concrete/docs/user/advanced_examples/QuantizedGeneralizedLinearModel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b760a0f6",
   "metadata": {},
   "source": [
    "# FIXME(Andrei): To be done with 979\n",
    "\n",
    "FIXME(Andrei): to be done with 979!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "253288cf",
   "metadata": {},
   "source": [
    "### Let's start by importing some libraries to develop our linear regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6200ab62",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f43e2387",
   "metadata": {},
   "source": [
    "### And some helpers for visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d104c8df",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53e676b8",
   "metadata": {},
   "source": [
    "### We need an inputset, a handcrafted one for simplicity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d451e829",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([[69], [130], [110], [100], [145], [160], [185], [200], [80], [50]], dtype=np.float32)\n",
    "y = np.array([181, 325, 295, 268, 400, 420, 500, 520, 220, 120], dtype=np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75f4fdb7",
   "metadata": {},
   "source": [
    "### Let's visualize our inputset to get a grasp of it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2a124a62",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.ioff()\n",
    "fig, ax = plt.subplots(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "edcd361b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.scatter(x[:, 0], y, marker=\"x\", color=\"red\")\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c8310ab",
   "metadata": {},
   "source": [
    "### Now, we need a model so let's define it\n",
    "\n",
    "The main purpose of this tutorial is not to train a linear regression model but to use it homomorphically. So we will not discuss about how the model is trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "91d4a1da",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model:\n",
    "    w = None\n",
    "    b = None\n",
    "\n",
    "    def fit(self, x, y):\n",
    "        a = np.ones((x.shape[0], x.shape[1] + 1), dtype=np.float32)\n",
    "        a[:, 1:] = x\n",
    "\n",
    "        regularization_contribution = np.identity(x.shape[1] + 1, dtype=np.float32)\n",
    "        regularization_contribution[0][0] = 0\n",
    "\n",
    "        parameters = np.linalg.pinv(a.T @ a + regularization_contribution) @ a.T @ y\n",
    "\n",
    "        self.b = parameters[0]\n",
    "        self.w = parameters[1:].reshape(-1, 1)\n",
    "\n",
    "        return self\n",
    "\n",
    "    def evaluate(self, x):\n",
    "        return x @ self.w + self.b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faa5247c",
   "metadata": {},
   "source": [
    "### And create one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "682fb2d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Model().fit(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "084fb296",
   "metadata": {},
   "source": [
    "### Time to make some predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4953b03e",
   "metadata": {},
   "outputs": [],
   "source": [
    "inputs = np.linspace(40, 210, 100).reshape(-1, 1)\n",
    "predictions = model.evaluate(inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f28155cf",
   "metadata": {},
   "source": [
    "### Let's visualize our predictions to see how our model performs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "111574ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.plot(inputs, predictions, color=\"blue\")\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23852861",
   "metadata": {},
   "source": [
    "### As a bonus let's inspect the model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7877cb2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.6698928]]\n",
      "-3.2299957\n"
     ]
    }
   ],
   "source": [
    "print(model.w)\n",
    "print(model.b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de63118c",
   "metadata": {},
   "source": [
    "They are floating point numbers and we can't directly work with them!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d959640",
   "metadata": {},
   "source": [
    "### So, let's abstract quantization\n",
    "\n",
    "Here is a quick summary of quantization. We have a range of values and we want to represent them using small number of bits (n). To do this, we split the range into 2^n sections and map each section to a value. Here is a visualization of the process!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9da2e1a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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fill=\"none\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"stroke\"/><path d=\"M 229.12 123 L 236.12 119.5 L 234.37 123 L 236.12 126.5 Z\" fill=\"#000000\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"all\"/><path d=\"M 246.88 123 L 239.88 126.5 L 241.63 123 L 239.88 119.5 Z\" fill=\"#000000\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"all\"/><rect x=\"108\" y=\"94\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 104px; margin-left: 109px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 12px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div>min(x)</div></div></div></div></foreignObject><text x=\"128\" y=\"108\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"12px\" text-anchor=\"middle\">min(x)</text></switch></g><rect x=\"228\" y=\"94\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 104px; margin-left: 229px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 12px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \">max(x)</div></div></div></foreignObject><text x=\"248\" y=\"108\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"12px\" text-anchor=\"middle\">max(x)</text></switch></g><path d=\"M 138 148 L 138 128\" fill=\"none\" stroke=\"#000000\" stroke-width=\"2\" stroke-miterlimit=\"10\" stroke-dasharray=\"2 6\" pointer-events=\"stroke\"/><rect x=\"118\" y=\"152\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 162px; margin-left: 119px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">Map</font></div><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">to 0<br style=\"font-size: 10px\"/></font></div></div></div></div></foreignObject><text x=\"138\" y=\"165\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">Map...</text></switch></g><rect x=\"148\" y=\"152\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 162px; margin-left: 149px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">Map</font></div><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">to 1<br style=\"font-size: 10px\"/></font></div></div></div></div></foreignObject><text x=\"168\" y=\"165\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">Map...</text></switch></g><path d=\"M 168 148 L 168 128\" fill=\"none\" stroke=\"#000000\" stroke-width=\"2\" stroke-miterlimit=\"10\" stroke-dasharray=\"2 6\" pointer-events=\"stroke\"/><path d=\"M 208 148 L 208 128\" fill=\"none\" stroke=\"#000000\" stroke-width=\"2\" stroke-miterlimit=\"10\" stroke-dasharray=\"2 6\" pointer-events=\"stroke\"/><path d=\"M 238 148 L 238 128\" fill=\"none\" stroke=\"#000000\" stroke-width=\"2\" stroke-miterlimit=\"10\" stroke-dasharray=\"2 6\" pointer-events=\"stroke\"/><path d=\"M 294.37 68.66 L 321.63 68.66\" fill=\"none\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"stroke\"/><path d=\"M 289.12 68.66 L 296.12 65.16 L 294.37 68.66 L 296.12 72.16 Z\" fill=\"#000000\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"all\"/><path d=\"M 326.88 68.66 L 319.88 72.16 L 321.63 68.66 L 319.88 65.16 Z\" fill=\"#000000\" stroke=\"#000000\" stroke-miterlimit=\"10\" pointer-events=\"all\"/><rect x=\"288\" y=\"18.66\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 29px; margin-left: 289px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 12px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><font style=\"font-size: 10px\">Distance<br/>Between<br/>Consecutive<br/>Values</font></div></div></div></foreignObject><text x=\"308\" y=\"32\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"12px\" text-anchor=\"middle\">Distan...</text></switch></g><rect x=\"188\" y=\"152\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 162px; margin-left: 189px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">Map</font></div><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">to 2</font></div></div></div></div></foreignObject><text x=\"208\" y=\"165\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">Map...</text></switch></g><rect x=\"218\" y=\"152\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 162px; margin-left: 219px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">Map</font></div><div style=\"font-size: 10px\"><font style=\"font-size: 10px\">to 3</font></div></div></div></div></foreignObject><text x=\"238\" y=\"165\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">Map...</text></switch></g><rect x=\"128\" y=\"174\" width=\"120\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 118px; height: 1px; padding-top: 184px; margin-left: 129px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \">(when n = 2)</div></div></div></foreignObject><text x=\"188\" y=\"187\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">(when n = 2)</text></switch></g><rect x=\"28\" y=\"94\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 104px; margin-left: 29px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \">0</div></div></div></foreignObject><text x=\"48\" y=\"107\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">0</text></switch></g><rect x=\"308\" y=\"18.66\" width=\"110\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 108px; height: 1px; padding-top: 29px; margin-left: 309px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div><font style=\"font-size: 12px\">= 1 / scale</font></div><div><font style=\"font-size: 12px\">= 1 / q</font></div></div></div></div></foreignObject><text x=\"363\" y=\"32\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">= 1 / scale...</text></switch></g><rect x=\"128\" y=\"24\" width=\"140\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 138px; height: 1px; padding-top: 34px; margin-left: 129px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><font style=\"font-size: 12px\">x =</font><font style=\"font-size: 12px\"> (x   + zp  ) / q </font></div></div></div></foreignObject><text x=\"198\" y=\"37\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">x = (x   + zp  ) / q </text></switch></g><rect x=\"167\" y=\"29\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 39px; margin-left: 168px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div><font style=\"font-size: 10px\">q</font></div></div></div></div></foreignObject><text x=\"187\" y=\"42\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">q</text></switch></g><rect x=\"199\" y=\"29\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 39px; margin-left: 200px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div>x</div></div></div></div></foreignObject><text x=\"219\" y=\"42\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">x</text></switch></g><rect x=\"227\" y=\"29\" width=\"40\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 38px; height: 1px; padding-top: 39px; margin-left: 228px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div>x</div></div></div></div></foreignObject><text x=\"247\" y=\"42\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">x</text></switch></g><rect x=\"48\" y=\"28\" width=\"80\" height=\"20\" fill=\"none\" stroke=\"none\" pointer-events=\"all\"/><g transform=\"translate(-0.5 -0.5)\"><switch><foreignObject style=\"overflow: visible; text-align: left;\" pointer-events=\"none\" width=\"100%\" height=\"100%\" requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"><div xmlns=\"http://www.w3.org/1999/xhtml\" style=\"display: flex; align-items: unsafe center; justify-content: unsafe center; width: 78px; height: 1px; padding-top: 38px; margin-left: 49px;\"><div style=\"box-sizing: border-box; font-size: 0; text-align: center; \"><div style=\"display: inline-block; font-size: 10px; font-family: Helvetica; color: #000000; line-height: 1.2; pointer-events: all; white-space: normal; word-wrap: normal; \"><div>zero point<br/></div><div>zp = 2</div></div></div></div></foreignObject><text x=\"88\" y=\"41\" fill=\"#000000\" font-family=\"Helvetica\" font-size=\"10px\" text-anchor=\"middle\">zero point...</text></switch></g></g><switch><g requiredFeatures=\"http://www.w3.org/TR/SVG11/feature#Extensibility\"/><a transform=\"translate(0,-5)\" xlink:href=\"https://www.diagrams.net/doc/faq/svg-export-text-problems\" target=\"_blank\"><text text-anchor=\"middle\" font-size=\"10px\" x=\"50%\" y=\"100%\">Viewer does not support full SVG 1.1</text></a></switch></svg>",
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import SVG\n",
    "SVG(filename=\"figures/QuantizationVisualized.svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45d12e7a",
   "metadata": {},
   "source": [
    "If you want to learn more, head to https://intellabs.github.io/distiller/algo_quantization.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "2541cdb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "class QuantizationParameters:\n",
    "    def __init__(self, q, zp, n):\n",
    "        # q = scale factor = 1 / distance between consecutive values\n",
    "        # zp = zero point which is used to determine the beginning of the quantized range\n",
    "        #     (quantized 0 = the beginning of the quantized range = zp * distance between consecutive values)\n",
    "        # n = number of bits\n",
    "        \n",
    "        # e.g.,\n",
    "        \n",
    "        # n = 2\n",
    "        # zp = 2\n",
    "        # q = 0.66\n",
    "        # distance between consecutive values = 1 / q = 1.5151\n",
    "        \n",
    "        # quantized 0 = zp / q = zp * distance between consecutive values = 3.0303\n",
    "        # quantized 1 = quantized 0 + distance between consecutive values = 4.5454\n",
    "        # quantized 2 = quantized 1 + distance between consecutive values = 6.0606\n",
    "        # quantized 3 = quantized 2 + distance between consecutive values = 7.5757\n",
    "        \n",
    "        self.q = q\n",
    "        self.zp = zp\n",
    "        self.n = n\n",
    "\n",
    "class QuantizedArray:\n",
    "    def __init__(self, values, parameters):\n",
    "        # values = quantized values\n",
    "        # parameters = parameters used during quantization\n",
    "        \n",
    "        # e.g.,\n",
    "        \n",
    "        # values = [1, 0, 2, 1]\n",
    "        # parameters = QuantizationParameters(q=0.66, zp=2, n=2)\n",
    "        \n",
    "        # original array = [4.5454, 3.0303, 6.0606, 4.5454]\n",
    "        \n",
    "        self.values = np.array(values)\n",
    "        self.parameters = parameters\n",
    "\n",
    "    @staticmethod\n",
    "    def of(x, n):\n",
    "        if not isinstance(x, np.ndarray):\n",
    "            x = np.array(x)\n",
    "\n",
    "        min_x = x.min()\n",
    "        max_x = x.max()\n",
    "\n",
    "        if min_x == max_x: # encoding single valued arrays\n",
    "            \n",
    "            if min_x == 0.0: # encoding 0s\n",
    "                \n",
    "                # dequantization = (x_q + zp_x) / q_x = 0 --> q_x = 1 && zp_x = 0 && x_q = 0\n",
    "                q_x = 1\n",
    "                zp_x = 0\n",
    "                x_q = np.zeros(x.shape, dtype=np.uint)\n",
    "                \n",
    "            elif min_x < 0.0: # encoding negative scalars\n",
    "                \n",
    "                # dequantization = (x_q + zp_x) / q_x = -x --> q_x = 1 / x & zp_x = -1 & x_q = 0\n",
    "                q_x = abs(1 / min_x)\n",
    "                zp_x = -1\n",
    "                x_q = np.zeros(x.shape, dtype=np.uint)\n",
    "                \n",
    "            else: # encoding positive scalars\n",
    "                \n",
    "                # dequantization = (x_q + zp_x) / q_x = x --> q_x = 1 / x & zp_x = 0 & x_q = 1\n",
    "                q_x = 1 / min_x\n",
    "                zp_x = 0\n",
    "                x_q = np.ones(x.shape, dtype=np.uint)\n",
    "                \n",
    "        else: # encoding multi valued arrays\n",
    "            \n",
    "            # distance between consecutive values = range of x / number of different quantized values = (max_x - min_x) / (2^n - 1)\n",
    "            # q = 1 / distance between consecutive values\n",
    "            q_x = (2**n - 1) / (max_x - min_x)\n",
    "            \n",
    "            # zp = what should be added to 0 to get min_x -> min_x = (0 + zp) / q -> zp = min_x * q\n",
    "            zp_x = int(round(min_x * q_x))\n",
    "            \n",
    "            # x = (x_q + zp) / q -> x_q = (x * q) - zp\n",
    "            x_q = ((q_x * x) - zp_x).round().astype(np.uint)\n",
    "\n",
    "        return QuantizedArray(x_q, QuantizationParameters(q_x, zp_x, n))\n",
    "\n",
    "    def dequantize(self):\n",
    "        # x = (x_q + zp) / q\n",
    "        # x = (x_q + zp) / q\n",
    "        return (self.values.astype(np.float32) + float(self.parameters.zp)) / self.parameters.q\n",
    "\n",
    "    def affine(self, w, b, min_y, max_y, n_y):\n",
    "        # the formulas used in this method was derived from the following equations\n",
    "        #\n",
    "        # x = (x_q + zp_x) / q_x\n",
    "        # w = (w_q + zp_w) / q_w\n",
    "        # b = (b_q + zp_b) / q_b\n",
    "        #\n",
    "        # (x * w) + b = ((x_q + zp_x) / q_x) * ((w_q + zp_w) / q_w) + ((b_q + zp_b) / q_b)\n",
    "        #             = y = (y_q + zp_y) / q_y\n",
    "        #\n",
    "        # So, ((x_q + zp_x) / q_x) * ((w_q + zp_w) / q_w) + ((b_q + zp_b) / q_b) = (y_q + zp_y) / q_y\n",
    "        # We can calculate zp_y and q_y from min_y, max_y, n_y. So, the only unknown is y_q and it can be solved.\n",
    "\n",
    "        x_q = self.values\n",
    "        w_q = w.values\n",
    "        b_q = b.values\n",
    "\n",
    "        q_x = self.parameters.q\n",
    "        q_w = w.parameters.q\n",
    "        q_b = b.parameters.q\n",
    "\n",
    "        zp_x = self.parameters.zp\n",
    "        zp_w = w.parameters.zp\n",
    "        zp_b = b.parameters.zp\n",
    "\n",
    "        q_y = (2**n_y - 1) / (max_y - min_y)\n",
    "        zp_y = int(round(min_y * q_y))\n",
    "\n",
    "        y_q = (q_y / (q_x * q_w)) * ((x_q + zp_x) @ (w_q + zp_w) + (q_x * q_w / q_b) * (b_q + zp_b))\n",
    "        y_q -= min_y * q_y\n",
    "        y_q = y_q.round().clip(0, 2**n_y - 1).astype(np.uint)\n",
    "\n",
    "        return QuantizedArray(y_q, QuantizationParameters(q_y, zp_y, n_y))\n",
    "\n",
    "class QuantizedFunction:\n",
    "    def __init__(self, table):\n",
    "        self.table = table\n",
    "\n",
    "    @staticmethod\n",
    "    def of(f, input_bits, output_bits):\n",
    "        domain = np.array(range(2**input_bits), dtype=np.uint)\n",
    "        table = f(domain).round().clip(0, 2**output_bits - 1).astype(np.uint)\n",
    "        return QuantizedFunction(table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab82ae87",
   "metadata": {},
   "source": [
    "### Let's quantize our model parameters\n",
    "\n",
    "Since the parameters only consist of scalars, we can use a single bit quantization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c8b08ef4",
   "metadata": {},
   "outputs": [],
   "source": [
    "parameter_bits = 1\n",
    "\n",
    "w_q = QuantizedArray.of(model.w, parameter_bits)\n",
    "b_q = QuantizedArray.of(model.b, parameter_bits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2528092",
   "metadata": {},
   "source": [
    "### And quantize our inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "affe644e",
   "metadata": {},
   "outputs": [],
   "source": [
    "input_bits = 6\n",
    "\n",
    "x_q = QuantizedArray.of(inputs, input_bits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5a50eb8",
   "metadata": {},
   "source": [
    "### Time to make quantized inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0fdfd3d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "output_bits = 7\n",
    "\n",
    "min_y = predictions.min()\n",
    "max_y = predictions.max()\n",
    "y_q = x_q.affine(w_q, b_q, min_y, max_y, output_bits)\n",
    "\n",
    "quantized_predictions = y_q.dequantize()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fb15eb4",
   "metadata": {},
   "source": [
    "### And visualize the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8076a406",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.plot(inputs, quantized_predictions, color=\"black\")\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af6bc89e",
   "metadata": {},
   "source": [
    "### Now it's time to make the inference homomorphic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "cbda8067",
   "metadata": {},
   "outputs": [],
   "source": [
    "q_y = (2**output_bits - 1) / (max_y - min_y)\n",
    "zp_y = int(round(min_y * q_y))\n",
    "\n",
    "q_x = x_q.parameters.q\n",
    "q_w = w_q.parameters.q\n",
    "q_b = b_q.parameters.q\n",
    "\n",
    "zp_x = x_q.parameters.zp\n",
    "zp_w = w_q.parameters.zp\n",
    "zp_b = b_q.parameters.zp\n",
    "\n",
    "x_q = x_q.values\n",
    "w_q = w_q.values\n",
    "b_q = b_q.values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8e95e3d",
   "metadata": {},
   "source": [
    "### Simplification to rescue!\n",
    "\n",
    "The `y_q` formula in `QuantizedArray.affine(...)` can be rewritten to make it easier to implement in homomorphically. Here is the breakdown.\n",
    "```\n",
    "(q_y / (q_x * q_w)) * ((x_q + zp_x) @ (w_q + zp_w) + (q_x * q_w / q_b) * (b_q + zp_b)) - (min_y * q_y)\n",
    "^^^^^^^^^^^^^^^^^^^    ^^^^^^^^^^^^   ^^^^^^^^^^^^   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^    ^^^^^^^^^^^^^\n",
    "constant (c1)          can be done    constant (c2)  constant (c3)                       constant (c4)\n",
    "                       on the circuit  \n",
    "                       \n",
    "                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "                       can be done on the circuit\n",
    "                       \n",
    "^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "cannot be done on the circuit because of floating point operation so will be a single table lookup\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6e101ae",
   "metadata": {},
   "source": [
    "### Let's import the Concrete numpy package now!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4da7aed5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import concrete.numpy as hnp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d3816fa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "c1 = q_y / (q_x * q_w)\n",
    "c2 = w_q + zp_w\n",
    "c3 = (q_x * q_w / q_b) * (b_q + zp_b)\n",
    "c4 = min_y * q_y\n",
    "\n",
    "f = lambda intermediate: (c1 * (intermediate + c3)) - c4\n",
    "f_q = QuantizedFunction.of(f, input_bits + parameter_bits, output_bits)\n",
    "\n",
    "table = hnp.LookupTable([int(entry) for entry in f_q.table])\n",
    "\n",
    "w_0 = int(c2.flatten()[0])\n",
    "\n",
    "def infer(x_0):\n",
    "    return table[(x_0 + zp_x) * w_0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01d67c28",
   "metadata": {},
   "source": [
    "### Let's compile our quantized inference function to it's homomorphic equivalent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "81304aca",
   "metadata": {},
   "outputs": [],
   "source": [
    "inputset = [int(x_i[0]) for x_i in x_q]\n",
    "\n",
    "circuit = hnp.compile_numpy_function(\n",
    "    infer,\n",
    "    {\"x_0\": hnp.EncryptedScalar(hnp.Integer(input_bits, is_signed=False))},\n",
    "    inputset,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c62af039",
   "metadata": {},
   "source": [
    "### Here are some representations of the fhe circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0c533af6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "%0 = Constant(1)                         # ClearScalar<Integer<unsigned, 8 bits>>\n",
      "%1 = x_0                                 # EncryptedScalar<Integer<unsigned, 7 bits>>\n",
      "%2 = Constant(15)                        # ClearScalar<Integer<unsigned, 8 bits>>\n",
      "%3 = Add(1, 2)                           # EncryptedScalar<Integer<unsigned, 7 bits>>\n",
      "%4 = Mul(3, 0)                           # EncryptedScalar<Integer<unsigned, 7 bits>>\n",
      "%5 = TLU(4)                              # EncryptedScalar<Integer<unsigned, 7 bits>>\n",
      "return(%5)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c1fc0f48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ffyxyzTXOD3rTpiLPPqvyHXq71jl3TiQjQ+SeexxzLYKq0fv1E9m0ybs2eYIiEflYRK4R5we9qYg8KyrfobdrnXMikiEi94hjrkVE1ej9RCQAit9dOK9nrA3FxSphztSpal1keRIS4JZboEcPSE01ogq4i4ICtRo/MxPWrIGsLCPAlo3ISBg0CJ56ClxEkfBrilEJc6ai1kWWJwG4BegBpGJEFXAXBajV+JnAGiALI8CWjUhgEPAUEGDFX1sy3CpGe7ZsgenTVcLRisIa1qunYpGmpKg1lPHxkJgIjRqpY1FRKiJbRIRazlVUBGfPqtfhw2rO6MGDavL29u2Qna1+EFzRrh2MHAmjR8MVV3jijn2LLcB0VMLRisIa1kPFIk1BraGMBxKBRtZjUaiIbBGo5VxFwFnr6zBqzuhB1OTt7UA26gfBFe2AkcBoIAiK/1LwnBhtlJSommrBAvjqK9i715NXOwPUByA8XC2U7tdPrTpxc9RGv6EEVVMtAL4CHIr/zBmoX98j1w1HLZTuh1p1EqTFXxM8L8byHDumxLl+varNtm1zDIF4KYSEQEzMeCIj9/Doo8tJTYWuXYMn5XlNOIYS58pffuHj5s2pu3AhZ3v3rtV3hgBNUTVsB1QTuCvBk/LcTXhfjK44cULFlDl+HI4eVc3PvDzVB7xwQb3HxkJYmMoBUq+e6n/Gx6v3li1h9eol9OvXj507d5YFONZUzKRJk3jnnXc4cuQIZ+vU4WfgOHAU1fzMQ/UBL1jfY4EwVA6Qeqj+Z7z1vSVaeG7AN8ToDkSE1q1bc+uttzJlyhSzzfFpiouLyxLWvPXWW2abo1FUvLjY37BYLPzhD39g9uzZnD171mxzfJoFCxZw7NgxxowZY7YpGjsCRowADz74IKWlpcyZM8dsU3yaqVOn0q9fP5o1a2a2KRo7AkqMcXFxDB8+nH/84x8ESOvb7Wzfvp01a9Ywfvx4s03RlCOgxAjw+OOPs3fvXr7++muzTfFJ/vGPf9CmTRu3JwXS1J6AE2Pbtm3p0aMHU6dONdsUnyM3N5d//etfjBs3zu2JZDW1J+DECDB+/HgWL17M/v37zTbFp/jwww8JCQlhhCdDomsumYAU45133kmTJk2YNm2a2ab4DKWlpUybNo3Ro0dTr149s83RuCAgxRgWFsaYMWP48MMPuXDhgtnm+ARLlixh//79PPLII2aboqmAgBQjwJgxY7h48SJz58412xSfYOrUqfzud7/Ts5N8mIAV45VXXsmQIUP0bBwgOzubr7/+Wg9n+DgBK0aAJ554gh9++IG1a9eabYqpTJ06lcTERG6//XazTdFUQkCLsVOnTtxwww1BPcxx7tw5Zs+ezfjx4wkNDTXbHE0lBLQYQQ1zfP755xw9etRsU0xh9uzZFBYWMnr0aLNN0VRBwItx6NChXH755UyfPt1sU0zh/fff57777uPyyy832xRNFQS8GCMiInjooYd4//33KSgoMNscr/L111+zfft2xo4da7YpmmoQ8GIEePTRRzl9+jSfB1nG16lTp5Kamsp1111ntimaahAUYmzSpAkDBgwIKkfOoUOHWLx4sR7O8COCQoygHDn//e9/2bRpk9mmeIX33nuPRo0acdddd5ltiqaaBI0Ye/bsSfv27fm///s/s03xOAUFBcyaNYuxY8cSHh5utjmaahI0YgTVd5w7dy6//PKL2aZ4lE8//ZTc3Fwefvhhs03R1ICgEuOIESOoW7cuH330kdmmeJRp06YxZMgQGjdubLYpmhoQVGKsU6cO999/P9OmTaO4otDjfs66devYtGmTdtz4IUElRlBN1SNHjvCf//ynVt+zdetW+vbtS1xcHLGxsfTu3Zt169a5ycpLZ+rUqVx33XV07dq1ynOXLl1KUlISYWFhXrBMUxVBJ8YWLVrQp0+fWg1zbNy4kW7duhEbG8uuXbvYv38/zZs3Jy0tjeXLl7vR2ppx/PhxFixYwOOPP17pefv27aN///48//zznDx50kvWaarEjNxXZrNs2TIB5Mcff6zx35aUlEjbtm0lPj5eLly4ULa/uLhYWrVqJYmJiZKfn+9Oc6vNyy+/LFdccYVcvHix0vOGDRsmb775phQVFUlCQoKEhoZ6yUJNJbgnP6O/UVpaKq1atZJHHnmkxn/7zTffCCCPPfaY07FXXnlFAJk/f747zKwRhYWFkpCQIC+88EKV59r/iGgx+gzpQddMBRV9fOzYsXzyySecOXOmRn+7atUqAK6//nqnY7Z9K1eurL2RNWT+/PmcOHGiWsMZ0dHRXrBIU1OCUoygoo+HhITw8ccf1+jvdu/eDcBVV13ldCwhIQGAPXv21Nq+mjJ16lQGDBhA06ZNvX5tjXsIWjHGxsYyfPhwpk6dSmlpabX/Ljc3F4C6LvLNxcTEAHD69Gm32Fhdtm7dyvr16/Vwhp8TtGIENV913759bvOAijWlgLcDBE+ZMoXk5GTS0tK8el2NewlqMSYnJ3PzzTfXaJgjLi4OgPPnzzsds+2zneMNTp8+zbx583jsscd0lHA/J6jFCKp2XLp0abX7ebZQh0eOHHE6ZgvtkeTFnOXTp08nIiKC++67z2vX1HiGoBdj//79ufrqq/nggw+qdf7NN98MwObNm52O2fZ5K6lMSUkJH3zwAaNHjy7rr2r8GLMHV3yBN954Q+Li4uTcuXNVnltSUiLJycnSpEkTh8H14uJiadOmjSQmJlY56O4uvvjiC7FYLPLTTz9d8nfocUafITjHGcvz8MMPk5+fz6efflrluSEhIcycOZOcnBxGjx7NiRMnOHXqFOPGjSM7O5sZM2YQFRXlBavVcMZtt93m1WaxxnNoMQJXXHEF99xzT7WTrHbt2pX169dz5swZWrVqRdOmTcnOzmb16tX8/ve/94LFsGvXLlatWnVJwxmLFy/GYrFgsVg4evQoJSUlZZ8//PBDD1irqQ4Wqc7TFwRs2bKF6667jtWrV9OzZ0+zzamS8ePH8+WXX7Jnzx5CQvRvagCQof8XrXTs2JEbb7zRL4JW5eXl8cknnzBu3DgtxABC/0/aMX78eBYuXOhy2MKXmDVrFsXFxYwaNcpsUzRuRIvRjiFDhtCwYUPef/99s02pEBFh2rRpjBw5kgYNGphtjsaNaDHaER4ezkMPPcT06dPJz8832xyXLF++nN27d+ukpwGIFmM5xo4dS25uLhkZGWab4pKpU6eSlpZG+/btzTZF42a0GMsRHx/PwIEDmTx5stmmOHHw4EGWLVumV2cEKFqMLhg/fjzff/893377rdmmODB16lQaN25M//79zTZF4wG0GF1w00030alTJ58a5rh48SKzZs3i0Ucf1VHCAxQtxgp45JFH+Oyzz3wmeto///lPzp07x4MPPmi2KRoPocVYAffeey+xsbE+Mz3s/fff55577qFRo0Zmm6LxEFqMFRAdHc0DDzzAe++9R1FRkam2ZGVl8f333zNu3DhT7dB4Fi3GShg3bhwnT55k0aJFptoxdepUunTpQufOnU21Q+NZtBgr4eqrr6Zv376mOnKOHTvGwoUL9XBGEKDFWAXjx48nMzOTH3/80ZTrv//++8TFxTF48GBTrq/xHlqMVdC7d29at27tkGT1yJEjvPjiiwwcONBt1zl69CidO3dm9uzZZVPxCgsLmTFjBmPHjvXagmWNiZgbacA/mDJlitSpU0f+/e9/y6BBgyQ0NFQAadGihduusX37dgHEYrFI/fr15fnnn5fJkydLWFiYHD582G3X0fgs6ToXWBUUFBQQHh5OdHQ0/fv3Jzw8nJKSEoAapwaoDFvgYxHhzJkz/O1vf6OoqIjmzZuzZcsWEhISdCjGAEc3Uyvg559/ZsKECTRq1Ihx48aVicV+mCMvL89t1ysfhbywsBAR4eDBg/Tv358WLVrw7rvvcu7cObddU+Nb6LAbLli5ciW33norFoulrBasiPz8fCIjI2t9zX/+85+MGjWqwlQDFosFEaFZs2b8+OOPOjRj4KHDbriiV69ePPvss9UKTmXLvVFbcnNzCQ0NrfSciIgIPvnkEy3EAEWLsQLefPNN7r///ioF4i4x5uTkVBrPxmKxMHfuXLp37+6W62l8Dy3GCrBYLEyfPp077rij0pz37so4lZubW2FNbLPFnUMpGt9Di7ESQkNDmTt3Lp07d65w2ZI7m6mu+qcWi4U33nhDr9YIArQYqyA6Opply5bRsmVLJ0FaLBa3ifH06dNOYgwJCWHs2LFMmDDBLdfQ+DZajNWgfv36rFixgoYNGzoIMiwszG3N1F9//dXhc1hYGIMHD/apBc4az6LFWE2aNGnC6tWriYmJKetDhoSEuNWBYyM8PJzu3bszZ84cHaQ4iND/0zXgmmuu4auvviI8PLxMJO7sM4ISYnJyMosXL3bL+KXGf9DT4WpI586d+fzzz+nXrx8FBQWc3r4d3nkHDhyAo0fh+HE4eRJyc6G0FPLyoLgY6tSByEiIioK4OIiPh4QEaNIEkpLIs4rxqquuYsWKFXossRocB7ZbXweAo9Z9J4FcoBTIA4qBOkAkEAXEAfFAAtAESAJSgGSgrvfMd0LPwKkuJSWwdStkZkJmJv9ctYqR584xCKhthNVS1K/iFcC3zZvT9JZboEcPSEuDxMRafntgUAJsBTKtr3XAKTdfw4ISZirQA0gDvFj6GVqMlVFYCCtXwhdfwKJF8MsvDof/DnwJLLftCAmBRo2gYUNo0ABCQyE2FsLC4MIFKCiAixchJ0fVomfPAupXvBmQhfqFduDaa2HgQLjrLkhxOhrQFAIrgS+ARcAvlZ9OCNAIaAg0AEKBWNQP3QWgALgI5KBq0bPVsOFaYCBwFy7+b9yLFqNL9u6F6dNh1iz47Tfn46GhSiSdOpFeVMTd990HrVpB48ZKeNXlwgU4dIjj69ax97//JTUvD9avh4oS73TsCGPHwr33QgA3Y/cC04FZgIvSJxQlkk5AO6At0ApoTM36XReAQ8BOYAequbseqCjtUUdgLHAv4IHS12J0YMMGmDQJli2D8sXSrBnceSf06gU33QT163vOjn37ICtL2bFsGZRfqVGvHowZA888o2rhAGEDMAlYBpR/KJsBdwK9gJsAD5Y++1CtlGXWV/l1MvWAMcAzqFrYTWToxcUiIps2idx2m4iSoPFq3FhkwgSR7783z7aLF0UWLRK5+26RiAhH++rWFXnmGZGcHPPscwObROQ2EaHcq7GITBARE0tfLorIIhG5W0QixNG+uiLyjIi4qfTTg1uMp0+LjBsnEhrq+JB37y6Sni5SWGi2hY6cOCHyxhsi8fGO9jZsKPLxxyKlpWZbWCNOi8g4EQkVx4e8u4iki4iPlb6cEJE3RCReHO1tKCIfi0gtSz+IxbhkiUijRo4PdY8eIitXmm1Z1Vy4IDJ5srMo09JE/CRExxIRaSSOD3UPEfGD0pcLIjJZnEWZJiK1KP0gFGNhocjLL4uEhBgPcZMmIrNnm21ZzTl/Xt1LZKRxL/Xrq1rdRykUkZdFJESMh7iJiPhh6ct5UfcSKca91BdVq18CQSbGnByR1FTjwbVYRJ54QuTcObMtqx07d4p06eJ4X6+9ZrZVTuSISKoYD65FRJ4QET8vfdkpIl3E8b4uofSDSIyHDom0bevYz1q61Gyr3EdhochzzznW+I88IlJcbLZlIiJySETaimM/K4BKXwpF5DlxrPEfEZEalH6QiPH4cZEWLYyHNCXFb/pWNeaLL0Sio417ffhh0x07x0WkhRgPaYrUqm/l03whItFi3OvDUm3HThCIMTdXpEMH4+Hs2VN5UQOZtWtFGjQw7nniRNNMyRWRDmI8nD1FeVEDmbUi0kCMe65m6QeBGAcMMB7Krl39v39YXTZsUOOQtnufN88UMwaI8VB2Ff/vH1aXDaLGIW33Xo3STw/sJVTTpqk5pQCtW8PixVDXzHn5XqRLF5g/35ieN2aMWlniRaah5pQCtAYWY+6qCG/SBZiPMT1vDGplSWUErhgPHICnn1bbUVGQng6XX26qSV7nttvgpZfU9pkz4MU4OgcAa+kTBaQDQVb63AZYS58zQFWlH7hinDhRrZAAeOutoFvxUMbEiWAL77hqlWodeOOyqBUSAG/h8RUPLlm6dClJSUmVRvfzNBMBW3DNVajWQUUE5kTxLVugUyfVW2rXTq1DrCL+qafo2rUrV1xxBYu9JAKXbNkC11+vFju3bQvbtoEH83ZsQa2oENSqiq2olRbeYt++ffzxj3/k4MGDHDhwgPPnz1NcXOxFCxzZAlyPWrfaFtiGWjtZjgCNKD5tmrHq4q23TBOiz9CxIwwbprZ37FALpD3INIxVF2/hXSECvPTSS3Tr1o3NmzcTGxvr5as70xGwlj47UIujXRF4Yrx4ETKsa++bN4fbbzfXHl/h8ceN7Y8+8thlLmJEPmgOmFH6M2fOZMKECaY2T8tjV/pUVPqBJ8YVK1T8GVAOC51GTXHDDUa/eeFCFUbEA6xARS4A5bAwo/Sjo6NNuGrl3IDRb16ICiNSnsAT49q1xrauFR2xlUdeHngoLbpd6ZtSK/oytvLIA1yVfuCJceNG9R4TE7we1Iro1s3Y3rDBI5ewlj4xmONB9WXsSh9Xpe87jWp3YYsfk5TkdcdNWFhYhfkcy2cdbtSoESdOnPCGWQbJycZ2RXF2aontW5PwvuPG17ErfZdxdgJPjLYAUlde6fVLu3Kf+8TQhg37SQ+uAm25Adu3er/0fR/7SQ+uSj/wmqm2gX4f7MSbjv1UwPPnPXIJ20C/Ln1n7KcCuir9wBPjZZepdzclpAkoTtmF/fXQ1EBr6aNL3xn7oMuuSj/wxGh7yE6eNNcOX8Q+CHODBh65hO0h06XvjH0QZlelH3hibNVKve/ZoyZHawy++87YbtPGI5ewlj57UJOjNQZ2pY+r0g88MdomRZeWGsMcGsX69cb2jTd65BK2SdGlGMMc3mbx4sVYLBYsFgtHjx6lpKSk7POHH35oklUqWrkNV6UfeBPFv/1WreUDNQPHxML3KfLzVdarnBwVHf3nnz1ymW9Ra/lAzcDRpa/IR2W9ykFFR3dR+gE4UbxzZzXGCPDZZ86h8YOVhQuVEAFGjPDYZTqjxhgBPsM5NH6wshAlRICKSj/wxGixwP33q+1z5+Ddd001xycoLYW331bbFguMGuWxS1mA+63b5wBd+qrJbi19LEBFpR94YgQVYsI2xPH2206p3IKOOXPUmkaAoUPVahYPMgZjiONtqk7lFujMQa1pBBiKWs3iisAUY4MG8MILavvsWXjkEXPtMZOTJ2HCBLUdEQGvvebxSzYArKXPWSCIS5+TgLX0iQAqK/3AFCPA+PEqCBXAggUwY4a59phBaSkMH26Muf7xj9CihVcuPR4VhApgARCEpU8pMBxjzPWPQKWl77lgdT7Ajz+KREWpUIURESJffWW2Rd7lySeNUI2dOokUFHj18j+KSJSoUIURIhJkpS9PihGqsZOIVFH6AR6qMSXFcFwUFsKQIbB5s7k2eYtXX4XJk9X2ZZfBvHmqmepFUjAcF4XAECBISp9XgcnW7cuAeahmaqV4/vfBB3j6aaOGiIkR+fJLsy3yHKWlKjOV7X6jo0Wyskw16WkxaogYEQng0pdSUZmpbPcbLSLVLP0giCguoh7QUaOMBzQy0j9TwFXF+fMiw4YZ9xkRobIem0ypiIwS4wGNFP9MAVcV50VkmBj3GSEq63E1CRIxijjXGCAyYoRIXp7ZlrmHnTtVQh/7FsCyZWZbVUb5GgMRGSEiAVL6slNUQh/7FkANSz+IxGjjnXdEwsKMh7ZlS5Hly8226tLJzxd5/XXHzFOJiSJbtphtmUveEZEwMR7aliLix6Uv+SLyujhmnkoUkS01/6ogFKOIyLp1Ildf7VhLDhkisn+/2ZbVjCVLRJKSHO9jwACRU6fMtqxS1onI1eJYSw4Rkf3mmXRJLBGRJHG8jwEicomlH6RiFFFZjEeOVFl+bQ9yeLjIQw+J/Pyz2dZVzrJlKqOWvQjj4kSmTTM9F2N1yRGRkaKy/Noe5HAReUhEfLz0ZZmojFr2IowTkWlS7VyMrghiMdrIynLsa4HK/tu7t0h6us9k/pUzZ0Q++MAx16R9rX7ihNkWXhJZ4tjXQlT2394iki41yvzrUc6IyAfimGvSvlZ3Q+lrMYqISFGRyMcfi1xzjfOD3rSpyLPPqnyH3q51zp0TycgQuecex1yLoGr0fv1ENm3yrk0eoEhEPhaRa8T5QW8qIs+Kynfo7Tr/nIhkiMg94phrEVE1ej8RcWPppwfeesbaUFwMc+fC1KlqXWR5EhLgllugRw9ITTWiCriLggK1Gj8zE9asgawsI8CWjchIGDQInnpKJfcJIIqBucBU1LrI8iQAtwA9gFSMqALuogC1Gj8TWANkYQTYshEJDAKeQiX3cSMZWowVsWULTJ+uEo5WFNawXj0VizQlRa2hjI+HxERo1Egdi4pSEdkiItRyrqIiNXH97Fk4fFjNGT14EHbuhO3bITtb/SAAe4Fr7K/Vrh2MHAmjR8MVV3j67k1nCzAdlXC0oqCS9VCxSFNQayjjgUSgkfVYFCoiWwRqOVcRauL6WeAwas7oQWAnsB3IRv0guKIdMBIYDXio9LUYq6SkRNVUCxbAV1/B3r0ev+R/Ub/861JS6HLvvTBwoLFgOsgoQdVUC4CvUD9SFVJY6LYpf+GohdL9gIEYC6Y9iBZjjTl2TIlz/XpVm23b5hgC8VIICYGmTVUN26EDpKbSa9IkcvPy+PbbbwkN9pR2dhxDiXM9qjbbhjUEYn4+NGwIn34K/frV6DtDgKaoGrYD6oewK15Pea7F6BZOnFAxZY4fh6NHVfMzL0/1AS9cUO+xsRAWpnKA1Kun+p/x8eq9ZUvHAMPAzp076dChA//4xz8YO3asSTfmH5wAPs/MZHxaGn/++WeKmzUjD9UHvGB9j0WFz49BNWETUM3aBKAlXheeKzICL7y/GTRurF5uJDk5mSeeeIIXXniBQYMGcaUJ6Qr8hcbAqcxMEhMT+UuzZmabc8kE9hIqP+fPf/4zderU4QVb1AJNhWRmZpKWlma2GbVCi9GHiY2N5a9//SsfffQRGzyUwi0QKCwsZMOGDfTs2dNsU2qF7jP6Ab169SI3N1c7cypg7dq1pKamkp2dzTXXXFP1H/gmARg3NQCZMmUK27ZtY0YwxvGpBpmZmcTHx/uzEAHdTPUL7J05v/76q9nm+ByZmZncfPPNZptRa7QY/QTtzHFNcXFxQPQXQYvRb9DOHNds2rSJvLw8LUaNd7nnnntIS0tj3LhxlJSUmG2OT7B69WoaN25MUgBMF9Ri9DO0M8eRzMxMevbsicViMduUWqPF6GdoZ45BcXEx69evD4gmKmgx+iXamaPYsmULZ8+e1WLUmId25ihWr17NlVdeSRsPpUT3NnoGjh8T7DNz7rjjDqKjo8nIyDDbFHegZ+D4M8HszCkpKWHdunUB00QF3Uz1a4LZmfPDDz+Qm5urxajxHYLVmZOZmUmDBg1o27at2aa4DS1GPydYnTmZmZn06NGDkJDAeYQD506CmGCbmVNaWsratWsDqokKWowBQzA5c7Zt28apU6f8fmV/ebQYA4RgcuZkZmZSv359UlJSzDbFrWgxBhDB4syx9RcDbWxVizGACAZnjogEZH8RtBgDDk84c7Zu3Urfvn2Ji4sjNjaW3r17s27dOrd8d03ZsWMHv/zyS5X9xaVLl5KUlERYmP9EI9ViDEDc6czZuHEj3bp1IzY2ll27drF//36aN29OWloay5cvd4O1NSMzM5N69erRoUMHl8f37dtH//79ef755zl58qR3jaslem5qgPLss88yc+ZMfvrpp0sOgFxaWkr79u3Jyclh3759REdHA2oqWtu2bblw4QLZ2dlERka60/RKufvuuzl//jxLlixxefzee++lffv2PPPMMzRt2pQTJ05QXFxROhufQs9NDVTc4czJyspix44dDB48uEyIAKGhoQwbNozDhw+zePFid5hbLUSErKysSvuLM2fOZMKECX7VPLWhxRiguMOZs2rVKgCuv/56p2O2fStXrrx0I2vI7t27OXnyZKVitP/R8De0GAOY2jpzdu/eDcBVV13ldCwhIQGAPXv21M7IGpCZmUlMTAzXXXed167pTbQYA5zaOHNyc3MBqFvXOUdTTEwMAKdPn66VfTUhMzOT7t27Ex4e7rVrehMtxgDHUzNzbH4/bwaCqqq/6O9oMQYBl+rMiYuLA+D8+fNOx2z7bOd4mj179nDs2DEtRo1/c6nOnNatWwNw5MgRp2NHjx4F8Fq80szMTOrUqePSmRQoaDEGCZfizLHlr9i8ebPTMdu+Xr16uc/ISsjMzKRbt25ERER45XpmoMUYRNicOdOnT6/W+T179iQ5OZn58+eTn59ftr+kpIR58+aRmJhI3759PWWuA2vWrAnoJipoMQYVycnJPPnkk0ycOLFazpyQkBBmzpxJTk4Oo0eP5sSJE5w6dYpx48aRnZ3NjBkziIqK8rjd+/bt49ChQ1qMmsCips6crl27sn79es6cOUOrVq1o2rQp2dnZrF69mt///vcetlaRmZlJVFQUnTt3rvLcxYsXY7FYsFgsHD16lJKSkrLPH374oResvXT03NQgZN68eQwfPpx169bRtWtXs82pklGjRnH48OGyGUEBip6bGoz4W8wcW3KbQEeLMUipqTPHLA4dOsTBgwe1GDWBS02dOWbxzTffEBkZSZcuXcw2xeNoMQYx/hAzJzMzky5duvj1aozqosUYxMTExPh8zJxg6S+C9qZq8N1sVkeOHCExMZGvv/7aazN9TER7UzW+68xZvXo1ERERfjH84g60GDU+68zJzMykc+fOLtdTBiJajBrAN505wdRfBC1GjRV7Z85///tfs83h+PHjZGdnB5UYtQNH44CvOHPmzp3LyJEjycnJITY21jQ7vIh24GgcmTp1qk84czIzM7n++uuDRYiAbqZqytGmTRufcOYEW38RtBg1LvCmM+f06dO89NJLfP3112VxdX755Rd++umnoBOj7jNqXGJbZrV27VpuvPFGp+MlJSVu6VMWFBQQHR2NiBAaGsp1111HQkIC//73vzl8+DBNmjSp9TX8hAwtRk2FuHLm7N+/nyeffJKRI0cyaNAgt1ynXr165OXllX0ODw+nqKiI0NBQ2rdvz+9+9zt69uxJampqIPchMxCNpgJ27twp4eHh8t5778nFixflL3/5i0RERAggzz33nNuu06JFCwEqfIWHhwsgf/vb39x2TR8kXdeMmkr505/+xCeffEKdOnU4ePBg2WLk1NRUsrKy3HKNnj17VvpdYWFhXHvttWzcuNGn5s66mQz/S9Wj8RpHjhzhwIEDnDhxgpCQEEpLS8uOff/995SWlhISUnsfYGJiotP322OxWJg9e3YgCxHQ3lSNCwoLC3n33Xdp2bIlCxcuBHASyvnz58nOznbL9Ro3blxh/ozQ0FBeeeUV2rZt65Zr+TK6ZtQ4cPDgQW6++WYOHDhAZT2YkJAQvvvuO1q1alXrazZq1MjltcLCwkhKSuLZZ5+t9TX8AV0zahy4+uqr+dOf/kRISEilzcKwsDC+++47t1yzcePGLrMLiwhz5swJ2KxT5dFi1DgxduxYvvnmG2JjYyvMAFxYWMi6devccr34+HinZnBoaCjPP/88nTp1css1/AHtTdVUyL59++jTpw8HDhygqKjI6XhERATnzp2rdc21fft2UlJSyj6HhYVx9dVXs337dq9ELPcR9ERxTcW0aNGCzZs306tXL5dN1sLCQnbs2FHr6zRu3Njhc0lJCbNnzw4mIQK6maqpgtjYWBYvXswzzzzjdMxd/cbLL7+8rDkcFhbGU089Rffu3Wv9vf6GFqOmSkJDQ3nrrbeYMWMGYWFhDrWkO8RosVho0KABAAkJCbz66qu1/k5/RA9taKrNQw89RJs2bejXrx95eXkUFxc7OHGOc5zt1n8HOMBRjnKc45zkJLnkUkopeeRRTDF1qEMkkUQRRRxxXGh0AX6F7rO7M6/OPFJIIZlk6hIc8W9AO3A0l8C+ffvoc3sfsvdkYwm1cHve7WyI3sApTl36l94BJALTjF0WLCSRRCqp9KAHaaSRSGJtzfdV9KoNTfUppJCVrOQLvmDhmYX8evevsBxYB3RzPj+EEBrRiIY0pAENCCWUWGIJI4wLXKCAAi5ykRxy+Pm1nyl4ogCqWJRxLdcykIHcxV2kkFL5yf6FFqOmavayl+lMZxaz+I3fjAMlwEQIaRJCh8c70IlOtKMdbWlLK1rRmMaEVbMnVFRURFF4EYc4xE52soMdbGc761nPEY64/JuOdGQsY7mXe4khxg13aipajJqK2cAGJjGJZSxDcHxMmtGMO7mTXvTi/x34f6Q09VwttY99ZJHFMuu/c5xzOF6PeoxhDM/wDA1p6DE7PIwWo8aZzWzmRV7kS7502N+YxtzP/dzN3XSkoym25ZPPcpbzKZ+ykIUUUlh2rC51eYRHeIEXuIzLTLGvFmgxagxyyeVFXuR93qcEI4lqd7rzBE9wJ3cSju/MEz3JST7iI6YwheMcL9vfkIa8zduMZCQWLCZaWCO0GDWKpSzlAR7gJCfL9vWgBy/zMrdwi4mWVc1FLjKd6fwP/+MgyjTS+IRPuIqrTLSu2ujpcMFOEUW8wiv0o1+ZEJvQhNnMJpNMnxciQDTRPMET7GUvL/MykUQCsJrVtKMdGWSYbGH10DVjEHOa0wxgAGtYA6hxvcd5nNd53a8H23exi9GMZiMbAXVfk5jERCaabFml6JoxWDnMYVJJLRNiQxqyhCVMZrJfCxGgDW1Ywxqe4zlCCEEQXuRFHuVRh76wr6FrxiDkBCe4iZvYxz4AUkhhKUv9pW9VIxaykHu5l4tcBOBhHuYDPvBFx46uGYONM5yhD33KhNiTnmSRFZBCBLiTO1nBChqgJqLPYAYv8ZLJVrlGizHIGMUotrIVgK50ZQlLiCPOVJs8TXe6s5SlZc3v13mdz/jMZKuc0WIMIqYxjUUsAqA1rVnMYr/vH1aXLnRhPvPLpueNYQwHOGCuUeXQYgwSDnCAp3kagCiiSCedy7ncZKu8y23cVtZEPcMZHuRBky1yRIsxSJjIxDInxlu8ZeqKhxYtWvDpp5+acu2JTKQ7KorAKlaxmMWm2OEKLcYgYAtbmMtcANrRjvGMN9WeqKgoIiMjTbl2KKFMYQoh1kd/AhOcJsGbhRZjEDCNaWUP3Fu8RSjeDZP/2Wefceutt/Ljjz8CEBkZSWRkJIWFhfz973/n5ptvprCwsIpvcR8d6cgwhgGwgx1kkum1a1eGFmOAc5GLZdPBmtOc27nd6zakpaWRmppKv379eOihh8jPz2fFihWkpKSwZs0aXnjhBa8HKn6cx8u2P+Ijr167QryW8EpjCotkkWD997q8bqot+fn5MnLkSAHkiiuukKysLFPtSZEUQZBYiZViKTbVFhFJ1zVjgLOWtWXbZtSKoNKCv/nmmyQnJxMWFkabNm0YNmwYDzzwAP3792f58uWV5vXwFLbyyCOPH/nR69cvjxZjgGObLB1DjGke1G+++YZVq1bxxRdfMHPmTKKiovjd737Hjh076NmzJ2+++aZX+4w2utkF7tnABq9fvzxajAGOLX5MEkled9zYGDp0KCtWrKB9+/YAFBQUUFBQQEREBE8//TTffPONKd7VZJLLtiuKs+NNtBgDHFsAqSu50mRLDAoKCsjPzzfbDIdJDw6BtkxCBzEOcGwD/dFEm2yJwd69e802AcBhKuB5zptoiULXjAGOLTDTaU6bbInvYR902RemBmoxBji2h8w+to1G8Qu/lG3blliZiRZjgNMKleZ7D3s4wxmTrfEtvsNI2tOGNiZaotBiDHBsk6JLKS0b5tAo1rO+bPtGbjTREoUWY4DTgx5l2+mkm2iJb5FPftnazmY084mEOlqMAU5nOpNEEgCf8ZlTaPxgZSELySEHgBGMMNkahRZjgGPBwv3cD8A5zvEu75prkA9QSilv8zagymcUo0y2SKHFGASMYUzZEMfbvO3gRQxG5jCHLWwBYChDaU5zky1SaDEGAQ1owAu8AMBZzvIIj5hskXmc5CQTmABABBG8xmsmW2SgxRgkjGc8rWkNwAIWMIMZJlvkfUopZTjDy8Zc/8gfaUELk60y0GIMEmxBqKKIApQ4l7PcZKu8y9M8zUpWAtCJTrzKqyZb5IgWYxCRQkqZ46KQQoYwhM1sNtkq7/AqrzKZyYCaIjiPeUQQYa5R5dBiDDIe47GykI1nOUsaaXzFVyZb5TkE4RVe4WVeBtSE+UUs4hquMdkyZ7QYg5D/5X/L3PnnOMcABjCHOSZb5X4ucIHhDOcv/AVQDpt5zCOVVJMtc40WYxBiwcIsZpXVFgUUMIpRjGRkwEwK2MUuutK1LERlDDEsYhH96W+yZRWjxRikWLDwCq/wDu+Uhbz/hE+4jutYwQqTrbt0CijgDd6gE53YxjYAEklkDWu4jdtMtq5ytBiDnCd5kkwyuZqrAcgmm1u5lbu52+dyUVTFUpbSnvYO0dMHMICtbKUDHcw1rhpoMWroRje2sIWRjCzLW5hBBkkk8TAPs5/9JltYOV/yJTdyI33pyx72ABBHHNOYxhd84RNrFauDTpaqcWANaxjHuLImHkAIIdzCLfyBPzCQgaYFtrLnLGeZxzymMa0sxZ2NIQxhClNoRCNzjLs0MrQYNU4UU8ynfMprvMZeHOPVNKUpQxjCIAZxAzd4NQPwec6zjGV8zuf8h/84xK2xYOEO7uBlXqYTnbxmkxvRYtRUTDHFzGUuU5nKt3zrdDyBBG7hFnrQg1RSy6IKuIsCCviO78gkkzWsIYussr6gjUgiGcQgnuIpfxWhDS1GTfXYwhamM535zK8wrGE96pFMMimkkEQS8cSTSCKNaEQ96hFFFHWpSwQRnOMcRRRx1vrvMIc5yUkOcpCd7GQ728kmm2KKXV6rHe0YyUhGM5oruMKTt+4ttBg1NaOEEjLJZAEL+IqvnJqxniKccDrTmX70YyADyxZMBxBajJracYxjZJLJetazne1sY5tDCEQndgOLgOcqPiWEEJrSlBRS6EAHUkmlK10DPeW5FqPG/ZzgBD/zM8c5zlGOcpKT5JFHAQXsSt/FmqFreEAeIIwwYoihHvVIIIF44kkggZa0DHThuSJDRxTXuJ3G1n+uSCedNaxhJjO9bJXvowf9NRofQYtRo/ERtBg1Gh9Bi1Gj8RG0GDUaH0GLUaPxEbQYNRofQYtRo/ERtBg1Gh9Bi1Gj8RG0GDUaH0GLUaPxEbQYNRofQYtRo/ERtBg1Gh9Bi1Gj8RG0GDUaH0GLUaPxEbQYNRofQYtRo/ERtBg1Gh9Bi1Gj8RG0GDU+ydatW+nbty9xcXHExsbSu3dv1q1bZ7ZZHkWLUeNzbNy4kW7duhEbG8uuXbvYv38/zZs3Jy0tjeXLl5ttnsfQEcU1XiU9PZ2hQ4dS0WNXWlpK+/btycnJYd++fURHRwNQUlJC27ZtuXDhAtnZ2URGRnrTbG+QoWtGjU+RlZXFjh07GDx4cJkQAUJDQxk2bBiHDx9m8eLFJlroObQYNT7FqlWrALj++uudjtn2rVy50qs2eQstRo1PsXv3bgCuuuoqp2MJCQkA7Nmzx6s2eQstRo1PkZubC0Ddus5ZqGJiYgA4ffq0N03yGlqMGr/B5vSxWCwmW+IZtBg1PkVcXBwA58+fdzpm22c7J9DQYtT4FK1btwbgyJEjTseOHj0KQFJSwKUQB7QYNT7GzTffDMDmzZudjtn29erVy6s2eQstRo1P0bNnT5KTk5k/fz75+fll+0tKSpg3bx6JiYn07dvXRAs9hxajxqcICQlh5syZ5OTkMHr0aE6cOMGpU6cYN24c2dnZzJgxg6ioKLPN9AhajBqfo2vXrqxfv54zZ87QqlUrmjZtSnZ2NqtXr+b3v/+92eZ5jDCzDdBoXNGxY0eWLl1qthleRdeMGo2PoMWo0fgIWowajY+gxajR+AhajBqNj6DFqNH4CFqMGo2PoMWo0fgIWowajY+gxajR+AhajBqNj6DFqNH4CFqMGo2PoMWo0fgIegmVxmMcPXqUlJQUioqKHPbXqVOH2NjYss8Wi4Ubb7yRr776ytsm+hRajBqPkZCQwDXXXMOmTZsqzK0BSox9+vTxomW+iW6majzKyJEjCQmp+jEbMmSIF6zxbbQYNR5l6NChlR4PCQmhR48eZaH7gxktRo1HufLKK0lLSyM0NNTlcYvFwogRI7xslW+ixajxOCNGjKiwz2ixWLjrrru8bJFvosWo8Th33XUXYWHOvsKwsDD69OlDgwYNTLDK99Bi1HiGUuA4sA3qZdejb5e+hIU6CrKkpIT7ut4Hm4Fs4KwJdvoQOo245tIpAHYC24DtwD6UAA8BJ4Fi49TP+ZwhDEEwHrdoovmN36hDHePEukAi0Bi4CmgDtANSgKZAYCagAsjQ44ya6nMAWA18A3wL7MVBcJXRl77UoQ7nUZmkwglnEIMchQhwHthtfZUnFiXMm4CeQA/rvgBB14yairkIfAn8GyXAg1WcHwo0AhKAeFQNdyUQBdSB++fez9zv5lJYXAjA0seW0qdZHygEzgFHUDXrEeAYUFVO1FCgE3ALMAhwzjzuT2RoMWocuQAsAeYDS1EiccXVQAdUTdXe+p5EpXO6li9fXhaev379+vz666+Eh4dX/AdngR2oZrCtKfw9Ffctm6JEORjogr81abUYNVaygZnADCDHxfF4VPOwN/A7oFnNL1FcXEyjRo3IycnhkUce4b333qv5l5SgmrDrgK+tL1c1aBLwAPAw4B/OWi3GoEaARcBUYJX1sz3XomqZQShHSkWUAPtRNdcB4Chwwu69ADgDlMLjZx5nSukUsqKySI1OVU3YaKA+0ATluEmwbicBbYGGlVy72Gr758AXwK/ljscA9wFPAK0r+R7z0WIMWv4D/BnYWm5/IvAH4B7gGhd/JygP6hpU7bQd2IUSXDVYz3ru4R4OcICQ6o6sXY4S5XVAKtAd1TctTwmQCcwBPgPy7Y6FAvei7tnVfZmPFmPQsQJ4EeUNtWEBegGPAv1RD649J1FOnCXAWuBUNa9lq+3qAPXU90qsMP3QdMY0HqMEfBElmt+s18mv8NscaQWkAQNQDpzIcsd/Az4C3kfV2jbCgJHAK6gfHt9BizFoOA48CaTb7bOgmqAvoxww9hwDPgUWAhtQg/iuSMQYC2yDago2QfUxo13/iYhgsVTgXcmx2noY5bzZhVH7VuS4iQVus97LnTgKsxTljPoLqka3EWPd9zi+spBQizHgEeAT4I84OmZ6A/+DavrZKEF5UD+0vpcfQwxB9SNTUc6cm1Ci8walKHFmoZrHWag+aXkuB0agHDfJ5f7+c+Al4Ce7/e2BD4Cu7je5hmgxBjTHgeGoMUIbbVFNt5vs9l1ECfCvqNkz9kShmrADUE1YV301s9iCckAtwrnvC6r5+gLKfhvFwBRU39E2bBOKarq/hHMT3XtoMQYs36CEeNz6ORr4E/A8RjPuPPAe8DdUf82eG1G1yxBUk87X2QfMsr6OlTt2IzAR6Gu37xgwAdVqsJEG/Avv1faOaDEGHAK8an3Z+nmdgblAC7tzPgOeRc12sVEHGA2MxbkP6S8Uo5rYU1BjkPb0Av6BY/M1A/Wjc8b6uTGqX53qWTNdoMUYUJSgPKLT7fb9AfVgRlg/bwfGo4YAbMRa/+4pKh/T8zc2Aq8DizHGUMNR9/8KysMLaprfUOv5oFoO/0SNsXqPDL2EKlDIRz08NiHGAAtQzokI1MP4N9T8TZsQw1CD4QeAtwgsIYKaEvdvYBNGH7kIeAc1le+/1n1Xo8pkjPVzATAMNTTiRbQYA4EC4A7UMATAFcBKwLaA/ihwK/AMxuD8zSgHyGT8ZbrYpXMdyvv6T9SwC6ixxx6o4Y1iVG34PjDJerwYeAg1O8lL6GaqvyPAKAxHRBPUSosU6+dNQD/UtDRQ6wXfQfWTgpGzqGaqvePmNlQ/0bYc62NU+RSjqqvP8EaTVTdT/Z5nMB6sBGA9hhC/RLn3bUK8HrWqPliFCKqfOAfluLG1CL4EumEM69yPaqJaUE6wEajpfx5Gi9GfmQH83bpdH+VFvNr6eRaq6Zpn/TwKNVjeypsG+jCDUQ6bJOvn7ag5r/usn0cAb1q381Eze8qPwboZLUZ/ZS/K+wnKQ5iBmk0Cqu/4B5R31YKa7jYLw6OqUVyDcuL0tH4+gupL20T3HGq6HKjZS8NRZeohtBj9kWLUsiDbDJK3UWsMAb5CuemLUUJ8D+XG96+Ftt6jAarMbNkFDlu3bZPh/4aaNABqkvxfPWeKFqM/8ibGmFgvjF/vw6hlQoXWz2+hBvA1lROJmrfaw/p5J6qZKqjhn08wnDt/RjVpPYAWo79xElUTAlyG8vyFoMbPhmBMBn8WNf1NUz2iUWOStplHyzBqwRbAu9btQtSUQg+gxehvvIrRPP0zKpwhqH6hrbbsgeF80FSf+qi+t20u7kSU9xnUNMFu1u3FqCh5bkaPM/oTP6PWDBaigi/tRjWx9qFWYxSg+kBbgP9njokBwTzUDBxQ/cV1qD53JmoyOagZPe4d7tDjjH7FBxj9wb9grL54GmNmzd/QQqwt96AmAoDytmZYt3tiOHrWon703IgWo79QglreA2oOqe2XeyNqPR+oaV8jvWxXoPI3jAgAL2CsgHnS7pzZ7r2kFqO/8BXGcqcRqLFFUPMpbbyNR/5HO3TogMViqfbrtddeIyYmxmn/X//qPC5w5MgRl9+xcOFCh/NefPFFp3N273YVdtxNJKP6iaC6ASus270xWh7/pNqBuKqFaPyD+0UE6+tH675cEalr3ddKREo9c+lrr71WMjIyHPaNGTNGAFm2bJnD/qFDh8qkSZNERGTLli0CyIABA6q8xty5cwWQ5557rtLzevbsKTNmzKjZDVwqP4hR5oPs9k+027/UbVdL1zWjv7DO+t4MY+7pArCmrlDzTfXAvntpj1qYDWrYw7YAub/dOevddznfiIulqZzfUNPfwHCvg1oWZKPybN21YuvWrdU+d968eZ4zxAyGAt+hxnHXoxw4HVHjkhcx1kS6AV0z+gP/xVip3sVuv8213gxjvFHjXuzDb9haJ+EYUfW+xW3zVbUY/YGf7bY7WN9PYaww6O5Va4KLjqg1oGBMqgDj/yEP+MU9l9Ji9AfsI3jbQmOcsNvnm+HqA4NwjGVp9mV+pd22q0RBl4AWoz9gL0bbgtjf7PZd4UVbghFb+VZU5tVNd1AFWoz+wBm77Tjre67dvsu8ZonHCA1V0YNLSirvgJWUlJSd6zVsP4D2NaB9mVeV1LWaaDH6A/aZti9Y3+va7TuP3xMTo2Znnz1bUUINRW5uLvXq1av0HLdjm5gf42IfOP5f1AItRn/gcrvtUy722Tef/JSkJBX/YseOHRWeU1BQwN69e2nZsqW3zFLYcj5W1DS1/7+oBVqM/oB9KEXbQ2D/YBzHbwkLC2P37t20aNGC1q1bs2HDBrKzs12em56ezpVXXkm7dl4Od24rXy1GjUPuB9tzehWGSDd41xxP8c477xASEkKfPn1YsGABOTk5lJSUcOzYMd577z3Gjx/P3//+d0JCvPjY7sMYukix22/7fwjD0bNaG9w2s07jOX4SYy7keLv9d1j3hYnIWe+YMmvWLEFNQXB45eXlOZxXt25dl+e5eu3atavs7zZv3iz33XefNG3aVCIjIyUiIkKuuuoqGTJkiKxbt847N2nPLDHK/hO7/Y2s+zq67UrpenGxPyCo8cXfgE6owMSg8itOsG7PRyUL1biXuzHWM+5HLereC9i6rY8C/+eWK+nFxX6BBSOZ548YDpu7MCaHf+hto4KA31ATxEEliW1q3V5pd44bk6xqMfoLt1vfizAWGSdhxPxcjkpgo3EfszDWK9pH2bMtKg7DCJHpBrQY/YV7USsFwHGFuS1UfykqKJXGPZzFiA4Xgyp/gD0YDrO+qHyObkKL0V+oj7GO7nvUagFQfZq21u1PUMt9NLXndQwv6pMYuRzfx1hBc797L6kdOP7E1xjNot4YoSAWozJNgerDrEGvVK0NO1BJgvJRNd8eVBDjI6iuwUVUtq8DGOFPao924PgVvVFZpUAJ05Ym+w4MkW4AXvSyXYHEeVRrI9/6+XWMaOKvoIQIKmat+4QI6JrR/9iAWu0vqDV136IeisOotXenUJ2PxRhhBTXV536MPnl/VBIhC/ADqrYsRg1r7MDdYtQ1o9/RFZWeDGArKsI4QCIq76Atp+AQjJXpmurxZwwhJmLkaMxHJRoqth57DbfXiqAdOP7JFIz5kG+gIl2DGv6wTQI4j/pl91CSloDj7xgpxOugMhnbyngCRjn2Qf3QeQAtRn8kAZhm3S5Fxfe0ef5eR+WiB7X+rheO4SI0zryJygANRq5L22D+QuAf1u1GqJrTQ1H4tBj9lSEY0cP3o8a8zqEelA9QIepBibQnKn+ExpFi1HS2F1B98BBUU982weI7VPNUUOX6Ie6bFO4CLUZ/ZhpGIs9NGElSbQ/VA9ZjBaisu69g9HuCnWPArRgtjGhU09T2I7YP5aW2Ldz+i/WzB9Fi9GfqoJpRLayfl6JmihSgmlszgcmo/+VS1APVHSMGa7CyEBWg+Bvr58tR0wltE+13o4aQbE3/h4GXPG+WFqO/0xCVh6OR9XMGyslgi17xBKqJWt/6+VvUyo//I/hqyZOooYu7MBYHX49qjt5k/bwJld/ykPXz7ahU7F5AizEQaIGaANDE+vkblOPGFlpwCGq1hy1N9llgPGqx7FfeM9M0ilCZh1thDF1YUOnX16GCQIPKVnwzRpiNAailaV6azaTFGCi0Q4Wfb2X9vAnVFFtu/fz/gFUob6stwNVuVB7CfgSmx7UItfKiLWp+qS3K3jWoZVDvAhEoB83/oMrBFmhqJEqI0XgNLcZA4mpU/g1bspZfUc2sV1F9xlCU53AXjmNli1Gu/N+hBOvvc7LOo5qWLVFOLFuIjBjUMMZ2VA0IqvXQGzWWWIKqMZ8HPsbr83v1dLhApAB4Cse+TnfUigP7WE7foPLWl0/ekoQaqxyFEcHcH9iEGn6Yi9FnBlX7jUQ5sGxNeUHlV3wGw1FTHzXrZqA3jHUiQ4sxkPkCVTPkWj+HocbVXscxBuhK1BSv1eX+PgLl/r8TNZvHg2Nsl8wPqMzNn6P6xfZEAQ8Cf8IxtfpeVDmssNvXETW0YV6qBC3GgGcf8AdU89NGU1QtMRzVdLWxETVhIB3nwMihqAnqt6IyM92AV/tTZZwA1qKa44tREx7K0wz1I/QQjot/f0X1DadirOAPB55GjcFGesTi6qLFGDRkAI+h3Ps2mqH6Sg/iKMqzqNAes1FDIaU4E4EaFrge5SBpi0q97a5UAwIcBHaiVkhsRzmoKhojjUENyj+A8iTbe0NyUFPa3sGx+XoTatDfy2FYK0CLMag4jVrrOAPlabSRjBrquA9j7Z6N46igTAtRfcyqctg3RMV5TUCNfV6FCn9fFyVg2/t5oBDlvSxC/Uj8Ahy1bh+i6rQFDVHN5wEoJ0xUuePZKLF9hGO+kiaoSeGj8aVsz1qMQcl+lIf1nzgO/NcDRqCCL7mqLS6gQn6sQzUV1+G2pC/VIh5Vm3W3vnfEeTygGNV8nYbqE9o/3Q1RLYGxmNPErhwtxqDmJ5QzJx3nGi8FGGx9JVfw96UoYe/EaE7+jKpNj2Gslq8Jl6FqriaoMdO2QBvUj0NFYfSLUH3i+SinVfkUbU1QA/zjcVuSGg+gxahBNQ9nopw3B10cT0aNV/ZEOW/quzjHFadRwryI0Sy1vcegnCe29waomq98U7Mifkat4/wGWIJzwlILkIbymt6JP8QE0mLU2FGCmmw+F9XUy3NxTiiqeZiKCvvRDlV7edITeQo1hLEdNZa4GhVmxBXNUbX5/aga1X/QYtRUQD7wJarptwTH5KzlCUPNdmmNCldha2ZehRqbrIPqo0VZtyMxHDdnUT8Ctlr0mPV1BCW4bVSdZaslasXFYNQkeP9Ei1FTDUpQ81jXoSakr8RteewvCZsjpzdqCl+zyk/3E7QYNZdACSqW6LZyr4PWY+6iDqq2TUE1h9tbt+Mr+yO/RYtR40ZKUGOER1BNy8Oo5u05lLf2AsqZk48aRgkF4lDDE3GoccnGqOZtExyTxAY+Gb7vY9L4D6EY/UVNjdFLqDQaH0GLUaPxEcIw8rJqNBrz2PD/AbetQncRG8WFAAAAAElFTkSuQmCC",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGBA size=227x423 at 0x7FF17C8E64F0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "file = Image.open(circuit.draw())\n",
    "file.show()\n",
    "file.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46753da7",
   "metadata": {},
   "source": [
    "### Finally, let's make homomorphic inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c0b246f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "homomorphic_predictions = []\n",
    "for x_i in (int(x_i[0]) for x_i in x_q):\n",
    "    inference = QuantizedArray(circuit.run(x_i), y_q.parameters)\n",
    "    homomorphic_predictions.append(inference.dequantize())\n",
    "homomorphic_predictions = np.array(homomorphic_predictions, dtype=np.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68f67b3f",
   "metadata": {},
   "source": [
    "### And visualize it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "92c7f2f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax.plot(inputs, homomorphic_predictions, color=\"green\")\n",
    "display(fig)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c18dbdd1",
   "metadata": {},
   "source": [
    "### Enjoy!"
   ]
  }
 ],
 "metadata": {
  "execution": {
   "timeout": 10800
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}