11a_generative_adversarial_network.ipynb

{
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  {
   "cell_type": "markdown",
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   "source": [
    "# Music machine learning - Adversarial learning\n",
    "\n",
    "### Author: Philippe Esling (esling@ircam.fr)\n",
    "\n",
    "Generative adversarial networks (GANs) are neural networks that generate material, such as images, music, speech, or text, that is similar to what humans produce.\n",
    "\n",
    "In this course we will cover\n",
    "1. The global principle of [adversarial learning](#adversarial)\n",
    "2. How to train your own GAN on a [toy dataset](#toy)\n",
    "3. A practical example on [MNIST](#mnist) using PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"adversarial\"></a>\n",
    "## Adversarial learning\n",
    "\n",
    "This is the code used in first example of the article [Generative Adversarial Networks: Build Your First Models](https://realpython.com/generative-adversarial-networks/) on Real Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from helper_plot import hdr_plot_style\n",
    "hdr_plot_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generative adversarial networks (GANs) are machine learning systems that can learn to mimic a given distribution of data. GANs consist of two neural networks, one trained to *generate* data and the other trained to *discriminate* fake data from real data (hence the “adversarial” nature of the model).\n",
    "\n",
    "GANs require to define two neural networks, one called the *generator* and the other called the *discriminator*. The role of the generator is to estimate the probability distribution of the real samples in order to provide generated samples resembling real data. The discriminator, in turn, is trained to estimate the probability that a given sample came from the real data rather than being provided by the generator.\n",
    "\n",
    "These two networks define a *zero-sum game* as they are trained to compete with each other: the generator tries to get better at fooling the discriminator, while the discriminator tries to get better at identifying generated samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training GANs on a toy dataset\n",
    "\n",
    "To understand how GAN training works, consider a toy example with a dataset composed of two-dimensional samples $(x_{1}, x_{2})$, with $x_{1}$ in the interval from $0$ to $2\\pi$ and $x_{2} = sin(x_{1})$, as illustrated in the following "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_data_length = 1024\n",
    "train_data = torch.zeros((train_data_length,2))\n",
    "train_data[:,0] = 2*math.pi*torch.rand(train_data_length)\n",
    "train_data[:,1] = torch.sin(train_data[:,0])\n",
    "train_labels = torch.zeros(train_data_length)\n",
    "trainset = [(train_data[i], train_labels[i]) for i in range(train_data_length)]\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(train_data[:, 0], train_data[:, 1], '.')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, we need to define a `DataLoader` that will provide us with the training data in different batches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 32\n",
    "train_loader = torch.utils.data.DataLoader(trainset, batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we define the generator, which is fed with random data from a latent space. Its role is to generate data resembling the real samples. In this example, you have a two-dimensional latent space, so that the generator is fed with random $(z_{1}, z_{2})$ pairs and is required to transform them so that they resemble the real samples.\n",
    "\n",
    "We can define any type of network in the generator, given that it has sufficient complexity to generate the underlying type of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Generator(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.model = nn.Sequential(\n",
    "            nn.Linear(2, 16),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(16, 32),\n",
    "            nn.ReLU(),\n",
    "            nn.Linear(32, 2),            \n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        output = self.model(x)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "generator = Generator()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In turn, the discriminator is fed with either real samples from the training dataset or generated samples provided by the generator. Its role will be to estimate the probability that the input belongs to the real dataset or is a generated one. The training is performed so that the discriminator outputs 1 when it is fed a real sample and 0 when it is fed a generated sample. Again, we can choose any architecture of our liking for this network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Discriminator(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.model = nn.Sequential(\n",
    "            nn.Linear(2, 256),\n",
    "            nn.ReLU(),\n",
    "            nn.Dropout(0.3),\n",
    "            nn.Linear(256, 128),\n",
    "            nn.ReLU(),\n",
    "            nn.Dropout(0.3),\n",
    "            nn.Linear(128, 64),\n",
    "            nn.ReLU(),\n",
    "            nn.Dropout(0.3),\n",
    "            nn.Linear(64, 1),\n",
    "            nn.Sigmoid()\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        output = self.model(x)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "discriminator = Discriminator()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now define our training hyper-parameters that will condition the learning procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.001\n",
    "num_epochs = 300\n",
    "loss_function = nn.BCELoss()\n",
    "optimizer_discriminator = torch.optim.Adam(discriminator.parameters(), lr=lr)\n",
    "optimizer_generator = torch.optim.Adam(generator.parameters(), lr=lr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training procedure is defined as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_d = torch.zeros(int(num_epochs / 10))\n",
    "loss_g = torch.zeros(int(num_epochs / 10))\n",
    "for epoch in range(num_epochs):\n",
    "    for n, (real_samples, _) in enumerate(train_loader):\n",
    "        \n",
    "        ######################\n",
    "        # YOUR CODE GOES HERE\n",
    "        ######################\n",
    "\n",
    "    # Show loss\n",
    "    if epoch % 10 == 0 and n == batch_size - 1:\n",
    "        loss_d[int(epoch / 10)] = loss_discriminator\n",
    "        loss_g[int(epoch / 10)] = loss_generator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we look at the evolution of different losses, we can clearly see the competing nature of both networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1450baa50>]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(loss_d.detach())\n",
    "plt.plot(loss_g.detach())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can visualize the samples that can be generated by drawing some random latent positions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "latent_space_samples = torch.randn(100, 2)\n",
    "generated_samples = generator(latent_space_samples)\n",
    "generated_samples = generated_samples.detach()\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(generated_samples[:,0], generated_samples[:,1], '.')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the randomly generated points closely follow the original distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Handwritten digits generator with GAN\n",
    "\n",
    "Generative adversarial networks can also generate high-dimensional samples such as images. In this example, we are going to define a GAN to generate images of handwritten digits. For that, we will train the models using the infamous MNIST dataset. \n",
    "\n",
    "Again, we are going to make use of `torch` and `torchvision` . Notably, we will use `transforms` to obtain the training data and perform image conversions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch import nn, optim\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import os"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this example uses images in the training set, the models need to be more complex, with a larger number of parameters. This makes the training process slower, taking about two minutes per epoch when running on CPU. To reduce the training time, you can use a GPU to train the model if you have one available. The following piece of code allows to automatically select the best device available on your system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "device = ''\n",
    "if torch.cuda.is_available():\n",
    "    device = torch.device('cuda')\n",
    "else:\n",
    "    device = torch.device('cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparing the training data\n",
    "\n",
    "The MNIST dataset consists of 28 × 28 pixel grayscale images of handwritten digits from 0 to 9. To use them with PyTorch, we need to convert them to Tensors. Also, in order to ensure adequate learning, it is always best to normalize the data. This is were we make use of `torchvision.transforms` in order to perfom thesse automatically while loading the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "transform = transforms.Compose(\n",
    "    [transforms.ToTensor(),\n",
    "     transforms.Normalize((0.5,), (0.5,))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, as usual, we can load both the *training* and *testing* data with the datasets objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 32\n",
    "# Load the training set\n",
    "train_set = torchvision.datasets.MNIST(root='./data', train=True, download=True, transform=transform)\n",
    "# Create a batched data loader\n",
    "train_loader = torch.utils.data.DataLoader(train_set, batch_size=batch_size, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we plot some examples of the train set, to better understand the underlying data that we are working with."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(20,5))\n",
    "real_samples, mnist_labels = next(iter(train_loader))\n",
    "for i in range(16):\n",
    "    ax = plt.subplot(1, 16, i+1)\n",
    "    plt.imshow(real_samples[i].reshape(28, 28), cmap='gray_r')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "plt.tight_layout()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing the discriminator and generator\n",
    "\n",
    "Here, we are going to first define our *discriminator*. In our case, we will use an MLP, that will be responsible for receiving the images and trying to find which images are fake. The model is defined as follows "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Discriminator(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        \n",
    "        ######################\n",
    "        # YOUR CODE GOES HERE\n",
    "        ######################\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = x.view(-1, 784)\n",
    "        output = self.model(x)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To input the image coefficients into the MLP neural network, you vectorize them so that the neural network receives vectors with 784 coefficients. The vectorization occurs in the first line of `.forward()`, as the call to `x.view()` converts the shape of the input tensor. In this case, the original shape of the input x is 32 × 1 × 28 × 28, where 32 is the batch size you’ve set up. After the conversion, the shape of x becomes 32 × 784, with each line representing the coefficients of an image of the training set.\n",
    "\n",
    "To run the discriminator model using the GPU, you have to instantiate it and send it to the GPU with .to(). To use a GPU when there’s one available, you can send the model to the device object you created earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "discriminator = Discriminator().to(device=device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the generator is going to generate more complex data, it’s necessary to increase the dimensions of the input from the latent space. In this case, the generator is going to be fed a 100-dimensional input and will provide an output with 784 coefficients, which will be organized in a 28 × 28 tensor representing an image. Here is the complete generator model code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Generator(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        \n",
    "        ######################\n",
    "        # YOUR CODE GOES HERE\n",
    "        ######################\n",
    "\n",
    "    def forward(self, x):\n",
    "        #x = x.view(x.size(0), 100)\n",
    "        output = self.model(x)\n",
    "        output = output.view(x.size(0), 1, 28, 28)\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "generator = Generator().to(device=device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, we define the training hyper-parameters that will condition our learning procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.0001\n",
    "num_epochs = 50\n",
    "loss_function = nn.BCELoss()\n",
    "optimizer_discriminator = torch.optim.Adam(discriminator.parameters(), lr=lr)\n",
    "optimizer_generator = torch.optim.Adam(generator.parameters(), lr=lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "latent_space_samples_plot = torch.randn((16, 100)).to(device=device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load trained NN when it exists, or train a new NN\n",
    "if os.path.isfile('discriminator.pt') and os.path.isfile('generator.pt'):\n",
    "    discriminator.load_state_dict(torch.load('./discriminator.pt'))\n",
    "    generator.load_state_dict(torch.load('./generator.pt'))   \n",
    "else:\n",
    "    for epoch in range(num_epochs):\n",
    "        for n, (real_samples, mnist_labels) in enumerate(train_loader):\n",
    "        \n",
    "            ######################\n",
    "            # YOUR CODE GOES HERE\n",
    "            ######################\n",
    "\n",
    "            # Show loss\n",
    "            if n == batch_size - 1:\n",
    "                print(f\"Epoch: {epoch} Loss D.: {loss_discriminator}\")\n",
    "                print(f\"Epoch: {epoch} Loss G.: {loss_generator}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "latent_space_samples = torch.randn(batch_size, 100).to(device=device)\n",
    "\n",
    "generated_samples = generator(latent_space_samples)\n",
    "generated_samples = generated_samples.cpu().detach()\n",
    "\n",
    "plt.figure(dpi=150)\n",
    "for i in range(16):\n",
    "    ax = plt.subplot(4, 4, i+1)\n",
    "    plt.imshow(generated_samples[i].reshape(28, 28), cmap='gray_r')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save trained NN parameters\n",
    "torch.save(generator.state_dict(), 'generator.pt')\n",
    "torch.save(discriminator.state_dict(), 'discriminator.pt')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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