Homework Hard.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sklearn.metrics import classification_report\n",
    "\n",
    "import torch\n",
    "from torch.utils.data import DataLoader\n",
    "from torchvision.datasets import MNIST\n",
    "from torchvision import transforms\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tqdm import tqdm\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Домашка №1\n",
    "# Усложненная\n",
    "### Эта домашка нужна для лучшего понимания, но она будет сложнее из-за использования классов и, возможно, пока непривычной форме с классами.\n",
    "Абстракции в этой домашке будут очень полезны для понимания того, что происходит в торче. Эта домашка прокачает вас гораздо сильнее, но и выполнить ее будет труднее. Вам нужно будет описать несколько слоев: `Linear`, `ReLU`, `BCELoss`.  Реализация `Sigmoid` уже есть в `our_library.layers`. Реализовав слои выше вы сможете сделать n-слойную нейронную сеть с любым количеством слоев. Это получается за счет того, что вы описали всю необходимую логику:\n",
    "- Как нужно обработать входные данные и передать их дальше;\n",
    "- Принять градиент с последующего слоя, сделать `backward` для текущего слоя и передать градиент предыдущему слою;\n",
    "- Как обновить веса, если в слоев есть обучаемые веса.\n",
    "\n",
    "Присылайте свои недоделанные сложные домашки, пусть они не пойдут совсем в стол. Я или ассистенты посмотрят, мы обсудим и доделаем.  \n",
    "Поверьте, эта домашка стоит того, чтобы ее сделать!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Датасет\n",
    "Мы его просто загрузим и здесь пока будет какая-то торчовая магия, которую мы разберем на следующем занятии"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Некоторые магические трансформации, о которых пока не стоит заморачиваться\n",
    "1. Перевод картинки в тензор\n",
    "1. Нормализация картинки"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "transform = transforms.Compose([\n",
    "    transforms.ToTensor(),\n",
    "    transforms.Normalize((0.1307,), (0.3081,))\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Загружаем датасет\n",
    "Конкретно эта часть кода понадобится нам один раз за курс и будет только в этой домашке"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bobazooba/opt/anaconda3/lib/python3.8/site-packages/torchvision/datasets/mnist.py:498: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  ../torch/csrc/utils/tensor_numpy.cpp:180.)\n",
      "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
     ]
    }
   ],
   "source": [
    "train_dataset = MNIST('.', train=True, download=True, transform=transform)\n",
    "test_dataset = MNIST('.', train=False, transform=transform)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Переводим его в два класса\n",
    "Это нужно для упрощения задачи до бинарной классификации. В этой домашке мы будем отличать две цифры: 1 и 7."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dataset.data = train_dataset.data[(train_dataset.targets == 3) | (train_dataset.targets == 7)]\n",
    "train_dataset.targets = train_dataset.targets[(train_dataset.targets == 3) | (train_dataset.targets == 7)]\n",
    "\n",
    "test_dataset.data = test_dataset.data[(test_dataset.targets == 3) | (test_dataset.targets == 7)]\n",
    "test_dataset.targets = test_dataset.targets[(test_dataset.targets == 3) | (test_dataset.targets == 7)]\n",
    "\n",
    "train_dataset.targets = (train_dataset.targets == 7).long()\n",
    "test_dataset.targets = (test_dataset.targets == 7).long()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Оборачиваем в итератор данных\n",
    "Далее в курсе мы поговорим о том, что это такое более подробно, а дальше в этой тетрадке будет несколько полезных деталей.  \n",
    "Пока что будет достаточно понимать, что мы обернули наши данные в некоторую абстракцию, итерация по которой дает нам батчи данных из нашего датасета.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_loader = DataLoader(train_dataset, batch_size=128, shuffle=True)\n",
    "test_loader = DataLoader(test_dataset, batch_size=128, shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Порисуем данные\n",
    "\n",
    "- классу 0 соответствует цифра 3\n",
    "- классу 1 соответствует цифра 7  \n",
    "\n",
    "Выбрал эти цифры, потому что на них хуже всего метрики"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x504 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = next(iter(train_loader))\n",
    "X = X.numpy()\n",
    "y = y.numpy()\n",
    "\n",
    "plt.figure(figsize=(6, 7))\n",
    "for i in range(25):\n",
    "    plt.subplot(5, 5, i+1)\n",
    "    plt.imshow(X[i].reshape(28, 28), cmap=plt.cm.Greys_r)\n",
    "    plt.title(y[i])\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Итерация по датасету\n",
    "- x - батч с данными\n",
    "- y - батч с таргетами к этим данным"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "for x, y in train_loader:\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### train_loader это итератор, при проходе по которому будут выдаваться батчи данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Размерность x\n",
    "- 128 - размер батча\n",
    "- 1 - количество каналов, у нас чернобелые картинки, поэтому канал 1\n",
    "- 28 - количество пикселей в длину\n",
    "- 28 - количество пикселей в ширину"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([128, 1, 28, 28])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]],\n",
       "\n",
       "\n",
       "        [[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]],\n",
       "\n",
       "\n",
       "        [[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]],\n",
       "\n",
       "\n",
       "        ...,\n",
       "\n",
       "\n",
       "        [[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]],\n",
       "\n",
       "\n",
       "        [[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]],\n",
       "\n",
       "\n",
       "        [[[-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          ...,\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242],\n",
       "          [-0.4242, -0.4242, -0.4242,  ..., -0.4242, -0.4242, -0.4242]]]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Просто выпрямим нашу матрицу в один вектор\n",
    "### То есть каждая фича в векторе это значение пикселя\n",
    "### Для нашей игрушечной задачи этого будет достаточно"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(128, 784)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.view(x.shape[0], -1).numpy().shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### x.numpy()\n",
    "Это перевод торчового тензора (некоторая абстракция, о которой мы будем говорить позже на курсе) в numpy массив"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "for x, y in train_loader:\n",
    "    x = x.view(x.shape[0], -1).numpy()\n",
    "    y = y.numpy()\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296],\n",
       "       [-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296],\n",
       "       [-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296],\n",
       "       ...,\n",
       "       [-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296],\n",
       "       [-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296],\n",
       "       [-0.42421296, -0.42421296, -0.42421296, ..., -0.42421296,\n",
       "        -0.42421296, -0.42421296]], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Размерность\n",
    "- количество примеров в батче\n",
    "- количество фичей"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(128, 784)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Таргеты\n",
    "- классу 0 соответствует цифра 3\n",
    "- классу 1 соответствует цифра 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1,\n",
       "       1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0,\n",
       "       0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1,\n",
       "       1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,\n",
       "       1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0,\n",
       "       0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Итерация по эпохам"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Эпоха - 1, прошли - 100.00 % датасета\n",
      "Эпоха - 2, прошли - 100.00 % датасета\n",
      "Эпоха - 3, прошли - 100.00 % датасета\n"
     ]
    }
   ],
   "source": [
    "# количество эпох - полных проходов по датасету\n",
    "epochs = 3\n",
    "\n",
    "for n_epoch in range(epochs):\n",
    "    \n",
    "    dataset_passed_samples = 0\n",
    "    \n",
    "    for x, y in train_loader:\n",
    "        \n",
    "        # вот здесь мы могли бы как-то манипулировать с данными\n",
    "        # например, учить, но пока этого делать не будет\n",
    "        # только демонстрация\n",
    "        \n",
    "        time.sleep(0.01)\n",
    "        \n",
    "        dataset_passed_samples += x.shape[0]\n",
    "        \n",
    "        dataset_passed_percent = dataset_passed_samples * 100 / train_loader.dataset.data.shape[0]\n",
    "        \n",
    "        print(f'Эпоха - {n_epoch + 1}, прошли - {dataset_passed_percent:.2f} % датасета', end='\\r')\n",
    "        \n",
    "    print('\\r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Небольшие пояснения по numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.56478083, 0.10829306, 0.74365169, ..., 0.8088915 , 0.64807257,\n",
       "        0.05161813],\n",
       "       [0.65053659, 0.65532038, 0.87362435, ..., 0.57765443, 0.10443366,\n",
       "        0.50475439],\n",
       "       [0.22490862, 0.03544221, 0.03582239, ..., 0.20402521, 0.8266479 ,\n",
       "        0.87001811],\n",
       "       ...,\n",
       "       [0.5378773 , 0.00818844, 0.3330567 , ..., 0.10227386, 0.31730248,\n",
       "        0.49914971],\n",
       "       [0.84405389, 0.15324776, 0.1637836 , ..., 0.87467301, 0.66455446,\n",
       "        0.39188532],\n",
       "       [0.67623825, 0.80341482, 0.46298484, ..., 0.89562697, 0.99304079,\n",
       "        0.19323015]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# таким образом мы создаем матрицу 64 на 512 с рандомными значениями\n",
    "x = np.random.rand(64, 512)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.25234015, -2.21118678,  0.25683531, ...,  0.44221499,\n",
       "        -0.01375455, -2.96121781],\n",
       "       [-0.00675987,  0.00681377,  0.62811471, ..., -0.21509481,\n",
       "        -2.24829688, -0.42890633],\n",
       "       [-1.44147719, -3.33859554, -3.32789891, ..., -1.54788543,\n",
       "         0.49297033,  0.61769026],\n",
       "       ...,\n",
       "       [-0.33081283, -4.80496439, -0.98851578, ..., -2.26964117,\n",
       "        -1.04721889, -0.44569877],\n",
       "       [ 0.54288802, -1.85221443, -1.78238414, ...,  0.6311477 ,\n",
       "         0.03299418, -0.78321194],\n",
       "       [ 0.06608834,  0.42659125, -0.55570602, ...,  0.69191638,\n",
       "         0.97914647, -1.60653542]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# большинство функций применяются к каждому элементу массива\n",
    "# здесь мы каждый элемент массива возвели в квадрат и прибавили к получившемуся значению логарифм элемента матрицы \n",
    "x ** 2 + np.log(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.random.rand(512, 1024)\n",
    "# скалярное произведение\n",
    "res = np.dot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[124.9963835 , 125.6381922 , 122.5550292 , ..., 130.0296717 ,\n",
       "        127.99131213, 121.92556557],\n",
       "       [130.20965094, 130.05690666, 125.54801086, ..., 130.11014374,\n",
       "        132.59473373, 126.4235058 ],\n",
       "       [130.01088871, 132.07814911, 128.45699434, ..., 133.08489523,\n",
       "        138.00152105, 125.55321896],\n",
       "       ...,\n",
       "       [117.8130419 , 118.35970453, 116.00727995, ..., 118.03895564,\n",
       "        121.92424887, 112.87873335],\n",
       "       [126.54614081, 124.80779786, 124.00512826, ..., 125.10906694,\n",
       "        131.29355405, 120.74645691],\n",
       "       [128.58085029, 127.77383613, 126.59390634, ..., 129.26212637,\n",
       "        134.43351828, 126.00669821]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.shape == (x.shape[0], y.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Импортируем нашу библиотеку\n",
    "В ней реализованы некоторые полезные методы, в модуле `layers` есть реализация сигмоиды. Остальное вам смотреть необязательно, это некоторые дополнения, упрощающие вам жизнь."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from our_library import layers, wrapper, tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Реализуйте слои:\n",
    "- Linear - линейная трансформация (не забудьте, что у нас в этом слое как раз есть обучаемые параметры)\n",
    "- ReLU\n",
    "- BCELoss - Binary Cross Entropy\n",
    "\n",
    "\n",
    "## Вы можете реализовать как здесь, так и в файла layers\n",
    "\n",
    "- TIP: np.expand_dims(y, 1) для BCE, так как BCE на вход принимает просто вектор размерностью (батч сайз, 1)\n",
    "\n",
    "## Также внутри layers есть код для Negative Log-Likelihood (сразу с софтмаксом) для примера"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Пример c сигмоидой\n",
    "В `our_library.layers` также это есть"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Sigmoid:\n",
    "\n",
    "    def __init__(self):\n",
    "\n",
    "        self._sigmoid_result = None\n",
    "\n",
    "    def forward(self, x):\n",
    "\n",
    "        self._sigmoid_result = 1 / (1 + np.exp(-x))\n",
    "\n",
    "        return self._sigmoid_result\n",
    "\n",
    "    def backward(self, grad):\n",
    "        \"\"\"\n",
    "        :grad: градиент от предыдущего слоя\n",
    "        :return: градиент для следующего слоя\n",
    "        \"\"\"\n",
    "\n",
    "        new_grad = self._sigmoid_result * (1 - self._sigmoid_result) * grad\n",
    "\n",
    "        return new_grad\n",
    "\n",
    "    def step(self, learning_step):\n",
    "\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тестирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[0.91551091, 0.15073826, 0.77137556, 0.59352491],\n",
    "              [0.81126142, 0.1194849 , 0.29651178, 0.19066982]])\n",
    "\n",
    "correct_forward_result = np.array([[0.71412654, 0.53761337, 0.68381838, 0.64417351],\n",
    "                                   [0.69237824, 0.52983574, 0.57358957, 0.54752357]])\n",
    "\n",
    "correct_backward_result = np.array([[0.20414982, 0.24858523, 0.2162108 , 0.229214  ],\n",
    "                                    [0.21299061, 0.24910983, 0.24458457, 0.24774151]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmoid_layer = Sigmoid()\n",
    "forward_result = sigmoid_layer.forward(x)\n",
    "backward_result = sigmoid_layer.backward(np.ones_like(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "assert np.allclose(correct_forward_result, forward_result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "assert np.allclose(correct_backward_result, backward_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Линейный слой"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Linear:\n",
    "\n",
    "    def __init__(self, in_features, out_features):\n",
    "        \n",
    "        # инициализируем веса\n",
    "        self.weight = ...\n",
    "        self.bias = ...\n",
    "        \n",
    "        # сохраняем градиент для весов\n",
    "        self._grad_weight = None\n",
    "        self._grad_bias = None\n",
    "\n",
    "    def forward(self, x):\n",
    "        ...\n",
    "\n",
    "    def backward(self, grad):\n",
    "        ...\n",
    "\n",
    "    def step(self, learning_rate):\n",
    "        ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тестирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "correct_forward_result = np.array([[0.01148086, 0.01477317, 0.00917651],\n",
    "                                   [0.00887036, 0.00972334, 0.00526646]])\n",
    "\n",
    "previous_grad = np.array([[0.01595814, 0.85148336, 0.9980065 ],\n",
    "                          [0.73044998, 0.18287682, 0.41246361]])\n",
    "\n",
    "correct_backward_result = np.array([[0.01089683, 0.00842654, 0.00822628, 0.00729307],\n",
    "                                    [0.00958704, 0.00833055, 0.00209236, 0.00543544]])\n",
    "\n",
    "correct_grad_weight = np.array([[0.60719574, 0.92790321, 1.24830165],\n",
    "                                [0.08968325, 0.15020214, 0.19972094],\n",
    "                                [0.22889674, 0.71103859, 0.89213814],\n",
    "                                [0.14874632, 0.54024567, 0.67098608]])\n",
    "\n",
    "correct_grad_bias = np.array([0.74640812, 1.03436018, 1.41047011])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "linear = Linear(in_features=4, out_features=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# так как внутри слоя мы объвяляем наши веса рандомно (домножая на 0.01), то давайте присвоим им для теста конкретные значения\n",
    "\n",
    "linear.weight = np.array([[0.00879391, 0.0075844 , 0.00430709],\n",
    "                          [0.00884834, 0.00921104, 0.00044317],\n",
    "                          [0.00011441, 0.00822498, 0.00122346],\n",
    "                          [0.00338301, 0.0001627 , 0.00711473]])\n",
    "\n",
    "linear.bias = np.array([0., 0., 0.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "forward = linear.forward(x)\n",
    "backward = linear.backward(previous_grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_forward_result, forward)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_backward_result, backward)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(linear._grad_weight, correct_grad_weight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(linear._grad_bias, correct_grad_bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ReLU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ReLU:\n",
    "\n",
    "    def __init__(self):\n",
    "        ...\n",
    "\n",
    "    def forward(self, x):\n",
    "        ...\n",
    "\n",
    "    def backward(self, prev_grad):\n",
    "        ...\n",
    "\n",
    "    def step(self, learning_rate):\n",
    "        ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тестирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[ 0.86811233, -0.23718669, -0.18401917, -0.37591633],\n",
    "              [-0.40626018,  0.37746975, -0.46929233,  0.79067681]])\n",
    "\n",
    "correct_forward_result = np.array([[0.86811233, 0.        , 0.        , 0.        ],\n",
    "                                   [0.        , 0.37746975, 0.        , 0.79067681]])\n",
    "\n",
    "previous_grad = np.array([[0.22436157, 0.61897707, 0.67895832, 0.72428618],\n",
    "                          [0.71231319, 0.87345215, 0.91129578, 0.90625846]])\n",
    "\n",
    "correct_backward_result = np.array([[0.22436157, 0.        , 0.        , 0.        ],\n",
    "                                    [0.        , 0.87345215, 0.        , 0.90625846]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "relu = ReLU()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "forward = relu.forward(x)\n",
    "backward = relu.backward(previous_grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_forward_result, forward)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_backward_result, backward)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BCE test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Не забудьте добавить np.expand_dims(y, 1) в forward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BCELoss:\n",
    "\n",
    "    def __init__(self):\n",
    "        ...\n",
    "\n",
    "    def forward(self, x, y):\n",
    "        y = np.expand_dims(y, 1)\n",
    "\n",
    "    def backward(self):\n",
    "        ...\n",
    "\n",
    "    def step(self, learning_rate):\n",
    "        ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Тестирование"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[0.76242307],\n",
    "              [0.0908412 ],\n",
    "              [0.60176646],\n",
    "              [0.09606798]])\n",
    "\n",
    "y = np.array([1, 0, 1, 0])\n",
    "\n",
    "correct_forward_result = 0.24384403491500606\n",
    "\n",
    "correct_backward_result = np.array([[-0.32790194],\n",
    "                                    [ 0.27497946],\n",
    "                                    [-0.41544356],\n",
    "                                    [ 0.27656947]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = BCELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "forward = loss.forward(x, y)\n",
    "backward = loss.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_forward_result, forward)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# значения должны быть близкими\n",
    "# assert np.allclose(correct_backward_result, backward)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Реализуйте обертку над слоями - нейронную сеть\n",
    "- TIP 1: modules - это список слоев, которые вы сделали выше. Порядок важен\n",
    "- TIP 2: обновление весов можно сделать циклом\n",
    "- TIP 3: forward идет в одну сторону по слоям, а backward в другую\n",
    "- TIP 4: В backward функции потерь мы не передаем предыдущий градиент, потому что это начало backward, то есть последний слой нашей сети\n",
    "- TIP 5: forward и backward ничего не должны отдавать, в них должны быть расчитаны градиенты для каждого слоя\n",
    "- TIP 6: в step нужно пройтись по всем слоям и обновить веса"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralNetwork:\n",
    "\n",
    "    def __init__(self, modules):\n",
    "\n",
    "        # список слоев\n",
    "        self.modules = modules\n",
    "\n",
    "    def forward(self, x):\n",
    "        ...\n",
    "\n",
    "    def backward(self, grad):\n",
    "        \"\"\"\n",
    "        :grad: градиент от функции потерь\n",
    "        :return: возвращать ничего не потребуется\n",
    "        \"\"\"\n",
    "        ...\n",
    "\n",
    "    def step(self, learning_rate):\n",
    "        ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Реализуйте обертку над моделью"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MNISTWrapper(wrapper.Wrapper):\n",
    "\n",
    "    def train_batch(self, x, y):\n",
    "        \"\"\"\n",
    "        Нужно реализовать одну итерацию обучения модели:\n",
    "        1. Рассчет forward\n",
    "        2. Рассчет функции потерь\n",
    "        3. Рассчет backward от функции потерь\n",
    "        4. Рассчет backward по модели, передавая туда значение градиента по функции потерь\n",
    "        5. Обновление весов с помощью step\n",
    "        :param x: входные данные np.array with shape (batch_size, n_features)\n",
    "        :param y: предсказания np.array with shape (batch_size, n_classes)\n",
    "        :return:\n",
    "        loss_batch - значение функции потерь, просто скаляр\n",
    "        prediction - матрица предсказаний вашей модели\n",
    "\n",
    "        напомню важные штуки, которые знает наш класс:\n",
    "        self.model\n",
    "        self.loss\n",
    "        self.learning_rate\n",
    "        \"\"\"\n",
    "        # КОД ЗДЕСЬ\n",
    "        ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# задайте гиперпараметры\n",
    "learning_rate = ...\n",
    "epochs = ...\n",
    "\n",
    "# задайте слои в свою нейронную сеть, например, 3 слоя\n",
    "neural_network = layers.NeuralNetwork(...)\n",
    "\n",
    "loss = BCELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier = MNISTWrapper(model=neural_network,\n",
    "                          loss=loss,\n",
    "                          learning_rate=learning_rate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Обучение модели"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier.train(train_loader, test_loader, epochs=epochs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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