4_02 - PyTorch Regression Example (with NN).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c84bb6fc-ed54-4d03-96f2-058776810719",
   "metadata": {},
   "source": [
    "# Искусственные нейронные сети в PyTorch\n",
    "\n",
    "На основе примитивов для операций над тензорами и инфраструктуры автоматического дифференцирования в PyTorch определены и базовые конструкции, позволяющие создавать и обучать нейронные сети (в первую очередь - это модуль `torch.nn`). В частности, PyTorch предлагает и базовую реализацию части тех классов, которые были самостоятельно \"придуманы\" и определены выше, например:\n",
    "\n",
    "- основные функции потерь: `torch.nn.MSELoss` (среднеквадратичная ошибка), `torch.nn.CrossEntropy` (кросс-энтропия) и др.;\n",
    "- оптимизаторы: `torch.optim.SGD` (стохастический градиентный спуск), `torch.optim.Adam` (Adam - adaptive moment estimation) и др.;\n",
    "\n",
    "Особого внимания заслуживает базовый класс `nn.Module`, предоставляющий основу для создания пользовательских нейронных сетей. Любая нейросетевая модель должна быть унаследована от `nn.Module`, что обеспечивает простоту взаимодействия с другими компонентами фреймворка.\n",
    "\n",
    "Воспроизведем пример выше, но уже используя более сложную \"неизвестную\" функцию и инструменты для создания и обучения нейронных сетей, предлагаемые PyTorch.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "24f94f00",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1cda67b",
   "metadata": {},
   "source": [
    "Создадим набор данных, порожденный некоторой линейной функцией $y = k x + b$. Для модели регрессии эта функция будет неизвестна, ее \"угадывание\" или восстановление как раз и будет происходить в ходе обучения регрессионной модели. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0d190252",
   "metadata": {},
   "outputs": [],
   "source": [
    "def true_fun(x):\n",
    "    return np.where(x < 0.5, np.sin(9.5*x)/2 + 0.5, (x - 0.5) ** 2)\n",
    "\n",
    "# Параметр, контролирующий шум, добавляемый к сгенерированным данным\n",
    "# (чтобы они отклонялись от уравнения, заданного в `true_fun`)\n",
    "NOISE_SIGMA = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9161c73d",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.random(80)\n",
    "y = true_fun(x) + np.random.normal(0, NOISE_SIGMA, x.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bb1885b",
   "metadata": {},
   "source": [
    "Вспомогательная функция для визуализации набора (и модели):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6db23c34",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(x, y, foo=None):\n",
    "    plt.scatter(x, y)\n",
    "    if foo is not None:\n",
    "        x_ = np.arange(0, 1.0, 0.05).reshape(-1, 1)\n",
    "        y_ = foo(torch.from_numpy(x_).to(torch.float32)).numpy(force=True).ravel()\n",
    "        plt.plot(x_, y_, color='orange')\n",
    "    plt.xlim([-0.1, 1.1])\n",
    "    plt.ylim([-0.1, 1.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "05486e6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14bffa6f",
   "metadata": {},
   "source": [
    "Определим класс `NeuralModel`, инкапсулирующий в себе нейросетевую модель, включающую один скрытый слой, состоящий из нескольких нейронов. Класс `NeuralModel` должен быть наследником `nn.Module`, а в качестве полей содержит набор преобразований исходных данных. Собственно параметры, изменение которых происходит во время обучения, находятся \"внутри\" `nn.Linear` (линейные полносвязные слои)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1d8f8c02",
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralModel(nn.Module):\n",
    "   \n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        # Слой обработки исходных данных\n",
    "        self.fc = nn.Linear(1, 3)\n",
    "        # Функция активации ReLU\n",
    "        self.relu = nn.ReLU()\n",
    "        # Слой формирования выходного значения\n",
    "        self.output = nn.Linear(3, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"Вычисление значения модели для заданного аргумента.\"\"\"\n",
    "        x = self.fc(x)\n",
    "        x = self.relu(x)\n",
    "        x = self.output(x)\n",
    "        return x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7a923af6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Создадим экземпляр модели\n",
    "model = NeuralModel()\n",
    "# Создадим экземпляр оптимизатора, связав его с\n",
    "# параметрами оцениваемой нейросетевой модели\n",
    "optimizer = torch.optim.Adam(model.parameters())\n",
    "# Функция потерь\n",
    "loss_fn = nn.MSELoss()\n",
    "\n",
    "# Исходные данные для обучения следует преобразовать\n",
    "# в тензоры. По сравнению с предыдущим примером, здесь имеет смысл\n",
    "# обратить внимание на два момента:\n",
    "#   1. преобразование формы входного тензора - чтобы все \n",
    "#      нейросетевые модули вели себя ожидаемо, первым измерением\n",
    "#      должны быть образцы, а остальными - описание этих образцов\n",
    "#   2. тип должен быть torch.float32\n",
    "#\n",
    "x_tensor = torch.from_numpy(x.reshape(-1, 1)).to(torch.float32)\n",
    "y_tensor = torch.from_numpy(y.reshape(-1, 1)).to(torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "26de1284",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "0.3324228525161743\n",
      "0.33109185099601746\n",
      "0.32977294921875\n",
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      "0.3258897662162781\n",
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      "0.3114425539970398\n",
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      "0.3069581389427185\n",
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      "0.025928843766450882\n",
      "0.025918442755937576\n",
      "0.025908062234520912\n",
      "0.025897711515426636\n",
      "0.025887370109558105\n",
      "0.025877054780721664\n",
      "0.025866765528917313\n",
      "0.025856494903564453\n",
      "0.025846246629953384\n",
      "0.025836020708084106\n",
      "0.02582581341266632\n",
      "0.025815632194280624\n",
      "0.02580547332763672\n",
      "0.025795334950089455\n",
      "0.025785217061638832\n",
      "0.02577511966228485\n",
      "0.025765055790543556\n",
      "0.025755038484930992\n",
      "0.02574503980576992\n"
     ]
    }
   ],
   "source": [
    "prev_loss = 1000.0\n",
    "\n",
    "while True:\n",
    "    # Сбросим градиент (чтобы результаты предыдущей\n",
    "    # итерации не влияли на направление изменения параметров)\n",
    "    optimizer.zero_grad()\n",
    "    # Получим предсказания\n",
    "    y_hat = model(x_tensor)\n",
    "    # Вычислим ошибку предсказаний модели\n",
    "    loss = loss_fn(y_hat, y_tensor)\n",
    "    print(loss.item())\n",
    "    # Вычислим градиент ошибки предсказаний модели по всем\n",
    "    # параметрам\n",
    "    loss.backward()\n",
    "    # Скорректируем значения параметров\n",
    "    optimizer.step()\n",
    "    # Условие останова - если ошибка перестает быстро уменьшаться\n",
    "    if abs(prev_loss - loss) < 1e-5:\n",
    "        break\n",
    "    prev_loss = loss.detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f3a0fe0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29802591-d230-4d9d-b354-d5a1ddda5181",
   "metadata": {},
   "source": [
    "Процесс обучения прошел, но и значение функции потерь достаточно высокое, и визуально выученная гипотеза далека от \"задуманной\". Это характерно для ситуации, когда модель (нейросетевая гипотеза) оказывается недостаточно выразительной для представления эмпирических данных. Увеличение мощности нейросетевой модели может быть достигнуто увеличением количества и размера слоев:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "94fddb23-c680-45b6-bfa2-62bc6e73da53",
   "metadata": {},
   "outputs": [],
   "source": [
    "class ImprovedNeuralModel(nn.Module):\n",
    "   \n",
    "    def __init__(self, n_hidden_layers, neurons_per_layer):\n",
    "        super().__init__()\n",
    "        layers = []\n",
    "        for i in range(n_hidden_layers):\n",
    "            if i == 0:\n",
    "                layers.append(nn.Linear(1, neurons_per_layer))\n",
    "            else:\n",
    "                layers.append(nn.Linear(neurons_per_layer, neurons_per_layer))\n",
    "            layers.append(nn.ReLU())\n",
    "        layers.append(nn.Linear(neurons_per_layer, 1))\n",
    "        # nn.Sequential - специальный модуль, который обеспечивает\n",
    "        # последовательное применение набора модулей к переданным\n",
    "        # входным данным\n",
    "        self.layers = nn.Sequential(*layers)\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"Вычисление значения модели для заданного аргумента.\"\"\"\n",
    "        return self.layers(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e9f28832-4c11-4e1d-b9d9-b8d7f64eac9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ImprovedNeuralModel(\n",
      "  (layers): Sequential(\n",
      "    (0): Linear(in_features=1, out_features=3, bias=True)\n",
      "    (1): ReLU()\n",
      "    (2): Linear(in_features=3, out_features=3, bias=True)\n",
      "    (3): ReLU()\n",
      "    (4): Linear(in_features=3, out_features=1, bias=True)\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "print(ImprovedNeuralModel(2, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7466558b-a626-4072-8f42-175b9891c490",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.14845725893974304\n",
      "0.14721015095710754\n",
      "0.1460188329219818\n",
      "0.1448785960674286\n",
      "0.1437833607196808\n",
      "0.14274147152900696\n",
      "0.14175885915756226\n",
      "0.14087410271167755\n",
      "0.14007484912872314\n",
      "0.13930851221084595\n",
      "0.13859179615974426\n",
      "0.13793030381202698\n",
      "0.13731113076210022\n",
      "0.13673418760299683\n",
      "0.1361975371837616\n",
      "0.13569961488246918\n",
      "0.13523419201374054\n",
      "0.1347949206829071\n",
      "0.13437049090862274\n",
      "0.13395662605762482\n",
      "0.13354678452014923\n",
      "0.1331336945295334\n",
      "0.13271227478981018\n",
      "0.13227704167366028\n",
      "0.13182048499584198\n",
      "0.13133634626865387\n",
      "0.13081757724285126\n",
      "0.1302611082792282\n",
      "0.1296617090702057\n",
      "0.12901614606380463\n",
      "0.12832069396972656\n",
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      "0.12677481770515442\n",
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    }
   ],
   "source": [
    "model = ImprovedNeuralModel(5, 20)\n",
    "optimizer = torch.optim.Adam(model.parameters())\n",
    "\n",
    "prev_loss = 1000.0\n",
    "\n",
    "while True:\n",
    "    # Сбросим градиент (чтобы результаты предыдущей\n",
    "    # итерации не влияли на направление изменения параметров)\n",
    "    optimizer.zero_grad()\n",
    "    # Получим предсказания\n",
    "    y_hat = model(x_tensor)\n",
    "    # Вычислим ошибку предсказаний модели\n",
    "    loss = loss_fn(y_hat, y_tensor)\n",
    "    print(loss.item())\n",
    "    # Вычислим градиент ошибки предсказаний модели по всем\n",
    "    # параметрам\n",
    "    loss.backward()\n",
    "    # Скорректируем значения параметров\n",
    "    optimizer.step()\n",
    "    # Условие останова - если ошибка перестает быстро уменьшаться\n",
    "    if abs(prev_loss - loss) < 1e-5:\n",
    "        break\n",
    "    prev_loss = loss.detach()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b6a009ab-79a4-4436-980a-86f7490aeb57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y, model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "823c8d72-d02e-47b8-8ec2-35196ec411f9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c69d75d6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}