{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mental rotation\n",
    "\n",
    "In this notebook we will show how we can enable a pretrained Generative Query Network (GQN) for the Shepard-Metzler mental rotation task. The problem is well studied in psychology to asses spatial intelligence. Mental rotation is a congitive hard problem as it typically requires the employment of both the ventral and dorsal visual streams for recognition and spatial reasoning respectively. Additionally, a certain degree of metacognition is required to reason about uncertainty.\n",
    "\n",
    "It turns out that the GQN is capable of this, as we will see in this notebook.\n",
    "\n",
    "<div class=\"alert alert-block alert-danger\">\n",
    "<strong>Note:</strong>\n",
    "This model has only been trained on around 10% of the data for $2 \\times 10^5$ iterations instead of the $2 \\times 10^6$ described in the original paper. This means that the reconstructions are quite bad and the samples are even worse. Consequently, this notebook is just a proof of concept that the model approximately works. If you have the computational means to fully train the model, then please feel free to make a pull request with the trained model, this will help me a lot.\n",
    "</div>\n",
    "\n",
    "You can download the pretrained model weights from here: [https://github.com/wohlert/generative-query-network-pytorch/releases/tag/0.1](https://github.com/wohlert/generative-query-network-pytorch/releases/download/0.1/model-checkpoint.pth)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "    \n",
    "# Load dataset\n",
    "from shepardmetzler import ShepardMetzler\n",
    "from torch.utils.data import DataLoader\n",
    "\n",
    "dataset = ShepardMetzler(\"/data/shepard_metzler_5_parts/\") ## <= Choose your data location\n",
    "loader = DataLoader(dataset, batch_size=1, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GenerativeQueryNetwork(\n",
       "  (generator): GeneratorNetwork(\n",
       "    (inference_core): Conv2dLSTMCell(\n",
       "      (forget): Conv2d(394, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (input): Conv2d(394, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (output): Conv2d(394, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (state): Conv2d(394, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (transform): Conv2d(128, 394, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "    (generator_core): Conv2dLSTMCell(\n",
       "      (forget): Conv2d(327, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (input): Conv2d(327, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (output): Conv2d(327, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (state): Conv2d(327, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "      (transform): Conv2d(128, 327, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    )\n",
       "    (posterior_density): Conv2d(128, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    (prior_density): Conv2d(128, 128, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))\n",
       "    (observation_density): Conv2d(128, 3, kernel_size=(1, 1), stride=(1, 1))\n",
       "    (upsample): ConvTranspose2d(128, 128, kernel_size=(4, 4), stride=(4, 4), bias=False)\n",
       "    (downsample): Conv2d(3, 3, kernel_size=(4, 4), stride=(4, 4), bias=False)\n",
       "  )\n",
       "  (representation): TowerRepresentation(\n",
       "    (conv1): Conv2d(3, 256, kernel_size=(2, 2), stride=(2, 2))\n",
       "    (conv2): Conv2d(256, 256, kernel_size=(2, 2), stride=(2, 2))\n",
       "    (conv3): Conv2d(256, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       "    (conv4): Conv2d(128, 256, kernel_size=(2, 2), stride=(2, 2))\n",
       "    (conv5): Conv2d(263, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       "    (conv6): Conv2d(263, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       "    (conv7): Conv2d(128, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       "    (conv8): Conv2d(256, 256, kernel_size=(1, 1), stride=(1, 1))\n",
       "    (avgpool): AvgPool2d(kernel_size=16, stride=16, padding=0)\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from gqn import GenerativeQueryNetwork, partition\n",
    "\n",
    "# Load model parameters onto CPU\n",
    "state_dict = torch.load(\"./model-checkpoint.pth\", map_location=\"cpu\") ## <= Choose your model location\n",
    "\n",
    "# Initialise new model with the settings of the trained one\n",
    "model_settings = dict(x_dim=3, v_dim=7, r_dim=256, h_dim=128, z_dim=64, L=8)\n",
    "model = GenerativeQueryNetwork(**model_settings)\n",
    "\n",
    "# Load trained parameters, un-dataparallel if needed\n",
    "if True in [\"module\" in m for m in list(state_dict.keys())]:\n",
    "    model = nn.DataParallel(model)\n",
    "    model.load_state_dict(state_dict)\n",
    "    model = model.module\n",
    "else:\n",
    "    model.load_state_dict(state_dict)\n",
    "    \n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load a batch of a single image containing a single object seen from 15 different viewpoints. We describe the whole set of image, viewpoint pairs by $\\{x_i, v_i \\}_{i=1}^{n}$. Whereafter we seperate this set into a context set $\\{x_i, v_i \\}_{i=1}^{m}$ of $m$ random elements and a query set $\\{x^q, v^q \\}$, which contains just a single element."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deterministic_partition(images, viewpoints, indices):\n",
    "    \"\"\"\n",
    "    Partition batch into context and query sets.\n",
    "    :param images\n",
    "    :param viewpoints\n",
    "    :return: context images, context viewpoint, query image, query viewpoint\n",
    "    \"\"\"\n",
    "    # Maximum number of context points to use\n",
    "    _, b, m, *x_dims = images.shape\n",
    "    _, b, m, *v_dims = viewpoints.shape\n",
    "\n",
    "    # \"Squeeze\" the batch dimension\n",
    "    images = images.view((-1, m, *x_dims))\n",
    "    viewpoints = viewpoints.view((-1, m, *v_dims))\n",
    "\n",
    "    # Partition into context and query sets\n",
    "    context_idx, query_idx = indices[:-1], indices[-1]\n",
    "\n",
    "    x, v = images[:, context_idx], viewpoints[:, context_idx]\n",
    "    x_q, v_q = images[:, query_idx], viewpoints[:, query_idx]\n",
    "\n",
    "    return x, v, x_q, v_q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 15 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "# Pick a scene to visualise\n",
    "scene_id = 0\n",
    "\n",
    "# Load data\n",
    "x, v = next(iter(loader))\n",
    "x_, v_ = x.squeeze(0), v.squeeze(0)\n",
    "\n",
    "# Sample a set of views\n",
    "n_context = 7 + 1\n",
    "indices = random.sample([i for i in range(v_.size(1))], n_context)\n",
    "\n",
    "# Seperate into context and query sets\n",
    "x_c, v_c, x_q, v_q = deterministic_partition(x, v, indices)\n",
    "\n",
    "# Visualise context and query images\n",
    "f, axarr = plt.subplots(1, 15, figsize=(20, 7))\n",
    "for i, ax in enumerate(axarr.flat):\n",
    "    # Move channel dimension to end\n",
    "    ax.imshow(x_[scene_id][i].permute(1, 2, 0))\n",
    "    \n",
    "    if i == indices[-1]:\n",
    "        ax.set_title(\"Query\", color=\"magenta\")\n",
    "    elif i in indices[:-1]:\n",
    "        ax.set_title(\"Context\", color=\"green\")\n",
    "    else:\n",
    "        ax.set_title(\"Unused\", color=\"grey\")\n",
    "    \n",
    "    ax.axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reconstruction\n",
    "\n",
    "Now we feed the whole set into the network and the network will perform the segregration of sets. The query image is then reconstructed in accordance to a given viewpoint and a representation vector that has been generated only by the context set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(12, 7))\n",
    "\n",
    "x_mu, r, kl = model(x_c[scene_id].unsqueeze(0), \n",
    "                    v_c[scene_id].unsqueeze(0), \n",
    "                    x_q[scene_id].unsqueeze(0),\n",
    "                    v_q[scene_id].unsqueeze(0))\n",
    "\n",
    "x_mu = x_mu.squeeze(0)\n",
    "r = r.squeeze(0)\n",
    "\n",
    "ax1.imshow(x_q[scene_id].data.permute(1, 2, 0))\n",
    "ax1.set_title(\"Query image\")\n",
    "ax1.axis(\"off\")\n",
    "\n",
    "ax2.imshow(x_mu.data.permute(1, 2, 0))\n",
    "ax2.set_title(\"Reconstruction\")\n",
    "ax2.axis(\"off\")\n",
    "\n",
    "ax3.imshow(r.data.view(16, 16))\n",
    "ax3.set_title(\"Representation\")\n",
    "ax3.axis(\"off\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualising representation\n",
    "\n",
    "We might be interested in visualising the representation as more context points are introduced. The representation network $\\phi(x_i, v_i)$ generates a single representation for a context point $(x_i, v_i)$ which is then aggregated (summed) for each context point to generate the final representation.\n",
    "\n",
    "Below, we see how adding more context points creates a less sparse representation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x504 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(1, 7, figsize=(20, 7))\n",
    "\n",
    "r = torch.zeros(128, 256, 1, 1)\n",
    "\n",
    "for i, ax in enumerate(axarr.flat):\n",
    "    phi = model.representation(x_c[:, i], v_c[:, i])\n",
    "    r += phi\n",
    "    ax.imshow(r[scene_id].data.view(16, 16))\n",
    "    ax.axis(\"off\")\n",
    "    ax.set_title(\"#Context points: {}\".format(i+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample from the prior.\n",
    "\n",
    "Because we use a conditional prior density $\\pi(z|y)$ that is parametrised by a neural network, we should be able to continuously refine it during training such that if $y = (v, r)$ we can generate a sample from the data distrbution by sampling $z \\sim \\pi(z|v,r)$ and sending it through the generative model $g_{\\theta}(x|z, y)$.\n",
    "\n",
    "This means that we can give a number of context points along with a query viewpoint and generate a new image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create progressively growing context set\n",
    "batch_size, n_views, c, h, w = x_c.shape\n",
    "\n",
    "f, axarr = plt.subplots(1, num_samples, figsize=(20, 7))\n",
    "for i, ax in enumerate(axarr.flat):\n",
    "    x_ = x_c[scene_id][:i+1].view(-1, c, h, w)\n",
    "    v_ = v_c[scene_id][:i+1].view(-1, 7)\n",
    "    \n",
    "    phi = model.representation(x_, v_)\n",
    "    \n",
    "    r = torch.sum(phi, dim=0)\n",
    "    x_mu = model.generator.sample((h, w), v_q[scene_id].unsqueeze(0), r)\n",
    "    ax.imshow(x_mu.squeeze(0).data.permute(1, 2, 0))\n",
    "    ax.set_title(\"Context points: {}\".format(i))\n",
    "    ax.axis(\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mental rotation task\n",
    "\n",
    "As an extension to the above mentioned sampling procedure, we can perform the mental rotation task by continuously sampling from the prior given a static representation $r$ and then varying the query viewpoint vector $v^q$ between each sample to \"rotate the object\".\n",
    "\n",
    "In the example below we change the yaw slightly at each frame for 8 frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Change viewpoint yaw\n",
    "batch_size, n_views, c, h, w = context_x.shape\n",
    "pi = 3.1415629\n",
    "\n",
    "x_ = x_c[scene_id].view(-1, c, h, w)\n",
    "v_ = v_c[scene_id].view(-1, 7)\n",
    "\n",
    "phi = model.representation(x_, v_)\n",
    "\n",
    "r = torch.sum(phi, dim=0)\n",
    "\n",
    "f, axarr = plt.subplots(2, num_samples, figsize=(20, 7))\n",
    "for i, ax in enumerate(axarr[0].flat):\n",
    "    v = torch.zeros(7).copy_(v_q[scene_id])\n",
    "    \n",
    "    yaw = (i+1) * (pi/8) - pi/2\n",
    "    v[3], v[4] = np.cos(yaw), np.sin(yaw)\n",
    "\n",
    "    x_mu = model.generator.sample((h, w), v.unsqueeze(0), r)\n",
    "    ax.imshow(x_mu.squeeze(0).data.permute(1, 2, 0))\n",
    "    ax.set_title(r\"Yaw:\" + str(i+1) + r\"$\\frac{\\pi}{8} - \\frac{\\pi}{2}$\")\n",
    "    ax.axis(\"off\")\n",
    "    \n",
    "for i, ax in enumerate(axarr[1].flat):\n",
    "    v = torch.zeros(7).copy_(v_q[scene_id])\n",
    "    \n",
    "    pitch = (i+1) * (pi/8) - pi/2\n",
    "    v[5], v[6] = np.cos(pitch), np.sin(pitch)\n",
    "\n",
    "    x_mu = model.generator.sample((h, w), v.unsqueeze(0), r)\n",
    "    ax.imshow(x_mu.squeeze(0).data.permute(1, 2, 0))\n",
    "    ax.set_title(r\"Pitch:\" + str(i+1) + r\"$\\frac{\\pi}{8} - \\frac{\\pi}{2}$\")\n",
    "    ax.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}