id=\"LineCollection_1\"/>\n",
|
||
" <g id=\"patch_9\">\n",
|
||
" <path d=\"M 152.815625 103.77 \n",
|
||
"L 154.854125 103.77 \n",
|
||
"L 156.892625 103.77 \n",
|
||
"L 156.892625 22.23 \n",
|
||
"L 154.854125 22.23 \n",
|
||
"L 152.815625 22.23 \n",
|
||
"L 152.815625 103.77 \n",
|
||
"z\n",
|
||
"\" style=\"fill: none; stroke: #000000; stroke-width: 0.8; stroke-linejoin: miter; stroke-linecap: square\"/>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" </g>\n",
|
||
" <defs>\n",
|
||
" <clipPath id=\"p3a36c213e6\">\n",
|
||
" <rect x=\"34.240625\" y=\"7.2\" width=\"111.6\" height=\"111.6\"/>\n",
|
||
" </clipPath>\n",
|
||
" <clipPath id=\"p81ac4143b7\">\n",
|
||
" <rect x=\"152.815625\" y=\"22.23\" width=\"4.077\" height=\"81.54\"/>\n",
|
||
" </clipPath>\n",
|
||
" </defs>\n",
|
||
"</svg>\n"
|
||
],
|
||
"text/plain": [
|
||
"<Figure size 180x180 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"needs_background": "light"
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"attention_weights = torch.eye(10).reshape((1, 1, 10, 10))\n",
|
||
"show_heatmaps(attention_weights, xlabel='Keys', ylabel='Queries')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0f6c23cb",
|
||
"metadata": {
|
||
"origin_pos": 9
|
||
},
|
||
"source": [
|
||
"后面的章节内容将经常调用`show_heatmaps`函数来显示注意力权重。\n",
|
||
"\n",
|
||
"## 小结\n",
|
||
"\n",
|
||
"* 人类的注意力是有限的、有价值和稀缺的资源。\n",
|
||
"* 受试者使用非自主性和自主性提示有选择性地引导注意力。前者基于突出性,后者则依赖于意识。\n",
|
||
"* 注意力机制与全连接层或者汇聚层的区别源于增加的自主提示。\n",
|
||
"* 由于包含了自主性提示,注意力机制与全连接的层或汇聚层不同。\n",
|
||
"* 注意力机制通过注意力汇聚使选择偏向于值(感官输入),其中包含查询(自主性提示)和键(非自主性提示)。键和值是成对的。\n",
|
||
"* 可视化查询和键之间的注意力权重是可行的。\n",
|
||
"\n",
|
||
"## 练习\n",
|
||
"\n",
|
||
"1. 在机器翻译中通过解码序列词元时,其自主性提示可能是什么?非自主性提示和感官输入又是什么?\n",
|
||
"1. 随机生成一个$10 \\times 10$矩阵并使用`softmax`运算来确保每行都是有效的概率分布,然后可视化输出注意力权重。\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "675bab48",
|
||
"metadata": {
|
||
"origin_pos": 11,
|
||
"tab": [
|
||
"pytorch"
|
||
]
|
||
},
|
||
"source": [
|
||
"[Discussions](https://discuss.d2l.ai/t/5764)\n"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"name": "python"
|
||
},
|
||
"required_libs": []
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |