{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "s4wplUzDYJcx"
   },
   "source": [
    "<h2 style=\"text-align: center;\"><b>Многослойная сеть на PyTorch</b></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "J2msuyHTYJcx"
   },
   "source": [
    "В этом ноутбке мы научимся писать свои нейросети на фреймворке PyTorch, конкретно - рассмотрим, как написать многослойную полносвязную сеть (Fully-Connected, FC)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9xJnMEZrYJcz"
   },
   "source": [
    "<h3 style=\"text-align: center;\"><b>Компоненты нейросети</b></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "InwacmvIYJc0"
   },
   "source": [
    "Здесь самое время напомнить о том, какие вещи играют принципиальную роль в построении любой ***нейронной сети*** (все их мы задаём *руками*, самостоятельно):  \n",
    "\n",
    "- непосредственно, сама **архитектура** нейросети (сюда входят типы функций активации у каждого нейрона);\n",
    "- начальная **инициализация** весов каждого слоя;\n",
    "- метод **оптимизации** нейросети (сюда ещё входит метод изменения `learning_rate`);\n",
    "- размер **батчей** (`batch_size`);\n",
    "- количество итераций обучения (`num_epochs`);\n",
    "- **функция потерь** (`loss`);  \n",
    "- тип **регуляризации** нейросети (для каждого слоя можно свой);  \n",
    "\n",
    "То, что связано с ***данными и задачей***:  \n",
    "- само **качество** выборки (непротиворечивость, чистота, корректность постановки задачи);  \n",
    "- **размер** выборки;  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tXujEOB0YJc1"
   },
   "source": [
    "<h3 style=\"text-align: center;\"><b>Многослойная нейронная сеть</b></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mnxH-DajYJc3"
   },
   "source": [
    "Как можно понять из названия, многослойная нейросеть состоит из нескольких **слоёв**. Каждый слой состоит из **нейронов**. Ранее мы уже писали свой нейрон на NumPy, вот из таких нейронов и состоит ***MLP (Multi-Layer Perceptron)***. Ещё такую многослойную нейросеть, у которой каждый нейрон на предыдущем уровне соединён с нейроном на следующем уровне, называют ***Fully-Connected-сетью*** (или ***Dense-сетью***).  \n",
    "\n",
    "Расмотрим их устройство более подробно:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "onjJUneMYJc5"
   },
   "source": [
    "* Вот так выглядит двухслойная нейросеть (первый слой - input layer - не считается, потому что это, по сути, не слой):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "owRRulLzYJc6"
   },
   "source": [
    "<img src=\"http://cs231n.github.io/assets/nn1/neural_net.jpeg\" width=300, height=200>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tFNxGGBEYJc8"
   },
   "source": [
    "* Так выглядит трёхслойная нейросеть:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zRaKX35eYJc9"
   },
   "source": [
    "<img src=\"http://cs231n.github.io/assets/nn1/neural_net2.jpeg\" width=400, height=300>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6w1FTkO1YJc-"
   },
   "source": [
    ".. и так далее для большего случая слоёв."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "8iKV7m5YYJc_"
   },
   "source": [
    "**Обратите внимание:** связи есть у нейронов со слоя $L_{i-1}$  и нейронов $L_{i}$, но между нейронами в одном слое связей **нет**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "URV9qWkfYJdA"
   },
   "source": [
    "**Входной слой** -- это данные (матрица $(n, m)$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zK8tWuHHYJdB"
   },
   "source": [
    "Слои, которые не являются входными или выходными, называются **скрытыми слоями (hidden layers)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fz9clUlCYJdC"
   },
   "source": [
    "При решении ***задачи регрессии*** на **выходном слое** обычно один нейрон, который возвращает предсказанные числа (для каждого объекта по числу).  \n",
    "\n",
    "В случае ***задачи классификации*** на **выходном слое** обычно один нейрон, если задача бинарной классификации, и $K$ нейронов, если задача $K$-класовой классификации."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "nJblXqY5YJdE"
   },
   "source": [
    "#### Forward pass в MLP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "D87xoAl8YJdF"
   },
   "source": [
    "Каждый слой многослойной нейросети - это матрица весов, столбцы которой -- это нейроны (один столбец - один нейрон). То есть один столбец -- это веса одного нейрона."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "RyXUqCfVYJdG"
   },
   "source": [
    "Допустим, мы решаем задачу $K$-классовой классификации (на последнем слое $K$ нейронов). Рассмотрим, как в таком случае выглядит `forward_pass` нейросети:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YO6gHbOjYJdH"
   },
   "source": [
    "* Вход: $$X =\n",
    "\\left(\n",
    "\\begin{matrix} \n",
    "x_{11} & ... & x_{1M} \\\\\n",
    "... & \\ddots  & ...\\\\\n",
    "x_{N1} & ... & x_{NM} \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "-- матрица $(N, M)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "XdImZiQkYJdI"
   },
   "source": [
    "* Структура сети - много слоёв, в слоях много нейронов. Первый слой (после входного) выглядит так:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "U2c2M4MJYJdJ"
   },
   "source": [
    "$$ W^1 =\n",
    "\\left(\n",
    "\\begin{matrix} \n",
    "w_{11} & ... & w_{1L_1} \\\\\n",
    "... & \\ddots  & ...\\\\\n",
    "w_{M1} & ... & w_{ML_1} \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "-- матрица $(M, L_1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UUCdeLN0YJdK"
   },
   "source": [
    "То есть это в точности $L_1$ нейронов, каждый имеет свои собственные веса, их $M$ штук."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ixHtlMwKYJdL"
   },
   "source": [
    "Мы помним, что нейрон - это линейное преобразование и потом нелинейная функция активации от этого преобразования. Однако в многослойных нейростеях часто отделяют `Linear` часть и `Activation`, то есть слоем считаем набор весов нейронов, а следующий слой всегда функция активации (у всех нейронов из слоя она одна и та же, обычно фреймворки не позволяют задавать конкретному нейрону в слое отличную от других нейронов в этом слое функцию активации, однако это легко сделать, объявив слой из одного нейрона)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AUt1NgTvYJdN"
   },
   "source": [
    "* Другие слои выглядит точно так же, как первый слой. Например, второй слой будет такой:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IdtSTvTmYJdN"
   },
   "source": [
    "$$ W^2 =\n",
    "\\left(\n",
    "\\begin{matrix} \n",
    "w_{11} & ... & w_{1L_2} \\\\\n",
    "... & \\ddots  & ...\\\\\n",
    "w_{L_11} & ... & w_{L_1L_2} \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "-- матрица $(L_1, L_2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "R3nGnHoLYJdP"
   },
   "source": [
    "То есть это в точности $L_2$ нейронов, каждый имеет свои собственные веса, их $L_1$ штук."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bQhOAQjSYJdR"
   },
   "source": [
    "* Выходной слой:  \n",
    "\n",
    "Пусть в нейросети до выходного слоя идут $t$ слоёв. Тогда выходной слой имеет форму:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fWvqm-K0YJdT"
   },
   "source": [
    "$$ W^{out} =\n",
    "\\left(\n",
    "\\begin{matrix} \n",
    "w_{11} & ... & w_{1K} \\\\\n",
    "... & \\ddots  & ...\\\\\n",
    "w_{L_t1} & ... & w_{L_tK} \n",
    "\\end{matrix}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "-- матрица $(L_t, K)$, где $L_t$ - количество нейронов в $t$-ом слое, а $K$ -- количество классов."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2z5tO89NYJdU"
   },
   "source": [
    "В итоге *для `forward_pass` нам нужно просто последовтельно перемножить матрицы друг за другом, применяя после каждого умножения соответсвующую функцию активации*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IZT4GgsCYJdV"
   },
   "source": [
    "*Примечание*: можно думать об умножении на очередную матрицу весов как на переход в **новое признаковое пространство**. Действительно, когда подаём матрицу $X$ и умножаем на матрицу первого слоя, мы получаем матрицу размера $(N, L_1)$, то есть как будто $L_1$ \"новых\" признаков (построенных как линейная комбинация старых до применения функции активации, и уже как нелинейная комбинация после активации). Здесь уместно вспомнить, что Deep Learning является пообластью Representation Learning, то есть позволяет выучивает новые представляения данных."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4RhJ4fsHYJdW"
   },
   "source": [
    "**Backward pass в MLP**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "MYN043DbYJdX"
   },
   "source": [
    "Обучается с помощью метода \"Error Backpropagation\" - [\"Обратное распространение ошибки\"](https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BE%D0%B1%D1%80%D0%B0%D1%82%D0%BD%D0%BE%D0%B3%D0%BE_%D1%80%D0%B0%D1%81%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B5%D0%BD%D0%B8%D1%8F_%D0%BE%D1%88%D0%B8%D0%B1%D0%BA%D0%B8), принцип распространения очень похож на то, как мы обучали один нейрон - это градиентный спуск, но по \"всей нейросети\" сразу.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "oK7Vi4bxYJdZ"
   },
   "source": [
    "Backpropagation работает корректно благодаря ***chain rule*** (=правилу взятия производной сложной функции):  \n",
    "\n",
    "Если $f(x) = f(g(x))$, то:  \n",
    "\n",
    "$$\\frac{\\partial{f}}{\\partial{x}} = \\frac{\\partial{f}}{\\partial{g}} \\frac{\\partial{g}}{\\partial{x}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "collapsed": true,
    "id": "WKvMsaEBYJda"
   },
   "source": [
    "Более подробно про backpropagation можно прочитать здесь (на английском):  https://mattmazur.com/2015/03/17/a-step-by-step-backpropagation-example/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "z5dyjPVNYJdc"
   },
   "source": [
    "<h3 style=\"text-align: center;\"><b>Многослойная нейросеть на PyTorch</b></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "T9ufk3ECYJde"
   },
   "source": [
    "Ешё раз напомним про основные компоненты нейросети:\n",
    "\n",
    "- непосредственно, сама **архитектура** нейросети (сюда входят типы функций активации у каждого нейрона);\n",
    "- начальная **инициализация** весов каждого слоя;\n",
    "- метод **оптимизации** нейросети (сюда ещё входит метод изменения `learning_rate`);\n",
    "- размер **батчей** (`batch_size`);\n",
    "- количетсво **эпох** обучения (`num_epochs`);\n",
    "- **функция потерь** (`loss`);  \n",
    "- тип **регуляризации** нейросети (для каждого слоя можно свой);  \n",
    "\n",
    "То, что связано с ***данными и задачей***:  \n",
    "- само **качество** выборки (непротиворечивость, чистота, корректность постановки задачи);  \n",
    "- **размер** выборки;  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9KrWarqTYJdf"
   },
   "source": [
    "Cоздадим двухслойную нейросеть из 100 нейронов:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bLjkPg19YJdg"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import torch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iCDVRvQJYJdl"
   },
   "source": [
    "Генерация и отрисовка датасета:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "k0J27RcLYJdm"
   },
   "outputs": [],
   "source": [
    "N = 100\n",
    "D = 2\n",
    "K = 3\n",
    "X = np.zeros((N * K, D))\n",
    "y = np.zeros(N * K, dtype='uint8')\n",
    "\n",
    "for j in range(K):\n",
    "    ix = range(N * j,N * (j + 1))\n",
    "    r = np.linspace(0.0, 1, N)\n",
    "    t = np.linspace(j * 4, (j + 1) * 4,N) + np.random.randn(N) * 0.2 # theta\n",
    "    X[ix] = np.c_[r * np.sin(t), r * np.cos(t)]\n",
    "    y[ix] = j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X9FHhqX_YJdp"
   },
   "source": [
    "Не забываем оборачивать данные (без этого градиенты не посчитать):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "pQINaQqZYJdq"
   },
   "outputs": [],
   "source": [
    "X = torch.autograd.Variable(torch.FloatTensor(X))\n",
    "y = torch.autograd.Variable(torch.LongTensor(y.astype(np.int64)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Who9mS8oYJdu",
    "outputId": "1ec6e30a-2cd9-4bd6-d0e0-3b7c936d1b8a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([300, 2]) torch.Size([300])\n"
     ]
    }
   ],
   "source": [
    "print(X.data.shape, y.data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "I-9dFW5CYJd0"
   },
   "source": [
    "Сама ячейка с нейросетью и обучением:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "kf-YapleYJd1",
    "outputId": "d71315ae-670a-48e3-bcf7-b425ebe198fe"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\izakharkin\\anaconda3\\envs\\vision\\lib\\site-packages\\torch\\nn\\functional.py:52: UserWarning: size_average and reduce args will be deprecated, please use reduction='sum' instead.\n",
      "  warnings.warn(warning.format(ret))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 330.8737487792969\n",
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   "source": [
    "# N - размер батча (batch_size, нужно для метода оптимизации); \n",
    "# D_in - размерность входа (количество признаков у объекта);\n",
    "# H - размерность скрытых слоёв; \n",
    "# D_out - размерность выходного слоя (суть - количество классов)\n",
    "N, D_in, H, D_out = 64, 2, 100, 3\n",
    "\n",
    "# Use the nn package to define our model and loss function.\n",
    "two_layer_net = torch.nn.Sequential(\n",
    "    torch.nn.Linear(D_in, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, D_out),\n",
    ")\n",
    "\n",
    "loss_fn = torch.nn.CrossEntropyLoss(size_average=False)\n",
    "\n",
    "learning_rate = 1e-4\n",
    "optimizer = torch.optim.SGD(two_layer_net.parameters(), lr=learning_rate)\n",
    "for t in range(500):\n",
    "    # forward\n",
    "    y_pred = two_layer_net(X)\n",
    "\n",
    "    # loss\n",
    "    loss = loss_fn(y_pred, y)\n",
    "    print('{} {}'.format(t, loss.data))\n",
    "\n",
    "    # зануляем градиенты (чтобы не было остатка с редыдущего шага)\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    # backward\n",
    "    loss.backward()\n",
    "\n",
    "    # обновляем\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zTQiN0bcYJd6"
   },
   "source": [
    "**Обратите внимание:** несмотря на то, что это задача 3-х классовой классификации и столбец $y$ нужно по-хорошему кодировать OneHotEncoding'ом, мы подали просто столбец из 0, 1 и 2 и всё отработало. Дело в том, что PyTorch сам делает OneHot в таком случае."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "apsWWq17YJd8"
   },
   "source": [
    "Проверим, насколько хороша наша сеть из 100 нейронов:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "X0ICB6Z-YJd-"
   },
   "outputs": [],
   "source": [
    "# Обратно в Numpy для отрисовки\n",
    "X = X.data.numpy()\n",
    "y = y.data.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JvjfvgbPYJeB",
    "outputId": "cf5545ff-3315-45c9-c674-af44f63a346b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = 0.02\n",
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "grid_tensor = torch.FloatTensor(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "Z = two_layer_net(torch.autograd.Variable(grid_tensor))\n",
    "Z = Z.data.numpy()\n",
    "Z = np.argmax(Z, axis=1)\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "\n",
    "plt.contourf(xx, yy, Z, cmap=plt.cm.rainbow, alpha=0.3)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "\n",
    "plt.title('Спираль', fontsize=15)\n",
    "plt.xlabel('$x$', fontsize=14)\n",
    "plt.ylabel('$y$', fontsize=14)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "G2wNgoh5YJeG"
   },
   "source": [
    "Подберём гиперпараметры получше:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = torch.autograd.Variable(torch.FloatTensor(X))\n",
    "y = torch.autograd.Variable(torch.LongTensor(y.astype(np.int64)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\izakharkin\\anaconda3\\envs\\vision\\lib\\site-packages\\torch\\nn\\functional.py:52: UserWarning: size_average and reduce args will be deprecated, please use reduction='sum' instead.\n",
      "  warnings.warn(warning.format(ret))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 329.6793212890625\n",
      "1 327.8143615722656\n",
      "2 326.1004943847656\n",
      "3 324.5147399902344\n",
      "4 322.9456787109375\n",
      "5 321.3118896484375\n",
      "6 319.5968933105469\n",
      "7 317.75592041015625\n",
      "8 315.75390625\n",
      "9 313.5726318359375\n",
      "10 311.1824645996094\n",
      "11 308.5584411621094\n",
      "12 305.68798828125\n",
      "13 302.5540771484375\n",
      "14 299.15460205078125\n",
      "15 295.4794006347656\n",
      "16 291.5202331542969\n",
      "17 287.2996826171875\n",
      "18 282.85137939453125\n",
      "19 278.21435546875\n",
      "20 273.4761657714844\n",
      "21 268.6789245605469\n",
      "22 263.89453125\n",
      "23 259.163818359375\n",
      "24 254.56350708007812\n",
      "25 250.1515655517578\n",
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    {
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     ]
    }
   ],
   "source": [
    "N, D_in, H, D_out = 64, 2, 100, 3\n",
    "\n",
    "better_net = torch.nn.Sequential(\n",
    "    torch.nn.Linear(D_in, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, D_out),\n",
    ")\n",
    "\n",
    "loss_fn = torch.nn.CrossEntropyLoss(size_average=False)\n",
    "\n",
    "learning_rate = 1e-3\n",
    "optimizer = torch.optim.SGD(better_net.parameters(), lr=learning_rate)\n",
    "for t in range(1000):\n",
    "    # forward\n",
    "    y_pred = better_net(X)\n",
    "\n",
    "    # loss\n",
    "    loss = loss_fn(y_pred, y)\n",
    "    print('{} {}'.format(t, loss.data))\n",
    "\n",
    "    # зануляем градиенты (чтобы не было остатка с редыдущего шага)\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    # backward\n",
    "    loss.backward()\n",
    "\n",
    "    # обновляем\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = 0.02\n",
    "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                     np.arange(y_min, y_max, h))\n",
    "grid_tensor = torch.FloatTensor(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "Z = better_net(torch.autograd.Variable(grid_tensor))\n",
    "Z = Z.data.numpy()\n",
    "Z = np.argmax(Z, axis=1)\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 8))\n",
    "\n",
    "plt.contourf(xx, yy, Z, cmap=plt.cm.rainbow, alpha=0.3)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.rainbow)\n",
    "\n",
    "plt.xlim(xx.min(), xx.max())\n",
    "plt.ylim(yy.min(), yy.max())\n",
    "\n",
    "plt.title('Спираль', fontsize=15)\n",
    "plt.xlabel('$x$', fontsize=14)\n",
    "plt.ylabel('$y$', fontsize=14)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предлагается самостоятельно проанализировать то, что было изменено, чтобы улучшить качество модели (и *обратить на это внимание*)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6N_9wfvPYJeK"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H_thmQJOYJeK"
   },
   "source": [
    "<h3 style=\"text-align: center;\"><b>Полезные ссылки</b></h3>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RpSrLf9FYJeL"
   },
   "source": [
    "1). *Примеры написания нейросетей на PyTorch (офийиальные туториалы) (на английском): https://pytorch.org/tutorials/beginner/pytorch_with_examples.html#examples  \n",
    "https://pytorch.org/tutorials/beginner/blitz/cifar10_tutorial.html*\n",
    "\n",
    "2). Курс Стэнфордского Университета:  http://cs231n.github.io/\n",
    "\n",
    "3). Практически исчерпывающая информация по основам нейросетей (из cs231n) (на английском):  \n",
    "\n",
    "http://cs231n.github.io/neural-networks-1/,  \n",
    "http://cs231n.github.io/neural-networks-2/,  \n",
    "http://cs231n.github.io/neural-networks-3/,  \n",
    "http://cs231n.github.io/neural-networks-case-study/#linear\n",
    "\n",
    "4). *Хорошие статьи по основам нейросетей (на английском):  http://neuralnetworksanddeeplearning.com/chap1.html*\n",
    "\n",
    "5). *Наглядная демонстрация того, как обучаются нейросети:  https://cs.stanford.edu/people/karpathy/convnetjs/*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1Qldb1U5YJeM"
   },
   "source": [
    "6). *Подробнее про backpropagation -- статья на Medium: https://medium.com/autonomous-agents/backpropagation-how-neural-networks-learn-complex-behaviors-9572ac161670*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "g1HSslRhYJeN"
   },
   "source": [
    "7). *Статья из интернета по Backprop: http://page.mi.fu-berlin.de/rojas/neural/chapter/K7.pdf*"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "[seminar]mlp_pytorch.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}