presentations/03 - Neural Networks/mnist.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SUa0f0Y_xlIj"
      },
      "source": [
        "# MNIST Dataset com MLP\n",
        "\n",
        "O dataset MNIST (Modified National Institute of Standards and Technology) é amplamente utilizado no campo de machine learning e visão computacional para o treinamento e teste de modelos de reconhecimento de padrões, especialmente redes neurais. Ele consiste em 70.000 imagens em escala de cinza de dígitos manuscritos (0 a 9), sendo 60.000 para treinamento e 10.000 para teste. Cada imagem tem uma resolução de 28x28 pixels, onde cada pixel possui um valor de intensidade variando de 0 (preto) a 255 (branco)."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Importe de Bibliotecas e Dowload do Dataset"
      ],
      "metadata": {
        "id": "kuhWg5D90amR"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "dF28F7XMxlIm"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torchvision\n",
        "import torchvision.models as models # Possibilita o save e load dos modelos\n",
        "import torch.nn.functional as F # Dá acesso às funções de ativação e de perda\n",
        "import torch.optim as optim # Dá acesso a diversos otimizadores\n",
        "import torch.nn as nn # Possiblita criar a rede neural\n",
        "from torchvision.transforms import ToTensor\n",
        "from torch.utils.data import DataLoader\n",
        "from torchvision import datasets\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Outra possibilidade de dataset é o Fashion MNIST. Neste caso, temos imagens 28x28 pixels em escala de cinza acerca de 10 categorias relacionadas a roupas, como camiseta, calça e tênis."
      ],
      "metadata": {
        "id": "00z5uMNEsj13"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "J5gADKP_xlIt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ff05e233-0e19-4700-aa1e-61489046cc02"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-images-idx3-ubyte.gz to data/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 9912422/9912422 [00:00<00:00, 17614102.58it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting data/MNIST/raw/train-images-idx3-ubyte.gz to data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/train-labels-idx1-ubyte.gz to data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 28881/28881 [00:00<00:00, 476014.50it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting data/MNIST/raw/train-labels-idx1-ubyte.gz to data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-images-idx3-ubyte.gz to data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 1648877/1648877 [00:00<00:00, 4434304.07it/s]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting data/MNIST/raw/t10k-images-idx3-ubyte.gz to data/MNIST/raw\n",
            "\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Failed to download (trying next):\n",
            "HTTP Error 403: Forbidden\n",
            "\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz\n",
            "Downloading https://ossci-datasets.s3.amazonaws.com/mnist/t10k-labels-idx1-ubyte.gz to data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 4542/4542 [00:00<00:00, 2939896.41it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Extracting data/MNIST/raw/t10k-labels-idx1-ubyte.gz to data/MNIST/raw\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\n"
          ]
        }
      ],
      "source": [
        "train_data = datasets.MNIST(\n",
        "    root = 'data',\n",
        "    train = True,\n",
        "    transform = ToTensor(),\n",
        "    download = True\n",
        ")\n",
        "\n",
        "test_data = datasets.MNIST(\n",
        "    root = 'data',\n",
        "    train = False,\n",
        "    transform = ToTensor(),\n",
        "    download = True\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u1qQqq0VxlIv",
        "outputId": "41e73ba0-31fd-4ed0-afef-f72d43e20878"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dataset MNIST\n",
              "    Number of datapoints: 60000\n",
              "    Root location: data\n",
              "    Split: Train\n",
              "    StandardTransform\n",
              "Transform: ToTensor()"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "train_data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5dshP-SyxlIx",
        "outputId": "912ec22f-6c75-43aa-d445-ac60c40723df"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dataset MNIST\n",
              "    Number of datapoints: 10000\n",
              "    Root location: data\n",
              "    Split: Test\n",
              "    StandardTransform\n",
              "Transform: ToTensor()"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "test_data"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Criação dos Dataloaders e Visualização dos Dados"
      ],
      "metadata": {
        "id": "aXwPfnyZ0qMn"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "WGXStyH4xlIy"
      },
      "outputs": [],
      "source": [
        "# batch_size: tamanho de cada lote\n",
        "# shuffle: embaralhamento do dataset após cada época de treinamento (ajuda a evitar overfitting)\n",
        "\n",
        "train_dataloader = DataLoader(train_data, batch_size=64, shuffle=True)\n",
        "test_dataloader = DataLoader(test_data, batch_size=64, shuffle=True)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for (data, target) in train_dataloader:\n",
        "    print('data:', data.size(), 'type:', data.type())\n",
        "    print('target:', target.size(), 'type:', target.type())\n",
        "    break\n",
        "\n",
        "pltsize=1\n",
        "plt.figure(figsize=(10*pltsize, pltsize))\n",
        "\n",
        "for i in range(10):\n",
        "    plt.subplot(1,10,i+1)\n",
        "    plt.axis('off')\n",
        "    plt.imshow(data[i,:,:,:].numpy().reshape(28,28), cmap=\"gray_r\")\n",
        "    plt.title('Classe: '+str(target[i].item()))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 160
        },
        "id": "jsKeAl0KXmlo",
        "outputId": "d3343622-e2e2-4d47-d1f9-170e742107d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "data: torch.Size([64, 1, 28, 28]) type: torch.FloatTensor\n",
            "target: torch.Size([64]) type: torch.LongTensor\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x100 with 10 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Criação da Rede"
      ],
      "metadata": {
        "id": "cNNeXCf30xgz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Outras funções de ativação comuns:\n",
        "\n",
        "\n",
        "*   nn.Sigmoid()\n",
        "*   nn.Softplus()\n",
        "*   nn.Tanh()\n",
        "\n"
      ],
      "metadata": {
        "id": "jMTEqQVyLZ2c"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "htuVjh9XxlIz"
      },
      "outputs": [],
      "source": [
        "# Criação de uma classe derivada de nn.Module\n",
        "class NetWork(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "\n",
        "        # Definição das camadas da rede\n",
        "        # nn.Flatten() converte a matriz da imagem para um vetor unidimensional\n",
        "        self.layers = nn.Sequential(\n",
        "            nn.Flatten(),\n",
        "            nn.Linear(28*28, 100),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(100, 50),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(50, 10)\n",
        "        )\n",
        "\n",
        "    # Definição da propagação dos inputs x pels rede\n",
        "    def forward(self, x):\n",
        "        return self.layers(x)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cross Entropy:\n",
        "  Dadas as saídas da última camada da rede, podemos utilizar algumas estratégias para melhorar a interpretabilidade dos dados. Dentre elas, está a aplicação da função de ativção softmax, conforme segue:\n",
        "\n",
        "  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)\n",
        "\n",
        "  Com isso, podemos aplicar a função CrossEntropy aos novos valores:\n",
        "\n",
        "  $$\n",
        "  CE(p_i) = -\\sum_{i = 1}^{n} P(i) \\cdot log(p(i))\n",
        "  $$"
      ],
      "metadata": {
        "id": "QaEbP3hROKFX"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "baW0pY_hxlI1",
        "outputId": "de112431-925f-447f-ed47-78621676414f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rodando na cuda\n",
            "NetWork(\n",
            "  (layers): Sequential(\n",
            "    (0): Flatten(start_dim=1, end_dim=-1)\n",
            "    (1): Linear(in_features=784, out_features=100, bias=True)\n",
            "    (2): ReLU()\n",
            "    (3): Linear(in_features=100, out_features=50, bias=True)\n",
            "    (4): ReLU()\n",
            "    (5): Linear(in_features=50, out_features=10, bias=True)\n",
            "  )\n",
            ")\n"
          ]
        }
      ],
      "source": [
        "# Verifica se é possível alocar uma GPU. Senão, aloca uma CPU\n",
        "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
        "print(f\"Rodando na {device}\")\n",
        "\n",
        "# Instancia o modelo e transfere para device\n",
        "model = NetWork().to(device)\n",
        "print(model)\n",
        "\n",
        "# Função de perda\n",
        "loss_function = nn.CrossEntropyLoss()\n",
        "\n",
        "# Otimizador (lr -> taxa de aprendizado)\n",
        "optimizer = optim.SGD(model.parameters(), lr = 0.001)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Treinamento do Modelo"
      ],
      "metadata": {
        "id": "SeIKWdmC4Go1"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "qVK8RqdfxlI2"
      },
      "outputs": [],
      "source": [
        "# Calcula a quantidade de predições acertadas\n",
        "def correct(output, target):\n",
        "    # Obtém o output de maior valor (predição)\n",
        "    predicted_digits = output.argmax(1)\n",
        "    correct_ones = (predicted_digits == target).type(torch.float)\n",
        "    return correct_ones.sum().item()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "R4Otf7EqxlI3"
      },
      "outputs": [],
      "source": [
        "# Define o treinamento do modelo\n",
        "def train(model, dataloader, lossfunc, optimizer):\n",
        "    model.train()\n",
        "\n",
        "    # Total de batches\n",
        "    num_batches = len(dataloader)\n",
        "\n",
        "    # Total de amostras no dataset\n",
        "    num_items = len(dataloader.dataset)\n",
        "\n",
        "    # Perda e precisão acumuladas\n",
        "    cum_loss = 0.0\n",
        "    cum_correct = 0.0\n",
        "\n",
        "    for data, target in dataloader:\n",
        "        data = data.to(device)\n",
        "        target = target.to(device)\n",
        "\n",
        "        # Obtém as saídas da última camada\n",
        "        output = model(data)\n",
        "\n",
        "        # Calcula a perda\n",
        "        loss = lossfunc(output, target)\n",
        "\n",
        "        cum_loss += loss\n",
        "        cum_correct += correct(output, target)\n",
        "\n",
        "        # Calcula as derivadas pelo backpropagation\n",
        "        loss.backward()\n",
        "\n",
        "        # Atualiza os pesos\n",
        "        optimizer.step()\n",
        "\n",
        "        # Zera as derivadas\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "    train_loss = cum_loss/num_batches\n",
        "    accuracy = cum_correct/num_items\n",
        "    print(f\"Perda Média: {train_loss:7f}, precisão: {accuracy:.2%}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GGqlZqHLxlI4",
        "outputId": "46ff7cfb-23ec-403c-98dd-ccc32147920f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training epoch: 1\n",
            "Perda Média: 2.295493, precisão: 11.37%\n",
            "Training epoch: 2\n",
            "Perda Média: 2.271132, precisão: 17.08%\n",
            "Training epoch: 3\n",
            "Perda Média: 2.234533, precisão: 27.66%\n",
            "Training epoch: 4\n",
            "Perda Média: 2.175642, precisão: 41.95%\n",
            "Training epoch: 5\n",
            "Perda Média: 2.081007, precisão: 55.04%\n",
            "Training epoch: 6\n",
            "Perda Média: 1.934949, precisão: 60.33%\n",
            "Training epoch: 7\n",
            "Perda Média: 1.728839, precisão: 63.64%\n",
            "Training epoch: 8\n",
            "Perda Média: 1.476353, precisão: 67.54%\n",
            "Training epoch: 9\n",
            "Perda Média: 1.221209, precisão: 72.22%\n",
            "Training epoch: 10\n",
            "Perda Média: 1.015930, precisão: 76.28%\n",
            "Training epoch: 11\n",
            "Perda Média: 0.870649, precisão: 78.96%\n",
            "Training epoch: 12\n",
            "Perda Média: 0.768918, precisão: 80.85%\n",
            "Training epoch: 13\n",
            "Perda Média: 0.694444, precisão: 82.17%\n",
            "Training epoch: 14\n",
            "Perda Média: 0.637888, precisão: 83.35%\n",
            "Training epoch: 15\n",
            "Perda Média: 0.593346, precisão: 84.36%\n",
            "CPU times: user 1min 55s, sys: 721 ms, total: 1min 56s\n",
            "Wall time: 1min 57s\n"
          ]
        }
      ],
      "source": [
        "%%time\n",
        "\n",
        "epochs = 15\n",
        "for epoch in range(epochs):\n",
        "    print(f\"Training epoch: {epoch+1}\")\n",
        "    train(model, train_dataloader, loss_function, optimizer)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Teste do Modelo"
      ],
      "metadata": {
        "id": "rBCZ7nmV4Kc7"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "rW47f5ALxlI5"
      },
      "outputs": [],
      "source": [
        "# Define o treinamento do modelo\n",
        "def test(model, dataloader, lossfunc):\n",
        "    model.eval()\n",
        "\n",
        "    num_batches = len(dataloader)\n",
        "    num_items = len(dataloader.dataset)\n",
        "\n",
        "    cum_loss = 0.0\n",
        "    cum_correct = 0.0\n",
        "\n",
        "    # Desabilita o cálculo do gradiente\n",
        "    with torch.no_grad():\n",
        "        for data, target in dataloader:\n",
        "            data = data.to(device)\n",
        "            target = target.to(device)\n",
        "\n",
        "            output = model(data)\n",
        "\n",
        "            loss = lossfunc(output, target)\n",
        "\n",
        "            cum_loss += loss\n",
        "            cum_correct += correct(output, target)\n",
        "\n",
        "    train_loss = cum_loss/num_batches\n",
        "    accuracy = cum_correct/num_items\n",
        "    print(f\"Perda Média: {train_loss:7f}, precisão: {accuracy:.2%}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iXexFf5WxlI5",
        "outputId": "beed6574-0cee-4064-f1c9-96c6a5347b1d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Perda Média: 0.555768, precisão: 85.14%\n"
          ]
        }
      ],
      "source": [
        "test(model, test_dataloader, loss_function)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Salvamento e Carregamento do Modelo"
      ],
      "metadata": {
        "id": "zDkaU1pV44so"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "torch.save(model.state_dict(), 'model_weights.pth')"
      ],
      "metadata": {
        "id": "h59eJGzC47T9"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model2 = NetWork()\n",
        "model2 = torch.load('model_weights.pth', weights_only=True)"
      ],
      "metadata": {
        "id": "mJlxn21dIMhu"
      },
      "execution_count": 14,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.10.12"
    },
    "colab": {
      "provenance": [],
      "gpuType": "T4"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}