{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution for Exercise 5 (Hopfield Network)\n", "\n", "https://neuronaldynamics-exercises.readthedocs.io/en/latest/exercises/hopfield-network.html" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# start with importing the libraries we need\n", "\n", "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from neurodynex3.hopfield_network import pattern_tools, plot_tools, network" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting started" ] }, { "cell_type": "code", "execution_count": 476, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
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\n", 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+sH4eOPGt/IJ/9iUwn/yfAV6VZF27muZVwGeSrEmyHiDJs4DfY/T7fj63yBj8mV4HfK7t673Ale1qlE3AZuCrI857skXnTzKW6X9zgXb0uJnpLyaXyzC3J5nxMzSinLNZdP6We22bXg+8Erh/JCmX81vmUT+YPp+4D3gI+CxwdhufAP5hYLl/B44BP2L6fNklbfxzwL1MF8s/Ac9bRdkvYLpgpoB/Btaeofv+j1rGKeANbey5wH7gHuAA8Lcsw9UnwOXAfzN91PTWNvYO4Pfb9HPavpxq+/aCgXXf2tZ7ELhshT7vi8oP/EHbz3cDdwGvOQOz/2r7fP8P039bOnC6z9BqyQ/8euuYr7fna0aV0d9QlaQO9XZaRpKE5S5JXbLcJalDlrskdchyl6QOWe6S1CHLXZI6ZLlLUof+D4Xk5cI0Ik23AAAAAElFTkSuQmCC\n", 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zmnWbU7y9aygiXoiIC4FTJe1TGt8NEXFFCvj/QTEPt0cXxjlm6xIR9wMnAD8AHqeYq78XWFpuJ+lDwH8HDo+IlV0eL1Rfo3aM6HnWBa7JUFnUpF8Cf0TS2621w9w+3mDXRcA+pePsBEwAHmyx642AndL9uynm6MaMquoSERdHxN4RsQ3wDWA6MK+0/2HAz4AZEXFPdx5dd3RQo3YsAnaSVH6HtA+jM7XVMddkqH6rSb9M6YxIers1klfmC4CbJb0XuB04HbikZg4NAEkHUtTxNmAcxVzfdsCtqckvgVNUfI3q2rR9JXDfCMbVFVXUBUDS/sCdwNbAD4HBdOaPpL9Ix/twRNw2grGMqg5qRJraG5cWJ0jaJCJeqNPHg5LuBL4h6R+Aw4G30/o3NyrlmgzVbzXZoM/wRyoiFlF8nfACYDnFHPXn129PH8B+LS1OoAizVcAy4APAERHxWDrWA8AngJ8ATwMzgSO7MH9fuTbrAvDPwGrgAYrH/tnStv8CbAHMKZ0NXTG6j6Ay6yjehgPcn5YBkPQTST8ptT2G4vOLp4EzgI9ExIqqBloh12Soymui9BUfMzPbwPkM38wsE10JfEnnSFouaWGD7ZL0vyQtlnS3pHd0o18zM2tdt87wzwUOG2b74cCu6TYL+HGX+jUzsxZ1JfAj4jrgqWGazATOj8ItwJaSJnejbzMza01VX8ucAjxaWl6a1j1ebiRpFsU7ACZOnLj/7rvvXtHwemfBggUrI2LYiyDlVpdOanLPstofJDb2tilbdDDK6jWri2tSX7265FqTrn1LR8XlPWdHxJBrpUiaDZwRETek5WuAv4+I+Y2ONzAwEPPnN9y8wZC0ICIGWm2fQ106qcn0U3/bcj9Lzjii/cH1UDt1cU3qW1+XXGtS1bd0lgHTSstT0zozM6tIVYE/CPyn9G2dA4FnIuLxZjuZmVn3dGUOX9KFwMHAtpKWUlw3ZSOAiPgJMIfiF6iLKf7TjE91o9+cbchvSc1sdHQl8CPi2CbbA/jP3ejLzMxGxr+0NTPLhAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0x0JfAlHSbpAUmLJZ1aZ/snJa2QdGe6ndiNfs3MrHUd/wcoksYBPwQOBZYC8yQNRsS9NU0vioiTOu3PzMxGphtn+AcAiyPi4Yh4CfgVMLMLxzUzsy7qRuBPAR4tLS9N62odLeluSRdLmtaFfs3MrA1VfWh7OTA9It4OXAWcV6+RpFmS5kuav2LFioqGNva5LkO5JkO5JvW5Lq/rRuAvA8pn7FPTutdExKqIeDEt/hzYv96BIuKsiBiIiIFJkyZ1YWgbBtdlKNdkKNekPtfldd0I/HnArpJ2lLQxcAwwWG4gaXJp8Ujgvi70a2Zmbej4WzoR8Yqkk4ArgXHAORGxSNLpwPyIGAS+IOlI4BXgKeCTnfZrIzP91N+23HbJGUeM4kjMrGodBz5ARMwB5tSsO610/6vAV7vRl5mZjYx/aWtmlgkHvplZJroypTPaPO9so8nPr/pcl6H6vSY+wzczy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsE31xaYWq9fvPp21s8/NrKNekvm7XxWf4ZmaZcOCbmWWiK4Ev6TBJD0haLOnUOtsnSLoobb9V0vRu9GtmZq3reA5f0jjgh8ChwFJgnqTBiLi31OwzwNMRsYukY4DvAh/rtO9mPC/YPSOtpf8OzMaObpzhHwAsjoiHI+Il4FfAzJo2M4Hz0v2LgUMkqQt9m5lZixQRnR1A+ghwWEScmJaPB94VESeV2ixMbZam5d+nNitrjjULmAWwww477P/II490NLaqjeRsVtKCiBgYrm2/16Vd/VKTqt+9NKtLv9UEOq+LnytDDVeTMfWhbUScFREDETEwadKkXg9nzHBdhnJNhnJN6nNdXteN7+EvA6aVlqemdfXaLJU0HtgCWNWFvscUz0HnxX/fQ7km9Y2VunTjDH8esKukHSVtDBwDDNa0GQROSPc/Avx7dDqXZGZmben4DD8iXpF0EnAlMA44JyIWSTodmB8Rg8DZwC8kLQaeonhRMDOzCnXl0goRMQeYU7PutNL9F4CPdqMvMzMbmTH1oa2ZmY0eB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5lloqPAl7S1pKskPZT+3KpBuz9KujPdav/7QzMzq0CnZ/inAtdExK7ANWm5nnURsW+6Hdlhn2ZmNgKdBv5M4Lx0/zzgQx0ez8zMRkmngb9dRDye7j8BbNeg3SaS5ku6RdKHGh1M0qzUbv6KFSs6HNqGw3UZyjUZyjWpz3V5XdPAl3S1pIV1bjPL7SIigGhwmLdExABwHPBPknau1ygizoqIgYgYmDRpUruPZYPlugzlmgzlmtTnurxufLMGEfH+RtskPSlpckQ8LmkysLzBMZalPx+WNBfYD/j9yIZsZmYj0emUziBwQrp/AnBZbQNJW0makO5vC7wbuLfDfs3MrE2dBv4ZwKGSHgLen5aRNCDp56nNHsB8SXcB1wJnRIQD38ysYk2ndIYTEauAQ+qsnw+cmO7fBLytk37MzKxz/qWtmVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZaKjwJf0UUmLJL0qaWCYdodJekDSYkmndtKnmZmNTKdn+AuBo4DrGjWQNA74IXA4sCdwrKQ9O+zXzMza1On/eHUfgKThmh0ALI6Ih1PbXwEz8f9ra2ZWqSrm8KcAj5aWl6Z1ZmZWoaZn+JKuBt5cZ9PXI+Kybg5G0ixgVlpcK+mBJrtsC6xss5uR7DOa+72l2QHarEuVj881qXa/YevimtRXQV36pyYR0fENmAsMNNj2p8CVpeWvAl/tUr/zq9inF/tVWZN+qWU/1KRf6tIvj60fniv9VJMqpnTmAbtK2lHSxsAxwGAF/ZqZWUmnX8v8sKSlFGfxv5V0ZVq/vaQ5ABHxCnAScCVwH/CvEbGos2GbmVm7Ov2WzqXApXXWPwZ8oLQ8B5jTSV8NnFXRPr3Yb6SqHKdrMjb2q7KvftlvpPrh38GIa6I0J2RmZhs4X1rBzCwTfRn4I7lUg6RzJC2XtLDNvqZJulbSvekyEie3uN8mkm6TdFfa71vt9Gtm1m19N6WTLtXwIHAoxY+45gHHRsSwv9yVdBCwFjg/IvZuo7/JwOSIuF3SZsAC4EMt9CdgYkSslbQRcANwckTc0mrfZmbd1I9n+K9dqiEiXgLWX6phWBFxHfBUu51FxOMRcXu6v4bim0ZNfykchbVpcaN0669XVzPboPRj4PfsUg2SpgP7Abe22H6cpDuB5cBVEdHSfmZmo6EfA78nJG0K/Br4YkQ828o+EfHHiNgXmAocIKnlqSQzs27rx8BfBkwrLU9N60ZNmoP/NXBBRFzS7v4RsRq4Fjisy0MzM2tZPwZ+pZdqSB++ng3cFxH/2MZ+kyRtme6/keJD5vtHZZBmZi3ou8Af6aUaJF0I3Ay8VdJSSZ9psct3A8cDfyHpznT7QLOdgMnAtZLupniRuioiZrfYp5lZ1/Xd1zLNzGxk+u4M38zMRsaBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZpn4f4TAAHdXeTU0AAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 1. -1. 1. -1. 1. -1. 1. -1. 1. -1. 1. -1. 1. -1. 1. -1. 1. -1.\n", " 1. -1. 1. -1. 1. -1. 1.]\n" ] } ], "source": [ "pattern_size = 5\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "# instantiate a pattern factory\n", "factory = pattern_tools.PatternFactory(pattern_size, pattern_size)\n", "# create a checkerboard pattern and add it to the pattern list\n", "checkerboard = factory.create_checkerboard()\n", "pattern_list = [checkerboard]\n", "\n", "# add random patterns to the list\n", "pattern_list.extend(factory.create_random_pattern_list(nr_patterns=3, on_probability=0.5))\n", "plot_tools.plot_pattern_list(pattern_list)\n", "# how similar are the random patterns and the checkerboard? Check the overlaps\n", "overlap_matrix = pattern_tools.compute_overlap_matrix(pattern_list)\n", "plot_tools.plot_overlap_matrix(overlap_matrix)\n", "\n", "# let the hopfield network \"learn\" the patterns. Note: they are not stored\n", "# explicitly but only network weights are updated !\n", "hopfield_net.store_patterns(pattern_list)\n", "\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),10)\n", "\n", "\n", "\n", "# create a noisy version of a pattern and use that to initialize the network\n", "noisy_init_state = pattern_tools.flip_n(checkerboard, nr_of_flips=8)\n", "hopfield_net.set_state_from_pattern(noisy_init_state)\n", "\n", "# from this initial state, let the network dynamics evolve. \n", "states = hopfield_net.run_with_monitoring(nr_steps=4)\n", "\n", "# each network state is a vector. reshape it to the same shape used to create the patterns.\n", "states_as_patterns = factory.reshape_patterns(states)\n", "# plot the states of the network\n", "plot_tools.plot_state_sequence_and_overlap(states_as_patterns, pattern_list, reference_idx=0, suptitle=\"Network dynamics\")\n", "\n", "\n", "# plt.figure()\n", "# plt.hist(hopfield_net.weights.flatten(), 20)\n", "\n", "print(states[4])\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single Pattern" ] }, { "cell_type": "code", "execution_count": 477, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pattern_size = 4 # we choose that since 4**2 = 16 = N \n", "nr_flips = [5, 7, 8, 9]\n", "# nr_flips = [8]\n", "\n", "\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "factory = pattern_tools.PatternFactory(pattern_size, pattern_size)\n", "checkerboard = factory.create_checkerboard()\n", "hopfield_net.store_patterns([checkerboard])\n", "\n", "for i in range(len(nr_flips)):\n", " noisy_init_state = pattern_tools.flip_n(checkerboard, nr_of_flips=nr_flips[i])\n", " hopfield_net.set_state_from_pattern(noisy_init_state)\n", " states = hopfield_net.run_with_monitoring(nr_steps=4)\n", "# print(factory.reshape_patterns(states)[0])\n", "\n", " # each network state is a vector. reshape it to the same shape used to create the patterns.\n", " states_as_patterns = factory.reshape_patterns(states)\n", " # plot the states of the network\n", " plot_tools.plot_state_sequence_and_overlap(states_as_patterns, [checkerboard], reference_idx=0, suptitle=\"nr flipped:{}\".format(nr_flips[i]))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After running the Hopfield network, while we increase the number of flipped pixels, we observe that when we reach 8 pixels flipped then our network fails to retrieve the stored pattern and the same holds for more noisy patterns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Weight Matrix" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The size of the network matrix is: (16, 16) elements\n", "The values that occur are: [-0.0625 0. 0.0625]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pattern_size = 4\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "print(\"The size of the network matrix is:\", hopfield_net.weights.shape, \" elements\")\n", "\n", "# instantiate a pattern factory\n", "factory = pattern_tools.PatternFactory(pattern_size, pattern_size)\n", "\n", "# weights at the initialization\n", "plot_tools.plot_network_weights(hopfield_net)\n", "plt.title('Weights at initialization')\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),20)\n", "\n", "# weights after storing a checkerboard pattern\n", "checkerboard = factory.create_checkerboard()\n", "hopfield_net.store_patterns([checkerboard])\n", "plot_tools.plot_network_weights(hopfield_net)\n", "plt.title('Weights with a checkerboard pattern')\n", "print(\"The values that occur are: \", np.unique(hopfield_net.weights)) # this command return the values that appear but only once\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),20);" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The values that occur are: [-0.0625 0. 0.0625]\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "\n", "# weights after storing an L shape pattern\n", "l_shaped = factory.create_L_pattern(l_width = 2)\n", "hopfield_net.store_patterns([l_shaped])\n", "print(\"The values that occur are: \", np.unique(hopfield_net.weights)) # this command return the values that appear but only once\n", "plot_tools.plot_network_weights(hopfield_net)\n", "plt.title('Weights with L shaped pattern')\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),20);" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The values that occur are: [-0.125 0. 0.125]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "\n", "# weights after storing a checkerboard and an L shape pattern\n", "l_shaped = factory.create_L_pattern(l_width = 2)\n", "checkerboard = factory.create_checkerboard()\n", "hopfield_net.store_patterns([l_shaped, checkerboard])\n", "print(\"The values that occur are: \", np.unique(hopfield_net.weights)) # this command return the values that appear but only once\n", "plot_tools.plot_network_weights(hopfield_net)\n", "plt.title('Weights with a checkerboard AND a L shaped pattern')\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can notice that the values that occur in the last matrix are double the values that occur in the previous cases. Although the number of 0s have increase drastically." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# here you can also see how the patterns look like \n", "plot_tools.plot_pattern_list([l_shaped, checkerboard])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Capacity of an N=100 Hopfield-network" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 7.4.1\n", "This means that when we experience something that is close enough to a memory that we already have, then neural dynamics transforms our current perception to an attractor state, i.e. the memory that we already had. \n", "\n", "Example: You see a house and if the appearance of the house is close enough with your house then you identify this house as your house." ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We can store 14.0 patterns in our network of 100 neurons\n", "Run 0\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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EqVZdXBM/Vyq5JrX55+cZHfuWjorLe14WEbvWaLsMODMifpOWrwT+LSLm1RtvaGgo5s0rmmec9JO16xefeUBH5tsvJN0QEUPN9h+ui2vyDD9XqrkmteX+89Otb+ksBaaXlqeldWZm1iXdCvw5wL+mb+vsBayMiGUjbWRmZp3TkXP4kr4HvB7YQtIS4DRgHYCI+AYwF3gTsBB4DHhHJ/ZrZmbN60jgR8SRI7QH8IFO7MvMzFrj37Q1M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTHQk8CXtJ+kOSQslnVSj/VhJKyT9Kd2O68R+zcyseW3/ARRJE4CvAvsCS4DrJc2JiFsruv4gIo5vd39mZtaaThzh7wksjIhFEfEk8H1gZgfGNTOzDupE4E8F7iktL0nrKh0q6WZJsyVN78B+zcxsFLr1oe2lwIyIeDFwBXB+rU6SZkmaJ2neihUrujS1/ue6VHNNqrkmtbkuz+hE4C8Fykfs09K6tSLiwYh4Ii2eDexRa6CIOCsihiJiaPLkyR2Y2mBwXaq5JtVck9pcl2d0IvCvB3aQtK2kdYEjgDnlDpKmlBYPBm7rwH7NzGwU2v6WTkSskXQ8cDkwATg3IhZIOgOYFxFzgBMkHQysAR4Cjm13v2ZmNjptBz5ARMwF5lasO7V0/2Tg5E7sy8zMWuPftDUzy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMdORaOlaYcdJP1t5ffOYBPZxJ/3BNqrkmtbku1TpdEx/hm5llwkf4bfARSTXXpLZyXazg50q1sa7JwAe+n1S1uS7VXJNqrkm18VyTgQ/80RrP/5ljxTWp5ppUq3wX47oU+um50pHAl7Qf8CWKv3h1dkScWdG+HnABxd+yfRA4PCIWd2Lf3dRP/3H9xKcrqvm5Us01qdbtmrQd+JImAF8F9gWWANdLmhMRt5a6vQv4a0RsL+kI4DPA4e3uuxWjKXCng6xfn/CjnVcnH0e/1gRaf664JqPv28n9dls7Pz/d3ncnvqWzJ7AwIhZFxJPA94GZFX1mAuen+7OBvSWpA/s2M7MmKSLaG0A6DNgvIo5Ly0cDL4+I40t95qc+S9LyX1KfByrGmgXMAth66633uOuuu2rus/JVrdErZjePQloZW9INETHUaJxm6tKoJrWW2513q1yT1sceqS6t/Pw00u13e62M7edKtUY16asPbSPiLOAsgKGhofZeiZrUb28Pa+l2XVyTaq5Jba5LtX6uSSdO6SwFppeWp6V1NftImghsTPHhrZmZdUknjvCvB3aQtC1FsB8BHFXRZw5wDHAdcBjwy2j3XFJJP7+i9kplTVwj16QW16C2QX2utB34EbFG0vHA5RRfyzw3IhZIOgOYFxFzgHOA70haCDxE8aLQskEpfie5JtVck9pcl2q51KQj5/AjYi4wt2LdqaX7fwPe2ol9mZlZa/rqQ9tBk8tRw2i4JtVck9pcl2rt1sRXyzQzy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMOPDNzDLhwDczy4QD38wsEw58M7NMtBX4kjaTdIWkO9O/m9bp93dJf0q3Oe3s08zMWtPuEf5JwJURsQNwZVqu5fGIeEm6HdzmPs3MrAXtBv5M4Px0/3zgzW2OZ2ZmY6TdwN8yIpal+8uBLev0W1/SPEm/k/TmeoNJmpX6zVuxYkWbUxscrks116Saa1Kb6/KMEQNf0i8kza9xm1nuFxEBRJ1htomIIeAo4IuStqvVKSLOioihiBiaPHnyaB/LwHJdqrkm1VyT2lyXZ4z4R8wjYp96bZLukzQlIpZJmgLcX2eMpenfRZKuAnYH/tLalM3MrBXtntKZAxyT7h8DXFLZQdKmktZL97cAXgXc2uZ+zcxslNoN/DOBfSXdCeyTlpE0JOns1GdnYJ6km4BfAWdGhAPfzKzLRjyl00hEPAjsXWP9POC4dP+3wIva2Y+ZmbXPv2lrZpYJB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmWgr8CW9VdICSU9LGmrQbz9Jd0haKOmkdvZpZmatafcIfz5wCHB1vQ6SJgBfBfYHdgGOlLRLm/s1M7NRavcvXt0GIKlRtz2BhRGxKPX9PjAT/11bM7Ou6sY5/KnAPaXlJWmdmZl10YhH+JJ+ATyvRtMpEXFJJycjaRYwKy2ulnRHRZctgAfqbN6obSy3bXfsFzRoA0asS78+rn6tSbtz62XNtmmw7VjWpJm59are/frz05+ZEhFt34CrgKE6ba8ALi8tnwyc3OJ+5rXSNpbbjvXYvapJP9e7nZoMas3Gsib9/Fzo15+ffq13N07pXA/sIGlbSesCRwBzurBfMzMrafdrmW+RtITiKP4nki5P67eSNBcgItYAxwOXA7cBP4yIBe1N28zMRqvdb+lcDFxcY/29wJtKy3OBue3sKzmrxbax3Hasxx7JeHxcvazJSO3jtWYjGa+Pa7z+/PRlvZXO+ZiZ2YDzpRXMzDIxLgK/0aUZJE2X9CtJt6bLPHyoxvYTJN0o6bIabZtImi3pdkm3SXpFRftH0rjzJf1F0v2S5pfaN5N0haQ7JS2VtKKi/XNp7JslLa5sL/U7UVJI2qLVOpmZNdL3gd/EpRnWACdGxC7AXsAHaly64UMUHxjX8iXgZxGxE7BbuZ+kqcAJFF853RW4K82l7CTgyojYAbgU+ElF+xXArhHxYuDaGu1Img68Ebi7zhzNzNrW94FP6dIMEfEkMHxpBgAiYllE/DHdX0UR2Gt/k1fSNOAA4OzKgSVtDLwWOCdt/2REPFzRbSLwbEkTgceARRXtM4Hz0/3TgdeUGyPi5+mbSgCzgU1qPMYvAB8H/IGKmY2Z8RD4TV+aQdIMYHfg96XVX6QI06drbLItsAL4djrlc7akScONEbEU+C+KI+9lwErgmooxtoyIZen+cmByg8fyTopfUivPeSawNCJuarCdmVnbxkPgN0XSBsCPgA9HxCNp3YHA/RFxQ53NJgIvBb4eEbsDj1Kcohkec1OKI/htga2AScCb680hiq881TxKl3QKxemnH5fWPQf4BHBqM4/RzKwd4yHwlwLTS8vT0rq1JK1DEfYXRsRFpaZXAQdLWkxxKuifJH231L4EWBIRw+8IZlO8AAzbB/i/iFgREU8BFwF7VMzvPklT0jymUOMaF5KOBQ4E3lbRtB3Fi8lNaY7TgD9KqnXtIjOztoyHwG94aQYV12Y+B7gtIj5f3jAiTo6IaRExI233y4h4e6l9OXCPpOGLDe3NP162+W5gL0nPSfvZG1hYMb85wDHp/jEUH9KuJWk/ilNKB0fEYxXzuyUinhsRM9IclwAvTfMyM+uotn7TthsiYo2k4UszTADOrbg0w6uAo4FbJP0prftE+u3eZnwQuDC9mCwC3lHa9+8lzQb+SHE6ZhLFt2m2SJeUOA04E/ihpHcBG6ZNNy+1nwysB1whaRtgXWDd4faIOGcU5TAza5l/09bMLBPj4ZSOmZl1gAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0w48M3MMvH/xJkyaxpedIkAAAAASUVORK5CYII=\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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\n", 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RTS+CVFUX18TPlVquSTW/fp7QsbN0VFze8+KI2KOi7WLg9Ij4TZq+DPi3iFjQaH1DQ0OxYEHRPOukH6+fv/T0gzsy3n4h6ZqIGGq1/3BdXJMn+LlSzzWplvvrp1tn6SwHZpamZ6R5ZmbWJd0K/HnAv6azdfYFVkfEipEWMjOzzunIMXxJ3wFeAWwjaRlwGrABQER8DZgPvBpYDDwEvKUT2zUzs9Z1JPAj4qgR2gN4Tye2ZWZmY+Nf2pqZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmOhL4kg6UdIukxZJOqmh/s6RVkv6Ubsd1YrtmZta6tv8DFEmTgC8DBwDLgKslzYuIG2u6fi8ijm93e2ZmNjad2MPfB1gcEUsi4lHgu8DsDqzXzMw6qBOBPx24ozS9LM2rdYSk6yXNlTSzA9s1M7NR6NaXthcBsyLiOcClwLlVnSTNkbRA0oJVq1Z1aWj9z3Wp55rUc02quS5P6ETgLwfKe+wz0rz1IuLeiHgkTZ4J7F21oog4IyKGImJo6tSpHRjaYHBd6rkm9VyTaq7LEzoR+FcDu0jaUdKGwJHAvHIHSdNKk4cBN3Vgu2ZmNgptn6UTEeskHQ9cAkwCzo6IRZI+DiyIiHnACZIOA9YB9wFvbne7ZmY2Om0HPkBEzAfm18w7tXT/ZODkTmzLzMzGxr+0NTPLhAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0w48M3MMuHANzPLhAPfzCwTDnwzs0w48M3MMtGRi6d126yTfrz+/tLTD+7hSPqHa1LPNanmutTLpSYTMvDHUy5/+NFwTeq5JvXKNQHXZVg/PVcc+B3UT3/YfuGa1HNNqrku9Tpdk4EPfD+Jqrku9VyTeq5JvYlck44EvqQDgS9Q/I9XZ0bE6TXtGwHnUfxftvcCb4iIpZ3Y9njyR9RqE/kJP15ck3quSbVe1qXtwJc0CfgycACwDLha0ryIuLHU7W3AXyNiZ0lHAp8C3tDutqvUhrQV/OKr55rUc02qDUqudOK0zH2AxRGxJCIeBb4LzK7pMxs4N92fC+wnSR3YtpmZtUgR0d4KpNcBB0bEcWn6GOAFEXF8qc/C1GdZmv5L6nNPzbrmAHMAtt9++71vu+22lsYwmr2S2r7juWwr65Z0TUQMNdvuWOrSrZrULl82kWtS279stMuOVNNWxzVSXdqtyUjbrxqrXz8TqyZ99aVtRJwBnAEwNDTU3jtRA+18TO3VR9zxrku7j6u8fLc++nb7uTLax9WL54pfP9X6+fUz4Y7hA8uBmaXpGWleVZ9lkiYDm1N8edtzPk5ZzzWp55pUc13q9XNNOhH4VwO7SNqRItiPBI6u6TMPOBa4Cngd8Ito91hSSa8K3M9/WNekXi/H1q91cU2qDerrp+3Aj4h1ko4HLqE4LfPsiFgk6ePAgoiYB5wFfEvSYuA+ijeFgdfPT+hecU3quSbVXJd67dakI8fwI2I+ML9m3qml+38DXt+JbZmZ2dj4aplmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkmHPhmZplw4JuZZcKBb2aWCQe+mVkm2gp8SVtJulTSrenfLRv0+7ukP6XbvHa2aWZmY9PuHv5JwGURsQtwWZqu8nBEPDfdDmtzm2ZmNgbtBv5s4Nx0/1zgNW2uz8zMxkm7gb9tRKxI91cC2zbot7GkBZJ+J+k1jVYmaU7qt2DVqlVtDm1wuC71XJN6rkk11+UJIwa+pJ9LWlhxm13uFxEBRIPV7BARQ8DRwOcl7VTVKSLOiIihiBiaOnXqaB/LwHJd6rkm9VyTaq7LEyaP1CEi9m/UJukuSdMiYoWkacDdDdaxPP27RNLlwF7AX8Y2ZDMzG4t2D+nMA45N948FflTbQdKWkjZK97cBXgzc2OZ2zcxslNoN/NOBAyTdCuyfppE0JOnM1OeZwAJJ1wG/BE6PCAe+mVmXjXhIp5mIuBfYr2L+AuC4dP+3wLPb2Y6ZmbXPv7Q1M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTDjwzcwy4cA3M8uEA9/MLBMOfDOzTLQV+JJeL2mRpMclDTXpd6CkWyQtlnRSO9s0M7OxaXcPfyFwOPDrRh0kTQK+DBwE7A4cJWn3NrdrZmaj1O7/eHUTgKRm3fYBFkfEktT3u8Bs/P/ampl1VTeO4U8H7ihNL0vzzMysi0bcw5f0c+BpFU2nRMSPOjkYSXOAOWlyraRbarpsA9zTYPFmbeO5bLvrfkaTNmDEuvTr4+rXmrQ7tl7WbIcmy45nTVoZW6/q3a+vn/7MlIho+wZcDgw1aHshcElp+mTg5DFuZ8FY2sZz2fFed69q0s/1bqcmg1qz8axJPz8X+vX106/17sYhnauBXSTtKGlD4EhgXhe2a2ZmJe2elvlaScso9uJ/LOmSNH87SfMBImIdcDxwCXAT8P2IWNTesM3MbLTaPUvnQuDCivl3Aq8uTc8H5rezreSMMbaN57Ljve6RTMTH1cuajNQ+UWs2kon6uCbq66cv6610zMfMzAacL61gZpaJCRH4zS7NIGmmpF9KujFd5uF9FctPknStpIsr2raQNFfSzZJukvTCmvYPpPUulPQXSXdLWlhq30rSpZJulbRc0qqa9s+kdV8vaWlte6nfiZJC0jZjrZOZWTN9H/gtXJphHXBiROwO7Au8p+LSDe+j+MK4yheAn0bEbsCe5X6SpgMnUJxyugdwWxpL2UnAZRGxC3AR8OOa9kuBPSLiOcCVFe1Imgm8Cri9wRjNzNrW94FP6dIMEfEoMHxpBgAiYkVE/DHdX0MR2Ot/yStpBnAwcGbtiiVtDrwMOCst/2hE3F/TbTLwZEmTgYeAJTXts4Fz0/2PAS8tN0bEz9KZSgBzgS0qHuPngA8D/kLFzMbNRAj8li/NIGkWsBfw+9Lsz1OE6eMVi+wIrAK+mQ75nClpynBjRCwH/otiz3sFsBq4omYd20bEinR/JTC1yWN5K8WP1Mpjng0sj4jrmixnZta2iRD4LZG0CfAD4P0R8UCadwhwd0Rc02CxycDzgK9GxF7AgxSHaIbXuSXFHvyOwHbAFOA1jcYQxSlPlXvpkk6hOPz0w9K8pwAfAU5t5TGambVjIgT+cmBmaXpGmreepA0owv78iLig1PRi4DBJSykOBf2TpG+X2pcByyJi+BPBXIo3gGH7A/8XEasi4jHgAmDvmvHdJWlaGsc0Kq5xIenNwCHAG2uadqJ4M7kujXEG8EdJVdcuMjNry0QI/KaXZlBxbeazgJsi4rPlBSPi5IiYERGz0nK/iIg3ldpXAndIGr7Y0H7842Wbbwf2lfSUtJ39gMU145sHHJvuH0vxJe16kg6kOKR0WEQ8VDO+GyLiqRExK41xGfC8NC4zs45q65e23RAR6yQNX5phEnB2zaUZXgwcA9wg6U9p3kfSr3tb8V7g/PRmsgR4S2nbv5c0F/gjxeGYKRRn02yTLilxGnA68H1JbwM2TYtuXWo/GdgIuFTSDsCGwIbD7RFx1ijKYWY2Zv6lrZlZJibCIR0zM+sAB76ZWSYc+GZmmXDgm5llwoFvZpYJB76ZWSYc+GZmmXDgm5ll4v8BIaA5NGrwTZAAAAAASUVORK5CYII=\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pattern_size = 10\n", "\n", "capacity = int(pattern_size**2 * 0.14)\n", "print(\"We can store {:.1f} patterns in our network of 100 neurons\".format(capacity))\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "# instantiate a pattern factory\n", "factory = pattern_tools.PatternFactory(pattern_size, pattern_size)\n", "\n", "for i in range(10): # run the script some times\n", " print('Run {}'.format(i))\n", " # create a checkerboard pattern and add it to the pattern list\n", " checkerboard = factory.create_checkerboard()\n", " pattern_list = [checkerboard]\n", " # add random patterns to the list\n", " pattern_list.extend(factory.create_random_pattern_list(nr_patterns=capacity-1, on_probability=0.5))\n", "\n", " # how similar are the random patterns and the checkerboard? Check the overlaps\n", " overlap_matrix = pattern_tools.compute_overlap_matrix(pattern_list)\n", " plot_tools.plot_overlap_matrix(overlap_matrix)\n", "\n", " # let the hopfield network \"learn\" the patterns. Note: they are not stored\n", " # explicitly but only network weights are updated !\n", " hopfield_net.store_patterns(pattern_list)\n", "\n", " # initialize with orig pattern\n", " hopfield_net.set_state_from_pattern(checkerboard)\n", " # from this initial state, let the network dynamics evolve. \n", " states = hopfield_net.run_with_monitoring(nr_steps=4)\n", "\n", " # each network state is a vector. reshape it to the same shape used to create the patterns.\n", " states_as_patterns = factory.reshape_patterns(states)\n", " # plot the states of the network\n", " plot_tools.plot_state_sequence_and_overlap(states_as_patterns, pattern_list, reference_idx=0, suptitle=\"Network dynamics\")\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After running the network several times, we observe that in the majority of times we successfully stay in the attractor state, as we are supposed to. However in sometimes we see that one pixel has flipped. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Non-random patterns\n", "We use letters to exemplify correlated patterns\n", "Note, the trajectory can go through a pattern without staying there. This is not a contradiction to the computation done in the class (book) where the overlap with a pattern is increasing because here we violate the assumption of zero overlap with other patterns. Furhtermore the decrease in energy is true only for the asynchronous update." ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the alphabet is stored in an object of type: \n", "letters are patterns of size: (10, 10). Create a network of corresponding size\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "# the letters we want to store in the hopfield network\n", "letter_list = ['A', 'B', 'C', 'S', 'X', 'Y', 'Z']\n", "\n", "# reproduce the same noise in the next run\n", "# numpy.random.seed(67)\n", "\n", "abc_dictionary =pattern_tools.load_alphabet()\n", "print(\"the alphabet is stored in an object of type: {}\".format(type(abc_dictionary)))\n", "# access the first element and get it's size (they are all of same size)\n", "pattern_shape = abc_dictionary['A'].shape\n", "print(\"letters are patterns of size: {}. Create a network of corresponding size\".format(pattern_shape))\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_shape[0]*pattern_shape[1])\n", "\n", "# create a list using Pythons List Comprehension syntax: \n", "pattern_list = [abc_dictionary[key] for key in letter_list ]\n", "plot_tools.plot_pattern_list(pattern_list)\n", "\n", "# store the patterns\n", "hopfield_net.store_patterns(pattern_list)\n", "\n", "# # create a noisy version of a pattern and use that to initialize the network\n", "noisy_init_state = pattern_tools.get_noisy_copy(abc_dictionary['A'], noise_level=0.2)\n", "hopfield_net.set_state_from_pattern(noisy_init_state)\n", "\n", "# from this initial state, let the network dynamics evolve. \n", "states = hopfield_net.run_with_monitoring(nr_steps=4)\n", "\n", "# each network state is a vector. reshape it to the same shape used to create the patterns.\n", "states_as_patterns = pattern_tools.reshape_patterns(states, pattern_list[0].shape)\n", "\n", "# plot the states of the network\n", "plot_tools.plot_state_sequence_and_overlap(\n", " states_as_patterns, pattern_list, reference_idx=0, suptitle=\"synchronous Network dynamics\")\n" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the alphabet is stored in an object of type: \n", "letters are patterns of size: (10, 10). Create a network of corresponding size\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# the letters we want to store in the hopfield network\n", "letter_list = ['A', 'B', 'C', 'S', 'X', 'Y', 'Z', 'R']\n", "\n", "# reproduce the same noise in the next run\n", "# numpy.random.seed(67)\n", "\n", "abc_dictionary =pattern_tools.load_alphabet()\n", "print(\"the alphabet is stored in an object of type: {}\".format(type(abc_dictionary)))\n", "# access the first element and get it's size (they are all of same size)\n", "pattern_shape = abc_dictionary['A'].shape\n", "print(\"letters are patterns of size: {}. Create a network of corresponding size\".format(pattern_shape))\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_shape[0]*pattern_shape[1])\n", "\n", "# create a list using Pythons List Comprehension syntax: \n", "pattern_list = [abc_dictionary[key] for key in letter_list ]\n", "plot_tools.plot_pattern_list(pattern_list)\n", "\n", "# store the patterns\n", "hopfield_net.store_patterns(pattern_list)\n", "\n", "# # create a noisy version of a pattern and use that to initialize the network\n", "noisy_init_state = pattern_tools.get_noisy_copy(abc_dictionary['A'], noise_level=0.2)\n", "hopfield_net.set_state_from_pattern(noisy_init_state)\n", "\n", "# from this initial state, let the network dynamics evolve. \n", "states = hopfield_net.run_with_monitoring(nr_steps=10)\n", "\n", "# each network state is a vector. reshape it to the same shape used to create the patterns.\n", "states_as_patterns = pattern_tools.reshape_patterns(states, pattern_list[0].shape)\n", "\n", "# plot the states of the network\n", "plot_tools.plot_state_sequence_and_overlap(\n", " states_as_patterns, pattern_list, reference_idx=0, suptitle=\"synchronous Network dynamics\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see from the evolution of the network above, the letter 'A' is not anymore a fixed point, as after some steps that we evolve the network then it becomes very fast unstable and actually it starts to converge towards letter 'R'.\n", "\n", "As we answered above, NO the overlap is not always decreasing as it converges to 'R' and then it stays stable.\n" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the alphabet is stored in an object of type: \n", "letters are patterns of size: (10, 10). Create a network of corresponding size\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# 7.5.3\n", "\n", "# the letters we want to store in the hopfield network\n", "letter_list = ['A', 'B', 'C','D']\n", "\n", "# reproduce the same noise in the next run\n", "# numpy.random.seed(67)\n", "\n", "abc_dictionary =pattern_tools.load_alphabet()\n", "print(\"the alphabet is stored in an object of type: {}\".format(type(abc_dictionary)))\n", "# access the first element and get it's size (they are all of same size)\n", "pattern_shape = abc_dictionary['A'].shape\n", "print(\"letters are patterns of size: {}. Create a network of corresponding size\".format(pattern_shape))\n", "\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_shape[0]*pattern_shape[1])\n", "\n", "# create a list using Pythons List Comprehension syntax: \n", "pattern_list = [abc_dictionary[key] for key in letter_list ]\n", "plot_tools.plot_pattern_list(pattern_list)\n", "\n", "# store the patterns\n", "hopfield_net.store_patterns(pattern_list)\n", "\n", "for reference_idx in range(len(pattern_list)):\n", " # # create a noisy version of a pattern and use that to initialize the network\n", " noisy_init_state = pattern_tools.get_noisy_copy(pattern_list[reference_idx], noise_level=0.2)\n", " hopfield_net.set_state_from_pattern(noisy_init_state)\n", "\n", " # from this initial state, let the network dynamics evolve. \n", " states = hopfield_net.run_with_monitoring(nr_steps=10)\n", "\n", " # each network state is a vector. reshape it to the same shape used to create the patterns.\n", " states_as_patterns = pattern_tools.reshape_patterns(states, pattern_list[0].shape)\n", "\n", " # plot the states of the network\n", " plot_tools.plot_state_sequence_and_overlap(\n", " states_as_patterns, pattern_list, reference_idx=reference_idx, suptitle=\"synchronous Network dynamics\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is not trivial to make a guess regarding the number of letters that we can retrieve successfully. As we saw from the previous question(7.5.2) our network cannot retrieve successfully all the letter even with 8 patterns stored in the weights, which significantly smaller from the theoretical capacity (14 patterns). This is due to the fact that the higher the correlation of the patterns the harder it is for the network to discriminate between them.\n", "\n", "Intuitive example: Sometimes it is difficult to discriminate monozygotic twins. However, if you become good friends or you see them more often, you could think as dedicating more neurons to them, you can finally discriminate between them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def my_bonus_update(state_s0, weights):\n", " random_neuron_idx_list = np.random.permutation(len(state_s0))\n", " state_s1 = state_s0.copy()\n", " for i in range(len(random_neuron_idx_list)):\n", " rand_neuron_i = random_neuron_idx_list[i]\n", " h_i = np.dot(weights[:, rand_neuron_i], state_s1)\n", " prop_state_s1_on = 0.5 * (1 + np.tanh(5*h_i)) # we consider temperature \\beta = 5\n", " # the update here is probabilistic and in the next line we do the inference step\n", " state_s1[rand_neuron_i] = 1 if prop_state_s1_on > np.random.rand() else -1 \n", " return state_s1\n", "\n", "pattern_size = 10\n", "# np.random.seed(0)\n", "# create an instance of the class HopfieldNetwork\n", "hopfield_net = network.HopfieldNetwork(nr_neurons= pattern_size**2)\n", "\n", "# here we update the update funcion \n", "hopfield_net.set_dynamics_to_user_function(my_bonus_update)\n", "# from this point on we can do the same analysis we did before\n", "\n", "plt.hist(hopfield_net.weights.flatten(),10)\n", "\n", "# instantiate a pattern factory\n", "factory = pattern_tools.PatternFactory(pattern_size, pattern_size)\n", "\n", "pattern_list = []\n", "# add random patterns to the list\n", "pattern_list.extend(factory.create_random_pattern_list(nr_patterns=14, on_probability=0.5))\n", "plot_tools.plot_pattern_list(pattern_list)\n", "# how similar are the random patterns and the checkerboard? Check the overlaps\n", "overlap_matrix = pattern_tools.compute_overlap_matrix(pattern_list)\n", "plot_tools.plot_overlap_matrix(overlap_matrix)\n", "\n", "# let the hopfield network \"learn\" the patterns. Note: they are not stored\n", "# explicitly but only network weights are updated !\n", "hopfield_net.store_patterns(pattern_list)\n", "\n", "plt.figure()\n", "plt.hist(hopfield_net.weights.flatten(),10)\n", "\n", "\n", "# create a noisy version of a pattern and use that to initialize the network\n", "noisy_init_state = pattern_tools.flip_n(pattern_list[0], nr_of_flips=5)\n", "# hopfield_net.set_state_from_pattern(noisy_init_state)\n", "hopfield_net.set_state_from_pattern(noisy_init_state)\n", "\n", "# from this initial state, let the network dynamics evolve. \n", "states = hopfield_net.run_with_monitoring(nr_steps=5)\n", "\n", "# each network state is a vector. reshape it to the same shape used to create the patterns.\n", "states_as_patterns = factory.reshape_patterns(states)\n", "# plot the states of the network\n", "plt.figure()\n", "plot_tools.plot_state_sequence_and_overlap(states_as_patterns, pattern_list, reference_idx=0, suptitle=\"Network dynamics\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }