notebooks/check_rotation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How does rotation distribution change during optimization training?\n",
    "* Under the normal training process the distribution of rotations the model is trained on should be uniformly distributed over $[0^{\\circ}, 360^{\\circ}]$. \n",
    "* Through the optimization process during training, we find that the model learns a more efficent representation where the digits of a given class are oriented at the same rotation. \n",
    "* We even find that the model learns to encode the \"6\" and \"9\" digits as $180^{\\circ}$ rotations of one another, as this is the most compressed representation of the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import pickle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "rot_hist_loc = '/media/rene/data/equivariance/mnist/batch_avae_mnist_L8_rotate_save_hist_correct/the_only_rot_history.pkl'\n",
    "with open(rot_hist_loc, 'rb') as f:\n",
    "    rot_hist = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>actual_rot</th>\n",
       "      <th>affine_rot</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>249.0</td>\n",
       "      <td>122.776927</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>140.0</td>\n",
       "      <td>46.770257</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>307.0</td>\n",
       "      <td>136.157572</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>230.0</td>\n",
       "      <td>137.621520</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.0</td>\n",
       "      <td>141.173986</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   actual_rot  affine_rot  target\n",
       "0       249.0  122.776927     4.0\n",
       "1       140.0   46.770257     1.0\n",
       "2       307.0  136.157572     1.0\n",
       "3       230.0  137.621520     9.0\n",
       "4        13.0  141.173986     6.0"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def reformat_rot_hist(rot_hist, epoch):\n",
    "    data = pd.DataFrame()\n",
    "    # 100 batches is enough\n",
    "    for batch_idx in range(100):\n",
    "        affine_params = rot_hist[epoch][batch_idx]\n",
    "        target = rot_hist[epoch][batch_idx]\n",
    "        rot = rot_hist[epoch][batch_idx]\n",
    "        # grab all the stuff from inside each batch\n",
    "        for img_idx in range(len(rot_hist[epoch][batch_idx][0])):\n",
    "            affine_params = rot_hist[epoch][batch_idx][0][img_idx]\n",
    "            target = rot_hist[epoch][batch_idx][1][img_idx]\n",
    "            rot = rot_hist[epoch][batch_idx][2][img_idx]\n",
    "            data = data.append({\n",
    "                                'actual_rot': rot,\n",
    "                                'affine_rot': math.acos(affine_params[0, 0])*180/math.pi,\n",
    "                                'target': target,\n",
    "                            }, ignore_index=True)    \n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25600 2555\n"
     ]
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    {
     "data": {
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>actual_rot</th>\n",
       "      <th>affine_rot</th>\n",
       "      <th>target</th>\n",
       "      <th>rot_off_center</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>247.0</td>\n",
       "      <td>44.732240</td>\n",
       "      <td>0.0</td>\n",
       "      <td>157.732240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>128.0</td>\n",
       "      <td>45.719237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>277.719237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>357.0</td>\n",
       "      <td>141.736323</td>\n",
       "      <td>0.0</td>\n",
       "      <td>144.736323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>243.0</td>\n",
       "      <td>44.049264</td>\n",
       "      <td>0.0</td>\n",
       "      <td>161.049264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>123.0</td>\n",
       "      <td>39.067359</td>\n",
       "      <td>0.0</td>\n",
       "      <td>276.067359</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    actual_rot  affine_rot  target  rot_off_center\n",
       "9        247.0   44.732240     0.0      157.732240\n",
       "16       128.0   45.719237     0.0      277.719237\n",
       "55       357.0  141.736323     0.0      144.736323\n",
       "61       243.0   44.049264     0.0      161.049264\n",
       "66       123.0   39.067359     0.0      276.067359"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ep1_data = reformat_rot_hist(rot_hist, epoch=1)\n",
    "ep1_data['rot_off_center'] = ep1_data['affine_rot'] - ep1_data['actual_rot']\n",
    "ep1_data['rot_off_center'] = ep1_data['rot_off_center'] % 360\n",
    "data = ep1_data[ep1_data['target'] == 0]\n",
    "print(len(ep1_data), len(data))\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution of Rotations Over Time\n",
    "* How does the distribution of rotations fed into the network change over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compare_rotations(rot_hist, epochs=[1, 15, 30, 59], target=1, save_loc=None):\n",
    "    plt.style.use('ggplot')\n",
    "    fig, ax = plt.subplots(len(epochs), 1, figsize=(8,10))#, sharex='col', sharey='row',figsize=(10,10))\n",
    "\n",
    "    for i,  epoch in enumerate(epochs):\n",
    "        data = reformat_rot_hist(rot_hist, epoch)\n",
    "        data = data[data['target'] == target]\n",
    "        data['rot_off_center'] = data['affine_rot'] - data['actual_rot']\n",
    "        data['rot_off_center'] = data['rot_off_center'] % 360\n",
    "        ax[i].set_ylabel(f'Epoch {epoch}', fontsize='large')  \n",
    "        ax[i].hist(data['rot_off_center'], 20, density=True, facecolor='g', alpha=0.75)\n",
    "        ax[i].yaxis.set_major_locator(plt.MultipleLocator(.002))\n",
    "    \n",
    "    ax[0].set_xticklabels([])\n",
    "    ax[1].set_xticklabels([])\n",
    "    ax[2].set_xlabel(f'Rotation', fontsize='large')  \n",
    "    plt.subplots_adjust(wspace=.1, hspace=.1)\n",
    "    plt.tight_layout()\n",
    "    if save_loc is not None:\n",
    "        plt.savefig(save_loc, bbox_inches='tight')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [],
   "source": [
    "rot_hist_loc = '/media/rene/data/equivariance/mnist/batch_avae_mnist_L8_rotate_save_hist_correct/the_only_rot_history.pkl'\n",
    "with open(rot_hist_loc, 'rb') as f:\n",
    "    rot_hist = pickle.load(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "compare_rotations(rot_hist, epochs=[1, 5, 30], target=1, \n",
    "                  save_loc='/media/rene/code/equivariance/imgs/rot_batch_opt_1.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_rotations(rot_hist, epochs=[1, 5, 30], target=8, \n",
    "                  save_loc='/media/rene/code/equivariance/imgs/rot_batch_opt_8.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _69(rot_hist, epochs=[1, 15, 30, 59], save_loc=None):\n",
    "    plt.style.use('ggplot')\n",
    "    fig, ax = plt.subplots(len(epochs), 2, figsize=(10,10))\n",
    "\n",
    "    for i,  epoch in enumerate(epochs):\n",
    "        data = reformat_rot_hist(rot_hist, epoch)\n",
    "        data['rot_off_center'] = data['affine_rot'] - data['actual_rot']\n",
    "        data['rot_off_center'] = data['rot_off_center'] % 360\n",
    "        data_6 = data[data['target'] == 6]\n",
    "        data_9 = data[data['target'] == 9]\n",
    "        ax[i, 0].hist(data_6['rot_off_center'], 20, density=True, facecolor='g', alpha=0.75)\n",
    "        ax[i, 1].hist(data_9['rot_off_center'], 20, density=True, facecolor='g', alpha=0.75)\n",
    "        ax[i, 0].yaxis.set_major_locator(plt.MultipleLocator(.002))\n",
    "        ax[i, 0].set_ylabel(f'Epoch {epoch}', fontsize='large')\n",
    "        ax[i, 1].set_yticklabels([])\n",
    "        if i < len(epochs)-1:\n",
    "            ax[i, 0].set_xticklabels([])\n",
    "            ax[i, 1].set_xticklabels([])\n",
    "            \n",
    "    ax[2, 0].set_xlabel(f'Rotation: Digit=\"6\"', fontsize='large')  \n",
    "    ax[2, 1].set_xlabel(f'Rotation: Digit=\"9\"', fontsize='large')  \n",
    "    plt.subplots_adjust(wspace=.1, hspace=.1)\n",
    "    if save_loc is not None:\n",
    "        plt.savefig(save_loc, bbox_inches='tight')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_69(rot_hist, epochs=[1, 5, 30], save_loc='/media/rene/code/equivariance/imgs/rot_batch_opt_69.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "HVAE",
   "language": "python",
   "name": "hvae"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}