tutorials/EGG walkthrough with a MNIST autoencoder.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "## Intro\n",
    "\n",
    "EGG provides multiple components to create different types of games. In particular, EGG has strong tooling for creating one-step Sender/Receiver games. In these games, two agents, Sender and Receiver, are trained to perform a common task while following a simple communication protocol:\n",
    "\n",
    " * Sender receives an input (e.g., an image) and sends a single message to Receiver;\n",
    " * Receiver obtains the message and (optionally) its own input, produces an output.\n",
    "\n",
    "This type of games includes, for instance, signaling games and discrete auto-encoders. In a nutshell, any Sender/Receiver game only differs in terms of (a) input data, (b) agents' architecture, (c) communication type (one-symbol, fixed-lentgh or variable-length multiple-symbol messages), (d) loss. EGG allows us to create new games by only specifying those components. \n",
    "\n",
    "In most cases, training of agents with discrete channel communication is done either via Gumbel-Softmax relaxation or by means of Reinforce. EGG allows to switch between the two with minimal changes in the logic.\n",
    "\n",
    "\n",
    "\n",
    "## MNIST Auto-encoder game\n",
    "\n",
    "In this  tutorial we will create a conceptually simple, but fully-featured Sender/Receiver game. In this game, Sender and Receiver are trained together such that Sender tries to encode a MNIST digit in a discrete message and Receiver will try to decode it from the message.\n",
    "\n",
    "While implementing this game, we will walk through several steps, typical for creating a new game:\n",
    " * pre-train a _vision_ module for the Sender agent by training it to classify digits;\n",
    " * use the pre-trained vision module to implement Sender and Receiver that communicate via a single symbol messages and analyse the trained models;\n",
    " * update the agents to allow variable-length multi-symbol messages.\n",
    "\n",
    "NB: depending on the computational resources you have available, this might be slow to run. To get at least a sense of the full pipeline, consider reducing the number of training epochs, or, alternatively, run a Google Colab version of the tutorial using a GPU.\n",
    "\n",
    "So let's start!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting git+https://github.com/facebookresearch/EGG.git\n",
      "  Cloning https://github.com/facebookresearch/EGG.git to /tmp/pip-req-build-o6iqeqi2\n",
      "  Running command git clone -q https://github.com/facebookresearch/EGG.git /tmp/pip-req-build-o6iqeqi2\n",
      "Requirement already satisfied (use --upgrade to upgrade): EGG==0.1.0 from git+https://github.com/facebookresearch/EGG.git in /private/home/kharitonov/work/myEGG\n",
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      "Building wheels for collected packages: EGG\n",
      "  Building wheel for EGG (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Stored in directory: /tmp/pip-ephem-wheel-cache-przkuffy/wheels/69/45/1b/d73e992bfa599a0e529de656c959a96277709640f819d1fc64\n",
      "Successfully built EGG\n"
     ]
    }
   ],
   "source": [
    "# if you are running this notebook via Google Colab, you have to install EGG first\n",
    "!pip install git+https://github.com/facebookresearch/EGG.git\n",
    "# also you'll need to change the runtime to GPU (Runtime -> Change runtime type -> Hardware Accelator -> GPU)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import egg.core as core\n",
    "\n",
    "from torchvision import datasets, transforms\n",
    "from torch import nn\n",
    "from torch.nn import functional as F\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import numpy as np\n",
    "\n",
    "from pylab import rcParams\n",
    "rcParams['figure.figsize'] = 5, 10\n",
    "\n",
    "# For convenince and reproducibility, we set some EGG-level command line arguments here\n",
    "opts = core.init(params=['--random_seed=7', # will initialize numpy, torch, and python RNGs\n",
    "                         '--lr=1e-3',   # sets the learning rate for the selected optimizer \n",
    "                         '--batch_size=32',\n",
    "                         '--optimizer=adam'])\n",
    "\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In most cases, we want to start a script by initializing EGG by calling `core.init` Typically, we use command-line arguments for that (see https://github.com/fairinternal/EGG/blob/master/egg/core/CL.md for more details)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we implement our ```Vision``` module (a part of a standard MNIST [model](https://github.com/pytorch/examples/blob/master/mnist/main.py)) that maps a MNIST image into a 500-dimensional vector.\n",
    "To pre-train this ```Vision``` module, we'll use the auxilary task of classifying MNIST digits. For this, we also define a ```PretrainNet``` model that takes the output of ```Vision``` and classifies images into 10 classes (0, 1, ..., 9)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Vision(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Vision, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(1, 20, 5, 1)\n",
    "        self.conv2 = nn.Conv2d(20, 50, 5, 1)\n",
    "        self.fc1 = nn.Linear(4*4*50, 500)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.conv1(x))\n",
    "        x = F.max_pool2d(x, 2, 2)\n",
    "        x = F.relu(self.conv2(x))\n",
    "        x = F.max_pool2d(x, 2, 2)\n",
    "        x = x.view(-1, 4*4*50)\n",
    "        x = F.relu(self.fc1(x))\n",
    "        return x\n",
    "\n",
    "class PretrainNet(nn.Module):\n",
    "    def __init__(self, vision_module):\n",
    "        super(PretrainNet, self).__init__()\n",
    "        self.vision_module = vision_module\n",
    "        self.fc = nn.Linear(500, 10)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = self.vision_module(x)\n",
    "        x = self.fc(F.leaky_relu(x))\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need DataLoaders for MNIST...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "kwargs = {'num_workers': 1, 'pin_memory': True} if torch.cuda.is_available() else {}\n",
    "transform = transforms.ToTensor()\n",
    "\n",
    "batch_size = opts.batch_size # set via the CL arguments above\n",
    "train_loader = torch.utils.data.DataLoader(\n",
    "        datasets.MNIST('./data', train=True, download=True,\n",
    "           transform=transform),\n",
    "           batch_size=batch_size, shuffle=True, **kwargs)\n",
    "test_loader = torch.utils.data.DataLoader(\n",
    "        datasets.MNIST('./data', train=False, transform=transform),\n",
    "           batch_size=batch_size, shuffle=False, **kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, everything is ready to actually run the pre-training. First, we instantiate the modules and then run 10 epochs of MNIST digit recognition by a PretrainNet instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "vision = Vision()\n",
    "class_prediction = PretrainNet(vision) #  note that we pass vision - which we want to pretrain\n",
    "optimizer = core.build_optimizer(class_prediction.parameters()) #  uses command-line parameters we passed to core.init\n",
    "class_prediction = class_prediction.to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run very typical Pytorch training loop to pretrain the vision module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train Epoch: 0, mean loss: 0.12150704449613889\n",
      "Train Epoch: 1, mean loss: 0.04163755515615145\n",
      "Train Epoch: 2, mean loss: 0.02630081065495809\n",
      "Train Epoch: 3, mean loss: 0.01954123163620631\n",
      "Train Epoch: 4, mean loss: 0.015052006431420644\n",
      "Train Epoch: 5, mean loss: 0.013803999131917953\n",
      "Train Epoch: 6, mean loss: 0.009823401796817779\n",
      "Train Epoch: 7, mean loss: 0.010111083876589934\n",
      "Train Epoch: 8, mean loss: 0.008516478467981021\n",
      "Train Epoch: 9, mean loss: 0.007413214242955049\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(10):\n",
    "    mean_loss, n_batches = 0, 0\n",
    "    for batch_idx, (data, target) in enumerate(train_loader):\n",
    "        data, target = data.to(device), target.to(device)\n",
    "        optimizer.zero_grad()\n",
    "        output = class_prediction(data)\n",
    "        loss = F.cross_entropy(output, target)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        mean_loss += loss.mean().item()\n",
    "        n_batches += 1\n",
    "        \n",
    "    print(f'Train Epoch: {epoch}, mean loss: {mean_loss / n_batches}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Awesome! Now ```vision``` is a pre-trained ```Vision``` module and we can proceed to actually implement the communication game."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single-symbol communication\n",
    "\n",
    "As said before, Sender/Receiver games only differ in the data used, the architecture of the agents, the type of the channel, and the loss.\n",
    "We will start with the simplest communication case, one-symbol communication.\n",
    "\n",
    "\n",
    "Let's define our Sender (that will re-use the pre-trained ```vision``` module) and Receiver. \n",
    "For implementing single-symbol games, EGG provides special wrappers, ```GumbelSoftmaxWrapper``` and ```ReinforceWrapper``` that wrap an agent and implement the required Gumbel-Softmax or Reinforce-specific logic. Both wrappers assume that the agent returns log-probabilities over all terms for the vocabulary.\n",
    "\n",
    "We start by defining the logic of our agents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Sender(nn.Module):\n",
    "    def __init__(self, vision, output_size):\n",
    "        super(Sender, self).__init__()\n",
    "        self.fc = nn.Linear(500, output_size)\n",
    "        self.vision = vision\n",
    "        \n",
    "    def forward(self, x):\n",
    "        with torch.no_grad():\n",
    "            x = self.vision(x)\n",
    "        x = self.fc(x)\n",
    "        return x\n",
    "    \n",
    "    \n",
    "class Receiver(nn.Module):\n",
    "    def __init__(self, input_size):\n",
    "        super(Receiver, self).__init__()\n",
    "        self.fc = nn.Linear(input_size, 784)\n",
    "\n",
    "    def forward(self, channel_input, receiver_input=None):\n",
    "        x = self.fc(channel_input)\n",
    "        return torch.sigmoid(x)\n",
    "\n",
    "sender = Sender(vision, output_size=400)\n",
    "receiver = Receiver(input_size=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While ```GumbelSoftmaxWrapper``` and ```ReinforceWrapper``` have the same interface to the user's defined Sender and Receiver, they do differ in their output.\n",
    "\n",
    "Since ```GumbelSoftmaxWrapper``` uses relaxation of the symbols, it doesn't output the index of the used symbol; instead, it outputs a tensor of dimensions (batch size; vocab size) with potentially all elements being non-zero. In evaluation mode, it outputs a tensor of the same dimensionality, but with the one-hot encoded symbol of highest probability. In contrast, ```ReinforceWrapper``` directly outputs the index of the transmitted symbol (plus other data to be discussed below). \n",
    "\n",
    "To make the change of wrappers simpler, we define a special helper layer, `core.RelaxedEmbedding` which behaves as a standard `torch.nn.Embedding` layer if the inputs are indexes (i.e. are of type torch.long), or provides their relaxation, if they are a tensor of floats. You don't have to use this, but it makes changing the training from GS-based to RF-based and vice-versa very simple, because you do not need to worry about the type of the input that the Receiver will get.\n",
    "\n",
    "Furthermore, you can also wrap your Receiver agent logic in the `core.SymbolReceiverWrapper`. This wrapper would embed the input symbol via the `core.RelaxedEmbedding` and pass the resulting embedding to the user-implement agent.\n",
    "\n",
    "(NB: `core.RelaxedEmbedding` has the same initialization as `torch.nn.Embedding` - different from that of `nn.Linear`!)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apart from specifying the agents' architecture, we have to define the loss that the agents experience. By default, EGG expects the loss function to take the following arguments: Sender's input, the message transmitted, the input of the receiver, the output of the receiver, and the labels provided from the dataset. \n",
    "Any of those can be used or ignored. In the case of our MNIST auto-encoder game, there is no specific input for Receiver, so the game mechanics passes `None` instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(sender_input, _message, _receiver_input, receiver_output, _labels):\n",
    "    loss = F.binary_cross_entropy(receiver_output, sender_input.view(-1, 784), reduction='none').mean(dim=1)\n",
    "    return loss, {}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this loss function is differentiable; it doesn't have to be differentiable if the training is done via Reinforce. However, if it is the case, the training of Receiver might be able to exploit that. See the [readme](https://github.com/facebookresearch/EGG/blob/master/README.md#an-important-technical-point) for more discussion.\n",
    "\n",
    "Another common parameter that would be shared across all the games we'll implement is the size of the vocabulary. We set it to 10 as MNIST has 10 digits; although it might be fun to play with other values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "vocab_size = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training with Gumbel-Softmax\n",
    "\n",
    "The next step is to actually create the agents. We first discuss how training can be done with Gumbel-Softmax. For that, we instantiate our Sender and Receiver and wrap Sender into `core.GumbelSoftmaxWrapper`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "sender = Sender(vision, vocab_size)\n",
    "sender = core.GumbelSoftmaxWrapper(sender, temperature=1.0) # wrapping into a GS interface, requires GS temperature\n",
    "receiver = Receiver(input_size=400)\n",
    "receiver = core.SymbolReceiverWrapper(receiver, vocab_size, agent_input_size=400)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have the agents created, we can adopt a pre-defined game logic which juggles the agents, messages, \n",
    "data, and the loss. Essentially, the game instance is also a `torch.nn.Module` - hence it can be handled as that, i.e.\n",
    "we can extract the trainable parameters of the agents, push it around devices, etc. Each game is expected to output a two-tuple. The first element of the tuple is a loss that is to be minimized. The second is a python dict `{}` of some auxilary values that are averaged over the epoch and printed. Accuracy or entropy of the communication channel are good examples of such auxilary data.\n",
    "\n",
    "\n",
    "Another entity that we will need is `core.Trainer`. Essentially, `Trainer` implements the training loop, handles checkpointing, etc.\n",
    "\n",
    "\n",
    "The Gumbel-Softmax distribution is parameterised by its temperature. In general, the latter has strong impact on training. To anneal the temperature of Sender, we create a callback that `trainer` invokes after each training epoch is over. In this snippet, the callback applies a multiplicative decay rule on the temperature value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "game = core.SymbolGameGS(sender, receiver, loss)\n",
    "optimizer = torch.optim.Adam(game.parameters())\n",
    "\n",
    "trainer = core.Trainer(\n",
    "    game=game, optimizer=optimizer, train_data=train_loader,\n",
    "    validation_data=test_loader, callbacks=[core.TemperatureUpdater(agent=sender, decay=0.9, minimum=0.1)]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yay, everything is ready for actual training!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "validation: epoch 1, loss 0.2278318554162979,  {}\n",
      "validation: epoch 2, loss 0.22411856055259705,  {}\n",
      "validation: epoch 3, loss 0.22268903255462646,  {}\n",
      "validation: epoch 4, loss 0.22037065029144287,  {}\n",
      "validation: epoch 5, loss 0.21967673301696777,  {}\n",
      "validation: epoch 6, loss 0.21596738696098328,  {}\n",
      "validation: epoch 7, loss 0.21486324071884155,  {}\n",
      "validation: epoch 8, loss 0.2144143283367157,  {}\n",
      "validation: epoch 9, loss 0.21371403336524963,  {}\n",
      "validation: epoch 10, loss 0.2130994349718094,  {}\n",
      "validation: epoch 11, loss 0.2131139636039734,  {}\n",
      "validation: epoch 12, loss 0.2130260020494461,  {}\n",
      "validation: epoch 13, loss 0.21324360370635986,  {}\n",
      "validation: epoch 14, loss 0.21285751461982727,  {}\n",
      "validation: epoch 15, loss 0.21280497312545776,  {}\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 15\n",
    "trainer.train(n_epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now when Sender and Receiver are trained, we firstly have a look at the codebook they came up with: what does Receiver output when given a particular word from a vocabulary? For that, we'll take every word in the vocabulary [0..9], wrap it into a tensor and pass it to Receiver:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "game.eval()\n",
    "\n",
    "for z in range(vocab_size):\n",
    "    t = torch.zeros(vocab_size).to(device)\n",
    "    t[z] = 1\n",
    "    with torch.no_grad():\n",
    "        # Receiver outputs a single tensor of predictions\n",
    "        sample = game.receiver(t).float().cpu()\n",
    "    sample = sample.view(28, 28)\n",
    "    plt.title(f\"Input: symbol {z}\")\n",
    "    plt.imshow(sample, cmap='gray')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, not too bad: some digits are vague, but others do resemble actual digits. Huh!\n",
    "\n",
    "\n",
    "Next, how good are our two agents at auto-encoding the images? Let's take some images from the validation set, feed them to Sender and look at (a) what messages are sent, (b) how does Receiver's output look like?\n",
    "\n",
    "First, we define a tiny, single-batch 10-digit test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_inputs = []\n",
    "for z in range(10):\n",
    "    index = (test_loader.dataset.targets[:100] == z).nonzero()[0, 0]\n",
    "    img, _ = test_loader.dataset[index]\n",
    "    test_inputs.append(img.unsqueeze(0))\n",
    "test_inputs = torch.cat(test_inputs)\n",
    "\n",
    "test_dataset = [[test_inputs, None]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we write a small helper function to dump and plot the input-outputs of the agents along with the communicated messages. We will use it throughout the tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(game, test_dataset, is_gs, variable_length):\n",
    "    sender_input, messages, _receiver_inputs, receiver_outputs, _labels = \\\n",
    "            core.dump_sender_receiver(game, test_dataset, is_gs, variable_length)\n",
    "\n",
    "    for z in range(10):\n",
    "        src = sender_input[z].squeeze(0)\n",
    "        dst = receiver_outputs[z].view(28, 28)\n",
    "        # we'll plot two images side-by-side: the original (left) and the reconstruction\n",
    "        image = torch.cat([src, dst], dim=1).cpu().numpy()\n",
    "\n",
    "        plt.title(f\"Input: digit {z}, channel message {messages[z]}\")\n",
    "        plt.imshow(image, cmap='gray')\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the left image is the original and the one on the right is the recovered one, each pair is labelled by the original class and the symbol sent over the channel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(game, test_dataset, is_gs=True, variable_length=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, not totally unreasonable! \n",
    "\n",
    "### Training with Reinforce\n",
    "What's the equivalent code when training by Reinforce?\n",
    "\n",
    "We create exactly the same Sender instance, but then feed it into ```core.ReinforceWrapper```. This wrapper implements the boilerplate code required for Reinforce-based optimization: samples from a distribution, records the log-probability of what was sampled, and reports the entropy of the distribution (*).\n",
    "\n",
    "Hence, each agent returns a tuple of three elements: the actual sampled output, the log-probability of the sampled output, and the entropy of the sampling distribution. During the evaluation, the sampling process is replaced by taking the most likely output.\n",
    "\n",
    "But what if an agent (e.g. Receiver) runs a deterministic function? In that case, we use a simple `core.ReinforceDeterministicWrapper` that appends zero entropy and log-probability tensors. `ReinforceDeterministicWrapper` can only be used if Receiver's parameters can be optimized via a gradient-based optimization, i.e. the loss function has to be differentiable.\n",
    "\n",
    "\n",
    "\n",
    "(*) Entropy regularization is used to encourage the agents to do some exploration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "sender = Sender(vision, output_size=vocab_size)\n",
    "sender = core.ReinforceWrapper(sender)  # wrapping into a Reinforce interface\n",
    "\n",
    "receiver = Receiver(input_size=400)\n",
    "receiver = core.SymbolReceiverWrapper(receiver, vocab_size, agent_input_size=400)\n",
    "receiver = core.ReinforceDeterministicWrapper(receiver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time we use the one-symbol game implementation with Reinforce logic, `core.SymbolGameReinforce`. It also consumes two entropy regularization terms, for Sender and Receiver. The entropies of the output distributions of the agents are weighted by these parameters and added to the loss.\n",
    "\n",
    "Note that we managed to change from Gumbel Softmax to Reinforce training by only (a) changing the agent wrappers, (b) changing the game type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "game = core.SymbolGameReinforce(sender, receiver, loss, sender_entropy_coeff=0.05, receiver_entropy_coeff=0.0)\n",
    "optimizer = torch.optim.Adam(game.parameters(), lr=1e-2) #  we can also use a manually set optimizer\n",
    "\n",
    "trainer = core.Trainer(game=game, optimizer=optimizer, train_data=train_loader,\n",
    "                           validation_data=test_loader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "validation: epoch 1, loss 0.21319255232810974,  {'baseline': 0.2360108992894489, 'loss': 0.22184547953331432, 'sender_entropy': tensor(0.2040, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 2, loss 0.21560125052928925,  {'baseline': 0.23067624203363962, 'loss': 0.2194550936214459, 'sender_entropy': tensor(0.0800, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 3, loss 0.21553604304790497,  {'baseline': 0.2272949881712599, 'loss': 0.2176427275132828, 'sender_entropy': tensor(0.0418, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 4, loss 0.21543172001838684,  {'baseline': 0.22536487936377558, 'loss': 0.2169620060501769, 'sender_entropy': tensor(0.0284, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 5, loss 0.21764248609542847,  {'baseline': 0.22452548109213571, 'loss': 0.2186968139947032, 'sender_entropy': tensor(0.0185, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 6, loss 0.2173253297805786,  {'baseline': 0.22372076069778793, 'loss': 0.21818101049040833, 'sender_entropy': tensor(0.0168, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 7, loss 0.2173387110233307,  {'baseline': 0.22309228002684606, 'loss': 0.21789990451198799, 'sender_entropy': tensor(0.0111, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 8, loss 0.21865805983543396,  {'baseline': 0.22259400611321206, 'loss': 0.21980801862649643, 'sender_entropy': tensor(0.0190, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 9, loss 0.22032047808170319,  {'baseline': 0.22239507810363085, 'loss': 0.22128786365635478, 'sender_entropy': tensor(0.0165, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 10, loss 0.216238871216774,  {'baseline': 0.22203840304295208, 'loss': 0.21704828101225174, 'sender_entropy': tensor(0.0137, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 11, loss 0.21599559485912323,  {'baseline': 0.22166442566351388, 'loss': 0.21658066686349936, 'sender_entropy': tensor(0.0111, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 12, loss 0.21750280261039734,  {'baseline': 0.22152219027611877, 'loss': 0.21823723937947148, 'sender_entropy': tensor(0.0114, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 13, loss 0.2165084183216095,  {'baseline': 0.22127741155868855, 'loss': 0.2171523759064202, 'sender_entropy': tensor(0.0111, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 14, loss 0.21709907054901123,  {'baseline': 0.22108858057260566, 'loss': 0.217593732019202, 'sender_entropy': tensor(0.0087, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n",
      "validation: epoch 15, loss 0.21726292371749878,  {'baseline': 0.22089879880534308, 'loss': 0.2179057683331517, 'sender_entropy': tensor(0.0100, device='cuda:0'), 'receiver_entropy': tensor(0., device='cuda:0')}\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 15\n",
    "trainer.train(n_epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's check what is in the communication code book and the quality of the auto-encoding. The dumping code is essentially the same as before, the only change is that Receiver returns a tuple of three elements, and we need only one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dMJY9+yHgoxFxLvAbwEcknQtcDzwQEYuAB6qfzaxPZYs9IrZHxMPV5b3AE8A84CpgRXWzFcC7upWkmdX3it6zS1oAXAD8GBiIiO1VaAeNw3wz61NjPjde0gzgm8B1ETHSPOdbRISkUd8US1oGLKubqJnVM6Y9u6RJNAr9axFxT3X1TkmDVXwQGBpt24hYHhFLImJJJxI2s/Zki12NXfgtwBMR8fmm0H3A0uryUuDezqdnZp0ylsP4S4D3A6slPVJddwNwE/ANSR8CNgNXdyfFsen2kMM6w0gXLFiQjA8MpD/uyA31TLX2cm27XMty9uzZyXiufXb66ae3/dg7d+5MxlNDWHPb79q1K7ntgQMHkvHc69qPQ2CzxR4RPwRaTcp+eWfTMbNu8Rl0ZoVwsZsVwsVuVggXu1khXOxmhXCxmxXiuJpKus6wwdxQz1zfNDXkMZdXrk+em1J58eLFyfiZZ57ZMpbrk9edajo3BDa1LPPGjRuT2+b67OvWrUvG169f3zJWt8+e+3vqR96zmxXCxW5WCBe7WSFc7GaFcLGbFcLFblYIF7tZIY6rPntKbvxwbsrk5mm2RrN///6WsVzPdtOmTcl4Tp1prusuJ713795k/KmnnkrGU73uVAxg5cqVyfhjjz2WjG/durVlLDcNde68i36cKjrHe3azQrjYzQrhYjcrhIvdrBAudrNCuNjNCuFiNyuExnN+61ZLRI3TYyfjuTnMU/3oXK861+ueOXNmre1T887PmTMnuW0u99zrtmfPnmR8aGjUhYIAGB4eTm6bi+d65amx9Lm/+36c932sImLUX5r37GaFcLGbFcLFblYIF7tZIVzsZoVwsZsVwsVuVohsn13SfOB2YAAIYHlEfFHSjcCfAUcHc98QEd/J3Ndx27zM9ZvrbNvNeN3zC3J/H7lx3al43V738dwL76ZWffaxFPsgMBgRD0uaCfwUeBdwNbAvIj471iRc7OMfd7GXp1WxZ2eqiYjtwPbq8l5JTwDpJUzMrO+8ovfskhYAFwA/rq66VtKjkm6VNKvFNsskrZK0qlamZlbLmM+NlzQD+AHw9xFxj6QBYJjG+/hP0zjU/2DmPo7b4y4fxo/Oh/H9p9a58ZImAd8EvhYR91R3uDMiDkfEEeBm4KJOJWtmnZctdjV2DbcAT0TE55uuH2y62buBNZ1Pz8w6ZSyfxl8K/A+wGjh6THYDcA1wPo3D+E3Ah6sP81L35eMusy5ru/XWSS52s+7zeHazwrnYzQrhYjcrhIvdrBAudrNCuNjNCuFiNyuEi92sEC52s0K42M0K4WI3K4SL3awQLnazQrjYzQqRnXCyw4aBzU0/z62u60f9mlu/5gXOrV2dzO2sVoFxHc/+Kw8urYqIJT1LIKFfc+vXvMC5tWu8cvNhvFkhXOxmheh1sS/v8eOn9Gtu/ZoXOLd2jUtuPX3Pbmbjp9d7djMbJy52s0L0pNglXSHpF5KelHR9L3JoRdImSaslPdLr9emqNfSGJK1pum62pPslrau+j7rGXo9yu1HStuq1e0TSlT3Kbb6k/5b0uKTHJP1ldX1PX7tEXuPyuo37e3ZJE4C1wFuBrcBK4JqIeHxcE2lB0iZgSUT0/AQMSb8F7ANuj4jXV9d9BtgdETdV/yhnRcTH+iS3G3mFy3h3KbdWy4x/gB6+dp1c/rwdvdizXwQ8GREbIuJF4G7gqh7k0fci4iFg9zFXXwWsqC6voPHHMu5a5NYXImJ7RDxcXd4LHF1mvKevXSKvcdGLYp8HbGn6eSv9td57AN+T9FNJy3qdzCgGmpbZ2gEM9DKZUWSX8R5Pxywz3jevXTvLn9flD+h+1aURcSHwduAj1eFqX4rGe7B+6p1+GVhIYw3A7cDneplMtcz4N4HrImKkOdbL126UvMbldetFsW8D5jf9fEZ1XV+IiG3V9yHgW/TfUtQ7j66gW30f6nE+v9RPy3iPtsw4ffDa9XL5814U+0pgkaTXSpoMvBe4rwd5/ApJ06sPTpA0HXgb/bcU9X3A0uryUuDeHubyMv2yjHerZcbp8WvX8+XPI2Lcv4AraXwivx74eC9yaJHX2cDPqq/Hep0bcBeNw7qXaHy28SFgDvAAsA74PjC7j3K7g8bS3o/SKKzBHuV2KY1D9EeBR6qvK3v92iXyGpfXzafLmhXCH9CZFcLFblYIF7tZIVzsZoVwsZsVwsVuVggXu1kh/h9wCZ6+ri5/SwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wspsVwsluVggnu1kh2lmyeSHwFWCIxhLNyyLi3yXNAu4BzqWxbPPVEZEuGA+wXJ390KFDLWO5uddzNdtVq9LL28+YMSMZP+2001rGUssWA0hKxnNLPqf2C6T3zebNm5Ntn3zyyWT8iSeeSMYff/zxlrGNGzcm2+aufcjNC9+POnpOO0f2I8DHIuIS4I3ARyVdAlwPPBgRFwIPVj+b2YDKJntEjETEo9XtMWA1MB+4ClhePWw58O5eddLM6ntJ79klnQu8DvgZMBQRI1VoK43TfDMbUG1fGy9pOvB14LqI2N38Xi8iQtK4b1IkLQWW1u2omdXT1pFd0iQaiX5HRHyjunubpLlVfC4w7ux+EbEsIhZFxKJudNjMOpNNdjUO4bcAqyPi5qbQfcCS6vYS4N7ud8/MukW5EoGkxcCPgceBY/WpG2i8b/8acDbwNI3S287Mcw1ePaKSK0GlhnLmlh7Olb8uuOCCZPw1r3lNMv7qV7+6Zeyiiy5Ktj311FOT8dwQ1rGxsWQ8Ncw0FQNYt25dMr5+/fpkfGRkpGVs7969yba5Iaq5Um0/S28RMe4fc/Y9e0T8BGiVCW+u0ykzmzi+gs6sEE52s0I42c0K4WQ3K4ST3awQTnazQmTr7F3d2ADX2euoM50ywJQpU5Lx2bNndxzPLak8efLkZDwnt2xyasrl3HTMuVp4blnkVK18kOvkdbWqs/vIblYIJ7tZIZzsZoVwspsVwsluVggnu1khnOxmhXCdfQDkxtLn4v167nak/r5yf3t146Vynd2scE52s0I42c0K4WQ3K4ST3awQTnazQjjZzQrR9vJP1juuJ9tE8JHdrBBOdrNCONnNCuFkNyuEk92sEE52s0I42c0KkU12SQsl/a+kJyU9Ielvq/tvlDQs6bHq68red9fMOpWdvELSXGBuRDwqaQbwC+DdwNXAnoj4bNsb8+QVZj3XavKK7BV0ETECjFS3xyStBuZ3t3tm1msv6T27pHOB1wE/q+66VtJKSbdKmtmizVJJKyStqNVTM6ul7TnoJE0HfgT8c0R8Q9IQsB0I4NM0TvU/lHkOn8ab9Vir0/i2kl3SJOB+4HsRcfM48XOB+yPidzPP42Q367GOJ5xUY/rRW4DVzYlefXB3zHuAVXU7aWa9086n8YuBHwOPA8fWub0BuAa4lMZp/CbgI9WHeann8pHdrMdqncZ3i5PdrPc8b7xZ4ZzsZoVwspsVwsluVggnu1khnOxmhXCymxXCyW5WCCe7WSGc7GaFcLKbFcLJblYIJ7tZIZzsZoWY6CWbtwNPN/08p7pvEA1q3wa1X+C+daqbfTunVWBCx7P/xsalFRGxqG8dSBjUvg1qv8B969RE9c2n8WaFcLKbFaLfyb6sz9tPGdS+DWq/wH3r1IT0ra/v2c1s4vT7yG5mE8TJblaIviS7pCskrZG0TtL1/ehDK5I2SXq8Woa6r+vTVWvojUpa1XTfLEkPSFpbfR93jb0+9W0glvFOLDPe133X7+XPJ/w9u6STgF8BbwW2AI8A10TEkxPakRYkbQIWRUTfL8CQ9EfAHuArx5bWkvQZYGdE3FT9o5wZER8fkL7dyEtcxrtHfWu1zPgH6eO+6+by553ox5H9MmBdRGyIiEPA3cBVfejHwIuIh4GdJ9x9FbC8ur2cxh/LhGvRt4EQESMR8Wh1eww4tsx4X/ddol8Toh/JPh/Y3PTzFgZrvfcAvi/pF5KW9rsz4xhqWmZrKzDUz86MI7uM90Q6YZnxgdl3nSx/Xpc/oPtNiyPi9cDbgY9Wp6sDKRrvwQapdvoF4HwaawCOAJ/rZ2eqZca/DlwXEbubY/3cd+P0a0L2Wz+SfRhY2PTzguq+gRARw9X3UeCbNN52DJJtx1bQrb6P9rk/vxYR2yLiaES8CHyJPu67apnxrwN3RMQ3qrv7vu/G69dE7bd+JPsjwIWSzpM0GXgfcF8f+vEbJE2rPjhB0jTgbQzeUtT3AUuq20uAe/vYl+MMyjLerZYZp8/7ru/Ln0fEhH8BV9L4RH498Il+9KFFv14F/LL6eqLffQPuonFad5jGZxsfBmYDDwJrgR8Aswaob7fTWNp7JY3Emtunvi2mcYq+Enis+rqy3/su0a8J2W++XNasEP6AzqwQTnazQjjZzQrhZDcrhJPdrBBOdrNCONnNCvH/04gBWrAijrMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "game.eval()\n",
    "\n",
    "for z in range(vocab_size):\n",
    "    t = torch.zeros(vocab_size).to(device)\n",
    "    t[z] = 1\n",
    "    with torch.no_grad():\n",
    "        sample, _1, _2 = game.receiver(t)\n",
    "        sample = sample.float().cpu()\n",
    "    sample = sample.view(28, 28)\n",
    "    plt.title(f\"Input: symbol {z}\")\n",
    "    plt.imshow(sample, cmap='gray')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ynhvb5OCDD65r+9u2bUvGc2ObrFy5MhnPHVduJqDctZn7ncjJVULljmv79u3JeO712rVrVzKeq3JplBbvwCXdDfwr8C5JyyRNp0jcH5T0MvCB8rmZmXWiFv+MRcT5mUXvb3BbzMysDv4kpplZRTmBm5lVlBO4mVlFeUaehAsvvDAZHzUq/XmlWbNmNWS/Y8eOTcZz1Rr1zhC0YsWKZPyOO+5Ixm+88cZkfNmyZXXtd968ecn4GWeckYyPGTMmGXcVSn793FgoI0aMSMZz13KuCiVXVbJxY3oIpNyMP7kxWHLtz1Wb5NbPVX3kZgjKxXP73bp1azLeVTP4+A7czKyinMDNzCrKCdzMrKKcwM3MKsoJ3MysolyFkjB16tS61n/55Zcbst9cVcnFF1+cjOfeyX744YeT8c9+9rPJ+HPPPdeK1rVdo85PT5SrKmlUtUluhp3ceD9vvfVWMr5p06ZkPFe1ktvvyJEjk/EhQ4Yk47mxUPr27ZuMv/HGG8l47nzmzkNufKPcdnK/i7kxUlyFYma2n3MCNzOrKCdwM7OKcgI3M6soJ3Azs4pyFUpCbkySRjniiCOS8fPOO6+u7dx8883J+GWXXZaM79y5s67td7RFixbVFd+f5MZCyY3RMXTo0GQ8N/ZIbjs7duxIxnNVE+PGjUvGc7Mw5WYIys0oVO/YI7mxUHLnIVd1k6tOyVXd1Dt2TaP4DtzMrKKcwM3MKsoJ3MysopzAzcwqygnczKyiWqxCkXQrcCawJiKOLmNXAxcBa8vVroyI/9tRjexsuXEZGvWO8qc//elkPPcO/V133ZWMf+pTn2pIezpa7ny+/fbbyXh3q5bpSLlrKjcGSK56ZPDgwXXFc9UUuf3mqlxy28+NhZKrNtmwYUMyvmrVqmQ8VyVS79gjjTr/uXh3qEKZA5yeiM+MiCnlV49J3mZmVdFiAo+IR4D0n0czM+sy7ekDv0TSryTdKildJQ9ImiFpgaQF7diXmZk109YE/i3g94EpwErg+tyKETErIo6LiOPauC8zM0toUwKPiNURsTsi9gA3Ayc0tllmZtaSNo2FImlMRKwsn34EeLZxTep6uXesGzWLxpgxY+rafm797iY3hsz06dOT8fvuu68jm1MJ9VYp5KodcjP15Ko+ctdarjolN+NPrj257a9bty4ZX7JkSTKeq0iq9zzkKrxy28/N7JM7PzkdXYXSmjLCu4FTgJGSlgF/A5wiaQoQwBIgPeeXmZl1mBYTeEScnwjP7oC2mJlZHfxJTDOzinICNzOrKCdwM7OK8ow8XeDii9Pv+Z588sl1xa+44opkfNasWcn4+vXrW9G6tstVlWzfvj0Zv/767McH9hu5ao09e/bUtZ3czDK57edmkDnggAOS8Vw1RW7GnNwYJps2bUrGN2/enIznqmhyVSW5mXf69u2bjK9ZsyYZz83sk5OrZqn3dayX78DNzCrKCdzMrKKcwM3MKsoJ3MysopzAzcwqar+uQsmN3dHRY4/kqkGOPfbYZHzevHnJ+DXXXJOMn356av4NOPPMM5PxLVu21LX+VVddlYxPnTo1Gb/22muT8ccffzwZ35/UO+5Obhajbdu21RXPzWiTq+LIVbnkqlNy+81VuRx22GHJ+OjRo5Px4cOHJ+O5dtY740+uKiY3lsuOHTuScVehmJlZkhO4mVlFOYGbmVWUE7iZWUU5gZuZVdR+XYWyYsWKZPzll19Oxg899NBk/NRTT03Gb7rppmQ8NzbIypUrk/Hjjz8+Gc9ViSxevDgZz40fkRuTJDeTTq79uWqTXLWM5atNcmNr5CqG6h1j5OCDD07Gc1UiQ4cOTcbrHZOkV6/0PWO9M+zkjjc3s08uvnbt2mQ8VymWG/tl165dyXijZvHK8R24mVlFOYGbmVWUE7iZWUU5gZuZVZQTuJlZRamld0klTQBuB0YBAcyKiG9IGg7cA0wClgDnRsTGFrbVsW/JNsj48eOT8Z/85CfJ+NFHH52MP/bYY8n4DTfckIznqlBypk2bloznqmJOPPHEZDw3nsWLL76YjH/pS19KxufOnZuMW17u3Pfr1y8Zz1WDHH744cn4UUcdlYwfc8wxyfjkyZOT8VGjRiXjufbnqmhyY7nUO7PPK6+8Ulf8+eefT8ZzlWi56p3cmCe5GXwaWIWyMCKOax5szR34LuBzEXEkcBLw15KOBC4HHoqIycBD5XMzM+skLSbwiFgZEYvKx1uAxcA44GzgtnK124BzOqqRZmb2u+r6II+kScBU4AlgVEQ0/c+/iqKLJfUzM4AZbW+imZmltPpNTEmDgR8An4mIvTqIoujoSXb2RMSsiDgu1X9jZmZt16oELqkvRfL+TkTcV4ZXSxpTLh8DrOmYJpqZWUprqlBE0ce9ISI+UxP/e2B9RFwn6XJgeER8oYVtVaIKJSc3U8/8+fOT8VxlQL1y7/Q36h3uOXPmJONf/OIXk/HcOBHWOLkxQ/r375+M58YkmThxYjJ+xBFHJOO5mXEmTZqUjOfGKslds7lxdOodw+T1119PxpcuXZqM52bSyc3gkxvbJFdt0gmSVSit6QM/Gfg48Iykp8rYlcB1wL2SpgOvAec2qqVmZtayFhN4RPwCSP85hfc3tjlmZtZa/iSmmVlFOYGbmVWUE7iZWUW1WIXS0J1VvAolJ1cBcN555yXjueqUiy66KBm/5ZZbkvF6X7vZs2cn4y+88EJd27Guk6tOaVTVypAhQ5LxgQMHJuO5MVtycmOk5MYeyc1A9Oabbybj9VaV7NmzJxnvhto8FoqZmXVDTuBmZhXlBG5mVlFO4GZmFeUEbmZWUa5CMevBcmOSdNX6Obk8VG9+6sx81slchWJm1pM4gZuZVZQTuJlZRTmBm5lVlBO4mVlF1TWpsZlVi6s4ejbfgZuZVZQTuJlZRTmBm5lVlBO4mVlFOYGbmVVUiwlc0gRJ8yU9L+k5SZeV8aslLZf0VPl1Rsc318zMmrSmjHAX8LmIWCRpCLBQ0gPlspkR8fWOa56ZmeW0mMAjYiWwsny8RdJiYFxHN8zMzPatrj5wSZOAqcATZegSSb+SdKukgzI/M0PSAkkL2tVSMzPbS6vHA5c0GPg58LWIuE/SKGAdEMA1wJiI+GQL2/DHvMzM6tf28cAl9QV+AHwnIu4DiIjVEbE7IvYANwMnNLK1Zma2b62pQhEwG1gcETfUxMfUrPYR4NnGN8/MzHJaU4VyMvBx4BlJT5WxK4HzJU2h6EJZAlzcIS00M7Mkz4lpZtb9eU5MM7OexAnczKyinMDNzCrKCdzMrKKcwM3MKsoJ3MysopzAzcwqygnczKyinMDNzCqqNR+lb6R1wGvl45Hl8/2Fj7fn2p+OFXy8XeHQVLBTP0q/146lBamPhvZUPt6ea386VvDxdifuQjEzqygncDOziurKBD6rC/fdFXy8Pdf+dKzg4+02uqwP3MzM2sddKGZmFeUEbmZWUZ2ewCWdLulFSb+WdHln778zSLpV0hpJz9bEhkt6QNLL5feDurKNjSJpgqT5kp6X9Jyky8p4Tz3eAZJ+Kenp8ni/UsZ/T9IT5XV9j6R+Xd3WRpHUW9KTkn5cPu/Jx7pE0jOSnpK0oIx122u5UxO4pN7AN4EPAUdSzKt5ZGe2oZPMAU5vFrsceCgiJgMPlc97gl3A5yLiSOAk4K/L17SnHu8O4NSIeDcwBThd0knA/wRmRsThwEZgehe2sdEuAxbXPO/JxwrwvoiYUlP73W2v5c6+Az8B+HVEvBIRO4HvAmd3chs6XEQ8AmxoFj4buK18fBtwTqc2qoNExMqIWFQ+3kLxiz6Onnu8ERFby6d9y68ATgW+X8Z7zPFKGg9MA24pn4seeqz70G2v5c5O4OOApTXPl5Wx/cGoiFhZPl4FjOrKxnQESZOAqcAT9ODjLbsUngLWAA8AvwE2RcSucpWedF3/A/AFYE/5fAQ991ih+GN8v6SFkmaUsW57LXf2WChGcRcnqUfVb0oaDPwA+ExEbC5u1Ao97XgjYjcwRdIwYC7wB13cpA4h6UxgTUQslHRKV7enk7wnIpZLOgR4QNILtQu727Xc2Xfgy4EJNc/Hl7H9wWpJYwDK72u6uD0NI6kvRfL+TkTcV4Z77PE2iYhNwHzgPwDDJDXdEPWU6/pk4MOSllB0d54KfIOeeawARMTy8vsaij/OJ9CNr+XOTuD/Bkwu38XuB3wUmNfJbegq84ALyscXAD/swrY0TNknOhtYHBE31Czqqcd7cHnnjaQDgA9S9PvPB/60XK1HHG9EXBER4yNiEsXv6sMR8ef0wGMFkDRI0pCmx8BpwLN042u50z+JKekMin613sCtEfG1Tm1AJ5B0N3AKxTCUq4G/Af4JuBeYSDGk7rkR0fyNzsqR9B7gX4Bn+G0/6ZUU/eA98XiPoXgjqzfFDdC9EfFVSYdR3KUOB54EPhYRO7qupY1VdqF8PiLO7KnHWh7X3PJpH+CuiPiapBF002vZH6U3M6sofxLTzKyinMDNzCrKCdzMrKKcwM3MKsoJ3MysopzAzcwqygnczKyi/j8ZBAFaf2FgAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(game, test_dataset, is_gs=False, variable_length=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not too bad either! Let us move to a more interesting case: variable-length messages. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Communication with variable-length messages\n",
    "\n",
    "This time, communication is carried out by RNNs. EGG provides pre-implemented code to use vanilla RNNs, GRUs, or LSTMs. There is also an experimental support for communication via Transformer-based blocks.\n",
    "\n",
    " Note that, when communicating over variable-length sequences, we need to define a special end-of-sequence symbol. The agents are trained such that the loss is calculated wrt to the Receiver output either after receiving the end-of-sequence symbol or after the maximal number of symbols were produced. EGG handles those scenarios, by defining special wrappers for agents, RnnSenderGS and RnnReceiverGS for Gumbel Softmax-based learning, and RnnSenderReinforce and RnnReceiverReinforce for Reinforce-based learning.\n",
    "\n",
    "By convention, the user-implemented Sender, after processing its input, outputs the initial hidden state vector for its RNN. EGG unrolls this RNN to produce a message. In turn, this message is fed into Receiver's RNN. The only thing that we need to implement for Receiver is how we map the Receiver RNN's hidden state to the Receiver's output.\n",
    "\n",
    "**Important points concerning end-of-sequence behaviour: (1) EGG assumes that the end-of-sequence symbol is always 0. (2) `vocab_size` always includes the end-of-sequence symbol - hence `vocab_size=2` specifies the unary encoding. (3) Communication stops immediately if the first symbol emitted by Sender is 0.**\n",
    "\n",
    "This time we'll have to specify some additional parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we start by defining the RNN parameters\n",
    "hidden_size = 20\n",
    "emb_size = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the same pre-trained vision module. Note, this time **Sender does not output a vector which will be casted as logits of probabilities over the vocab - it only outputs the initial hidden state for its RNN cell**!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest is pretty much the same as before: we instantiate the instances and put them into wrappers (note that we set the RNN cell types to 'rnn' and maximal communication length `max_len=2`!)\n",
    "\n",
    "First, we'll go through Gumbel Softmax-based training.\n",
    "\n",
    "\n",
    "### Variable-length messages with Gumbel Softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "sender = Sender(vision, hidden_size)\n",
    "receiver = Receiver(hidden_size)\n",
    "\n",
    "sender_rnn = core.RnnSenderGS(sender, vocab_size, emb_size, hidden_size,\n",
    "                                   cell=\"gru\", max_len=2, temperature=1.0)\n",
    "receiver_rnn = core.RnnReceiverGS(receiver, vocab_size, emb_size,\n",
    "                    hidden_size, cell=\"gru\")\n",
    "\n",
    "game_rnn = core.SenderReceiverRnnGS(sender_rnn, receiver_rnn, loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that sometimes specifying different learning speeds for the two agents aids learning; this can be done as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.Adam([\n",
    "        {'params': game_rnn.sender.parameters(), 'lr': 1e-3},\n",
    "        {'params': game_rnn.receiver.parameters(), 'lr': 1e-2}\n",
    "    ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can train the agents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "validation: epoch 1, loss 0.21742498874664307,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 2, loss 0.20543161034584045,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 3, loss 0.19978027045726776,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 4, loss 0.19766512513160706,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 5, loss 0.19549231231212616,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 6, loss 0.19639243185520172,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 7, loss 0.1945004165172577,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 8, loss 0.194252610206604,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 9, loss 0.19360794126987457,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 10, loss 0.19458362460136414,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 11, loss 0.192210853099823,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 12, loss 0.19272926449775696,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 13, loss 0.19325990974903107,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 14, loss 0.19270439445972443,  {'mean_length': tensor(2., device='cuda:0')}\n",
      "validation: epoch 15, loss 0.19333335757255554,  {'mean_length': tensor(2., device='cuda:0')}\n"
     ]
    }
   ],
   "source": [
    "trainer = core.Trainer(game=game_rnn, optimizer=optimizer, train_data=train_loader,\n",
    "                           validation_data=test_loader)\n",
    "trainer.train(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Heh, the validation loss is lower than it used to be with one symbol communication. Let's see how it works. Again, the original image is on the left, the transmitted and decoded - on the right. The communicated message is in the title. Note that since default `vocab_size` is 10 and 0 is used for end-of-sequence, Sender has an effective vocabulary of 9 symbols.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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B5UoSzwEjzGzf2GnYWRT60BERkV1TWS43uftWM/saoUOqdsAd7t6UbrNFRKQNq8gvrnVPQkSkWWa7++GtuUD94lpERLKUJEREJEtJQkREspQkREQkS0lCRESylCRERCRLSUJERLKUJEREJEtJQkREslqtF1gR2fW1a9eupHjO9u3bk/FcDxClji/lo5qEiIhkKUmIiEiWkoSIiGQpSYiISJaShIiIZKl1UxvUtWvXZPxHP/pRMn7RRRcl47Nnz07Gv/CFLyTjCxYsaELpZFdkZsl4rlVSjx49kvF+/fol44MHD07Gc+PvsUf6/HTNmjXJ+BtvvJGML1++PBlfv359Mv7ee+8l49u2bUvGRTUJERFpgJKEiIhkKUmIiEiWkoSIiGQpSYiISJaVq+8TM6sF3gG2AVvd/fAGxlWHKw0YPnx4Mj537tyS5pNrQXLppZcm45MmTSpp/tL25FoxdejQIRnv3bt3Mn7IIYeUJd6zZ89kPNfKKNe6Kdfybs6cOSWN/+qrrybjGzZsSMbbYKun2Q0dW1tCuZvAftrdV5V5niIiUiG63CQiIlnlTBIOPGJms81sfP2BZjbezGaZ2awyLlNERFpQOS83HeXuS8xsb+BRM5vn7k/WDXT3ycBk0D0JEZFdRdlqEu6+JP5fATwIHFGueYuISGWUpSZhZl2BPdz9nfj6ROB75Zh3Nevbt28yPnXq1FYuiexqSu2LqXv37sn4AQcckIyPHTs2GR85cmQyXmorprfffjsZb98+fUgaM2ZMSeV54YUXkvFcn04LFy5MxvVEvPJdbuoHPBh33PbA3e7+mzLNW0REKqQsScLd5wOHlmNeIiLSdqgJrIiIZClJiIhIlpKEiIhk6cl0rSDXV9Jpp52WjB9xRMu2Hj766KOT8VxfTy+99FIy/uSTTybjUjm51k19+vRJxg89NH0rcfTo0cl4x44dk/H58+cn43/961+T8c2bNyfjgwYNSsZHjRqVjO+7777J+MaNG5PxXKun3BPutmzZkoy3wT6dWoxqEiIikqUkISIiWUoSIiKSpSQhIiJZShIiIpKl1k2t4MYbb0zGc/3CtLTPfe5zJcVzT/k688wzk/HZs2c3r2DSZLm+m3KtjwYOHJiM556C2KNHj2Q818fRU089lYwvWrQoGc+Vf9Wq9DPLcq22ampqkvHBgwcn4wMGDEjG582bl4y/++67yXiu/NXYp5NqEiIikqUkISIiWUoSIiKSpSQhIiJZShIiIpKl1k1lNGPGjGQ81ydSS3vrrbeS8dzTuYYOHZqM5/rHmTlzZjKea4ki5ZPbxrknxB1yyCHJeK51U66Vzuuvv56M51o9rVixIhnv1KlTMp57Ml2uldR+++2XjA8bNiwZP/DAA5PxXJ9O69atS8ZzfUNVI9UkREQkS0lCRESylCRERCRLSUJERLKUJEREJKuk1k1mdgdwMrDC3Q+OsRrgF8AwoBY4w93XlLeYbcsxxxyTjI8cOTIZz/XRVK6+m2699dZk/JFHHknG33777WT8uOOOS8avuuqqksrz1a9+NRm/5ZZbSpqP5FvG5VoH7b///sn4Rz7ykZLmv3LlymQ895TCxYsXJ+MbNmxIxjt37lxSeZYtW1bScvv375+Mf/SjH03Gcy31ctth06ZNyXg1PrGu1JrEncC4erErgcfcfQTwWHwvIiJVoKQk4e5PAqvrhU8FpsbXU4H0g5tFRGSXU44f0/Vz96Xx9TKgX2okMxsPjC/D8kREpJWU9RfX7u5mlvypprtPBiYD5MYREZG2pRytm5ab2QCA+D/9O3wREdnllKMmMR04D7g+/v9VGebZJuT6f7n33nuT8T59+pRlubknwU2bNi0Zv+aaa5LxXMuSUpc7fnz6KmHfvn2T8YkTJybjuRY5N998czK+ZcuWZHx3UmrrpkGDBpU0fk6uL6ZcH0q5Po5yfUDl+mhasybdMLK2tjYZz+2DI0aMSMZzT6wbO3ZsMp57ymLuc8m1WNyVn1hXUk3CzO4B/giMNLPFZnYhITn8rZm9CpwQ34uISBUoqSbh7mdnBh1fhrKIiEgbo19ci4hIlpKEiIhkKUmIiEiWnkzXgFwLjHK1YnriiSeS8bPOOisZX7VqVVmWm5Nr3XTdddcl4zfccEMy3qVLl2Q81+pp+vTpyXjuKWjVyMxKGj+3jTt27JiM5/blXF9DL774YjKee9rh1q1bk/Hcem3evDkZz7VoW726fkcPwfz585PxJUuWJONDhgxJxnNP9OvatWsyntsO1Ug1CRERyVKSEBGRLCUJERHJUpIQEZEsJQkREclS66ZWMGvWrGT8ggsuSMZbuhVTqXKtj84555xk/GMf+1hLFqcq5fr2KbXvpt69eyfjPXr0SMbffPPNZHzOnDnJeK4/sFz5c62bSu2Xa+PGjcl4rs+o5cuXlxTPbc+amppkPNe31a7cR1OOahIiIpKlJCEiIllKEiIikqUkISIiWUoSIiKSpdZNzZBrcZJz5JFHtlBJWkeuhUpuO5S6fa6++upk/Nxzzy1pPtUoty07d+6cjPfv3z8Zz7XeeeWVV5LxtWvXJuOltt7J9Q1Vamuu3D6Yi69fvz4Zf+edd5Lxd999NxmvxifNlUo1CRERyVKSEBGRLCUJERHJUpIQEZEsJQkREckqqXWTmd0BnAyscPeDY+xq4CvAyjjaBHefUc5CVsrFF1+cjOdaPFSrU045JRkfM2ZMMp7bPrl4rnWTlN53U79+/ZLxTZs2JeO5J6yV+qS83Geba91ULt26dUvGc0+Uy7VuWrZsWTKe6xtqdzoGlFqTuBMYl4jf6O6Hxb+qSBAiIlJiknD3J4H0w2ZFRKTqlOuexNfM7GUzu8PMeqVGMLPxZjbLzNL9ZouISJtTjiRxC7A/cBiwFPjX1EjuPtndD3f3w8uwTBERaQU7nSTcfbm7b3P37cBtwBE7XywREWkLdrrvJjMb4O5L49vPAn/a2Xm2FblWPbu6vn37JuOjRo1KxidMmFCW5a5cuTIZL/UpZdWo1P6xunfvnoznWvVs3rw5Gc+10mnXrl0y3tJy69u+ffpQlevDKrcdcq2Vcq28cn067U5KbQJ7D3As0MfMFgPfBY41s8MAB2qBi8pcRhERqZCSkoS7n50ITylTWUREpI3RL65FRCRLSUJERLKUJEREJEtPptsNXXXVVcn4JZdcUpb519bWJuPnnXdeMr5w4cKyLLca5Vr19OnTJxnv0KFDMr5hw4aSlptr3ZQrz9atW0uaf64V05577llSvEuXLiXFc+XMtWLauHFjMq4n04mIiKAkISIiDVCSEBGRLCUJERHJUpIQEZEstW6qYjNmpJ//NHLkyBZd7pw5c5Lxp59+ukWXuysrte+m3JPpck9qy/XdlGvFlJt/rnVTqeXPtcLKLTfX39h+++2XjPfqlXxiAa+++moyvmjRomQ890Q/tW4SERFBSUJERBqgJCEiIllKEiIikqUkISIiWWrd1IBSW2zknHTSSSWNP3ny5GR84MCBJc0nV87c08jKpVqf6FcJuc9w9erVyXjuCWu5Vkk1NTXJeK7vo1wfSrnWU7lWTLlWWHvvvXcyPnbs2GR89OjRJZVnwYIFyfibb76ZjKt1k2oSIiLSACUJERHJUpIQEZEsJQkREclSkhARkawmt24ys8HAT4F+gAOT3f0mM6sBfgEMA2qBM9x9TfmL2vpuueWWZHzixIklzefhhx9OxkttZVSuVknlms+tt95alvlIvrVMrpXO8uXLk/GVK1cm4wMGDEjGR4wYkYyvXbs2Gc9Zsyb9le/cuXMy3r9//2T84IMPTsaPPPLIZDzX99TcuXOT8RdeeCEZz223bdu2JeO7k1JqEluBy919FPBx4BIzGwVcCTzm7iOAx+J7ERGpAk1OEu6+1N2fj6/fAeYCg4BTgalxtKnAaeUupIiIVEazfkxnZsOAMcCzQD93XxoHLSNcjkpNMx4Y35zliYhIZZR849rMugHTgK+7+7riMA8XVpMXV919srsf7u6HN6ukIiLS6kpKEmbWgZAg7nL3B2J4uZkNiMMHACvKW0QREamUUlo3GTAFmOvuNxQGTQfOA66P/39V1hJW0AMPPJCMf+Mb30jGc0/PamtyLTlyLULGj09fJVy6dGkyLuWzZcuWZDzXd9Nrr72WjA8ZMiQZz7Um6t69ezI+dOjQZHzVqlXJeK6/scGDB5cU37BhQzI+c+bMZPzRRx9Nxmtra5Nx9dGUV8o9iU8C5wKvmNmLMTaBkBzuM7MLgQXAGeUtooiIVEqTk4S7Pw2ku0WF48tTHBERaUv0i2sREclSkhARkSwlCRERybJK3L03s126ycDRRx+djJ92WvrH5pdddlky3tJPiMs91ezSSy9NxidNmtSSxZFmyD3Zba+99krGDzzwwGT89NNPT8ZzfSLl+lzKtQLKlTM3n40bNybjixcvTsafeOKJkuLz5s1LxnOtpFr6u1hGs1v7t2aqSYiISJaShIiIZClJiIhIlpKEiIhkKUmIiEiWWje1gnHjxiXjuT6RTjnllGR8+vTpyfjkyZOT8dDd1ofNmTMnGV+4cGEyLpWT+ww7deqUjPfq1SsZ33fffZPxsWPHJuOjR49OxnNPsttzzz2T8VxrolmzZiXjzzzzTDKee6Jcrs+o9957Lxmvgr6Y1LpJRETaDiUJERHJUpIQEZEsJQkREclSkhARkSy1bhKpIu3atUvGc30rdevWraR4TU1NMp5rhbVmzZqS4rnWUFu3bk3Gc30uVUErphy1bhIRkbZDSUJERLKUJEREJEtJQkREspQkREQkq8mtm8xsMPBToB/gwGR3v8nMrga+AqyMo05w9xmNzKtqmx6I7I5yrZuquJVRpbR666b2JYy7Fbjc3Z83s+7AbDN7NA670d3/pfzFExGRSmpyknD3pcDS+PodM5sLDGqpgomISOU1656EmQ0DxgDPxtDXzOxlM7vDzJJ9FZvZeDObZWbpPoJFRKTNKfkX12bWDXgCuNbdHzCzfsAqwn2K7wMD3P2CRuahC5UiVUT3JFpN2/7FtZl1AKYBd7n7AwDuvtzdt7n7duA24IjyF1NERCqhyUnCwqnCFGCuu99QiA8ojPZZ4E/lK56I7ArcPfknu75SWjd9EjgXeMXMXoyxCcDZZnYY4XJTLXBRWUsoIiIVo15gRUR2HW37noSIiOxelCRERCRLSUJERLKUJEREJEtJQkREspQkREQkS0lCRESylCRERCRLSUJERLJK6ZajnFYBC+LrPvH97kLrW912p/XdndYV2sb6Dm3tBVakW44dCmA2q7V/Zl5JWt/qtjut7+60rrD7rW8dXW4SEZEsJQkREclqC0licqUL0Mq0vtVtd1rf3WldYfdbX6AN3JMQEZG2qy3UJEREpI1SkhARkayKJgkzG2dmfzGz18zsykqWpSWY2R1mtsLM/lSI1ZjZo2b2avzfq5JlLBczG2xmj5vZHDP7s5ldFuPVur6dzGymmb0U1/eaGN/XzJ6N+/QvzKxjpctaLmbWzsxeMLOH4/uqXVcAM6s1s1fM7EUzmxVjVbk/N6RiScLM2gGTgJOAUYRnZY+qVHlayJ3AuHqxK4HH3H0E8Fh8Xw22Ape7+yjg48Al8fOs1vXdBBzn7ocChwHjzOzjwA+BG919OLAGuLCCZSy3y4C5hffVvK51Pu3uhxV+H1Gt+3NWJWsSRwCvuft8d98M3AucWsHylJ27Pwmsrhc+FZgaX08FTmvVQrUQd1/q7s/H1+8QDiaDqN71dXdfH992iH8OHAfcH+NVs75mtg/wd8Dt8b1RpevaiKrcnxtSySQxCFhUeL84xqpdP3dfGl8vA/pVsjAtwcyGAWOAZ6ni9Y2XX14EVgCPAq8Da919axylmvbpfwO+CWyP73tTvetax4FHzGy2mY2Psardn3Mq1XeTEM5Gzayq2iCbWTdgGvB1d18XTjiDaltfd98GHGZmPYEHgY9UuEgtwsxOBla4+2wzO7bS5WlFR7n7EjPbG3jUzOYVB1bb/pxTyZrEEmBw4f0+MVbtlpvZAID4f0WFy1M2ZtaBkCDucvcHYrhq17eOu68FHgc+AfQ0s7qTr2rZpz8J/L2Z1RIuCx8H3ER1ruv73H1J/MOMPH4AAAEeSURBVL+CcBJwBLvB/lxfJZPEc8CI2EKiI3AWML2C5Wkt04Hz4uvzgF9VsCxlE69RTwHmuvsNhUHVur59Yw0CM+sM/C3hPszjwOlxtKpYX3f/lrvv4+7DCN/T37n7OVThutYxs65m1r3uNXAi8CeqdH9uSEV/cW1mnyFc62wH3OHu11asMC3AzO4BjiV0Mbwc+C7wEHAfMITQXfoZ7l7/5vYux8yOAp4CXuGD69YTCPclqnF9DyHcuGxHONm6z92/Z2b7Ec62a4AXgC+6+6bKlbS84uWmK9z95Gpe17huD8a37YG73f1aM+tNFe7PDVG3HCIikqVfXIuISJaShIiIZClJiIhIlpKEiIhkKUmIiEiWkoSIiGQpSYiISNZ/AZ0NR7ipdS6iAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(game_rnn, test_dataset, is_gs=True, variable_length=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems to work better than with length-one!\n",
    " \n",
    "We can also enumerate all possible 10x10 messages of length two {x = first symbol, y = second symbol} and check the Receiver's interpretation of the code, as shown next. NB: When x=0, the second symbol is ignored, as 0 is interpreted as end-of-sequence. For this reason, in this case Receiver generates the same image irrespective of y's value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 100 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(10, 10, sharex=True, sharey=True)\n",
    "\n",
    "for x in range(10):\n",
    "    for y in range(10):\n",
    "            \n",
    "        t = torch.zeros((1, 2, vocab_size)).to(device)\n",
    "        t[0, 0, x] = 1\n",
    "        t[0, 1, y] = 1\n",
    "\n",
    "        with torch.no_grad():\n",
    "            sample = game_rnn.receiver(t).float().cpu()\n",
    "            # 0 is the end-of-sequence symbol, hence we stop immediately when x == 0\n",
    "            output_index = (0 if x == 0 else 1)\n",
    "            sample = sample[0, output_index, :].view(28, 28)\n",
    "            ax[x][y].imshow(sample, cmap='gray')\n",
    "            \n",
    "            if y == 0:\n",
    "                ax[x][y].set_ylabel(f'x={x}')\n",
    "            if x == 0:\n",
    "                ax[x][y].set_title(f'y={y}')\n",
    "            \n",
    "            ax[x][y].set_yticklabels([])\n",
    "            ax[x][y].set_xticklabels([])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For completeness, we re-iterate by training with Reinforce.\n",
    "\n",
    "### Variable-length messages with Reinforce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "sender = Sender(vision, hidden_size)\n",
    "receiver = Receiver(hidden_size)\n",
    "\n",
    "sender_rnn = core.RnnSenderReinforce(sender, vocab_size, emb_size, hidden_size,\n",
    "                                   cell=\"gru\", max_len=2)\n",
    "receiver_rnn = core.RnnReceiverDeterministic(receiver, vocab_size, emb_size,\n",
    "                    hidden_size, cell=\"gru\")\n",
    "\n",
    "game_rnn = core.SenderReceiverRnnReinforce(sender_rnn, receiver_rnn, loss, \n",
    "                                           sender_entropy_coeff=0.015, \n",
    "                                           receiver_entropy_coeff=0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = torch.optim.Adam([\n",
    "        {'params': game_rnn.sender.parameters(), 'lr': 1e-3},\n",
    "        {'params': game_rnn.receiver.parameters(), 'lr': 1e-2}\n",
    "    ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "validation: epoch 1, loss 0.2565174102783203,  {'loss': 0.2565174956862538, 'sender_entropy': 2.2664143376457044, 'receiver_entropy': 0.0, 'original_loss': 0.2626750760565931, 'mean_length': 1.91573482428115, 'baseline': 0.2665747605323788}\n",
      "validation: epoch 2, loss 0.2739541828632355,  {'loss': 0.27395415767884485, 'sender_entropy': 1.7809024584559967, 'receiver_entropy': 0.0, 'original_loss': 0.23955688666040525, 'mean_length': 1.9765375399361023, 'baseline': 0.26017114344835174}\n",
      "validation: epoch 3, loss 0.24810554087162018,  {'loss': 0.24810550002434764, 'sender_entropy': 1.2814037411357648, 'receiver_entropy': 0.0, 'original_loss': 0.22273309257464668, 'mean_length': 1.996305910543131, 'baseline': 0.25191662189165703}\n",
      "validation: epoch 4, loss 0.24316313862800598,  {'loss': 0.24316317742815413, 'sender_entropy': 1.260018523127888, 'receiver_entropy': 0.0, 'original_loss': 0.21547606120856044, 'mean_length': 1.9461861022364217, 'baseline': 0.24481843697031405}\n",
      "validation: epoch 5, loss 0.23483553528785706,  {'loss': 0.23483556256697963, 'sender_entropy': 1.0939484882278565, 'receiver_entropy': 0.0, 'original_loss': 0.21071830191932167, 'mean_length': 1.9548722044728435, 'baseline': 0.23936161725362132}\n",
      "validation: epoch 6, loss 0.22579450905323029,  {'loss': 0.2257945630401849, 'sender_entropy': 1.1128935061704617, 'receiver_entropy': 0.0, 'original_loss': 0.20786746203328094, 'mean_length': 1.932108626198083, 'baseline': 0.23515459575520517}\n",
      "validation: epoch 7, loss 0.22017540037631989,  {'loss': 0.22017540166172356, 'sender_entropy': 1.0588102053148678, 'receiver_entropy': 0.0, 'original_loss': 0.20727013575192837, 'mean_length': 1.9538738019169328, 'baseline': 0.23183678805487623}\n",
      "validation: epoch 8, loss 0.21277719736099243,  {'loss': 0.21277726753451193, 'sender_entropy': 1.0349600800690941, 'receiver_entropy': 0.0, 'original_loss': 0.2060841450961634, 'mean_length': 1.9582667731629393, 'baseline': 0.2292043217917271}\n",
      "validation: epoch 9, loss 0.21209080517292023,  {'loss': 0.21209088258278636, 'sender_entropy': 1.001563546947016, 'receiver_entropy': 0.0, 'original_loss': 0.2053085954520649, 'mean_length': 1.9476837060702876, 'baseline': 0.22707213690722475}\n",
      "validation: epoch 10, loss 0.2051154226064682,  {'loss': 0.20511536490612517, 'sender_entropy': 0.9530502578701836, 'receiver_entropy': 0.0, 'original_loss': 0.20388677630561608, 'mean_length': 1.955870607028754, 'baseline': 0.22521642385164858}\n",
      "validation: epoch 11, loss 0.20468834042549133,  {'loss': 0.20468838189166194, 'sender_entropy': 0.9330115741053329, 'receiver_entropy': 0.0, 'original_loss': 0.20377666924517757, 'mean_length': 1.957867412140575, 'baseline': 0.2235411122423223}\n",
      "validation: epoch 12, loss 0.20152722299098969,  {'loss': 0.20152711411253713, 'sender_entropy': 0.9225771691852485, 'receiver_entropy': 0.0, 'original_loss': 0.20283753379655722, 'mean_length': 1.9571685303514377, 'baseline': 0.22209183168477342}\n",
      "validation: epoch 13, loss 0.19603195786476135,  {'loss': 0.1960319806687748, 'sender_entropy': 0.8981294245384752, 'receiver_entropy': 0.0, 'original_loss': 0.20255296960615884, 'mean_length': 1.9551717252396166, 'baseline': 0.2208238242675106}\n",
      "validation: epoch 14, loss 0.19801713526248932,  {'loss': 0.19801711602904165, 'sender_entropy': 0.9188079405516482, 'receiver_entropy': 0.0, 'original_loss': 0.20194000672227658, 'mean_length': 1.9587659744408945, 'baseline': 0.2197114532726152}\n",
      "validation: epoch 15, loss 0.19692060351371765,  {'loss': 0.1969206130352264, 'sender_entropy': 0.9277436312395163, 'receiver_entropy': 0.0, 'original_loss': 0.20232746576348815, 'mean_length': 1.9554712460063899, 'baseline': 0.2187220226754079}\n"
     ]
    }
   ],
   "source": [
    "trainer = core.Trainer(game=game_rnn, optimizer=optimizer, train_data=train_loader,\n",
    "                           validation_data=test_loader)\n",
    "trainer.train(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can check how the auto-encoding is done and the emerging protocol.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(game_rnn, test_dataset, is_gs=False, variable_length=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 100 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(10, 10, sharex=True, sharey=True)\n",
    "\n",
    "for x in range(10):\n",
    "    for y in range(10):\n",
    "            \n",
    "        t = torch.zeros((1, 2)).to(device).long()\n",
    "        t[0, 0] = x\n",
    "        t[0, 1] = y\n",
    "\n",
    "        with torch.no_grad():\n",
    "            sample = game_rnn.receiver(t)[0].float().cpu()\n",
    "            sample = sample[0, :].view(28, 28)\n",
    "            ax[x][y].imshow(sample, cmap='gray')\n",
    "            \n",
    "            if y == 0:\n",
    "                ax[x][y].set_ylabel(f'x={x}')\n",
    "            if x == 0:\n",
    "                ax[x][y].set_title(f'y={y}')\n",
    "            \n",
    "            ax[x][y].set_yticklabels([])\n",
    "            ax[x][y].set_xticklabels([])\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Not surprisingly, the results are different. \n",
    "Sometimes (eg `x=3`, `x=7`) it looks like the first symbol in the message (x) encodes which digit Receiver should reproduce, while the second (y) has more effect on the style of the digit. But is it true? How would we check that? 🤔\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (advanced under the hood stuff, may be skipped): optimization with stochastic nodes via Reinforce\n",
    "\n",
    "When we apply the differentiable relaxation of the communication channel by replacing the discrete messages with their Gumbel Softmax approximations, we make the entire Sender->Receiver pipeline differentiable. In contrast, Reinforce-based training doesn't make any relaxations. Instead, it effectively \"smoothes\" the channel by operating with a randomized distribution of messages, parameterised by Sender's output distribution.\n",
    "\n",
    "However, things might get more tricky with Reinforce-based training. In particular, it can happen that the loss on the Receiver's side is differentiable (as in our MNIST example above), and, in this case, we can train Receiver using the standard backprop. It might also happen that the loss is not differentiable (imagine 0-1 accuracy loss). In the latter case, Receiver also has to randomise its outputs.\n",
    "\n",
    "*EGG handles both cases with the same API*, however, it can be useful to know how it operates internally.\n",
    "\n",
    "Now, let's have a closer look at the optimisation problem. By $\\theta_s$ and $\\theta_r$ we denote the parameters of Sender and Receiver, respectively; $m$ is the message sent, and it comes from Sender's output distribution $P(m | i, \\theta_s)$; $R(m, \\theta_r)$ is Receiver's output, and $i$ is Sender's input. \n",
    "\n",
    "### Deterministic Receiver\n",
    "When Receiver is deterministic, we want to minimize the following aggregate loss for an input $i$:\n",
    "\n",
    "$$L = \\mathbb{E}_{m \\sim P(m | i, \\theta_s)}~ l(R(m, \\theta_r), m, i)$$\n",
    "\n",
    "The gradient wrt to ${\\theta_r}$ would be:\n",
    "\n",
    "$$\\nabla_{\\theta_r} L = \\nabla_{\\theta_r}\\mathbb{E}_{m \\sim P(m | i, \\theta_s)}~ l(R(m, \\theta_r), m, i) = \\mathbb{E}_{m \\sim P(m | i, \\theta_s)}~ \\nabla_{\\theta_r} l(R(m, \\theta_r), m, i) = \\mathbb{E}_{m \\sim P(m | i, \\theta_s)} \\frac{\\partial}{\\partial r } l(r, m, i) \\cdot \\nabla_{\\theta_r} R(m, \\theta_r)\n",
    "$$\n",
    "\n",
    "We can estimate it by sampling $N$ messages from Sender:\n",
    "$$\\frac{1}{N} \\sum_m \\frac{\\partial}{\\partial r } l(r, m, i) \\cdot \\nabla_{\\theta_r} R(m, \\theta_r)\n",
    "$$\n",
    "Note that this gradient of $\\theta_r$ is obtained by standard back-propogation from the loss with the messages sampled from Sender. By using the Reinforce trick, we estimate the second gradient by sampling $N$ messages from $P(m | i, \\theta_s)$:\n",
    "\n",
    "$$\\nabla_{\\theta_s} L = \\frac{1}{N} \\sum_m l(R(m, \\theta_r), m, i) \\nabla_{\\theta_s} \\log P(m | i, \\theta_s) $$\n",
    "\n",
    "**In this case, in Pytorch the gradients of both agents can be obtained by differentiating the sum**\n",
    "\n",
    "```(l.mean() + (l.detach() * log_prob_sender).mean()).backwards()```\n",
    "\n",
    "(note: EGG also utilizes the mean baseline to reduce variance of the gradient estimate, but we omit that here for simplicity).\n",
    "\n",
    "\n",
    "### Stochastic Receiver\n",
    "When the loss $l$ is not differentiable, and we sample output $o$ from Receiver $o \\sim P(o | m, \\theta_r)$, the expected loss becomes:\n",
    "\n",
    "$$L = \\mathbb{E}_{m, o \\sim P(m, o | i, \\theta_s, \\theta_r)} ~ l(o, m, i)$$\n",
    "\n",
    "The gradient wrt $\\theta_r$ would be\n",
    "$$\\nabla_{\\theta_r} L = \\mathbb{E}_{m, o \\sim P(m, o | i, \\theta_s, \\theta_r)} l(o, m, i) ~ \\nabla_{\\theta_r} log P(m, o | i, \\theta_s, \\theta_r) = \\mathbb{E}_{m, o \\sim P(m, o | i, \\theta_s, \\theta_r)} l(o, m, i) ~ \\nabla_{\\theta_r} log P(o | m, \\theta_r)$$\n",
    "\n",
    "By sampling $N$ $(m, o)$ pairs, we get\n",
    "$$\\nabla_{\\theta_r} L \\approx \\frac{1}{N} \\sum_{o, m} l(o, m, i) ~ \\nabla_{\\theta_r} log P(o | m, \\theta_r)$$\n",
    "\n",
    "and similarly, \n",
    "$$\\nabla_{\\theta_s} L \\approx \\frac{1}{N} \\sum_{o, m} l(o, m, i) ~ \\nabla_{\\theta_s} log P(m | i, \\theta_s)$$\n",
    "\n",
    "\n",
    "**In this case, in Pytorch the gradients of both agents can be obtained by differentiating the sum**\n",
    "\n",
    "```(l.detach() * (log_prob_sender + log_prob_receiver).mean()).backwards()```\n",
    "\n",
    "\n",
    "### Putting it all together\n",
    "\n",
    "Now, we can notice that if `l` is not differentiable, the gradient of `l.mean()` would be zero. Conversely, if Receiver is deterministic, `log_prob_receiver` would be the zero constant, hence its gradient is zero, too.\n",
    "\n",
    "Thus, both cases can be covered by minimizing the loss:\n",
    "\n",
    "```(l.mean() + (l.detach() * (log_prob_sender + log_prob_receiver).mean())).backwards()```\n",
    "\n",
    "And that is what EGG does internally. Depending on whether Receiver is wrapped in `ReinforceDeterministicWrapper`/`RnnReceiverDeterministic` or in `ReinforceWrapper`/`RnnReceiverReinforce` defines which part of the loss would be effective for training Receiver. \n",
    "\n",
    "\n",
    "Overall, this makes it hard to implement a general Reinforce interface for all possible losses. Some involved cases might require re-implementing game mechanics or resorting to Gumbel Softmax relaxation, which doesn't have this problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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