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{
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"# 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",
"![由于突出性的非自主性提示（红杯子），注意力不自主地指向了咖啡杯](../img/eye-coffee.svg)\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",
"![依赖于任务的意志提示（想读一本书），注意力被自主引导到书上](../img/eye-book.svg)\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",
"![注意力机制通过注意力汇聚将*查询*（自主性提示）和*键*（非自主性提示）结合在一起，实现对*值*（感官输入）的选择倾向](../img/qkv.svg)\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"
]
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"id": "58a7898f",
"metadata": {
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"source": [
"import torch\n",
"from d2l import torch as d2l"
]
},
{
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"id": "6e9e92fc",
"metadata": {
"origin_pos": 5
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"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": {
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"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);"
]
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"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"
]
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"attention_weights = torch.eye(10).reshape((1, 1, 10, 10))\n",
"show_heatmaps(attention_weights, xlabel='Keys', ylabel='Queries')"
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"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"
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{
"cells": [
{
"cell_type": "markdown",
"id": "e2119702",
"metadata": {
"origin_pos": 0
},
"source": [
"# 注意力机制\n",
":label:`chap_attention`\n",
"\n",
"灵长类动物的视觉系统接受了大量的感官输入，\n",
"这些感官输入远远超过了大脑能够完全处理的程度。\n",
"然而，并非所有刺激的影响都是相等的。\n",
"意识的聚集和专注使灵长类动物能够在复杂的视觉环境中将注意力引向感兴趣的物体，例如猎物和天敌。\n",
"只关注一小部分信息的能力对进化更加有意义，使人类得以生存和成功。\n",
"\n",
"自19世纪以来，科学家们一直致力于研究认知神经科学领域的注意力。\n",
"本章的很多章节将涉及到一些研究。\n",
"\n",
"首先回顾一个经典注意力框架，解释如何在视觉场景中展开注意力。\n",
"受此框架中的*注意力提示*（attention cues）的启发，\n",
"我们将设计能够利用这些注意力提示的模型。\n",
"1964年的Nadaraya-Waston核回归（kernel regression）正是具有\n",
"*注意力机制*（attention mechanism）的机器学习的简单演示。\n",
"\n",
"然后继续介绍的是注意力函数，它们在深度学习的注意力模型设计中被广泛使用。\n",
"具体来说，我们将展示如何使用这些函数来设计*Bahdanau注意力*。\n",
"Bahdanau注意力是深度学习中的具有突破性价值的注意力模型，它双向对齐并且可以微分。\n",
"\n",
"最后将描述仅仅基于注意力机制的*Transformer*架构，\n",
"该架构中使用了*多头注意力*（multi-head attention）\n",
"和*自注意力*（self-attention）。\n",
"自2017年横空出世，Transformer一直都普遍存在于现代的深度学习应用中，\n",
"例如语言、视觉、语音和强化学习领域。\n",
"\n",
":begin_tab:toc\n",
" - [attention-cues](attention-cues.ipynb)\n",
" - [nadaraya-waston](nadaraya-waston.ipynb)\n",
" - [attention-scoring-functions](attention-scoring-functions.ipynb)\n",
" - [bahdanau-attention](bahdanau-attention.ipynb)\n",
" - [multihead-attention](multihead-attention.ipynb)\n",
" - [self-attention-and-positional-encoding](self-attention-and-positional-encoding.ipynb)\n",
" - [transformer](transformer.ipynb)\n",
":end_tab:\n"
]
}
],
"metadata": {
"language_info": {
"name": "python"
},
"required_libs": []
},
"nbformat": 4,
"nbformat_minor": 5
}
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{
"cells": [
{
"cell_type": "markdown",
"id": "36341c1f",
"metadata": {
"origin_pos": 0
},
"source": [
"# 多头注意力\n",
":label:`sec_multihead-attention`\n",
"\n",
"在实践中，当给定相同的查询、键和值的集合时，\n",
"我们希望模型可以基于相同的注意力机制学习到不同的行为，\n",
"然后将不同的行为作为知识组合起来，\n",
"捕获序列内各种范围的依赖关系\n",
"（例如，短距离依赖和长距离依赖关系）。\n",
"因此，允许注意力机制组合使用查询、键和值的不同\n",
"*子空间表示*（representation subspaces）可能是有益的。\n",
"\n",
"为此，与其只使用单独一个注意力汇聚，\n",
"我们可以用独立学习得到的$h$组不同的\n",
"*线性投影*（linear projections）来变换查询、键和值。\n",
"然后，这$h$组变换后的查询、键和值将并行地送到注意力汇聚中。\n",
"最后，将这$h$个注意力汇聚的输出拼接在一起，\n",
"并且通过另一个可以学习的线性投影进行变换，\n",
"以产生最终输出。\n",
"这种设计被称为*多头注意力*（multihead attention）\n",
" :cite:`Vaswani.Shazeer.Parmar.ea.2017`。\n",
"对于$h$个注意力汇聚输出，每一个注意力汇聚都被称作一个*头*（head）。\n",
" :numref:`fig_multi-head-attention`\n",
"展示了使用全连接层来实现可学习的线性变换的多头注意力。\n",
"\n",
"![多头注意力：多个头连结然后线性变换](../img/multi-head-attention.svg)\n",
":label:`fig_multi-head-attention`\n",
"\n",
"## 模型\n",
"\n",
"在实现多头注意力之前，让我们用数学语言将这个模型形式化地描述出来。\n",
"给定查询$\\mathbf{q} \\in \\mathbb{R}^{d_q}$、\n",
"键$\\mathbf{k} \\in \\mathbb{R}^{d_k}$和\n",
"值$\\mathbf{v} \\in \\mathbb{R}^{d_v}$，\n",
"每个注意力头$\\mathbf{h}_i$（$i = 1, \\ldots, h$）的计算方法为：\n",
"\n",
"$$\\mathbf{h}_i = f(\\mathbf W_i^{(q)}\\mathbf q, \\mathbf W_i^{(k)}\\mathbf k,\\mathbf W_i^{(v)}\\mathbf v) \\in \\mathbb R^{p_v},$$\n",
"\n",
"其中，可学习的参数包括\n",
"$\\mathbf W_i^{(q)}\\in\\mathbb R^{p_q\\times d_q}$、\n",
"$\\mathbf W_i^{(k)}\\in\\mathbb R^{p_k\\times d_k}$和\n",
"$\\mathbf W_i^{(v)}\\in\\mathbb R^{p_v\\times d_v}$，\n",
"以及代表注意力汇聚的函数$f$。\n",
"$f$可以是 :numref:`sec_attention-scoring-functions`中的\n",
"加性注意力和缩放点积注意力。\n",
"多头注意力的输出需要经过另一个线性转换，\n",
"它对应着$h$个头连结后的结果，因此其可学习参数是\n",
"$\\mathbf W_o\\in\\mathbb R^{p_o\\times h p_v}$：\n",
"\n",
"$$\\mathbf W_o \\begin{bmatrix}\\mathbf h_1\\\\\\vdots\\\\\\mathbf h_h\\end{bmatrix} \\in \\mathbb{R}^{p_o}.$$\n",
"\n",
"基于这种设计，每个头都可能会关注输入的不同部分，\n",
"可以表示比简单加权平均值更复杂的函数。\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "dc55ba33",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:01:32.189972Z",
"iopub.status.busy": "2023-08-18T07:01:32.189240Z",
"iopub.status.idle": "2023-08-18T07:01:34.516491Z",
"shell.execute_reply": "2023-08-18T07:01:34.515475Z"
},
"origin_pos": 2,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"import math\n",
"import torch\n",
"from torch import nn\n",
"from d2l import torch as d2l"
]
},
{
"cell_type": "markdown",
"id": "b51ca181",
"metadata": {
"origin_pos": 5
},
"source": [
"## 实现\n",
"\n",
"在实现过程中通常[**选择缩放点积注意力作为每一个注意力头**]。\n",
"为了避免计算代价和参数代价的大幅增长，\n",
"我们设定$p_q = p_k = p_v = p_o / h$。\n",
"值得注意的是，如果将查询、键和值的线性变换的输出数量设置为\n",
"$p_q h = p_k h = p_v h = p_o$，\n",
"则可以并行计算$h$个头。\n",
"在下面的实现中，$p_o$是通过参数`num_hiddens`指定的。\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1bb10990",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:01:34.521491Z",
"iopub.status.busy": "2023-08-18T07:01:34.521131Z",
"iopub.status.idle": "2023-08-18T07:01:34.530492Z",
"shell.execute_reply": "2023-08-18T07:01:34.529556Z"
},
"origin_pos": 7,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"#@save\n",
"class MultiHeadAttention(nn.Module):\n",
" \"\"\"多头注意力\"\"\"\n",
" def __init__(self, key_size, query_size, value_size, num_hiddens,\n",
" num_heads, dropout, bias=False, **kwargs):\n",
" super(MultiHeadAttention, self).__init__(**kwargs)\n",
" self.num_heads = num_heads\n",
" self.attention = d2l.DotProductAttention(dropout)\n",
" self.W_q = nn.Linear(query_size, num_hiddens, bias=bias)\n",
" self.W_k = nn.Linear(key_size, num_hiddens, bias=bias)\n",
" self.W_v = nn.Linear(value_size, num_hiddens, bias=bias)\n",
" self.W_o = nn.Linear(num_hiddens, num_hiddens, bias=bias)\n",
"\n",
" def forward(self, queries, keys, values, valid_lens):\n",
" # queries，keys，values的形状:\n",
" # (batch_size，查询或者“键－值”对的个数，num_hiddens)\n",
" # valid_lens　的形状:\n",
" # (batch_size，)或(batch_size，查询的个数)\n",
" # 经过变换后，输出的queries，keys，values　的形状:\n",
" # (batch_size*num_heads，查询或者“键－值”对的个数，\n",
" # num_hiddens/num_heads)\n",
" queries = transpose_qkv(self.W_q(queries), self.num_heads)\n",
" keys = transpose_qkv(self.W_k(keys), self.num_heads)\n",
" values = transpose_qkv(self.W_v(values), self.num_heads)\n",
"\n",
" if valid_lens is not None:\n",
" # 在轴0，将第一项（标量或者矢量）复制num_heads次，\n",
" # 然后如此复制第二项，然后诸如此类。\n",
" valid_lens = torch.repeat_interleave(\n",
" valid_lens, repeats=self.num_heads, dim=0)\n",
"\n",
" # output的形状:(batch_size*num_heads，查询的个数，\n",
" # num_hiddens/num_heads)\n",
" output = self.attention(queries, keys, values, valid_lens)\n",
"\n",
" # output_concat的形状:(batch_size，查询的个数，num_hiddens)\n",
" output_concat = transpose_output(output, self.num_heads)\n",
" return self.W_o(output_concat)"
]
},
{
"cell_type": "markdown",
"id": "9ab1c33b",
"metadata": {
"origin_pos": 10
},
"source": [
"为了能够[**使多个头并行计算**]，\n",
"上面的`MultiHeadAttention`类将使用下面定义的两个转置函数。\n",
"具体来说，`transpose_output`函数反转了`transpose_qkv`函数的操作。\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b2af5ed8",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:01:34.534820Z",
"iopub.status.busy": "2023-08-18T07:01:34.534308Z",
"iopub.status.idle": "2023-08-18T07:01:34.540852Z",
"shell.execute_reply": "2023-08-18T07:01:34.539927Z"
},
"origin_pos": 12,
"tab": [
"pytorch"
]
},
"outputs": [],
"source": [
"#@save\n",
"def transpose_qkv(X, num_heads):\n",
" \"\"\"为了多注意力头的并行计算而变换形状\"\"\"\n",
" # 输入X的形状:(batch_size，查询或者“键－值”对的个数，num_hiddens)\n",
" # 输出X的形状:(batch_size，查询或者“键－值”对的个数，num_heads，\n",
" # num_hiddens/num_heads)\n",
" X = X.reshape(X.shape[0], X.shape[1], num_heads, -1)\n",
"\n",
" # 输出X的形状:(batch_size，num_heads，查询或者“键－值”对的个数,\n",
" # num_hiddens/num_heads)\n",
" X = X.permute(0, 2, 1, 3)\n",
"\n",
" # 最终输出的形状:(batch_size*num_heads,查询或者“键－值”对的个数,\n",
" # num_hiddens/num_heads)\n",
" return X.reshape(-1, X.shape[2], X.shape[3])\n",
"\n",
"\n",
"#@save\n",
"def transpose_output(X, num_heads):\n",
" \"\"\"逆转transpose_qkv函数的操作\"\"\"\n",
" X = X.reshape(-1, num_heads, X.shape[1], X.shape[2])\n",
" X = X.permute(0, 2, 1, 3)\n",
" return X.reshape(X.shape[0], X.shape[1], -1)"
]
},
{
"cell_type": "markdown",
"id": "0e31b376",
"metadata": {
"origin_pos": 15
},
"source": [
"下面使用键和值相同的小例子来[**测试**]我们编写的`MultiHeadAttention`类。\n",
"多头注意力输出的形状是（`batch_size`，`num_queries`，`num_hiddens`）。\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d06baadf",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:01:34.545405Z",
"iopub.status.busy": "2023-08-18T07:01:34.544605Z",
"iopub.status.idle": "2023-08-18T07:01:34.571251Z",
"shell.execute_reply": "2023-08-18T07:01:34.570476Z"
},
"origin_pos": 17,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"text/plain": [
"MultiHeadAttention(\n",
" (attention): DotProductAttention(\n",
" (dropout): Dropout(p=0.5, inplace=False)\n",
" )\n",
" (W_q): Linear(in_features=100, out_features=100, bias=False)\n",
" (W_k): Linear(in_features=100, out_features=100, bias=False)\n",
" (W_v): Linear(in_features=100, out_features=100, bias=False)\n",
" (W_o): Linear(in_features=100, out_features=100, bias=False)\n",
")"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"num_hiddens, num_heads = 100, 5\n",
"attention = MultiHeadAttention(num_hiddens, num_hiddens, num_hiddens,\n",
" num_hiddens, num_heads, 0.5)\n",
"attention.eval()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8da65afc",
"metadata": {
"execution": {
"iopub.execute_input": "2023-08-18T07:01:34.574642Z",
"iopub.status.busy": "2023-08-18T07:01:34.574021Z",
"iopub.status.idle": "2023-08-18T07:01:34.588848Z",
"shell.execute_reply": "2023-08-18T07:01:34.587945Z"
},
"origin_pos": 20,
"tab": [
"pytorch"
]
},
"outputs": [
{
"data": {
"text/plain": [
"torch.Size([2, 4, 100])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"batch_size, num_queries = 2, 4\n",
"num_kvpairs, valid_lens = 6, torch.tensor([3, 2])\n",
"X = torch.ones((batch_size, num_queries, num_hiddens))\n",
"Y = torch.ones((batch_size, num_kvpairs, num_hiddens))\n",
"attention(X, Y, Y, valid_lens).shape"
]
},
{
"cell_type": "markdown",
"id": "c228d916",
"metadata": {
"origin_pos": 22
},
"source": [
"## 小结\n",
"\n",
"* 多头注意力融合了来自于多个注意力汇聚的不同知识，这些知识的不同来源于相同的查询、键和值的不同的子空间表示。\n",
"* 基于适当的张量操作，可以实现多头注意力的并行计算。\n",
"\n",
"## 练习\n",
"\n",
"1. 分别可视化这个实验中的多个头的注意力权重。\n",
"1. 假设有一个完成训练的基于多头注意力的模型，现在希望修剪最不重要的注意力头以提高预测速度。如何设计实验来衡量注意力头的重要性呢？\n"
]
},
{
"cell_type": "markdown",
"id": "bfae5c77",
"metadata": {
"origin_pos": 24,
"tab": [
"pytorch"
]
},
"source": [
"[Discussions](https://discuss.d2l.ai/t/5758)\n"
]
}
],
"metadata": {
"language_info": {
"name": "python"
},
"required_libs": []
},
"nbformat": 4,
"nbformat_minor": 5
}
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