00-logic_neuron_programming.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code your own neuron and neural net\n",
    "The parts of code that look like\n",
    "```python\n",
    "pass  # ⬅️✏️\n",
    "```\n",
    "need to be filled in before moving to the next cell.\n",
    "\n",
    "Check out the slides and / or corresponding video lecture for more instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Define two vectors (lists): input my_x, weights my_w\n",
    "my_x = [0, 1, 1]\n",
    "my_w = [-10, 10, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multiply two lists element wise\n",
    "def mul(a, b):\n",
    "    \"\"\"\n",
    "    return a list c, same length as a, element c[i] = a[i] * b[i]\n",
    "    \"len(list)\" and \"[0] * n\" may be useful\n",
    "    \"\"\"\n",
    "    \n",
    "    n = len(a)\n",
    "    c = [0] * n\n",
    "    \n",
    "    if n == len(b):\n",
    "        c = [a[i] * b[i] for i in range(n)]\n",
    "            \n",
    "    return c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 10, 5]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test mul() function\n",
    "mul(my_x, my_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Define a scalar: bias b\n",
    "my_b = -5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Neuron linear (internal) potential\n",
    "def linear_neuron(x, weights, bias):\n",
    "    \"\"\"\n",
    "    return a scalar value representing a scalar neuron\n",
    "    \"sum(list)\" computes the sum of the elements in a list\n",
    "    \"\"\"\n",
    "    \n",
    "    return sum(mul(x, weights)) + bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test linear_neuron() function\n",
    "linear_neuron(my_x, my_w, my_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Import exp() function (safe on lists)\n",
    "from numpy import exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Logistic sigmoid\n",
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    return the logistic sigmoid (use exp())\n",
    "    \"\"\"\n",
    "    return 1 / (1 + exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0066928509242848554\n",
      "0.5\n",
      "0.9933071490757153\n"
     ]
    }
   ],
   "source": [
    "# Try out σ() for different z values\n",
    "for z in (-5, 0, 5): print(sigmoid(z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import some plotting stuff to graph sigmoid()\n",
    "from numpy import linspace\n",
    "from matplotlib.pyplot import plot, axhline, axvline, grid, style\n",
    "style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get a pair of axis and grid lines centred in (0, 0)\n",
    "axhline(c='.2'); axvline(color='.2')\n",
    "grid(c='.1', ls='--')\n",
    "\n",
    "# Plot across a span of numbers\n",
    "z = linspace(-7.5, 7.5)\n",
    "plot(z, sigmoid(z));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Full neuron function\n",
    "def neuron(x, weights, bias):\n",
    "    \"\"\"\n",
    "    Return a classical neuron output (reuse code above)\n",
    "    \"\"\"\n",
    "    return sigmoid(linear_neuron(x, weights, bias))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999546021312976"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test neuron() function\n",
    "neuron(my_x, my_w, my_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Package OR neuron weights and bias\n",
    "def or_neuron(x):\n",
    "    \"\"\"\n",
    "    Return x1 OR x2 (x1 + x2)\n",
    "    \"\"\"\n",
    "    return x[0] or x[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defina a collection of inputs to test OR and AND\n",
    "my_x_collection = [\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1],\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking OR neuron output\n",
      "[0, 0] 0.000\n",
      "[0, 1] 1.000\n",
      "[1, 0] 1.000\n",
      "[1, 1] 1.000\n"
     ]
    }
   ],
   "source": [
    "print('Checking OR neuron output')\n",
    "for my_x in my_x_collection:\n",
    "    print(my_x, f'{or_neuron(my_x):.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Package AND neuron weights and bias\n",
    "def and_neuron(x):\n",
    "    \"\"\"\n",
    "    Return x1 AND x2 (x1 * x2)\n",
    "    \"\"\"\n",
    "    return x[0] and x[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking AND neuron output\n",
      "[0, 0] 0.000\n",
      "[0, 1] 0.000\n",
      "[1, 0] 0.000\n",
      "[1, 1] 1.000\n"
     ]
    }
   ],
   "source": [
    "print('Checking AND neuron output')\n",
    "for my_x in my_x_collection:\n",
    "    print(my_x, f'{and_neuron(my_x):.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [],
   "source": [
    "# Package NOT neuron weight and bias\n",
    "def not_neuron(x):\n",
    "    \"\"\"\n",
    "    Return NOT x1 (x1_)\n",
    "    \"\"\"\n",
    "    return not x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "lines_to_next_cell": 1
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Checking NOT neuron output\n",
      "[0] 1.000\n",
      "[1] 0.000\n"
     ]
    }
   ],
   "source": [
    "print('Checking NOT neuron output')\n",
    "for my_x in [[0], [1]]:\n",
    "    print(my_x, f'{not_neuron(my_x):.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![X-OR](res/x-or_circuit.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Combine OR, AND, and NOT into a XOR neuron\n",
    "def xor_neuron(x):\n",
    "    \"\"\"\n",
    "    Return x1_ * x2 + x1 * x2_\n",
    "    \"\"\"\n",
    "    return (not x[0])*x[1] + x[0]*(not x[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "encoding": "# -*- coding: utf-8 -*-"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}