rnn.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recurrent Neural Network"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RNN（Recurrent Neural Network, 再帰型ニューラルネットワーク）\n",
    "\n",
    "![](https://cdn-ak.f.st-hatena.com/images/fotolife/n/nkdkccmbr/20161006/20161006221349.png)  \n",
    "RNNのイメージ 出典：[３層パーセプトロン -- ニューラルネットワーク・DeepLearningなどの画像素材　プレゼン・ゼミなどに【WTFPL】](https://nkdkccmbr.hateblo.jp/entry/2016/10/06/222245)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "# packageのimport\n",
    "from typing import Any, Union, Callable, Type, TypeVar\n",
    "from tqdm.std import trange,tqdm\n",
    "import numpy as np \n",
    "import numpy.typing as npt\n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt \n",
    "import plotly.express as px\n",
    "import seaborn as sns\n",
    "plt.style.use(\"bmh\")\n",
    "\n",
    "# pytorch関連のimport\n",
    "import torch\n",
    "import torch.nn as nn \n",
    "import torch.nn.functional as F \n",
    "import torch.optim as optim \n",
    "from torch.utils.data import Dataset, DataLoader"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## RNNとは"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RNNのイメージと再帰構造"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RNNとは，時系列構造をもつデータをニューラルネットワークでうまく扱うことができる枠組みです．RNNというとネットワークの中に閉路があるだけでそれだと認識されるので，順伝搬において信号の伝搬路の中にループがあれば全てRNNと言われます．ここでは以下のようなネットワーク（エルマン型）を紹介します．  \n",
    "\n",
    "> ![](https://www.acceluniverse.com/blog/developers/LSimage_2.png)\n",
    "RNNのイメージ  \n",
    "出典：[Long Short-Term Memory](http://axon.cs.byu.edu/~martinez/classes/778/Papers/lstm.pdf)\n",
    "\n",
    "※$x$の添字が0からスタートするか1からスタートするのかについてはあまり頓着せずに，左の図を展開すると右になることに納得してほしいです．\n",
    "\n",
    "\n",
    "時系列データ$\\mathbf{x}=( x_1,x_2, \\cdots,x_t, \\cdots, x_{T} ) \\in \\mathbb{R}^T$が与えられた時，$x_t$までの情報を使って$x_{t+1}$を予測したい場合や，$\\mathbf{x}$に対応した別の時系列データ$\\mathbf{y}$を予測したい場合などが考えられます．\n",
    "\n",
    "「$x_{t-1}$までの情報を使って$o_{t}$を予測したい場合」，これまでの情報$x_1 \\cdots x_t$を通常のMLPでうまく扱うことは難しいです．そこで，RNNでは$t-1$時点のMLPの中間層の出力を$t$時点のMLPの入力に利用します．__RNNでは単位時間ごとのMLPは全てパラメータを共有しており__，これまでと異なるのは$h_t$時点の隠れ層出力が$(x_{t}\\cdot {W^{(x,h)}}^{\\top} + h_{t-1}\\cdot W^{(h,h)}+b)$として次の隠れ層の入力となることだけです．\n",
    "\n",
    "![](./figs/rnn/elman_arch_x0.png)\n",
    "\n",
    "つまり$h_t$は活性化関数がtanhの時，以下のようにして求められます：\n",
    "\n",
    "$$\n",
    "h_{t} := \\operatorname{tanh}(x_{t}\\cdot {W^{(x,h)}}^{\\top} + h_{t-1}\\cdot W^{(h,h)}+b)\n",
    "$$\n",
    "\n",
    "ただし，$h_0$にはゼロ行列を使います．  \n",
    "また，ここで使われているtanhをはじめとした双曲線関数 $\\sinh$ （ハイパボリックサイン）, $\\cosh$（ハイパボリックコサイン）,$\\tanh$（ハイパボリックタンジェント） は以下の式で定義されます：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sinh x & =\\frac{e^x-e^{-x}}{2} \\\\\n",
    "\\cosh x & =\\frac{e^x+e^{-x}}{2} \\\\\n",
    "\\tanh x & =\\frac{\\sinh x}{\\cosh x}=\\frac{e^x-e^{-x}}{e^x+e^{-x}}\n",
    "\\end{aligned}\n",
    "$$\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "特にtanhに着目すると，これはsigmoid関数に非常によく似た形になっている（取り得る範囲が0~1と-1~1の違い）ことがわかります．そのため，ニューラルネットワークの実装ではsigmoidの代わりにtanhを利用することもよくあります．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "x = np.linspace(-2,2,100)\n",
    "plt.plot(x,np.sinh(x), label=\"sinh\")\n",
    "plt.plot(x,np.cosh(x), label=\"cosh\")\n",
    "plt.plot(x,np.tanh(x), label=\"tanh\")\n",
    "plt.legend()\n",
    "plt.title(\"hyperbolic functions\")\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "x = np.linspace(-10,10,100)\n",
    "plt.plot(x,np.tanh(x), label=\"tanh\")\n",
    "plt.plot(x, (lambda x: 1/(1+np.exp(-x)))(x), label=\"sigmoid\")\n",
    "plt.legend()\n",
    "plt.title(\"Hyperbolic tangent & Logistic sigmoid\")\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### フォワードプロパゲーションの流れ"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上述した通り，ここで紹介するRNNでは時間方向の影響をモデル化した隠れ層を利用しています．これを使ったRNNフォワードプロパゲーションの全体像を見ておきましょう．$f$と$g$は任意の活性化関数です．\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&\\text{input layer: } \\quad  x_t \\\\\n",
    "&\\text{hidden layer:} \\quad h_{t} = \\operatorname{f}(x_{t}\\cdot {W^{(x,h)}} + h_{t-1}\\cdot W^{(h,h)}+b^{x,h}) \\\\\n",
    "&\\text{output layer:} \\quad o_{t} = \\operatorname{g}(h_t \\cdot W^{(h,o)}+b^{(h,o)})\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    ":::{hint}\n",
    "\n",
    "例えば文書生成などがRNNを使う例として考えられます．入力データとして，ある文書に登場する単語一つ一つを$x_1,x_2,\\cdots,x_{T-1}$として入力して，それぞれの出力を$\\hat{x_2},\\hat{x_3},\\cdots, \\hat{x_T}$としましょう．この時出力値はそれぞれ「入力された単語の次に出現する単語」に相当します．\n",
    "\n",
    ":::"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "（以下は疑似コードの形の方が理解しやすい人向け）"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RNNの疑似コード {prf:ref}`rnn-forward-prop`を作るために，以下の様に定義します．\n",
    "\n",
    "- $M$: バッチサイズ\n",
    "- $T$: 時間\n",
    "- $K$: 特徴数\n",
    "- $C$: クラス数\n",
    "- $H$: 隠れ層の次元数\n",
    "\n",
    "\n",
    "また，$\\operatorname{softmax}$は最もネストの深い軸（axis=-1）を基準に計算しているとします．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "::::{prf:algorithm} Forward propagation of RNN\n",
    ":label: rnn-forward-prop\n",
    "\n",
    "**Input:** $\\mathbf{X} \\in \\mathbb{R}^{M \\times T \\times K}$: mini-batch データ, $\\Theta$: モデルパラメータの集合\n",
    "\n",
    "ここで, $\\Theta$には以下のパラメータが含まれている．\n",
    "\n",
    "- $\\mathbf{W}^{(x,h)} \\in \\mathbb{R}^{K \\times H}$: 入力層→隠れ層の重み\n",
    "- $\\mathbf{W}^{(h,h)} \\in \\mathbb{R}^{H \\times H}$: 隠れ層→隠れ層の重み\n",
    "- $\\mathbf{W}^{(h,o)} \\in \\mathbb{R}^{H \\times C}$: 隠れ層→出力層の重み\n",
    "- $\\mathbf{b}^{(x,h)} \\in \\mathbb{R}^{H}$: 入力層→隠れ層のバイアス\n",
    "- $\\mathbf{b}^{(h,o)} \\in \\mathbb{R}^{C}$: 隠れ層→出力層のバイアス\n",
    "\n",
    "**Output:** $\\hat{\\mathbf{Y}} \\in \\mathbb{R}_{>0}^{M \\times T \\times C}$: 各クラスへの所属確率\n",
    "\n",
    "1. 全ての要素を0で初期化 \n",
    "    $\\mathbf{H} \\leftarrow \\mathbf{O} \\in \\mathbb{R}^{M \\times T \\times H}$\n",
    "2. $\\hat{\\mathbf{H}}_{0} \\leftarrow \\mathbf{O} \\in \\mathbb{R}^{M \\times H}$\n",
    "3. **For** $t = 1:T$ **do**:\n",
    "4. &nbsp;&nbsp;&nbsp;&nbsp;$t$時点の隠れ層出力を算出 $\\hat{\\mathbf{H}}_{t} \\leftarrow \\operatorname{tanh}(\\mathbf{X}_{:,t,:} \\cdot \\mathbf{W}^{(x,h)}+\\mathbf{h}_{t-1}\\cdot \\mathbf{W}^{(h,h)} + \\mathbf{b}^{(x,h)})$\n",
    "5. &nbsp;&nbsp;&nbsp;&nbsp;全ての時点の出力を一つの配列に保存 $\\mathbf{H}_{:,t,:} \\leftarrow \\hat{\\mathbf{H}}_{t}$     \n",
    "6. 出力を算出\n",
    "    $\\hat{\\mathbf{Y}} \\leftarrow \\operatorname{softmax}(\\mathbf{H} \\cdot  \\mathbf{W}^{(h,o)} + \\mathbf{b}^{(h,o)})$\n",
    "\n",
    "::::"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BPTT（Backpropagation through time）"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "学習ではunfold（展開）したネットワークに対して，一番最後の出力から遡ってBack Propagationしていきます．この手法のことを __Back Propagation Through Time（BPTT）__ と呼びます．\n",
    "\n",
    "> ![](https://camo.qiitausercontent.com/b0c4040112f747cc634270019bfb3b91b0f88f6e/68747470733a2f2f71696974612d696d6167652d73746f72652e73332e61702d6e6f727468656173742d312e616d617a6f6e6177732e636f6d2f302f3536383638382f33396539396631322d303561632d383831312d663663332d6461383962316538396565362e706e67)  \n",
    "[出典: PyTorchを使ってジャパリパークの歌詞みたいなやつを生成させたい](https://qiita.com/kibounoasa/items/78fb5a217232de863b00)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "パラメータの更新は以下のように行います：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathrm{w}_{\\mathrm{ji}}^{(\\mathrm{l}) \\text { new }} & =\\mathrm{w}_{\\mathrm{ji}}^{(\\mathrm{l}) \\text { old }}-\\eta \\frac{\\partial \\mathrm{L}}{\\partial \\mathrm{W}_{\\mathrm{ji}}^{(l)}} \\\\\n",
    "\\mathrm{w}_{\\mathrm{jj}}^{(\\mathrm{l}) \\text { new }} & =\\mathrm{w}_{\\mathrm{jj}}^{(\\mathrm{l}) \\text {,old }}-\\eta \\frac{\\partial \\mathrm{L}}{\\partial \\mathrm{w}_{\\mathrm{jj}}^{(l)}} \\\\\n",
    "\\mathrm{L} & =\\sum_{\\mathrm{t}=1}^T \\mathrm{~L}^{(\\mathrm{t})}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "損失関数は全ての出力値から計算したものを合計して利用します．それ以外は普通のMLPと同様です．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- BPTTの利点\n",
    "    - これまでのMLPの訓練方法の通りである\n",
    "- BPTTの欠点\n",
    "    - 計算グラフが大きくなるので勾配消失問題や勾配爆発問題が起こりやすい\n",
    "    \n",
    "この問題を解決するために，ある程度遡ったら途中で勾配を切り捨てる様なBPTTの拡張として，__Truncated BPTT__ が提案されています．\n",
    "\n",
    "> ![](https://qiita-user-contents.imgix.net/https%3A%2F%2Fqiita-image-store.s3.ap-northeast-1.amazonaws.com%2F0%2F568688%2Faace0b89-3603-bfcd-5cbe-307f55fc0049.png?ixlib=rb-4.0.0&auto=format&gif-q=60&q=75&w=1400&fit=max&s=779bd53f95eef72ccd37d19819cd4c69)  \n",
    "[出典: PyTorchを使ってジャパリパークの歌詞みたいなやつを生成させたい](https://qiita.com/kibounoasa/items/78fb5a217232de863b00)\n",
    "\n",
    "\n",
    "遡るタイムステップ数 $\\tau$ を限定したBPTTを Truncated BPTT といいます。\n",
    "\n",
    "- Truncated BPTTの利点\n",
    "    - 勾配消失や勾配爆発をある程度抑制できる．\n",
    "- Truncated BPTTの欠点\n",
    "    - 任意の範囲で勾配履歴を切り落としてしまう．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 例：文書生成モデル"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### データローダー"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "文書数: 564194, 語彙数: 63269\n"
     ]
    }
   ],
   "source": [
    "with open(\"./data/ja.text8\") as f:\n",
    "    text8 = f.read()\n",
    "\n",
    "import re\n",
    "def build_simply_dictionary(texts):\n",
    "    token_set = set(token for text in texts for token in text.split())\n",
    "    word2id = {token:id for id, token in enumerate(token_set)}  \n",
    "    return word2id\n",
    "\n",
    "def my_analyzer(text):\n",
    "    #text = code_regex.sub('', text)\n",
    "    tokens = text.split()\n",
    "    tokens = filter(lambda token: re.search(r'[ぁ-ん]+|[ァ-ヴー]+|[一-龠]+', token), tokens)\n",
    "    return tokens \n",
    "\n",
    "def build_dictionary(texts, min_df=1):\n",
    "    from sklearn.feature_extraction.text import CountVectorizer\n",
    "    countvectorizer = CountVectorizer(min_df=min_df, analyzer=my_analyzer)\n",
    "\n",
    "    X = countvectorizer.fit_transform(texts)\n",
    "    id2word = {id:w for id,w in enumerate(countvectorizer.get_feature_names_out())}\n",
    "    word2id = {w:id for id,w in id2word.items()}\n",
    "    return id2word, word2id, X\n",
    "\n",
    "texts = text8.split(\"。\")\n",
    "id2word, word2id,X = build_dictionary(texts,5)\n",
    "V = len(id2word)\n",
    "D = len(texts)\n",
    "print(f\"文書数: {D}, 語彙数: {V}\")\n",
    "\n",
    "WINDOW_SIZE = 11\n",
    "\n",
    "preprocessed_texts = [[word2id[w] for w in text.split() if w in word2id] for text in texts]\n",
    "preprocessed_texts = [text for text in preprocessed_texts if len(text) > WINDOW_SIZE]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_word2id_seq(corpus ,word2id, max_length=10):\n",
    "    tmp = []\n",
    "    for doc in corpus:\n",
    "        line = [word2id[w] for w in doc.split() if w in word2id]\n",
    "        # もしmax_lengthよりも単語数が多ければ切り捨て，\n",
    "        if len(line) >= max_length:\n",
    "            line = line[:max_length]\n",
    "        # もしmax_lengthよりも単語数が少なければ0で穴埋め,\n",
    "        elif len(line) <= max_length:\n",
    "            line += [0]* (max_length - len(line))\n",
    "        tmp.append(line)\n",
    "    return tmp \n",
    "\n",
    "def make_id2word_seq(id_seqs, id2word):\n",
    "    tmp = []\n",
    "    for id_seq in id_seqs:\n",
    "        line = [id2word[id] for id in id_seq  if id in id2word]\n",
    "        tmp.append(\" \".join(line))\n",
    "    return tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyDataset(Dataset):\n",
    "    def __init__(self, id_data):\n",
    "        super().__init__()\n",
    "        self.data_length = len(id_data)\n",
    "        # 訓練データ。例：［'僕', 'は', 'カレー', 'が', '好き']\n",
    "        self.x = [row[0:-1] for row in id_data]\n",
    "        # 正解ラベル。例：['は', 'カレー', 'が', '好き', '。']\n",
    "        self.y = [row[1:] for row in id_data]\n",
    "    \n",
    "    def __len__(self):\n",
    "        return self.data_length\n",
    "    \n",
    "    def __getitem__(self, idx):\n",
    "        return torch.tensor(self.x[idx]), torch.tensor(self.y[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "BS = 2\n",
    "dataset = MyDataset(make_word2id_seq(texts, word2id))\n",
    "dl = DataLoader(dataset, batch_size=BS, shuffle=True, drop_last=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文書生成RNNの作成"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RNN(nn.Module):\n",
    "    def __init__(self, vocab_size, embedding_dim, hidden_size, batch_size, num_layers=1) -> None:\n",
    "        super().__init__()\n",
    "        self.hidden_size = hidden_size\n",
    "        self.batch_size = batch_size\n",
    "        self.num_layers = num_layers\n",
    "        self.device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "        self.embedding = nn.Embedding(vocab_size, embedding_dim, padding_idx=0)\n",
    "        self.rnn = nn.RNN(embedding_dim, hidden_size, batch_first=True, num_layers=self.num_layers)\n",
    "        self.fc = nn.Linear(hidden_size, vocab_size)\n",
    "        \n",
    "    def init_hidden(self, batch_size=None):\n",
    "        if not batch_size:\n",
    "            batch_size = self.batch_size\n",
    "        self.hidden_state = torch.zeros(self.num_layers, batch_size,\n",
    "                                        self.hidden_size).to(self.device)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.embedding(x)\n",
    "        x, self.hidden_state = self.rnn(x, self.hidden_state)\n",
    "        x = self.fc(x)\n",
    "        return x\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 訓練スクリプト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": [
     "hide-output"
    ]
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[13], line 44\u001b[0m\n\u001b[1;32m     41\u001b[0m criterion \u001b[39m=\u001b[39m nn\u001b[39m.\u001b[39mCrossEntropyLoss()\n\u001b[1;32m     42\u001b[0m optimizer \u001b[39m=\u001b[39m optim\u001b[39m.\u001b[39mAdam(model\u001b[39m.\u001b[39mparameters(), lr\u001b[39m=\u001b[39m\u001b[39m0.01\u001b[39m)\n\u001b[0;32m---> 44\u001b[0m losses \u001b[39m=\u001b[39m train(model, dataloader, criterion, optimizer, EPOCHS, VOCAB_SIZE)\n",
      "Cell \u001b[0;32mIn[13], line 24\u001b[0m, in \u001b[0;36mtrain\u001b[0;34m(model, dataloader, criterion, optimizer, epochs, vocab_size)\u001b[0m\n\u001b[1;32m     22\u001b[0m     running_loss \u001b[39m+\u001b[39m\u001b[39m=\u001b[39m loss\u001b[39m.\u001b[39mitem()\n\u001b[1;32m     23\u001b[0m     loss\u001b[39m.\u001b[39mbackward()\n\u001b[0;32m---> 24\u001b[0m     optimizer\u001b[39m.\u001b[39;49mstep()\n\u001b[1;32m     25\u001b[0m losses\u001b[39m.\u001b[39mappend(running_loss \u001b[39m/\u001b[39m cnt)\n\u001b[1;32m     27\u001b[0m \u001b[39mprint\u001b[39m(\u001b[39m'\u001b[39m\u001b[39m+\u001b[39m\u001b[39m'\u001b[39m, end\u001b[39m=\u001b[39m\u001b[39m'\u001b[39m\u001b[39m'\u001b[39m)\n",
      "File \u001b[0;32m~/.pyenv/versions/miniforge3-4.10.3-10/envs/datasci/lib/python3.10/site-packages/torch/optim/optimizer.py:280\u001b[0m, in \u001b[0;36mOptimizer.profile_hook_step.<locals>.wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    276\u001b[0m         \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    277\u001b[0m             \u001b[39mraise\u001b[39;00m \u001b[39mRuntimeError\u001b[39;00m(\u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39m{\u001b[39;00mfunc\u001b[39m}\u001b[39;00m\u001b[39m must return None or a tuple of (new_args, new_kwargs),\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m    278\u001b[0m                                \u001b[39mf\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mbut got \u001b[39m\u001b[39m{\u001b[39;00mresult\u001b[39m}\u001b[39;00m\u001b[39m.\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[0;32m--> 280\u001b[0m out \u001b[39m=\u001b[39m func(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m    281\u001b[0m \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_optimizer_step_code()\n\u001b[1;32m    283\u001b[0m \u001b[39m# call optimizer step post hooks\u001b[39;00m\n",
      "File \u001b[0;32m~/.pyenv/versions/miniforge3-4.10.3-10/envs/datasci/lib/python3.10/site-packages/torch/optim/optimizer.py:33\u001b[0m, in \u001b[0;36m_use_grad_for_differentiable.<locals>._use_grad\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[1;32m     32\u001b[0m     torch\u001b[39m.\u001b[39mset_grad_enabled(\u001b[39mself\u001b[39m\u001b[39m.\u001b[39mdefaults[\u001b[39m'\u001b[39m\u001b[39mdifferentiable\u001b[39m\u001b[39m'\u001b[39m])\n\u001b[0;32m---> 33\u001b[0m     ret \u001b[39m=\u001b[39m func(\u001b[39mself\u001b[39;49m, \u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m     34\u001b[0m \u001b[39mfinally\u001b[39;00m:\n\u001b[1;32m     35\u001b[0m     torch\u001b[39m.\u001b[39mset_grad_enabled(prev_grad)\n",
      "File \u001b[0;32m~/.pyenv/versions/miniforge3-4.10.3-10/envs/datasci/lib/python3.10/site-packages/torch/optim/adam.py:141\u001b[0m, in \u001b[0;36mAdam.step\u001b[0;34m(self, closure)\u001b[0m\n\u001b[1;32m    130\u001b[0m     beta1, beta2 \u001b[39m=\u001b[39m group[\u001b[39m'\u001b[39m\u001b[39mbetas\u001b[39m\u001b[39m'\u001b[39m]\n\u001b[1;32m    132\u001b[0m     \u001b[39mself\u001b[39m\u001b[39m.\u001b[39m_init_group(\n\u001b[1;32m    133\u001b[0m         group,\n\u001b[1;32m    134\u001b[0m         params_with_grad,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    138\u001b[0m         max_exp_avg_sqs,\n\u001b[1;32m    139\u001b[0m         state_steps)\n\u001b[0;32m--> 141\u001b[0m     adam(\n\u001b[1;32m    142\u001b[0m         params_with_grad,\n\u001b[1;32m    143\u001b[0m         grads,\n\u001b[1;32m    144\u001b[0m         exp_avgs,\n\u001b[1;32m    145\u001b[0m         exp_avg_sqs,\n\u001b[1;32m    146\u001b[0m         max_exp_avg_sqs,\n\u001b[1;32m    147\u001b[0m         state_steps,\n\u001b[1;32m    148\u001b[0m         amsgrad\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mamsgrad\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    149\u001b[0m         beta1\u001b[39m=\u001b[39;49mbeta1,\n\u001b[1;32m    150\u001b[0m         beta2\u001b[39m=\u001b[39;49mbeta2,\n\u001b[1;32m    151\u001b[0m         lr\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mlr\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    152\u001b[0m         weight_decay\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mweight_decay\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    153\u001b[0m         eps\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39meps\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    154\u001b[0m         maximize\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mmaximize\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    155\u001b[0m         foreach\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mforeach\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    156\u001b[0m         capturable\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mcapturable\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    157\u001b[0m         differentiable\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mdifferentiable\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    158\u001b[0m         fused\u001b[39m=\u001b[39;49mgroup[\u001b[39m'\u001b[39;49m\u001b[39mfused\u001b[39;49m\u001b[39m'\u001b[39;49m],\n\u001b[1;32m    159\u001b[0m         grad_scale\u001b[39m=\u001b[39;49m\u001b[39mgetattr\u001b[39;49m(\u001b[39mself\u001b[39;49m, \u001b[39m\"\u001b[39;49m\u001b[39mgrad_scale\u001b[39;49m\u001b[39m\"\u001b[39;49m, \u001b[39mNone\u001b[39;49;00m),\n\u001b[1;32m    160\u001b[0m         found_inf\u001b[39m=\u001b[39;49m\u001b[39mgetattr\u001b[39;49m(\u001b[39mself\u001b[39;49m, \u001b[39m\"\u001b[39;49m\u001b[39mfound_inf\u001b[39;49m\u001b[39m\"\u001b[39;49m, \u001b[39mNone\u001b[39;49;00m),\n\u001b[1;32m    161\u001b[0m     )\n\u001b[1;32m    163\u001b[0m \u001b[39mreturn\u001b[39;00m loss\n",
      "File \u001b[0;32m~/.pyenv/versions/miniforge3-4.10.3-10/envs/datasci/lib/python3.10/site-packages/torch/optim/adam.py:281\u001b[0m, in \u001b[0;36madam\u001b[0;34m(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps, foreach, capturable, differentiable, fused, grad_scale, found_inf, amsgrad, beta1, beta2, lr, weight_decay, eps, maximize)\u001b[0m\n\u001b[1;32m    278\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    279\u001b[0m     func \u001b[39m=\u001b[39m _single_tensor_adam\n\u001b[0;32m--> 281\u001b[0m func(params,\n\u001b[1;32m    282\u001b[0m      grads,\n\u001b[1;32m    283\u001b[0m      exp_avgs,\n\u001b[1;32m    284\u001b[0m      exp_avg_sqs,\n\u001b[1;32m    285\u001b[0m      max_exp_avg_sqs,\n\u001b[1;32m    286\u001b[0m      state_steps,\n\u001b[1;32m    287\u001b[0m      amsgrad\u001b[39m=\u001b[39;49mamsgrad,\n\u001b[1;32m    288\u001b[0m      beta1\u001b[39m=\u001b[39;49mbeta1,\n\u001b[1;32m    289\u001b[0m      beta2\u001b[39m=\u001b[39;49mbeta2,\n\u001b[1;32m    290\u001b[0m      lr\u001b[39m=\u001b[39;49mlr,\n\u001b[1;32m    291\u001b[0m      weight_decay\u001b[39m=\u001b[39;49mweight_decay,\n\u001b[1;32m    292\u001b[0m      eps\u001b[39m=\u001b[39;49meps,\n\u001b[1;32m    293\u001b[0m      maximize\u001b[39m=\u001b[39;49mmaximize,\n\u001b[1;32m    294\u001b[0m      capturable\u001b[39m=\u001b[39;49mcapturable,\n\u001b[1;32m    295\u001b[0m      differentiable\u001b[39m=\u001b[39;49mdifferentiable,\n\u001b[1;32m    296\u001b[0m      grad_scale\u001b[39m=\u001b[39;49mgrad_scale,\n\u001b[1;32m    297\u001b[0m      found_inf\u001b[39m=\u001b[39;49mfound_inf)\n",
      "File \u001b[0;32m~/.pyenv/versions/miniforge3-4.10.3-10/envs/datasci/lib/python3.10/site-packages/torch/optim/adam.py:345\u001b[0m, in \u001b[0;36m_single_tensor_adam\u001b[0;34m(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps, grad_scale, found_inf, amsgrad, beta1, beta2, lr, weight_decay, eps, maximize, capturable, differentiable)\u001b[0m\n\u001b[1;32m    343\u001b[0m \u001b[39m# Decay the first and second moment running average coefficient\u001b[39;00m\n\u001b[1;32m    344\u001b[0m exp_avg\u001b[39m.\u001b[39mmul_(beta1)\u001b[39m.\u001b[39madd_(grad, alpha\u001b[39m=\u001b[39m\u001b[39m1\u001b[39m \u001b[39m-\u001b[39m beta1)\n\u001b[0;32m--> 345\u001b[0m exp_avg_sq\u001b[39m.\u001b[39;49mmul_(beta2)\u001b[39m.\u001b[39;49maddcmul_(grad, grad\u001b[39m.\u001b[39;49mconj(), value\u001b[39m=\u001b[39;49m\u001b[39m1\u001b[39;49m \u001b[39m-\u001b[39;49m beta2)\n\u001b[1;32m    347\u001b[0m \u001b[39mif\u001b[39;00m capturable \u001b[39mor\u001b[39;00m differentiable:\n\u001b[1;32m    348\u001b[0m     step \u001b[39m=\u001b[39m step_t\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "EMBEDDING_DIM = 300\n",
    "HIDDEN_SIZE = 300\n",
    "NUM_LAYERS = 1\n",
    "VOCAB_SIZE = len(word2id)# + 1\n",
    "\n",
    "def train(model, dataloader, criterion, optimizer, epochs, vocab_size):\n",
    "    device = model.device\n",
    "    model.train()\n",
    "    losses = []\n",
    "\n",
    "    for epoch in range(EPOCHS):\n",
    "        running_loss = 0\n",
    "        for cnt, batch in enumerate(dataloader):\n",
    "            (X_train, y_train) = batch\n",
    "            optimizer.zero_grad()\n",
    "            X_train, y_train = X_train.to(device), y_train.to(device)\n",
    "            model.init_hidden()\n",
    "            outputs = model(X_train)\n",
    "            outputs = outputs.reshape(-1, vocab_size)\n",
    "            y_train = y_train.reshape(-1)\n",
    "            loss = criterion(outputs, y_train)\n",
    "            running_loss += loss.item()\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "        losses.append(running_loss / cnt)\n",
    "\n",
    "        print('+', end='')\n",
    "        if epoch % 50 == 0:\n",
    "            print(f'\\nepoch: {epoch:3}, loss: {loss:.3f}')\n",
    "\n",
    "    print(f'\\nepoch: {epoch:3}, loss: {loss:.3f}')\n",
    "    return losses\n",
    "\n",
    "# 実行は以下のコードを叩くことで可能です．\n",
    "\n",
    "EPOCHS = 1\n",
    "model = RNN(VOCAB_SIZE, EMBEDDING_DIM, HIDDEN_SIZE, BS, NUM_LAYERS)\n",
    "BS = 2\n",
    "dataset = MyDataset(make_word2id_seq(texts, word2id))\n",
    "dataloader = DataLoader(dataset, batch_size=BS, shuffle=True, drop_last=True)\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.01)\n",
    "\n",
    "losses = train(model, dataloader, criterion, optimizer, EPOCHS, VOCAB_SIZE)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "言語モデルの学習には非常に時間がかかります．寝る前に回してみましょう．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
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