AIML421-ASS4-Part3-optimisation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "36ba499a",
   "metadata": {},
   "source": [
    "## Part 3 Optimisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "53a2848a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#conda install pytorch torchvision -c pytorch\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "85551cdc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "39a9d735",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.03833254277706147,\n",
       " 1.0418675154447556,\n",
       " -0.043163859844207765,\n",
       " 1.0164278388023376)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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09TMgxVBCr1BSffRN502xYfs+lq27lZXrd9Q+YSUZptQU63yDauSSJ63lUrHO+mhTzgocpswQ83yDauSSF43QAxLrKLTbMGWGXsletWaRpymhByTmUWinYcoMqjWLDKaSS0Ca1PGQtcwQwxrkoXTphBKH5E8JPSBrVy1fVEMHjUI71bnWHMr8SChxSDFUcgmIOh7iFcr8SChxSDE0Qg9MXUehOozvL5T5kVDikGIooUtm3cn7NWct4Zbd8zqM7yOU+ZFQ4pBiqOQimSSdsfnFnQ/U8jB+y555Vq7fUcpJXKF06YQShxRDI3TJJKkG2704/oKQD+PLnhwMpUsnlDikGObe6+tYrJmZGZ+dna3kuSW7hTJL0uF6L1OTE3x/3YUFRjW8let3JP4tIccsAmBmu919JukxjdBloO7RbBrjx1mlh/GDJmk1ORgWTarnQwldBkoqs3QaP854Ejj6ZMfRXu8rERYuTTlFk4PhUG98fjQpKgP1G7VOTU5w0jOOX5zMgcNHvbJJ0TS91pocDId64/OjhC4D9Rq1LtSbDxw8nPh4VeWLtFcB0klcYVD5Kz8quchAg5YkCK18kTaeup7EFZvQPj91phG6DDRoNBta+SK0eKQ/vV/50QhdUkkazXZ2JjxrYpxnjB/HgYOHK+9SUK91vej9yo/60GUoW/bMs/bf7+Bwx2To+HHGhrecqy+iSIH69aGr5CJDuWbr3kXJHODwk841W/dWFJGIKKHLUA4cSu5s6XW/iBRPCV1EJBJK6DKUk08cz3S/iBRPCb0Bilgm9hOvO4fxscXn94+PGZ943Tkj/24RGY7aFiNX1DoZajWTUWlBrvwpoUeu3zoZo355dKalDEsLchVDCT1yVa6ToRGY9FLkQKPJlNAjV9U6GUWPwLSzqDctyFUMTYpGrqp1MopcEjXpuqZXb76r0GuChqbM66EWodeAQgtyjUYJPXJVLRNb5Ais6etnx7BD04JcxUhVcjGzi4FrgTHgendf3/X4O4CPtm/+L/BX7n5HnoHK8KqYvCyy1NP0w/UY6s/qkirGwIRuZmPAdcBFwBywy8y2uvs9HZv9HPhjd3/czC4BNgEXFBGw1MOgNdRH0fT1s2PZoalLKn9pSi7nA/vd/X53fwK4CbiscwN3/4G7P96+uRM4Pd8wpW6KLPU0/XBd9WfpJU3JZQp4sOP2HP1H3+8Fvj5KUBKHokZgTT9cL/LoR+otTUJPun574iLqZvYaWgn9lT0eXwOsAZienk4ZoqTVpFa+Jh+uN32HJr2lSehzwBkdt08HHureyMxeAlwPXOLuv0r6Re6+iVZ9nZmZmWqurBEpnXnXLE3eoUlvaWrou4AzzWyZmZ0AXA5s7dzAzKaBzcA73f2+/MOUQZreyiciKUbo7n7EzK4CttNqW7zB3fea2ZXtxzcCHweeA3zWzACO9LpEkhQjls4HERleqj50d98GbOu6b2PHz+8D3pdvaJJFla18Tardi4RMa7nUQJqEWVXng2r35dBOU9JQQg9c2oRZVedDDGct9hNCItVOU9JSQg9cloRZRedDzLX7UBJp7DtNyY8SeuCGTZhljSxjPg0/ayIt6jWPeacp+dJqi4Eb5jTvMlfjq8Np+MMuNZslkSa95h/+8u289JPfHPl116n+kpYSeuCGSZhl9qRXtTxvWqPs3LIk0qTXHODAocMj70zrsNOUMKjkErhhJjvLPkQP+azFUerPWTqH+r22o9a7+30GQpi0lXAooddA1oQZc107q1F2bguv+TVb93Lg0GEAnjGefFDb6zXP8nyDYun+DIQyaSvhUMklQjpEf1oe9ef/O/LkUz8/fjC5hJL0mg/7fGlpuQfppoQeodDr2mUadeeWNmkuvOYnnzh+zO8oameq7hfpppJLpEKua5dp1BOu0ibNhVr2gYOHmZwYxwwOHDysllEplRJ6xGKeMMvyt42yc0uTNLtr2QcOHWZifIx/eetLC329daEL6aaSS6RiuDJ8L6H12VdVy65raW3Y8wJkMI3QIxXz6eJl/m1pSjZV1rLrVlpTZ06xlNAjFfOEWWh99qplpxfKcgqxUsklUjGfLh7a36Y20fRGXU4hlrJhUZTQI7NQn5w/cOiYq3vHkmTKSKBZ6ryDatmqGT9t1OUU1Gffn0ouEemuTzpg7X+nug5XRz2UrfJQuOi134ep8/Yqy6hmvFgeyynEUDYsihJ6RJJGNAvJ/PvrLnzqvlGTTAhJqsjJwDwnXWOenB5Glp2x5iayU0KPSNoRzahJJvYklefIUKPMY6XdGavPPjvV0COStj45apKJPUnlOeka2gRundS1z75KGqHXVFINO+2IZtRD2dgPhfMcGWqUOZq69dlXTSP0GurVzgWkGtGM2iUSe5teniNDjTKlTObulTzxzMyMz87OVvLcdbfQltite/Kznzp3ucSmDq9lHWJsCjPb7e4zSY+p5FJDedSwRz2U1aFwPkLoGBqkDjFKi0ouNaSJtnjU4eSZOsQoLUroNRR7DbtJ6tAxVIcYpUUllxoq+kxJKc+oHUNl1LZj72qKiRJ6TamGHYdR2hrLqm2r9bI+lNAlOE3qqBjlaKusM3aHjbFJ72MolNAlKE3sqBj2aKvM2nbWGJv4PoZAk6ISFHVUpBdyt5Pex2qkGqGb2cXAtcAYcL27r+963NqPXwocBN7j7j/JOVZpAHVU9NZdwnjNWUu4Zfd8kLVtvY/VGDhCN7Mx4DrgEuBs4G1mdnbXZpcAZ7b/WwN8Luc4pSFCHnVWKWm5h1t2z/Om86aCXFZA72M10ozQzwf2u/v9AGZ2E3AZcE/HNpcBN3prHYGdZjZpZqe6+8O5RyxRU0dFsl4ljG//16Opl3sok97HaqRJ6FPAgx2354ALUmwzBSihSybqsU9WtxKG3sdqpEno3ZemhNaFcLJug5mtoVWSYXp6OsVTSxOpx/5YdTy5R+9j+dJ0ucwBZ3TcPh14aIhtcPdN7j7j7jNLlizJGqtIY2m5B0kjTULfBZxpZsvM7ATgcmBr1zZbgXdZyyuA36h+LpIfrasuaQwsubj7ETO7CthOq23xBnffa2ZXth/fCGyj1bK4n1bb4hXFhSzSTCphyCCp+tDdfRutpN1538aOnx34QL6hiYhIFjpTVEQkEkroIiKRUEIXEYmEErqISCSsNZ9ZwRObPQr8ssCnOAV4rMDfnwfFmA/FmA/FmI+iY/x9d088kaeyhF40M5t195mq4+hHMeZDMeZDMeajyhhVchERiYQSuohIJGJO6JuqDiAFxZgPxZgPxZiPymKMtoYuItI0MY/QRUQaJZqEbmbPNrNvmdlP2/+enLDNGWb2bTO718z2mtmHSojrYjPbZ2b7zWxdwuNmZv/afvxOM3tZ0TENEeM72rHdaWY/MLNzQ4uxY7uXm9lRM3tzmfG1n3tgjGb2ajO7vf35+25oMZrZs8zsa2Z2RzvG0hfaM7MbzOwRM7u7x+MhfGcGxVjNd8bdo/gP+EdgXfvndcA/JGxzKvCy9s/PBO4Dzi4wpjHgZ8AfACcAd3Q/H61VKr9O6yIhrwB+VPLrlibGPwRObv98SYgxdmy3g9ZCcm8OLUZgktalG6fbt58bYIx/s/DdAZYAvwZOKDnOPwJeBtzd4/FKvzMpY6zkOxPNCJ3WdU2/0P75C8Dq7g3c/WF3/0n75/8B7qV1qbyiPHU9Vnd/Ali4Hmunp67H6u47gUkzO7XAmDLH6O4/cPfH2zd30rqASZnSvI4AHwRuAR4pM7i2NDG+Hdjs7g8AuHvZcaaJ0YFnmpkBJ9FK6EfKDNLdb2s/by9Vf2cGxljVdyamhP48b19Uo/3vc/ttbGZLgRXAjwqMqde1VrNuU6Ssz/9eWqOjMg2M0cymgDcAG6lGmtfxBcDJZvYdM9ttZu8qLbqWNDF+BnghrSuO3QV8yN2fLCe81Kr+zmRV2ncm1XrooTCz/wB+L+Ghj2X8PSfRGsl92N1/m0dsvZ4q4b6hrsdaoNTPb2avofXhfGWhESU8dcJ93TF+Gvioux9tDS5LlybG44HzgNcCE8APzWynu99XdHBtaWJcBdwOXAg8H/iWmX2v4O9JVlV/Z1Ir+ztTq4Tu7n/S6zEz+28zO9XdH24ffiUezprZOK1k/kV331xQqAtyux5rgVI9v5m9BLgeuMTdf1VSbAvSxDgD3NRO5qcAl5rZEXffUkqE6d/rx9z9d8DvzOw24FxaczllSBPjFcB6bxV/95vZz4GzgB+XE2IqVX9nUqniOxNTyWUr8O72z+8Gvtq9Qbsu+G/Ave7+zyXEVIfrsQ6M0cymgc3AO0scTWaK0d2XuftSd18K3Ay8v8RknipGWp/JV5nZ8WZ2InABrXmckGJ8gNYRBGb2PGA5cH+JMaZR9XdmoMq+M2XPDhf1H/Ac4D+Bn7b/fXb7/tOAbe2fX0nr0OxOWoeVtwOXFhzXpbRGYD8DPta+70rgyvbPBlzXfvwuYKaC125QjNcDj3e8ZrOhxdi17ecpucslbYzAWlqdLnfTKvkFFWP7+/LN9mfxbuAvK4jxS8DDwGFao/H3BvidGRRjJd8ZnSkqIhKJmEouIiKNpoQuIhIJJXQRkUgooYuIREIJXUQkEkroIiKRUEIXEYmEErqISCT+H60Gsb2/N7VUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make up some data for x \n",
    "D=2\n",
    "x= torch.rand(100,D)\n",
    "plt.scatter(x[:,0],x[:,1])\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f439a566",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.060148739814758295,\n",
       " 1.9257378339767457,\n",
       " 0.04752920866012572,\n",
       " 1.9129040360450744)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x[:,0] = x[:,0] + x[:,1] \n",
    "x[:,1] = 0.5*x[:,0] + x[:,1]\n",
    "plt.scatter(x[:,0],x[:,1])\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8a825160",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.6754, 0.4923])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "18b4b69d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def encoder(x,w,b):\n",
    "    return x[:,0]*w[0]+x[:,1]*w[1]+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "926e90da",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decoder(z,w,b):  \n",
    "    x = torch.ones(100,2)\n",
    "    x[:,0] = z*w[:,0] + b[:,0]\n",
    "    x[:,1]= z*w[:,1] + b[:,1]          \n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f7df7f93",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "loss_func = torch.nn.MSELoss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bb13daa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss vs epochs - SGD')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "losses=[]\n",
    "epochs=[]\n",
    "wEncoder = torch.randn(D,1, requires_grad=True)\n",
    "wDecoder = torch.randn(1,D, requires_grad=True)\n",
    "bEncoder = torch.randn(1, requires_grad=True)\n",
    "bDecoder = torch.randn(1,D, requires_grad=True)\n",
    "opt=torch.optim.SGD([wEncoder,bEncoder,wDecoder,bDecoder], lr=0.01)\n",
    "steps=1000\n",
    "for i in range(steps):     \n",
    "    opt.zero_grad()\n",
    "    z=encoder(x,wEncoder,bEncoder)\n",
    "    y=decoder(z,wDecoder,bDecoder)\n",
    "    loss=loss_func(y,x)\n",
    "    loss.backward()\n",
    "    opt.step()  \n",
    "    losses.append(loss.item())\n",
    "    epochs.append(i+1)\n",
    "#print(losses)\n",
    "plt.plot(epochs,losses)\n",
    "plt.title('Loss vs epochs - SGD')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a931dedf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SGD - Input data / constructed data / encoder weights')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iAijQu4GadES6lIY07j4KfJEO837CT3eL/9+fMU8ypHF6sLQFKPQ7nQJfpIO8H/gSO/vNb4v3S0NfQxp3JwW+SAdZmPP4lxndfLMqZz6dSNXZFPgiHSTvjNjtjG6+sZz5dCJVZ1Pgi3SQvDNiSzm7hr5OpOp8CnyRDrKg8iw7ODqRqtvUJfDN7Doze9LM7s+ZfpyZPW1my+Pf39RjvSLtolFdIK8G3sfOmn4vsEfOvDMpf2ET6Tz1quFfD5xUYZ6fuvuR8e8TdVqvSEtbBEwBzqZxXSCvBrbGdW0lHLCdWDLPRNR8043qcqatu99uZrPqsSyRTpH0dS/t/gg7u0A2qlbtFe7XamjZMJcsfoANm7cAsM+kPj72hsOYN3uwTmuQempkG/4xZnavmf2rmR2WN5OZLTCzpWa2dO3atQ0snkh9ZfV1T2tUF8iLgC0lj21h7H3uh5YNc/4/3rsj7AFGNm3h/H+6l6Flw2NcuoyHRgX+PcBMdz8C+DwwlDejuy909znuPmfq1KkNKp5I/VUK9B6qb9Ov5VhAXp/7vMcruXhoBQdeeDPn3bicLdt3/a2wZZtzxZKVNS5dxlNDAt/dn3H3jfH2zUCfmU1pxLpFmqVSn/ZtVNemnzUcwjmEXjazcp6/iPw+91ZgnaUuHlrBDXc+yjYv3yi0ZsPmKpcsjdCQwDez/czM4u2j4nrzrpks0hHyxpjPCuBKwxosAt7Brk1ESezm7TQuIr+93oEPUewXw9CyYWZ/4hZuuLNYQ9S0gf5C80lj1eWgrZl9CzgOmGJmq4GPAX0A7n4N8GbgfWa2FdgMvNW9QhVBpM3ljTF/ds78eU0sSc0+7yzaRNaB4ErxvI6dNa9kp0FqGaUHZYvo6zXOP/HgwvNL41gr5+6cOXN86dKlzS6GSF1NIDu8ewndKEvNonh7uxH61dfy3ETSP39o2TAX3rSCzVsq7Wp2Ui+d5jOzu919TtY0XQBFpMHy4jPv8Wp685QeN7iU/K6heZL1XbFkZeGwP3vuDD417/Aq1iLNoKEVRBpsZpWPFx3QLGssnPnsvBYt7DwDdybherXl1lf0wKvCvn2ohi/SYFm17nIDl50CXMPog6+TCAdxbyb/GrSJvEsXJscGWDbMPktW0rthM9sH+jnjxINh9iDTBvoZLhP6fT3GFWccoeabNqLAF2mwIhcMTywCvsbosDdC2F89xnI8OLSCqSW9bno3bOb7N63gWOD8Ew/ObcMf6O/jkjeqrb7dKPBFmqDoBcOzztZ1Qs2+VkPLhvnoTfexacv2zOmbt2zjiiUr+fkFrwVCW/6aDZuZNtDP+ScerJBvYwp8kRaWd8C21mEZdva8yQ77RNJ+P2/2oAK+g+igrUgLyztgW+uVqYr2vNGJU51JNXyRFlbtAd60oWXDXLFkJcMbNtNrVnE4hER/X69OnOpQquGLNEgtA5+lu1VWc2Wq+dfewXk3Lt/Ry6Zo2O8xsZfLTj9czTgdSjV8kQYoHRs/axiDPEUP8EKo1Z934/Kqy2cG849Wf/pOp8AXaYCs3jb1vAhKpZ43WQzU86bLKPBFGqDevW3SkguRZI1Nn2dwoH9Ht0vpHmrDF2mAeve2SR8POG/JyqrCXgdlu5cCX6QKeQdesx5PLmBu5I9YuZHqL0KyCPizZcNsvfxHTL/gB3gVFxsZ6O/TQdkupiYdkYLyDrz+nDD8QfrxdxFGv6zU430dxQ/eJi5aNsyeN62gp4phi3sMrjzzSAV9l1PgixSUd+B1IbsG+wtVLLfag7dbl6xkQhVhf+yBk1n0nmOqKJF0KgW+SIlFZA9slneAtXj05stbdnLyVHosmwkFmnB0IRLJosAXSSnXX34G2W3xvYw99LMO3pZecWp4w2YuvGkFkyb1sWnTrpccHBjoZ7l63kgZCnyRlHL95fOGOTgG+GHGsoz8C4iXOiV1Oz0kQqnNW7YxMKGHLX29bEk16/T19XKJet5IBQp8kZRy/eXzxrG/KOc5k+P/dTnT074DLL72Dnp/sx4IO4s8T2/ewlVvOVLDFkvVFPgiKXnNNkmTS9YwB+fkLGs9Oy8oPitnuYndLr2V3mdfKBv0iWkD/Rq2WGqiwBdJqWV0yrydRE/8y5s+KXVpQShfq0/opCkZCwW+SEo1lx9MZO0kYOeB3FWMbs/fZ2gFe8VLCxYJ+cSgmm5kjBT40tXyumBWM6BZ6U6ih1177Tgh3Adi2FcT9P19GrJY6kNDK0jXSrpgriIEctIFs9qhDiCE/iOENvu88Sr7lw2zdxVh70BPDwp7qRvV8KVrjdeQxek2+3Q7fTW1egf23msiKy46YQwlERlNNXzpWtUOWVxp4DQj1KCSNvtJy4bZ96YVTKgy7HvNOGfuDIW91J1q+NK1KnXBTCs6cNo2kqC/D9uyvaqgN+Cqt2iAMxk/danhm9l1Zvakmd2fM93M7HNm9pCZ3Wdmr6rHekXG4lJCl8u0vC6Yec0/Xyp5fJ+hFUy5cTk9VYb9HhN7FfYy7upVw78e+ALw9ZzpJwMHxb+jCd+To+u0bpGaZHXBPCXeP5udY+TMpPxJUxC7Wt71KHjxrpbqfSONVpfAd/fbzWxWmVlOA77u7g7caWYDZra/uz9ej/WL1CrdBbO02SavH33a1GvvoL/AcAiJZDnqUy/N0Kg2/EHgsdT91fGxXQLfzBYQByicMaPWC8CJVC+r2SZRLuyrabpRs400U6N66WR9JzIHEnT3he4+x93nTJ06dZyLJbJTkQuKG6H5ZsaFN1cd9kfNncF5swd36eUj0iiNquGvBqan7h8ArGnQukUKyeu1A7WNe5Mw4A/mzuAH8w7PHGc/r89/3lnAIrVqVOAvBj5oZt8mHKx9Wu330moyB05bNszkf3mAnk1bqj5xyvt62Hj6K/n87MGqT/IqdyEWhb7Uqi6Bb2bfAo4DppjZauBjQB+Au18D3EzoAPEQ4TN8bj3WK1JP6V47a2sMeghhv/nAyayN15F9B/lXxMprRhqvs4Clu9Wrl85ZFaY78IF6rEtkPM0H9ii5tGBRDngPrDvjSDalDsxuI7+XTw+hNl8a4tWeBSxShM60FUkZWjbMR75zL9u86MUJg7PnzuCGeYfnBnIyWmbpUreR3VRTzVnAIkVpLB2RKLloeDVh72YwdwaHzDs888zdUfMSTuYqlTTVpFVzFrBIUarhS1cbWjbMJYsfYMPmLYWf09/fxxNvPIyRVLPNAmBh/Mtrs59J8aaaWi7EIlKJAl+60sVDK1h016NU03Iz0N/HJW88jPNmDzJSMi2ppT8S7+ddJvEiijfVVHshFpFKFPjSdU648jb+68nnCs/fa8anzzxixxmyp+fMl9TSK9XOS3cGE4GN7Lz+rWryMl4U+NIVamm6gewBzspdtDzpcZNXOy/dGUwGngHWxcfV317Gkw7aSse7eGgF5924vOqwHxzozxzNMu/gbNLjptKQCenLIe4JlJYq6yCuSD2ohi8da2jZMB//lwcY2VRd0Pf1Gle8+YjcQc6SmnfWwdlqT45Sf3tpJAW+dJzQvfI+Nm/Ju5x4vn0m9fGxNxxWcUTL+cA5OdOqCWv1t5dGUuBLxxhaNsx5Ny6v6bkHvWgPbv3wcVU9px5hnTl+D+pvL+NDgS9tr9YDssnZr2fHE6dmUV2f93qEtfrbSyMp8KVtDS0b5i9uXJ59YYUyHPCJvWx80+F8Pjbd1DIyZb3CWv3tpVHMqxwzpJHmzJnjS5cubXYxpAXV3HzT38faNx7G87MHd1yvdiM7u0WmzWTniVQi7cLM7nb3OVnTVMOXtnLx0Aq+edejbK+hnpI03Sxg9PVq86wieyRLkXalwJe2cPHQCm64s/rOig70GFx1ZriW7Czyr1ubRSdBSSfRiVfS0oaWDfOyi26uOuyTHwAHHjiZ31526o5ultXuMvJOglpEuC6trk8r7UQ1fGlZtdbqAT77liMz+9KXu25tntIS6PKD0q4U+NJyam2nT7pZfiYn7CG7K2Ulpf3qdflBaVdq0pGWktTqqwl7B9xg89wZXHr5qWXPkp1PGLN+ZsFlZ/Wrr2U4BDUBSStQDV+abmjZMFcsWcmaDZur7lNPXw/rTn8lU2YPchUh0BdRvm980u+9h+zrzEL4pZDXr77oGbZJOVYx+vKGagKSZlHgS1MN1XjB8GMPnMyi9xyzy+PVtK/nBXel/vdFzrAtLUfpjkVNQNIMCnxpiqRWP7xhc9XPPXvuDD417/BdHl9EdSNY1jo0QpEzbLPa+UtpRExpNAW+NNzFQytYdOejVTXfOLB9Uh/PveEwDsloo09q1Hm/E7LCtejQCHlNROVq50XCXCNiSqMp8KVhah7krMd46owj2BSDvrS2nlezT8sL10rBXWsXzErdPzUipjSDAl/G3dCyYT56031sKjg+fV+PsefuE1i/aQvbBvoZOfHgHWEPo2vPlWr2EA6Y1hqutXbBzGouSg7czkQjYkpzKPBlXFV78tTgQD/nn3gwz80e5Byye9Gka+tF2sqd2sM1r5Ze6eQtDXssrUiBL+OmmrA34KrUCVOzyA770tp6kbNmewldMGsJ3V6yfz30Fniuhj2WVqMTr2RcDC0bZlEVYT9/7oxRJ0zlPTNdWy968tK2+Lyk/T39vEonROU1FVXXiVSkNdSlhm9mJwGfJVR8vuLul5dMPw74HvDb+NBN7v6JeqxbWkf6BKoes0K9cPKuIVuuj3ziQxWWnVU730Q4wHsOMBl4Gtgap60C3hVvJzuVmTnlgLCDUDONtJMx1/DNrBf4InAycChwlpkdmjHrT939yPinsO8wyQlUw/Fs2W0FLqxz9twZLPub12cOhXApoSdLWmnPlqyLliQcyDtEnNT417Ez7BMvMHpHklWOxCrCjsPQcAnSHurRpHMU8JC7P+zuLwDfBk6rw3KljVyxZGXhs2X7+3r4zFuOzDx5KpEe88bi/4VUV5uutZ97ekdSaeyd0uESFPrSyuoR+IPAY6n7q+NjpY4xs3vN7F/N7LC8hZnZAjNbamZL165dW4fiSSOsKXDGbHLB8Ac/eXLZAc4S8wlDHGyP/0vDPu/DmzxernZejaQcVmG+vLHzRVpFPQI/63tQ+nv+HmCmux8BfB4YyluYuy909znuPmfq1Kl1KJ40wrSB/szHe80wQnfLqyrU6quV12SznZ1nx26iWI+atH1zHi/yi0HDJUgrq0fgrwamp+4fAKxJz+Duz7j7xnj7ZqDPzKbUYd3SIs4/8WD6+0ZHa39fL58+8wh+e/mp/PyC1xaq1SeKDCec18yyL6F5JTnYuo3KtfNEH6H3QZYivxg0XIK0snoE/q+Ag8zsJWY2EXgrsDg9g5ntZ2YWbx8V11vumJu0mXmzB7ns9MMZHOjfUaO/7PTDqwr5RHL27Cryu1NC/oFd2PVkrCI9hmYC/0D+cYLS9vzSnYiGS5BWZ16gN0XFhZidAnyG8Ov5One/1MzeC+Du15jZB4H3ETpFbAY+7O6/qLTcOXPm+NKlS8dcPmkvsyg+bHHWwGZ5Z+hWUm4M/CyVxt0XaQYzu9vd52ROq0fgjxcFfnfKuzCJkd9unzaL6q9bmzaJ6nsEibSKcoGvM22l5eS1gzvF+rtfSmiLL9VLsbZ89baRTqXAl5ZT6WSndHt+1sHd+cDeGc+tZjgE9baRTqTB06TlpEeazGqaSdfA88aqX5+z7KINmOptI51INXxpqrzul5VOdnqU8mPV5wV2kT756m0jnUqBL01TpPtlXnDPIL/Z5VHyu2wuoHw7fi1DOIi0CwW+NE25Gnqi3CBq5XYGeWPxXE1+s46RPYSDSKdQG740TbkaeqLSlaNKLyOYbo7JuwBJ3pDHareXTqcavjTFIvI/fKXBmzeIWq0jahYZelmkEynwpSHSB2enAOeS3U2y2uCtNKJm3nPGOvSySDtSk46Mu+TgbNL0kjeIUi+NC15db1a6kWr4Mu6yDs5m2UYYB2cWupCIyHhQ4Mu4q+as1XKjY4rI2CjwZdzV0vtF49mI1J8CX8ZdrZcaXEX5C6CISHUU+NIQ2RdArExNPCL1o8CXcZX00Cl3ebMeKv8CUBOPyNgp8GVcFemhs53R/eLzaMhikbFR4Mu4KhLSMxl9AlXexck19IHI2Cjwpe7SZ9VW+oBlnVmroQ9ExocCX+qqdMjjrOETkmabvCENNPSByPjQ0ApSV3lt9r2E5prS0S7zaOgDkfpT4Etd5bXZb49/ItI8atKRuip3URIRaS4FvtSVDriKtC4FvtSVDriKtC614Uvd6YCrSGtSDV9EpEvUJfDN7CQzW2lmD5nZBRnTzcw+F6ffZ2avqsd6RUSkuDEHvpn1Al8ETgYOBc4ys0NLZjsZOCj+LQC+NNb1iohIdepRwz8KeMjdH3b3F4BvA6eVzHMa8HUP7gQGzGz/OqxbGumZZ2D5cnjuuWaXRERqUI/AHwQeS91fHR+rdh5pdXfdBbNnwz33NLskIlKDegR+1oi2XsM8YUazBWa21MyWrl27dsyFkzoaGQn/99mnueUQkZrUI/BXA9NT9w8A1tQwDwDuvtDd57j7nKlTp9aheFI3SeBPntzccohITeoR+L8CDjKzl5jZROCtwOKSeRYDb4+9deYCT7v743VYtzSSavgibW3MJ165+1Yz+yCwhDAo4nXu/oCZvTdOvwa4GTgFeIgwmOK5Y12vNMH69bDbbtBf6xVqRaSZ6nKmrbvfTAj19GPXpG478IF6rEuaaGREzTkibUxn2kpxIyNqzhFpYwp8KW79egW+SBtT4EtxquGLtDUFvhSnNnyRtqbAl+JUwxdpawp8KWbr1jCWjgJfpG0p8KWYDRvCfzXpiLQtBb4Uo7NsRdqeAl+KWb8+/Ffgi7QtBb4Uoxq+SNtT4EsxGilTpO0p8KUY1fBF2p4CX4pRG75I21PgSzEjI7DHHjBxYrNLIiI1UuBLMTrLVqTtKfClGI2UKdL2FPhSjGr4Im1PgS/FaKRMkbanwJdiVMMXaXsKfClGbfgibU+BL5W98AJs2qQmHZE2p8CXynSWrUhHUOBLZTrLVqQjKPClMtXwRTqCAl8q00iZIh1BgS+VqYYv0hEU+FKZ2vBFOoICXypLavgDA00thoiMzYSxPNnMJgM3ArOAR4Az3X0kY75HgGeBbcBWd58zlvVKg42MwN57w4QxfVxEpMnGWsO/APihux8E/DDez/O/3f1IhX0b0lm2Ih1hrIF/GvC1ePtrwLwxLk9akcbREekIYw38F7v74wDx/4ty5nPgFjO728wWlFugmS0ws6VmtnTt2rVjLJ7UhUbKFOkIFRtlzezfgf0yJl1UxXqOdfc1ZvYi4FYz+7W73541o7svBBYCzJkzx6tYh4yXkRE45JBml0JExqhi4Lv78XnTzOwJM9vf3R83s/2BJ3OWsSb+f9LMvgscBWQGvrQgteGLdISxNuksBt4Rb78D+F7pDGa2h5ntldwGXg/cP8b1SiOpSUekI4w18C8HTjCz/wJOiPcxs2lmdnOc58XAz8zsXuCXwA/c/d/GuF5plM2b4fnnVcMX6QBj6ljt7uuA12U8vgY4Jd5+GDhiLOuRJtJZtiIdQ2faSnkaR0ekYyjwpTyNlCnSMRT4Up5q+CIdQ4Ev5akNX6RjKPClPDXpiHQMBb6UNzICZmG0TBFpawp8KW/9+jAOfo8+KiLtTt9iKU8jZYp0DAW+lKdhFUQ6hgJfylMNX6RjKPClPI2UKdIxFPhSnpp0RDqGAl/yuatJR6SDKPAl38aNsHWrAl+kQyjwJZ/G0RHpKAp8yadhFUQ6igJf8qmGL9JRFPiSTyNlinQUBb7kU5OOSEdR4Es+NemIdBQFvuRbvx56e2HPPZtdEhGpAwW+5Hv5y+Gss8J4+CLS9hT4ku/tb4dvfKPZpRCROlHgi4h0CQW+iEiXUOCLiHQJBb6ISJdQ4IuIdAkFvohIl1Dgi4h0CQW+iEiXMHdvdhlymdlaYFUDVzkFeKqB62tH2kbFaDtVpm1UTLXbaaa7T82a0NKB32hmttTd5zS7HK1M26gYbafKtI2Kqed2UpOOiEiXUOCLiHQJBf5oC5tdgDagbVSMtlNl2kbF1G07qQ1fRKRLqIYvItIlFPgiIl1CgV/CzM4wswfMbLuZqctYipmdZGYrzewhM7ug2eVpRWZ2nZk9aWb3N7ssrcrMppvZj83swfhd+1Czy9RqzGx3M/ulmd0bt9HH67FcBf6u7gdOB25vdkFaiZn1Al8ETgYOBc4ys0ObW6qWdD1wUrML0eK2Ah9x90OAucAH9FnaxfPAa939COBI4CQzmzvWhSrwS7j7g+6+stnlaEFHAQ+5+8Pu/gLwbeC0Jpep5bj77cD6Zpejlbn74+5+T7z9LPAgMNjcUrUWDzbGu33xb8w9bBT4UtQg8Fjq/mr0JZUxMrNZwGzgriYXpeWYWa+ZLQeeBG519zFvowljLlUbMrN/B/bLmHSRu3+v0eVpE5bxmPr0Ss3MbE/gn4Hz3P2ZZpen1bj7NuBIMxsAvmtmr3D3MR0b6srAd/fjm12GNrQamJ66fwCwpkllkTZnZn2EsF/k7jc1uzytzN03mNlthGNDYwp8NelIUb8CDjKzl5jZROCtwOIml0nakJkZ8FXgQXe/stnlaUVmNjXW7DGzfuB44NdjXa4Cv4SZvcnMVgPHAD8wsyXNLlMrcPetwAeBJYSDbN9x9weaW6rWY2bfAu4ADjaz1Wb2p80uUws6FjgHeK2ZLY9/pzS7UC1mf+DHZnYfobJ1q7t/f6wL1dAKIiJdQjV8EZEuocAXEekSCnwRkS6hwBcR6RIKfBGRLqHAFxHpEgp8EZEu8T9wFe1jRs6gRQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x[:,0],x[:,1], color='cyan')\n",
    "plt.scatter(y[:,0].detach().numpy(),y[:,1].detach().numpy())\n",
    "plt.plot([0,wEncoder[0,0].detach().numpy()],[0,wEncoder[1,0].detach().numpy()],'-r')\n",
    "plt.axis('equal')\n",
    "plt.title('SGD - Input data / constructed data / encoder weights')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "08331aad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.052501105 1.36625\n"
     ]
    }
   ],
   "source": [
    "#ratio of weight in the encoder vs decoder for each dimensions\n",
    "print(wEncoder[0,0].detach().numpy()/wDecoder[0,0].detach().numpy(),wEncoder[1,0].detach().numpy()/wDecoder[0,1].detach().numpy())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac92ecb",
   "metadata": {},
   "source": [
    "Now, add momentum and do the same process as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2012f3bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss vs epochs - SGD with momentum')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "losses=[]\n",
    "epochs=[]\n",
    "wEncoder = torch.randn(D,1, requires_grad=True)\n",
    "wDecoder = torch.randn(1,D, requires_grad=True)\n",
    "bEncoder = torch.randn(1, requires_grad=True)\n",
    "bDecoder = torch.randn(1,D, requires_grad=True)\n",
    "opt=torch.optim.SGD([wEncoder,bEncoder,wDecoder,bDecoder], lr=0.01, momentum=0.9)\n",
    "steps=1000\n",
    "for i in range(steps):     \n",
    "    opt.zero_grad()\n",
    "    z=encoder(x,wEncoder,bEncoder)\n",
    "    y=decoder(z,wDecoder,bDecoder)\n",
    "    loss=loss_func(y,x)\n",
    "    loss.backward()\n",
    "    opt.step()  \n",
    "    losses.append(loss.item())\n",
    "    epochs.append(i+1)\n",
    "#print(losses)\n",
    "plt.plot(epochs,losses)\n",
    "plt.title('Loss vs epochs - SGD with momentum')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f989a5be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'SGD with momentum - Input data / constructed data / encoder weights')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cU4qCbytZTETkblxFnchcdS4VdXdhxhSwPYD/tkBXEh4HHuvtRBQ7X7S7vy/+nohrr1mfr8/vGy3njckzVf0nrgmAKXKq+uPeTkOJ2Bv3nHYwrgj6a6ramK8Pt2JMY4wxJc+KMY0xxpS8ki7GHDJkiI4YMaK3k2GMMUXjueeee0NVq9MvWVxKOtiNGDGCZcuW9XYyjDGmaIhIXE82RcuKMY0xxpQ8C3bGGGNKngU7Y4wxJc+CnTHGmJJnwc4YY0zJK+namMaYvqe+McGchmY2tLQytKqSmRNGMXlcTfoVTUmzYGeMKRn1jQlmL2yidZsb7SXR0srshU0AFvD6OCvGNMaUjDkNze2BLql1WxtzGqLGiDZ9hQU7Y0zJ2NDSmtV003dYsDPGlIyhVZVZTTd9hwU7Y0zJmDlhFJUV5R2mVVaUM3NCtoN0m1JjFVSMMUVrZmOCexqa0ZZWpKqSUyaM4qopY6w2punEgp0xpijNbEywYGETsq0NAWhpZcHCJpgyhqdmje/t5JkCY8WYxpiidE9DM5JS81K2tXFPmpqX84ARuIvfCP/elD7L2RljipK2tLocXcj0KPOAGcBW//4V/x5gek5TZwqNBTtjTNEI9o4iIqDaaRmJqXl5ETsDXdJWP92CXWmzYGeMKVjzcIFoLVDbmKBiYRPbkkWXqih0yN1pRTmnxtS8XJvldFM6LNgZYwrSPOAs4H3/fntDM6Q+owMQQVWRqkpOnTCKOTE1L2txRZdh001ps2BnjClIF7Az0PVrTFAe8SxOVFlz9QkZbfMKOj6zA+jnp5vSlrdgJyK3AZ8DXlfVj4XMn8nOYvNdgAOAalXdLCJrgLeBNmC7qtblJ9XGmN6yyf+vvuUZKldvDq2MAtn1jpK8wLQXjeICnT2vK335bHpwOzAxaqaqzlHVsao6FpgNPKGqmwOLHO3nW6Azpo8YWN8UG+i60jvKdGANsMP/t0DXN+Qt2Knqk8DmtAs604A7ezA5xpgCNxgY8Oy6yEAHcNWUMe29o1j7OROn4BqVi0g/XA7w94HJCjwsIs+JyIzwNdvXnyEiy0Rk2caNG3syqcaYHlLfmGDY1UtCmxYkVVVVdgh0M3CVT5Sd7ecs4Jmkggt2wInAUylFmEeo6sHA8cDXReQzUSur6lxVrVPVuurq6p5OqzEmx5IDsLZENBoHF9DWThjVHszi2s8ZA4UZ7E4jpQhTVTf4/68Di4BDeiFdxpg8CBuANUiB1v0HsWVcTXsws/ZzJp2CCnYisgdwJHBvYFp/ERmQfA0cBzzfOyk0xvS0qIFWFVAR3j6slo3nHA7sDGZR7eSs/ZxJymfTgzuBo4AhIrIeuASoAFDVm/xiXwAeVtV3A6vuBSwSkWR656vqQ/lKtzEmv4ZWVZIICXhtVZUkUkYzSAYzaz9n0slbsFPVaRksczuuiUJw2kvAQT2TKmNMoZk5YRTfXNhEWaAoc0dFOVtSmhgEg5m1nzPpFFQxpjHGTB5XQ9mUMWyvqkSB7VWVbJoyhq3jaijHdRE2HJhLx2Bm7edMHOsuzBhTcK4YV8OMcTWdiiVTA5wxmbKcnTGm4EzHBbbhROfkjMmG5eyMMXkXHJduaFUlMyeMam8gnjQdC24mdyzYGWPyKtloPNmWLtHSyuyFTQCdAp4xuWLFmMaYvAprNN66rY05Dc29lCLTF1iwM8bkVVSj8fUtrdaBs+kxFuyMMXkVNf5cW1WldeBseowFO2NMTpyHqwQg/v95EcvNnDCKyoryDtOCjcatA2fTE6yCijGm284Dbgy8bwu8Py6k5uVVU8Ywp6GZ9S2ttFVVsmXCKLYGKqdYB84m10RjxosqdnV1dbps2bLeToYxJW8XXIBLtXtjgmGBmpfgRhdPDro6Ajf2XKrhuF5QTP6JyHOqWtfb6cg1K8Y0xnRbWKDr15hg0IIVoTUvL2xoZh6u/8p+qethHTib3LNgZ4zptvKU9/0aEwxZsByJKDnSllZm+NfWU4rJB3tmZ4zpthl0fGY3+HcrkJgnJG1Vle0VUdZgwc30PAt2xphu+6X/f0djgqo/rETaoiNdsOalVUQx+WLFmMaYnDjOV0Yp37oNiVhGoX24HrCRxE3+WLAzxuTEpYtXdqqM0onQHuisIorJp7wFOxG5TUReF5HnI+YfJSJvishy/3dxYN5EEWkWkVUiMitfaTamEM0DRuB+vCMojN5G6hsTtLRuS7ucHFprFVFMr8hnzu52YGKaZf6kqmP932UAIlIO3AAcD4wGponI6B5NqTEFJhngBDgD1zZN/f9C6F4rk06cP7T/IJg8Jg+pMaazvAU7VX0S2NyFVQ8BVqnqS6r6PnAXcFJOE2dMAZuHC2jJxtepVT8KoXutqM6dAaoqKzhl6liePefwggvSpu8otGd2h4vIChF5UEQO9NNqgHWBZdb7aaFEZIaILBORZRs3buzJtBqTFxfhAlqc3q7VGNW588B+FSy/5DjuGVfTaR8KIUibvqOQgt3fgOGqehBwPVDvp4dV7Iqs16yqc1W1TlXrqqurc59KY/Isk0DW27Uawzp3rqwo55IT3T1r1D70dpA2fUfBBDtVfUtV3/GvHwAqRGQILie3b2DRYcCGXkiiMb0iXSBL1mrMZcWVbLc1eVwNV00ZQ01VJQLUVFW29385j+gLzaBupNGYbBRMo3IR2Rt4TVVVRA7B/T42AS3ASBHZD0gApwH/1WsJNSbPrsA93woWAwqueGM4O6vvB5dJPhOD7Gs8Jp8RZrutyeNqmDyu4xOG5LaiGiS87ZexWpmmp+Wz6cGdwDPAKBFZLyJni8i5InKuX+Rk4HkRWQFcB5ymznbgfKABeAFYoKor85VuY3rbdDr3H3kHLtit8fPDnut19ZlY1LYuIPucY7rnje9jz+1MftgQP8aUgKgeSwTYkcV25gGnR8zr15hgYEMz5X4Muq0TRnH9uJrYXFkZMQ/YQ9I4Dxf81uKKb6/Acn35ZkP8GGMK0jyig102FVeSRY5hBtY3MeTu5ezS0upGIm9pZfeFTVzUmIjdZiafn1wm2MTCmieYXLNgZ0yRu4jw3JOQXXdcUUWO/RoTDFi6tlNALdvWxvY0jcnDxqvrsO1AGnNZFGtMKgt2xhS5qOr7SnZFgFHbGdjQHJlz3CWmMTl0ft442P+FdRlmzRNMTyqY2pjGmK6pZWfvKkHDc7Cdfo2J2IBWFdGYPGg6mQXdqP3o7TaEpjRYzs6YIhdWVNiVEQVSt9OvMcGQhU2x61zqx6XLhVzthzFhLNgZU+TCmiZ0ZUSB1O1UNzQjEUP2CHD6YbWd2tV1R672w5gwVoxpTAnItKgwm+3s19Ia2Wzg2qljcxrowj7fmFyynJ0xBujcRdgeEc/jaqoqeyTQGdOTLGdnjNnZxq4xwdCGZrSllc39KtilTNixY2f+rrKinJk5fE5nTL5YsDPGuLZsjQkGL2yizD+nk63b2FEuVFVW8GbrNoZWVTJzwijL1ZmiZMHOGMMbjQmGLFiBpHYf2Kb0320Xll9yXO8kzJgcsWBnTB83/ZZnGLJ6c+T8uFHIjSkWVkHFmD5s+i3P8FRMoIPoUciNKSYW7Izpo75X35Q20FmFFFMqLNgZU4S6Oyp5fWOCeUvje50sF2kfbdyYYmfP7IwpMl0dSTxoTkNz2nHmfnrqQRboTMmwnJ0xRSYXQ+Gkq3RyxP6DLNCZkpK3YCcit4nI6yLyfMT86SLyd//3tIgcFJi3RkSaRGS5iNjQ46ZPy8VQOHGVTo7YfxDzzjk8qzQZU+jymbO7HZgYM/9l4EhV/TjwQ1wfsEFHq+rYUhwu3phsRA15k81QODMnjKKyorzDtGTnzhboTCnK2zM7VX1SREbEzH868HYpMKzHE2VMEbqCjs/sIPuhcJJFlHMamtnQ0mq9o5iSV6gVVM4GHgy8V+BhEVHgZlVNzfW1E5EZ+Of1tbU27KMpPclKKBfhii5rcYEu29ECJo+ryTi4zcvB5xnTmwqugoqIHI0Ldv8vMPkIVT0YOB74uoh8Jmp9VZ2rqnWqWlddXd3DqTWm+zJpRpC6DMAaYIf/35OBJ1n78xXcXWey9me2zR2M6U0FFexE5OPArcBJqropOV1VN/j/rwOLgEN6J4XGZC8umGUSSNIt0902d+nkovanMb2tYIoxRaQWWAicoar/DEzvD5Sp6tv+9XHAZb2UTGOykq5NXFwgme7XPxNIHS88GGzCtr+8McHTOXoel4van8b0trwFOxG5EzgKGCIi64FLgAoAVb0JuBgYDPxSRAC2+5qXewGL/LRdgPmq+lC+0m1Md6QLZnGBJBkoUwNdcJmw7dOY4J6FTeCH6km0tDJ7YRNAlwJeLS6Ihk03pliIpg7pUULq6up02TJrlmd6TxmE9lQiuOdtIwgPJMP9/7B5wWXWpmx/YH0TA5auRUKWr6mq5KlZ49OmOVVq7hRc7c+5WCWVUiQiz5ViE6+CemZnTDHJ5FlZujZxV+ACR1CyGUFcMWFymeD24wIddH2onum4wDYcF6SHY4HOFB8LdsZ0QaY1FOOCGcQHkqhAWR5YJrj9Ac9GBzro3lA908lf7U9jeoIFO2O6INMait3JFUUFyl8H1p+Oq8DSvzERXl7q2VA9pq8rmNqYxhSTbGooTic6uGUygkFYY+5gI++B9U0Mjim+BGyoHtPnWc7OmC7IRf+UkD6HGFZ8GCxCrapvYvc0ga5fRZkFOtPnWbAzpgvSPYvLVFfasCUDZLoKKQAisHXKxykDhvi/nmp8bkwhs2BnTBfkqoZiV3KIa4F+jYm0gQ4R3jx1LK+Mq0GBTf7PuvwyfZEFO2O6KBc1FNPlEMOaN9TWNzHk7uXxgQ7g1IPYElN8aV1+mb7Egp0xvSguhxjWvOFb9U2QLkeHG5dubQbP6azLL9NXWLAzppdF5RDDKq9UPrsu7fZOP6yWyyePyaiyjHX5ZfoKC3bGROjp0QTSSc11Daxvgpju/ZIjjV8+eQwQXkQa1JUKNcYUK2tnZ0yITNq/9bRgB8yZ1Ly8durYDk0MUtvpDfLvN2MDsJq+x3J2xoQohDHcsukK7PTDakPb0gWLSN/wf9bll+mLLGdnTIhCGMOtPWfWmIgrvexQdGmMCWc5O2NC5KqHlHSjlEfNS5oO1DQ0R+bqykUs0BmTAQt2xoTIRQ8pcSMjhM07A1fJZAQdA1/c0DzTDt03ixQZ03dZMaYxIeI6Yc5Uuud+qfOSJZWvAN9oTDCnoZk3W1opE6EtpByzX0WZ5eqMyZAFO2MixI1WkImo53txo48DVN/yDJWrN9Pi34cFusqKcq6cYoHOmEzlrRhTRG4TkddF5PmI+SIi14nIKhH5u4gcHJg3UUSa/bxZ+UqzMd3RlQbbe1/zOJWrN4c+oysXQYCaqkobsseYLOXzmd3twMSY+ccDI/3fDOBGABEpB27w80cD00RkdI+m1Jg0gpVLokYTSNeoO9XA+iZ2ff3dyMooO1R5+eoTeGrWeAt0xmQpb8WYqvqkiIyIWeQk4DeqqsBSEakSkX1w149VqvoSgIjc5Zf9Rw8n2ZhQqQ3ONwXmRQ2+mq7oUkjflm5oVWWWKTXGJBVSbcwaINjx33o/LWp6KBGZISLLRGTZxo0beyShpm8Lq3gSFDb46vCIZYcDixoTfPSyh5GYtnQAMyeMyiqdxpidCinYhd3Uasz0UKo6V1XrVLWuuro6Z4kzJimThuWvkL5Isx9wSH0TF969nK1bt8Vu74j9B1nRpTHdUEjBbj0QbDQ0DNgQM92YXpFpxZNgu7qwoXzOa0zwl6XpQ+fIPfsz75zDO0zr7U6qjSk2hRTsFgNf9LUyDwPeVNVXgb8CI0VkPxHZFTjNL2tMr8im4klYkWayb8pHFq9Mu35FRRmP/PdRHabFNVY3xoTLZ9ODO4FngFEisl5EzhaRc0XkXL/IA8BLwCrgFuA8AFXdDpwPNAAvAAtUNf1VwpgekppLG+z/okTl3Vpa44sud1SUs2nKxzsFsVx2Um05RNNXiMb1MFvk6urqdNmyZb2dDNNHjCC81uVwXE6u0/Kz7o/clgq8cepYto6r6bR+GeEPrQWXa8xUaq1ScDnW5Ejppm8SkedUta6305FrhVSMaUxRy7Y/zYH9KkKnKzsDHXTOGeaqk+pCGMbImHyxYGdMjoRVQonLJV1y4oFUlHesbKzA24fVtgc6cD/SYDFjLjqphsIYxsiYfLFiTGPyoL4xwcx7lrMtUM54xP6DOKWuljkNzWxoaWWPqkrWThjFlpgmBsliRuj+COQjyK7Y1fQNpVqMaR1BG9PDvlffxG9Dmhg8tXqz+z9rfPu0eewMYmVAW8o6yWLGNbiAlvrcLawHlyhXEP7MLtscojHFwIoxjelB9Y2J0ECXlAx4ScHmCVGVTYJb685zt2yLXY0pZpazM6YH/eAPXW8lU0t4MWOwIkp3n7t1dxgjY4qF5eyM6UFb0nQDpkS3bcukIkquamYaU+os2BnTA+obExxx9ZLYZRRo3X9QZJFjJsWMuaqZaUyps2JMY3KsvjHB7IVNtG5LrV6yUzLQbTzn8NhhfdIVMwaHEVpLdrUxjelLLGdnTI7NaWiODXQ7yoQ3po5lo+/cubtFjql9biYDnXUFZsxOlrMzJkfqGxPMaWgm0dIauUxbVSWbJ4xqbzTeU0WO3WmSYEwpspydMTmQLLqMC3Q1VZVcPWs81eNq2juQrgTOIPc5L+sKzJiOLNiZPi8XxX3pii4rK8qZOWFUe5HjHUArsImeGabHugIzpiMLdqZPy8XYcPWNibQ5uqumjOkw0nhP57ysSYIxHVmwM31ad4NOsvgySk1VJU/NGt8h0EHP57ysSYIxHVmwM31ad4NOXPFlsugyTE/nvKwrMGM6smBn+rTuBp0NMcWXqUWXQfnIeUU1STCmL8prsBORiSLSLCKrRGRWyPyZIrLc/z0vIm0iMsjPWyMiTX6ejdtj0sqk4kl3g87QqsrQ6TVVlZGBDiznZUy+5S3YiUg5cANwPDAamCYio4PLqOocVR2rqmOB2cATqhrsFv5oP7/kxloyuZVpxZNMg05U4Jw5YRSVFeUdlo0rvkz97DVYzsuYfMjb4K0icjhwqapO8O9nA6jqVRHLzwceU9Vb/Ps1QJ2qvpHpZ9rgrX3XCHI3MGkycNKYYNAfVlLmO3fuV1nBVZ8/EKB9ANahVZXMnDAqNldnTCGzwVu7rwZYF3i/Hjg0bEER6QdMBM4PTFbgYRFR4GZVnRux7gz8tam21ipa91W5rO14EUBjgiG/W4G07bw5bG3dxsx7VjDnlIM6DMBqjCk8+XxmF9bfbVS28kTgqZQizCNU9WBcMejXReQzYSuq6lxVrVPVuurq6u6l2BStrlQ8iSqqXAsM+sPKDoEuadsOZU5Dc5fTaYzJj3wGu/XAvoH3w4ANEcueBtwZnKCqG/z/14FFwCE9kEZTROIqoGRb8STuGV9tY6K96DJMoqXVOlk2psDlM9j9FRgpIvuJyK64gLY4dSER2QM4Erg3MK2/iAxIvgaOA57PS6pNQUpXASXb2o6RjcsbE8iCFbHD8GyvqsxpV1/GmNzL2zM7Vd0uIucDDUA5cJuqrhSRc/38m/yiXwAeVtV3A6vvBSwSkWSa56vqQ/lKuyk8cT2fJANaurHggsKe5e19zePo6++GzNlpR5mwZcKoTp9tjCkseauN2RusNmbpKiP8ga/gqvJnawQda2/ufc3j7Pr6u7E5OgXemDq2fbieTD57HjbQqilspVob03pQMUUp191tBZ/x9WtMpA10OyrKOwS6TD47F51OG2O6xoKdKUq57m4r+IxvYENzbKBDhHemjOkQ6DL5bBtjzpjeY8HOFKWe6G4r2aNJRUx/lwpw6kFcP64m68+2MeaM6T0W7EzR6nZ3W62t8Le/tb+tb0xwxNVLIht/AlAmrB1X06XPzlXRay4GmzWmr7FgZ/qm996DKVPgyCNh48b2ceniBmFV4I1TDsrJc8GkbIte7bmfMV1jwc6UvNSc0J3//jecfDI89BD8/OdQXR05Lp36v7Z+FbwxdSyMq8nJc8FMiz9T034B9tzPmK7IZ9+YxuRdMieUDBAb3n+f3adOhfvvh5tugrPOctMjcnQCcPUJJMhNU4Fs2v6lpj2sY+ske+5nTDzL2ZmSE8wNncnOYLHLtm3cOW0aJ957L9//xS/gq19tXyduXLo19M4wPGG1N6NYl+fGxLOcnSk43Wl4nZobShZMlm/fzm9PP53/XLiQC372M+6o+QzzZz9AmyrlIhz2oYFsfvf9DkWZmY5L11Myza3leoRzY0qR5exMQeluBYyw3FBZWxu/PvNMpi5YwLd/8hPuGD6eDy5dS5vvPahNladWb+bg2j2oqapEcDm6q6aMyXpculzWlIzKrQ3GRjg3JluWszMFJZM+L8Mkc4Opz7XK2tq47ayzmD5/PrOuuoprvv1tamfdH7qNpS9tYfVVk7qY8vBnbDP8664EoytStgcuF/fzLm7PmL7McnamoHSl4XUwNxgkO3Ywd8YMzvzNb/j+ZZdx/YQzGP79ByN7R2nrZj+xue4hpScazhvTV1nOzhSUQcCmkOlxFTDCgozs2MGNX/saZ992Gz+4+GKu+dxZDF7YBNuiu2oul9hOwtKKqi0ZV4synWxqbxpjolnOzhSMecBbIdN3Jb4CRqdcnyrXf+MbfHXuXK6cPZtLL72UwXcvpyykHV3QtEP3jZ2fTnmW040x+WPBzhSMi4Cw8cAHEJ+76ZDrU+VnF17I13/5S348cyYXXXEFQ6/8Y3zHzrhiwssnj8kuwSmiQml8iDXG5IMFO1Mwop7LbU6z3iR8429V5sycyQXXXcfPL7yQH//oRwy893kq3n4/bbCbflj3W6oNz3K6MSZ/LNiZgtGVjpLnAbcCqspVs2fznZ/+lOvPP5/ma67h3Huf54NL41urKcBhtd3O1UHuhx0yxuROXoOdiEwUkWYRWSUis0LmHyUib4rIcv93cabrmuLXlWBxAa7o87KLL2bWj37Ejeeeyzevu46Fyzfw2zSBDqCtqpK1EYHuPFwNLvH/z0uzrbjakzZSgTG9K2+1MUWkHLgBOBZYD/xVRBar6j9SFv2Tqn6ui+uaIpZ8LpdN7ymbgO9fdhnfv/xybvnKV/j6DTeACBV/WJn28xTYMmEUtXTuteXDwKOBZduAG/3rX6bZh9T05rr9nTEme/nM2R0CrFLVl1T1feAu4KQ8rGuKSLbjxM2+8kouu+QSfvWlL/HVm29Gy8rY+5rHKdsaVtXFUb/95CgGk+jca8ujEevOzWJfkqLa352O5fKMyZd8BrsaYF3g/Xo/LdXhIrJCRB4UkQOzXBcRmSEiy0Rk2caNG3ORblOo5szhyosu4o7TT+crt96KlpVRfcsz7Pr6u7EVUqSijPVXn0D1uBrmAg+QeYfLXalZGVeYauPRGZMf+Qx2Ydef1C4r/gYMV9WDgOuB+izWdRNV56pqnarWVVdXdzWtptBdey38z//w19NO48u/+hU7ysvp15igcvXm2EBXBvxsysc75ByzGR6nK23m0tXztPHojOl5+Qx264Fgq91hwIbgAqr6lqq+418/AFSIyJBM1jV9yPXXw3//N5x8MqfdcQdtu+zCwPomhty9PD5HB1wzdWyHzp3nkd2PYEb6RToJq3iTysajM6Zn5TPY/RUYKSL7iciuwGnA4uACIrK3iOuzSUQO8enblMm6po+48Ub45jfhC1+A+fN5eZdd6NeYYMDStWnb0l0bEuhmEF00Kez8gZQDXyO+ckqUYC3NKDYenTE9K2/BTlW3A+cDDcALwAJVXSki54rIuX6xk4HnRWQFcB1wmjqh6+Yr7aZA3HILnHcenHgi3HUXVFRQ25hgyIIVaQNd9Z79uXBcTYeq/+kGR1VccYIC2+laoEtKVrz5LdYWz5jeINrNnt4LWV1dnS5btqy3k2EyFDto669+BWefDRMnwqJFsNtu1DcmmLmwiW1p+rz80P6DePacwzsNlZNppZRc/0K6MzitMT1NRJ5T1breTkeuWQ8qpiDEDtp6xx0u0H32s7BwIey2GwBzGprTBrqqygpeSgl04AJdJpVNhNzXlMy2eYUxpvss2JmCENUW7dk774QvfQmOPhruvRc+8IH2+RtaWmO3WSZw6ecPjKz80Ub6iiPq02Y9oBhT3CzYmYIQFpBOvucerjnjDPj0p2HxYqisBKC+McERVy+JLV4c2K+Ca051FVKiKn8ku/NKdu8VJZnLDM11GmOKggU7UxBSA9LkRYu4c9o0/nb44XDffdC/P+AC3eyFTSQicnWVFeX8bOpYGi8+rr3m5RVARcpyFex8VrYGV6QYVVuynNyOQG6MyT8LdqYgBNuinbh4MQtOPZXnPvlJXn7gAdh99/bl5jQ00xrxnK6mqpKrpozp0LwgKTXnFpaTmxSRtqingtY2zpjikbeOoI2Jk6yk8cgDDzD35JNZOW4cdz/0EAsHDGAaO2stRj2nE+CpWeND510EvJ8y7X0/PVg55IGItJUTHvCsbZwxxcOCnSkY0x9+mOlTpsCYMfzz4Ye5eY892AoMrG9Cn13Hd1Ujn61tq6pkBOHV+KNyYKnT01VkSW26YG3jjCkeVoxpCsOjj8JJJ8EBB8Ajj/A/VVXtgW7A0rVITKDbUVHOlgmjIiuOZDoobKYVWYLj1BljioMFO9P7Hn/c9YoyciQ88ggMGtSeyxrw7LrYmpLbqyrZNGUMW/1zurCKI5kOChv1zG4S1jbOmGJnwc7kRWQ7tT/9CT73OdhvP/jjH2HIECCQy4rp4Wft1SeQmDW+PdC1T09ZLm4E8aCoZ3ZR040xxcOCnelxUb2jNDz9NEyaBMOGuWLMPfdsX6c9Nybh+bpykYyLJyGznFmmz/aMMcXHgp3pcWG9o3zs2Wf5j4kTYZ99YMkS2HvvDvOTuTE5dN/QxuPTDt034+LJTGUTPI0xxcWCnelxqTmjTyxbRsOECbxeXe0C3dChoetNB9ZMHsMZh9VS7nN45SKcflgtl08ek3HxZKZyHTyNMYXDRj0wPW4ErugSYGxjI48ecwxv7rEH0594gqdrCyvfZCMSmL7ORj0wJkvJSimv4HJeY/7+dx459ljeHjCASY89xtcLLNCB1bo0plRZo3LTI5KVUpLP6g5YuZJHjzmG9z7wAc5YsoTvjRhhgcQYkzcW7ExOpBb/vcPOQPfRF15gyfjxbKuo4PTHHuPJ/ffvsG59Y4I5Dc1saGllaFUlMyeMCu3f0hhjuiqvxZgiMlFEmkVklYjMCpk/XUT+7v+eFpGDAvPWiEiTiCwXEXsQV0DCmhZs8vNG/vOfLBk/HhVh/JIlPDlyZId1g6MYKJBoaWX2wibqGxP53AVjTInLW7ATkXLgBuB4YDQwTURGpyz2MnCkqn4c+CGucl3Q0ao6thQfnhazsKYFAB9avZol48dT3tbG+CVLaP7oRztV4w8bxaB1WxtzGpp7KrnGmD4on8WYhwCrVPUlABG5CzgJ+EdyAVV9OrD8UmBYHtNnuiis0fWIl1/msaOP5gPvvcfRjz3GC6NH0w/X9dYI4I3GBEMamiFiFIN0o5AbY0w28hnsaoB1gffrgUNjlj8beDDwXoGHRUSBm1U1NddnekktO5sWANS+8gqPHX00A955h+lLlrByzBiG4wLdr4H+tzzD4NWbY7c5tKqy5xJsjOlz8hnswvp9Cm3kJyJH44LdpwKTj1DVDSKyJ/CIiLyoqk+GrDsD9wiJ2gKs2l6KrmBnzcth69axZPx49njzTf7z0Uc5e+zY9r4lRwC71TdRuXpzbOfOlRXlzJwwqodTbYzpS/JZQWU9sG/g/TBgQ+pCIvJx4FbgJFVN1nNAVTf4/68Di3DFop2o6lxVrVPVuurq6hwm30RJ9mRyYCLBkvHjGfLGGxz38MM8dvDBHYbcWUtmoxi0ThnDu1Yb0xiTQ/kMdn8FRorIfiKyK3AasDi4gIjUAguBM1T1n4Hp/UVkQPI1cBzwfN5SbtKa/uqr3Dt+PHv/619MfOghln3yk4DL7V3gl6mF2FEMtldVkpg1nlfG1YSOS2eMMV2Vt2JMVd0uIucDDUA5cJuqrhSRc/38m4CLgcHAL8X1hbjd17zcC1jkp+0CzFfVh/KVdpPGa6/BMcewVyLBxIceYunhh3eYvQmY2ZigqqGZLRGbUGBLoOgyOS6dNTw3xuSC9Y1puuV3b7zBx44+mtrVq/ncgw/y2JFHdpjfrzHBoMUrKW/dFrkNBVr3H8TGczoGScF122WMyZ9S7RvTelAxXXbPpk2M+uxnGb5qFSfcf39ooBt8zwrKdkTfUJWL0HbovmycPKbTPKteZIzJFQt2pmu2bOGAY4/lwy++yIl/+AOPjR/faZFBi1fGBjoBVl81qVM/mmBD6xhjcstGPTDZa2mB445j5MqVfGHRIv547LGhi5XFFF3CzrZ0uR6XzhhjUlnOzmTnrbdg4kRYsYLzfv97Hjr++E6LDAZ2J6IRpZfalm46FtyMMT3HcnYmI/OA0e+8w58nTWLbc8/xxIIFjD/xxNCRvb/cmKDm6iWR7enKBK6aMsZGNjDG5I0FO5PWPODCd9/lxhNO4LClS5l2551MmjwZ6Fz8eF5jgvv8KAZhKsqFa04da4HOGJNXVoxp0vrh1q3cfeKJfOrPf+a/5s/n9yefDLh2cGvoWPx4RMgoBkk1NladMaaXWLAz8Vpbuf6kkzjq8cc54447WDB1avussNEOokYrEOCpWZ1rbBpjTD5YMaaJ9t57MGUKxzz6KF/+1a+YP71jFZKwdnBRoxXYKAbGmN5kOTsT7t//hpNPhoce4i+33srvzjyzw+xkO7j6xgRzGprZ0NLK0KpKjv5oNb9/LtGhKNNGMTDG9DbL2ZnOtm2DqVPh/vvhpps47OyzQ9vB9W9MMNtXRlEg0dLK759L8J+fqKGmqhLBPaezmpfGmN5mOTvT0bZtMG0a3Hsv/OIX8NWvAuHt4MIqo7Rua+OxFzfa8zljTEGxnJ3Zaft2OOMM+P3v4dpr4etfj108qjJK1HRjjOktFuyM09YGZ54Jd98Nc+bAhRemXcUqoxhjioUFO+MC3Vlnwfz5cOWV8J3vZLTazAmjqKwo7zDNKqMYYwqRPbPr63bsgBkz4De/gcsug9mzM141WekkWBvTGo0bYwqRBbu+TBXOOw9uuw2+/333l6XJ42osuBljCp4VY/ZVqvCNb8DNN7vc3A9+0NspMsaYHpPXYCciE0WkWURWiciskPkiItf5+X8XkYMzXddkQRW+9S244Qb3fO6KK0Cixigwxpjil7dgJyLlwA3A8cBoYJqIjE5Z7HhgpP+bAdyYxbomE6owcyb8/OeuxuWPf2yBzhhT8vKZszsEWKWqL6nq+8BdwEkpy5wE/EadpUCViOyT4bomE9/7Hvz0p3D++XDNNRbojDF9Qj6DXQ2wLvB+vZ+WyTKZrAuAiMwQkWUismzjxo3dTnTJ+chHXKWU666zQGeM6TPyGezCrqya4TKZrOsmqs5V1TpVrauurs4yiX3AmWe6Z3UW6IwxfUg+mx6sB/YNvB8GbMhwmV0zWNcYY4wJlc+c3V+BkSKyn4jsCpwGLE5ZZjHwRV8r8zDgTVV9NcN1jTHGmFB5y9mp6nYROR9oAMqB21R1pYic6+ffBDwATAJWAVuBL8etm6+0G2OMKW6iGvroqyTU1dXpsmXLejsZxhhTNETkOVWt6+105Jr1oGKMMabkWbAzxhhT8izYGWOMKXkW7IwxxpS8kq6gIiIbgVdysKkhwBs52E6hKLX9gdLbp1LbH7B9KgZDgP6qWnI9cpR0sMsVEVlWSrWTSm1/oPT2qdT2B2yfikGp7U+QFWMaY4wpeRbsjDHGlDwLdpmZ29sJyLFS2x8ovX0qtf0B26diUGr7086e2RljjCl5lrMzxhhT8izYGWOMKXkW7FKIyCAReURE/s//Hxix3BoRaRKR5SJSkL1Ni8hEEWkWkVUiMitkvojIdX7+30Xk4N5IZ6Yy2J+jRORNf06Wi8jFvZHOTInIbSLyuog8HzG/qM4PZLRPxXaO9hWRx0TkBRFZKSIXhCxTVOcpw30qqvOUEVW1v8Af8GNgln89C/hRxHJrgCG9nd6Y/SgHVgMfwg1+uwIYnbLMJOBB3EjwhwHP9na6u7k/RwH39XZas9inzwAHA89HzC+a85PFPhXbOdoHONi/HgD8s5h/R1nsU1Gdp0z+LGfX2UnAr/3rXwOTey8p3XIIsEpVX1LV94G7cPsWdBLwG3WWAlUisk++E5qhTPanqKjqk8DmmEWK6fwAGe1TUVHVV1X1b/7128ALQE3KYkV1njLcp5Jjwa6zvdSNjo7/v2fEcgo8LCLPiciMvKUuczXAusD79XT+QmeyTKHINK2Hi8gKEXlQRA7MT9J6TDGdn2wU5TkSkRHAOODZlFlFe55i9gmK9DxFydtI5YVERP4I7B0y66IsNnOEqm4QkT2BR0TkRX9XWygkZFpqO5NMlikUmaT1b8BwVX1HRCYB9cDInk5YDyqm85OpojxHIrI78HvgQlV9K3V2yCoFf57S7FNRnqc4fTJnp6qfVdWPhfzdC7yWLILw/1+P2MYG//91YBGumK2QrAf2DbwfBmzowjKFIm1aVfUtVX3Hv34AqBCRIflLYs4V0/nJSDGeIxGpwAWFeaq6MGSRojtP6fapGM9TOn0y2KWxGDjTvz4TuDd1ARHpLyIDkq+B44DQ2me96K/ASBHZT0R2BU7D7VvQYuCLvjbZYcCbySLcApR2f0RkbxER//oQ3Pd7U95TmjvFdH4yUmznyKf1f4EXVPWaiMWK6jxlsk/Fdp4y0SeLMdO4GlggImcDa4FTAERkKHCrqk4C9gIW+e/CLsB8VX2ol9IbSlW3i8j5QAOuJuNtqrpSRM71828CHsDVJFsFbAW+3FvpTSfD/TkZ+JqIbAdagdPUVy0rRCJyJ67W2xARWQ9cAlRA8Z2fpAz2qajOEXAEcAbQJCLL/bTvArVQtOcpk30qtvOUlnUXZowxpuRZMaYxxpiSZ8HOGGNMybNgZ4wxpuRZsDPGGFPyLNgZY4wpeRbsjDHGlDwLdsYYY0re/wfsniTECMXHwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x[:,0],x[:,1], color='cyan')\n",
    "plt.scatter(y[:,0].detach().numpy(),y[:,1].detach().numpy())\n",
    "plt.plot([0,wEncoder[0,0].detach().numpy()],[0,wEncoder[1,0].detach().numpy()],'-r')\n",
    "plt.axis('equal')\n",
    "plt.title('SGD with momentum - Input data / constructed data / encoder weights')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e66115c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8811451 0.78346264\n"
     ]
    }
   ],
   "source": [
    "#ratio of weight in the encoder vs decoder for each dimensions\n",
    "print(wEncoder[0,0].detach().numpy()/wDecoder[0,0].detach().numpy(),wEncoder[1,0].detach().numpy()/wDecoder[0,1].detach().numpy())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23ce17af",
   "metadata": {},
   "source": [
    "Now switch to RMSprop and do the same process as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "53cfeed8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Loss vs epochs - RMSprop')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "losses=[]\n",
    "epochs=[]\n",
    "wEncoder = torch.randn(D,1, requires_grad=True)\n",
    "wDecoder = torch.randn(1,D, requires_grad=True)\n",
    "bEncoder = torch.randn(1, requires_grad=True)\n",
    "bDecoder = torch.randn(1,D, requires_grad=True)\n",
    "opt=torch.optim.RMSprop([wEncoder,bEncoder,wDecoder,bDecoder], lr=0.01, momentum=0.9)\n",
    "steps=1000\n",
    "for i in range(steps):     \n",
    "    opt.zero_grad()\n",
    "    z=encoder(x,wEncoder,bEncoder)\n",
    "    y=decoder(z,wDecoder,bDecoder)\n",
    "    loss=loss_func(y,x)\n",
    "    loss.backward()\n",
    "    opt.step()  \n",
    "    losses.append(loss.item())\n",
    "    epochs.append(i+1)\n",
    "#print(losses)\n",
    "plt.plot(epochs,losses)\n",
    "plt.title('Loss vs epochs - RMSprop')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "29d6700a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'RMSprop - Input data / constructed data / encoder weights')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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oynimT4wtaZY+Uo7WR0cQngm7wsyWR9M+TzRuubtfQxg5cRphNMKthNEjRUQ6NLe0cvHCFbRvCyM7t7a1c/HCFQAKDBVUclCInoyW9pAOosHOzi91WyIycF2xeFVHQMhp37aDKxavUlCoIA1zISKZa25ppbWtPXbeuoTp0jcUFEQkU7lioyT7NjZUMDWioCAimZkHfCqm2Cinob6Oi6b09EFoUoqqHhBPRAaui1pauXnxKga1tSdWSl524gTVJ1SYcgoiUnHNLa3csnAFdSkBoamxgZcmNjGOcKEaR8hZSN9STkFEKqq5pZX/nL88dZmG+jreOWU8Mwlt2AGeBmZGr2f0XfJqnnIKIlIR84BxLa38x/zl8WPcEI1909jAZSdO4JaJTR0BIWcrMLsvEynKKYhI35sHfBTYa9FK6lKW29nYwOWzjmY6cGLCMs+UO3HSiXIKItLnPgns1tLKoPZtqcudNmV8R9HQ2IRlkqZLeSgoiEifa29pZcTCFalDH+wYUs8tE5s6KpPnAEMKlhkSTZe+o+IjEelzwxavYlBCXwQIdQmb3ncQW+lamTybUGQ0lhAQVMnct5RTEJE+NQ+oSxmqwoEtk8eyNeqPkF+ZPANYTXj4+2oUECpBOQUR6VOzgR2NDewWExjcjA2nHNwREHJUmZwdBQUR6RO5ZyN4Wzs2pJ6dg4xBO3c1Rt1ZX8fGEyd0CQigyuQsKSiISNnlPxvBgLqt2/A6Y0dDPYPat7GjsYHNU8bHBgRVJmdLQUFEyi7u2Qi2w/HX7MYzX3oPRqhL2I/w9K07UGVytVBQEJGyS3oGQl1bO/uhC381U1AQkbLIf77yIDN2eNfBLEY3NvD7DNIm3aegICI9No/QS3lj9H6f5hUMXrqrzdAOd5zOz+n1aJA7qW7qpyAiPTIPOJtdAWFY8wrql3ZtRGqAW6g72N7YwIZokDupbsopiEiPzAZyIxgNa17B0KXPJA9f4fDM5cd3vFX/g+qnnIKI9Ejuwj6kpTU9IMRQ/4Pqp6AgIj2Su7APX7SyaEDYOaS+47X6H/QPZQkKZvYjM3vOzB5LmH+UmT1vZsujvy+WY7sikmwe9MmjLOcA9VB0GOzcIHdG6I8wFzVD7Q/KVadwPfBd4IaUZR5w9/eWaXsikqCwZRCU91GWuc9/PmWZ3CB3oyY2sbrE7UlllSWn4O73A5vKsS4R6b15hIv/xph55XyU5QxgeF7RUD4HNpx6CJunT2BambYnlVPJOoXDzewRM7vTzA5KWsjMZprZMjNbtn79+gomT6T/mw1dnmuc72l6X5zU3NLKEZffyxtm3c4Rl9/L8W/bh/q6zrUKXmdsOPWQjjGNFvRwG5K9SgWFPwP7ufvBwHeA5qQF3X2uu09y90mjRo2qUPJEBobuNPl0dhUnpQWGTnUSLa18+pZHaG1rx4HWtnbm/3ENp/7LGBobG3b1RTip8zDYG4tsQ6pPRfopuPsLea/vMLPvmdlId99Qie2L1IqxhAt+d+SKkwrrGOLqJHYsWgk7Ow9bsW2nc9sjz9L2pfekBqMzgQ+jwe76i4rkFMxsbzOz6PWh0Xbjij1FpARxzzVOU3gxj6uTGNLSmtjSqK19W9HcyQ66nzuR7JUlp2BmNwFHASPNbC3wJUKrNdz9GuAk4BNmth1oB05zjxktS0RKEvdc4xdJvgMr7ExWWCcxpKWVEQtXpPZHKEfuRKpHWYKCu59eZP53CU1WRaSPzaDzRTetOKCwM1nhXf+wxasYVPBchE7zh9RzISEHkFbBnbYNqS4a+0hkgEu6kx9B1zv23LJDWloZtngVdQnPRQCorzO+9L6DmB69nx19to5QZJT7H5ceqV4a5kJkgIurZxgCfCtm2WnA7i2tjFywnN3a2hOLjcyMK046mOlRS6MZwGqiEVGj/z9J2K6GuqhuyimIDHBx9QxxrYDmAbdet4QRT25KrUOor6/jihMndASEUrcr1cWqub530qRJvmzZsqyTIVITxl23BC8SEJoaG7hoyviiAUGyY2YPu/uk3n5eOQURASgaEAB+P+voiqRFsqM6BZEBrCcjpRYLCNaTBydIv6WcgsgAleuIlmsqWupIqTMOU7uhWqCcgsgAFTc4XtpIqUfsPzxxXWdMHsul0yeUKWVSzRQURAaopE5iSdPnnXN4l8BwxP7DWX358QoINUTFRyIDVFKntVwhUHNLK1csXsW6tnb2jVoVzTvn8C7Lz0PNSmuJgoJIPxF3caZg2jTCMwzSRpt8uaWVA3+1kq1bdw1y19rWzsULVwB0am5a7noJqX7qpyDSDxRenCGMOGnAqz1Yz7DmFQxd+kxiS6OmxoZOzU7HEZ/b2A/0mM0qpX4KIjUgrtI4fjDrZMUCAsC6grGOelovIf2fKppFqkxc34JSL8JDWlqLBgSAfRsbOr1PaoSqxqkDl4KCSBXJFRM9TecH0yQ3Fu2eEQsfLRoQGurruGjK+E7TkgbT06B2A5eCgkgVSepbAD17olq+Yc0rsG07iy53WcwgdzOAuYQ6BIv+z0WVzAOZgoJIFUkqJtpE14tzd3SnHsGBDacewm8SBrnLDYu9M/qvgDCwKSiIVJG0MvzCi3NSYKgjBI69r7yvWwFhy+SxvDSxiWvQ85NFQUEkU4WVytPofhl+XHk/hKedjbxuCYOfe6lbAWFz1FvZSR4CQ2qHgoJIRuIqlX8CnEn3yvALy/vr8uY1FBkGuzAg5KipqaifgkhGkiqV76D7HcNmsCtg9OQOLy4ggJqaioKCSGZ60jGsO0Nc7NXSSv2ilQxqT+/WdsbksWyaPoFrCDmGHDU1FVBQEMlMsQHrcuLGHzqbzkNcrG9pZcT85UVzCwfstXvHiKdHoIHupKuy1CmY2Y/M7DkzeyxhvpnZt83sCTN71MzeXo7tivRn3e0YljTERf6YRyNuKR4Qjth/OHd9+qiO92pqKnHKlVO4HvgucEPC/OOAA6K/w4DvR/9FalbuIlw4yuls4AxCxfGObqxn1HVLsJS+aQb8/fLjS0mq1JCy5BTc/X5C/5okJwA3eLAUaDSzfcqxbZH+LP9ufQ6h9VGuSKm7AaFYS6PC8YxE0lSqSWoTsCbv/dpoWhdmNtPMlpnZsvXr11ckcSLVIK6YqJhiAQGgdcr4ToPriaSpVFCI+93GPsjB3ee6+yR3nzRq1Kg+TpZI9eiLPgI7DZ6e2NRpcD0FBklTqaCwFhiT9340sK5C2xbpF3rSR2DUdUsYO+v21GUc2HjKIZ2mbSW+13LccN1SmyoVFBYBH4laIU0Gnnf3Zyu0bZF+IWnYikL7zrmro9goqegoN8jd1phB7gpzJEnDdSsw1KaytD4ys5uAo4CRZrYW+BLhaYG4+zWETprTgCcINytnl2O7IgNJfmukuP4LEHII9VvSH8CZFhCg67MZknpWz0bNVGtRWYKCu59eZL4D55djWyIDWf6wFYWd1oa0tNLwZHIjPwd2NDawecr4xIAAsCVad247euSm5NOAeCJVqnDAu1GLVxVvaTTr6NSAAKHTW369gh65KfkUFESqWK4fw8KWVmhrT1325f27/9DO/FyAHrkp+RQURKpcc0srFy9ckTjfAYYO5spzDu9ycU/KWQxiV0sj0CM3ZRcFBZEq1tzSymcWPEL7tvj+zQ607z+cp2cfC3S9uJ9L8oN48lsagcZBkkBBQaTCutsn4AvNK/jP+cvZ4bH9PDtaGa0/53Ag/uL+PZIfxJOT1HdBapOCgkgFdbdPQHNLK/OWPhPf7T+yo7GhU6Vy0sU9f3ylpHHz1NJIchQURCoorU9AvisWr0oNCDvr69g8ZXyX6cUu7mppJMUoKIj0gaQiomJ9Ar7QvIL9L76D1pSWRnVmDDpxQmzT02IXd7U0kmL05DWRMot7UlquvD/paWvDgXHXLcGLjHpqwDdOOZiXJjZ12gZ07+Ie9wwHPXFN8ikoiJRZWhHRHOhyMa8HtrW0disgzJg8lul5OYTeXNzze02LFFJQECnRPDpfnJPGLXqGXRfjTwIbo9evaWmlcf7y1IDQ1NjARVPGdwoIurhLX1BQEClBXFGREf+wkPzy/lyNwZCWVoYVCQhuxnmzjmZ6qYkV6QZVNIuUIK6oyOnakzi/vD//MyPmL089CR3YctiYTq2T9OwD6UsKCiIlSGpN5CQPG5H7zLDmFek5BEJv5c3TJ3R8Rs8+kL6moCBSgqQmoPuRPGzEWEKx0dClz6QGhZ1D6jt6K+e2091+DiK9paAgUoLetPufAwwvMgy2A5ved1CX9RXr55BftDQy+lMxk/SEgoJICQqfeZBfVJRU9j8DqEvpnObAq3vtTvvEpi5FT2k9kguLljZGfypmkp4wTxhsqxpMmjTJly1blnUyRHpkHp2bnOYMa2ll+C8eZfv2pBGIdgWE13z6KFYnrDuu09pc0h/jmZMr1pKBy8wedvdJvf28cgoiPVCs5U/uol0YEIa0tDJ0wfKiAWHL5LG88OmjOoqLCrcHyTmT7gxqp4HvpBj1UxDpprThK/I7pRVWBA9paWVkkb4INDawccp4Rk5s6uiZnLS9ucTf7ad1nMtfRiSNcgoi3RR3wc9v+TOP+BxC0YAArJ51NC9ObOrUUqmnLY3iKr07pQUNfCfFKSiIdEPcBT8nVyQTd7Ee0Y2AkCTprj9pemGl94joT4/YlJ5Q8ZFIN6T1A8gVyRRerPe+8r5uBYQj9h8eO72O8NjMuOlJNB6SlKosOQUzm2pmq8zsCTObFTP/KDN73syWR39fLMd2RSolrYJ2DnBewbS9r7yPwc+9VDQoDN9/OPPPORwj3KHlryf+qcxh+jjUvFT6RslBwczqgKuB44ADgdPN7MCYRR9w90Oiv6+Uul2RSkqqoB3BrmKbnO4EBAdemDyWlnMO77j47wC+z67AsF/K558GziB0TlNwkHIqR07hUOAJd3/K3V8FbgZOKMN6RapGUs/lb0Wvcxf2Yc0ruhUQtg8dzObpE2Ln5wJMsYpjCPUc6pQm5VSOoNAErMl7vzaaVuhwM3vEzO40s4OSVmZmM81smZktW79+fRmSJ1K6tJ7LOd0Zz8iBHa+pY93sYxOXyQWY/G2m0dhHUk7lCApx50BhN+k/A/u5+8HAd4DmpJW5+1x3n+Tuk0aNGlWG5ImUxwySB7kDGP6rlUUDwqt77U7rl6embie/Ijm3zWKBQZ3SpFzKERTWAmPy3o8G1uUv4O4vuPuL0es7gHozG1mGbYtURLGezPsBg7ZuS12HA//49FFFtzUzZlqxoiR1SpNyKUdQ+BNwgJm9wcwGA6cBi/IXMLO9zcyi14dG201q9i1SVYo9w6C5pZXGy+9NXYcDG089pFvbu4OuQSdXlDQiZnl1SpNyKjkouPt24AJgMfA4sMDdV5rZuWZ2brTYScBjZvYI8G3gNK/mkfhE8qT1LG5uaeXihStoa2tPLDrKjWm0dWJcVVtXSSOazgA2ADeSXrchUgqNkipSxCDin7k8rHkFr1uaXpqfCwhJLY3SaERT6Y1SR0lVj2aRIuIGmhvWvIKhRQLCzmiQu+7mEAqp8liyoLGPRIqIq+Qd+tCa1JZGOxobWDPr6F4HBFDlsWRDQUGkQNozDDqkFLvurK9j05TxiWMUpY1dlKPKY8mKgoJInqSWRlDQX8Di8wkObDxxAlsnNrGD+F7QcU1O86nyWLKkoCCSp9gzDHJFSVsOG9Ol8rmwlVHu4l7YUuh7xDctzX1mNQoIkh1VNItE5pH8rIINLa0csXgV69raOaCxgbYp43kBeN1Da8AdN2PLYWM6Whnlin+ShrL+FvHPWlaRkWRNQUFq2jx2PfA+qeJ4SEsrIxeuoHVbGJWora2dhoUruOrECUyPgkBuPW2ECuJcQEiS/3S1Z7r5GZFKUD8FqVmFz0COM6SllZELHsFizpOmxgZ+P+vovkqeSK+on4JIL8XVH+Qb0tKa+jjNdW3tfZAqkWypollqVrHOYSMWPpp6guzb2FDO5IhUBQUFqVlpncOGtLRi23Ymzq+vr+OiKePLnyiRjCkoSM2aljB91HVLGJlSbJTri/BSCb2VRaqVgoLUpHnAT2KmD2teQcOTm1KHsMBg88QmPe1MBiQFBalJSZXMxcY0cmDLYaHgSQPWyUCkoCA1Ke6CPqSlNXVMo8JhsDVgnQxECgpSM/IHuiv84Q9paWXEwhWp9QgbTj2kS49lkYFGQUFqQuFAdzsK5g9bvIpB2wqn7rL//sMZNbFJTzuTAU+d16QmJNUh7NHSyp6LV7FbSke0MyaP5dJePDlNpD9SUJCakFSHMGzhitQcQlNjgwKC1BQVH0lNiKsULlZk1KAOalKDFBSkJsQ9UrMupcioqbGBy06cwHR1UJMao+IjqQlxQ1U3NjbQFhMYNPqp1DLlFKRmzCA81Wxn9P+SKeNpqO/8xGQVGUmtK0tQMLOpZrbKzJ4ws1kx883Mvh3Nf9TM3l6O7YqUYvrEJi47cQJNjQ0YKjISgTIUH5lZHXA1cCywFviTmS1y97/kLXYccED0dxjw/ei/SHnt3AmDun+vM31ik4KASJ5y5BQOBZ5w96fc/VXgZuCEgmVOAG7wYCnQaGb7lGHbIrtcey1MmQJbtmSdEpF+qxxBoQlYk/d+bTStp8sAYGYzzWyZmS1bv359GZInNeHOO+H882HwYGjQw29EeqscQSFuuJjCUcW6s0yY6D7X3Se5+6RRo0aVnDipAcuXwymnwIQJMH8+7KZGdSK9VY6gsBYYk/d+NLCuF8uI9NzatXD88dDYCLfdBnvskXWKRPq1cgSFPwEHmNkbzGwwcBqwqGCZRcBHolZIk4Hn3f3ZMmxbatkLL4SAsGUL3H47NKnCWKRUJeez3X27mV0ALAbqgB+5+0ozOzeafw1wB+Hph08QxiU7u9TtSo3bti0UGa1cCXfcAW97W9YpEhkQylL46u53EC78+dOuyXvtwPnl2JYI7qFSefFiuO46eM97sk6RyIChHs3S/3ztayEYXHwxfPzjWadGZEBRUJD+Zf58mDULTjsNLr0069SIDDgKCtJ//P73cOaZcOSR8OMf96jnsoh0j84q6R/+9jc44QQYOxaam+G1r806RSIDkoKCVL8NG2DaNDALLY1GjMg6RSIDlrp+SnV7+eWQQ1izBu69F974xqxTJDKgKShI9dq5E846C/7wB1iwAN75zqxTJDLgqfhIqtfs2aG10de+BiefnHVqRGqCgoJUp7lz4fLL4dxz4cILs06NSM1QUJDq8+tfw3nnwXHHwXe+EyqYRaQiFBSkujzySCgqeutbNQy2SAYUFKR6tLaGUU/33DOMejp0aNYpEqk5ug2T6rBlSwgIL7wADz6oYbBFMqKgINnbvj0Mg/3YYyGHoGGwRTKjoCDZcocLLgiVy9deC1OmZJ0ikZqmOgXJ1te/HoLBrFkwc2bWqRGpeQoKkp1bboHPfhZOPRXmzMk6NSKCgoJk5Q9/gA9/GI44Aq6/XsNgi1QJnYlSeU88Ae9/P4wZo2GwRaqMgoJU1saNYRhsCMNgjxyZbXpEpBO1PpLKefllmD4dnnkG7rkHDjgg6xSJSAEFBamMnTvh7LNDx7T580NdgohUHRUfSWV84Qtw881h5NNTTsk6NSKSoKScgpkNB+YD44DVwCnuvjlmudXAFmAHsN3dJ5WyXelnfvADuOyy0A/hs5/NOjUikqLUnMIs4B53PwC4J3qf5N/c/RAFhBrzm9+EZyJMnQpXX61hsEWqXKlB4QTgJ9HrnwDTS1yfDCSPPgonnRSGwV6wQMNgi/QDpQaF17v7swDR/70SlnPgN2b2sJmljmVgZjPNbJmZLVu/fn2JyZPMrFsXRj0dOhRuu03DYIv0E0Vv3czsbmDvmFmze7CdI9x9nZntBdxlZn919/vjFnT3ucBcgEmTJnkPtiHVIjcMdlsbPPAAjB6ddYpEpJuKBgV3PyZpnpn908z2cfdnzWwf4LmEdayL/j9nZrcChwKxQUH6ue3b4bTTYMUK+NWv4JBDsk6RiPRAqcVHi4Azo9dnAr8sXMDMdjezobnXwHuAx0rcrlQjd/j3fw89lb/3vfCMZRHpV0oNCpcDx5rZ34Bjo/eY2b5mdke0zOuBB83sEeCPwO3u/usStyvV6BvfgGuugc99TsNgi/RTJTUHcfeNwLtjpq8DpkWvnwIOLmU70g/8/Odw0UWhY9pXv5p1akSkl9SjWUq3ZEkYBvud79Qw2CL9nM5eKc2TT4ZhsEePhl/+Ehoask6RiJRAQUF6LzcMtruGwRYZINTFVHrnlVfgAx+A1as1DLbIAKKgID2XGwb7gQfgppvgyCOzTpGIlImKj6TnvvjFEAwuuyx0VBORAUNBQXrmhz+EOXPgnHNCfwQRGVAUFKT77roL/t//gylTNAy2yACloCDds2JFGAb7wAPDMNj19VmnSET6gIKCFJcbBnuPPeD22+F1r8s6RSLSR9T6SNK9+CK8972weXNobTRmTNYpEpE+pKAgyXLDYD/6qIbBFqkRCgoSzx0++clQXPT972sYbJEaoToFiffNb4ZnIlx0EZx7btapEZEKUVCQrn7xC7jwwtDa6PLLs06NiFSQgoJ0tnQpnHEGTJ4MN9ygYbBFaozOeNnlqafCMNhNTRoGW6RGKShIsGlTGAZ7x44wDPaoUVmnSEQyoNZHsmsY7L//He6+G970pqxTJCIZUVCode7w0Y/C/ffDz34G73pX1ikSkQyp+KjWffGLIRh89atw+ulZp0ZEMqagUMt+/GO49FL42Mdg1qysUyMiVUBBoVbdfTfMnAnHHht6LGsYbBGhxKBgZieb2Uoz22lmk1KWm2pmq8zsCTPTLWnWHnsMPvhBeMtb4JZbNAy2iHQoNafwGHAicH/SAmZWB1wNHAccCJxuZgeWuF3prWefDU1Pd989jGu0555Zp0hEqkhJrY/c/XEASy96OBR4wt2fipa9GTgB+Esp25ZeyA2DvWmThsEWkViVqFNoAtbkvV8bTYtlZjPNbJmZLVu/fn2fJ65m7NgRWhctXw7z58PEiVmnSESqUNGcgpndDewdM2u2u/+yG9uIy0Z40sLuPheYCzBp0qTE5aQHcsNg33ZbeLby8cdnnSIRqVJFg4K7H1PiNtYC+eUUo4F1Ja5TeuKqq0IwuPBCOO+8rFMjIlWsEsVHfwIOMLM3mNlg4DRgUQW2KwC33gqf+UxobfQ//5N1akSkypXaJPUDZrYWOBy43cwWR9P3NbM7ANx9O3ABsBh4HFjg7itLS7Z0y0MPwYwZcNhh8NOfahhsESnK3Ku32H7SpEm+bNmyrJPRPz31VHgmwtChsGQJ7LVX1ikSkQows4fdPbHfWDG6dRyINm8Olcnbt4dhsBUQRKSbNErqQPPKK3DiiSGncNddMH581ikSkX5EQWEgcYePfxzuuw/mzYN//desUyQi/YyKjwaSSy6BG28MI59+6ENZp0ZE+iEFhYHi+uvhK18JD8z5/OezTo2I9FMKCgPBPffAOefAMcfANddoGGwR6TUFhYFg5MgQEH7+cw2DLSIlUUXzQHDwwXDnnVmnQkQGAOUURESkg4KCiIh0UFAQEZEOCgoiItJBQUFERDooKIiISAcFBRER6aCgICIiHar6ITtmth54uhcfHQlsKHNy+ota3nfQ/mv/a3f/c/u+n7uP6u1Kqjoo9JaZLSvlyUP9WS3vO2j/tf+1u//l2ncVH4mISAcFBRER6TBQg8LcrBOQoVred9D+a/9rV1n2fUDWKYiISO8M1JyCiIj0goKCiIh0GJBBwcyuMLO/mtmjZnarmTVmnaZKMrOTzWylme00s5ppnmdmU81slZk9YWazsk5PJZnZj8zsOTN7LOu0VJqZjTGz35rZ49Hv/pNZp6mSzOy1ZvZHM3sk2v8vl7K+ARkUgLuAt7r724D/BS7OOD2V9hhwInB/1gmpFDOrA64GjgMOBE43swOzTVVFXQ9MzToRGdkOfMbd3wJMBs6vse/+FeBodz8YOASYamaTe7uyARkU3P037r49ersUGJ1leirN3R9391VZp6PCDgWecPen3P1V4GbghIzTVDHufj+wKet0ZMHdn3X3P0evtwCPA03ZpqpyPHgxelsf/fW6BdGADAoFPgroAcYDXxOwJu/9WmrowiCBmY0DJgIPZZyUijKzOjNbDjwH3OXuvd7/3cqWqgozs7uBvWNmzXb3X0bLzCZkLedVMm2V0J39rzEWM03trWuIme0B/AL4lLu/kHV6KsnddwCHRPWnt5rZW929V/VL/TYouPsxafPN7EzgvcC7fQB2xii2/zVoLTAm7/1oYF1GaZEKM7N6QkCY5+4Ls05PVty9zczuI9Qv9SooDMjiIzObCnwOeL+7b806PVIRfwIOMLM3mNlg4DRgUcZpkgowMwN+CDzu7ldmnZ5KM7NRuRaWZtYAHAP8tbfrG5BBAfguMBS4y8yWm9k1WSeokszsA2a2FjgcuN3MFmedpr4WNSy4AFhMqGhc4O4rs01V5ZjZTcASYLyZrTWzj2Wdpgo6AvgwcHR0vi83s2lZJ6qC9gF+a2aPEm6O7nL323q7Mg1zISIiHQZqTkFERHpBQUFERDooKIiISAcFBRER6aCgICIiHRQURESkg4KCiIh0+P9E0wHKi/n2gAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x[:,0],x[:,1], color='cyan')\n",
    "plt.scatter(y[:,0].detach().numpy(),y[:,1].detach().numpy())\n",
    "plt.plot([0,wEncoder[0,0].detach().numpy()],[0,wEncoder[1,0].detach().numpy()],'-r')\n",
    "plt.axis('equal')\n",
    "plt.title('RMSprop - Input data / constructed data / encoder weights')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "12e97a23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.523778 2.5225258\n"
     ]
    }
   ],
   "source": [
    "#ratio of weight in the encoder vs decoder for each dimensions\n",
    "print(wEncoder[0,0].detach().numpy()/wDecoder[0,0].detach().numpy(),wEncoder[1,0].detach().numpy()/wDecoder[0,1].detach().numpy())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83d04553",
   "metadata": {},
   "source": [
    "I noticed couple of things after running the code above a few times:\n",
    "\n",
    "1. The learned weight is different each time, this is due to the random start point\n",
    "2. The Converging speed of the loss function depends on where it starts as well\n",
    "3. The plot of loss function vs epochs using SGD is very smooth, while the other two is a bit bumpy.\n",
    "4. It looks like the learning speed of SGD with momentum is faster than without momentum\n",
    "5. The constructed data using RMSprop is almost perfectly linear with the input data which suggests it has the best performance\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9aa8329c",
   "metadata": {},
   "source": [
    "## AIML420 ONLY\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83357931",
   "metadata": {},
   "source": [
    "1.In a text cell: explain the relationship between the above autoencoder and PCA.\n",
    "\n",
    "The above autoencoder is a linear autoencoder. It encodes the data to a lower dimension then decode the data back to it's original dimension space, the way autoencoder works is not the same as PCA. PCA learns a linear transformation that projects the data to a differen space which are the components. We can then choose a smaller number of components to reduce the dimentionality. But autoencoder can be used to model complext non linear functions.\n",
    "\n",
    "PCA is faster and computationally cheaper than autoencoders.\n",
    "\n",
    "However, an one layer autoencoder with linear activation function is almost equivlant to PCA. In the above autoencoder, the activatio function is linear, so if we want to transfor X->z->x1, then we can write x1=w2*Z = w2* w1*x which is the same as how PCA transforms the data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1423e00d",
   "metadata": {},
   "source": [
    "2. In a text cell: in the notebook with the Week 9 tutorial, you may have noticed how the RMSprop and Adam optimisers seem to prefer travelling along diagonal lines. Why does this happen?\n",
    "\n",
    "RmsProp and Adam optimisers are adaptive Learning Algorithms while SGD with momentum uses constant learning rate.\n",
    "Algorithms using constant learning rate is like letting a ball rolling down a hill. They take large steps when the direction is the same, but small steps if the direction changes.\n",
    "RmsProp and Adam optimisers adapts their learning rate using a moving average of their gradient's square value. As this value increase, the learning rate becomes smaller allowing the algorithm to converge.This allows RMSProp and Adam to escape a saddle point much better. They will take a straight path whereas gradient descent takes the approach of “let the ball rolls down the steep slope first and worry about the slower direction later”\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e252713",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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