From c48b05c0e043366b4dfb69880a0044944228e3cf Mon Sep 17 00:00:00 2001 From: Alfredo Canziani Date: Wed, 30 Oct 2019 01:50:18 -0400 Subject: [PATCH] Add new logic neuron programming --- 00-logic_neuron_programming.ipynb | 442 ++++++++++++++++++++++++++++++ res/adder_circuit.png | Bin 0 -> 129069 bytes res/half-adder_circuit.png | Bin 0 -> 121031 bytes res/x-or_circuit.png | Bin 0 -> 70596 bytes slides/00 - Logic neurons.pdf | Bin 0 -> 554712 bytes 5 files changed, 442 insertions(+) create mode 100644 00-logic_neuron_programming.ipynb create mode 100644 res/adder_circuit.png create mode 100644 res/half-adder_circuit.png create mode 100644 res/x-or_circuit.png create mode 100644 slides/00 - Logic neurons.pdf diff --git a/00-logic_neuron_programming.ipynb b/00-logic_neuron_programming.ipynb new file mode 100644 index 000000000..47aa911e1 --- /dev/null +++ b/00-logic_neuron_programming.ipynb @@ -0,0 +1,442 @@ +{ + "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": null, + "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": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Test mul() function\n", + "mul(my_x, my_w)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "source": [ + "# Define a scalar: bias b\n", + "my_b = -5" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Test linear_neuron() function\n", + "linear_neuron(my_x, my_w, my_b)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "source": [ + "# Import exp() function (safe on lists)\n", + "from numpy import exp" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Logistic sigmoid\n", + "def sigmoid(z):\n", + " \"\"\"\n", + " return the logistic sigmoid (use exp())\n", + " \"\"\"\n", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Try out σ() for different z values\n", + "for z in (-5, 0, 5): print(sigmoid(z))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "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": null, + "metadata": {}, + "outputs": [], + "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": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Full neuron function\n", + "def neuron(x, weights, bias):\n", + " \"\"\"\n", + " Return a classical neuron output (reuse code above)\n", + " \"\"\"\n", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Test neuron() function\n", + "neuron(my_x, my_w, my_b)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "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": null, + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "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": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "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": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "lines_to_next_cell": 1 + }, + "outputs": [], + "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": null, + "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", + " pass # ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Checking XOR neuron output')\n", + "for my_x in my_x_collection:\n", + " print(my_x, f'{xor_neuron(my_x):.3f}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Half-adder](res/half-adder_circuit.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Combine a XOR and an AND into a half-adder\n", + "# ⬅️✏️" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "![Adder](res/adder_circuit.png)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# Combine two half-adders and an OR into a (full) adder\n", + "# ⬅️✏️" + ] + }, + { + "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": "3.7.4" + } + }, + "nbformat": 4, + 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