{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Two Spirals\n", "\n", "This notebook explores the two-spirals category task. This is a good example of how to make a problem difficult for humans and neural networks." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Using TensorFlow backend.\n", "ConX, version 3.7.4\n" ] } ], "source": [ "import conx as cx\n", "import math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This task involves separating two categories, A and B, where the two sets spiral around each other.\n", "\n", "First, let's make the dataset:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def spiral_xy(i, spiral_num):\n", " \"\"\"\n", " Create the data for a spiral. \n", " \n", " Arguments:\n", " i runs from 0 to 96\n", " spiral_num is 1 or -1\n", " \"\"\"\n", " φ = i/16 * math.pi\n", " r = 6.5 * ((104 - i)/104)\n", " x = (r * math.cos(φ) * spiral_num)/13 + 0.5\n", " y = (r * math.sin(φ) * spiral_num)/13 + 0.5\n", " return (x, y)\n", "\n", "def spiral(spiral_num):\n", " return [spiral_xy(i, spiral_num) for i in range(97)]" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = [\"A\", spiral(1)]\n", "b = [\"B\", spiral(-1)]\n", "\n", "cx.scatter([a,b])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, there it is: given the (x,y) coordinates of a point, can you determine if it belongs to category A or B. This is fairly easy to do given the picture. But very difficult only given the coordinates.\n", "\n", "Nonetheless, this was an early challenge problem for neural networks, and much research was done in order to learn the task.\n", "\n", "Many things were tried, with various levels of success!\n", "\n", "For an overview of the task, and solutions see, for example:\n", "\n", "https://www.researchgate.net/publication/220233514_Variations_of_the_two-spiral_task\n", "\n", "Here is an attempt using so-called \"shortcut\" connections:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "net = cx.Network(\"Two-Spirals\")\n", "net.add(\n", " cx.Layer(\"input\", 2),\n", " cx.Layer(\"hidden1\", 5, activation=\"sigmoid\"),\n", " cx.Layer(\"hidden2\", 5, activation=\"sigmoid\"),\n", " cx.Layer(\"hidden3\", 5, activation=\"sigmoid\"),\n", " cx.Layer(\"output\", 2, activation=\"softmax\")\n", ")\n", "net.connect(\"input\", \"hidden1\")\n", "net.connect(\"input\", \"hidden2\")\n", "net.connect(\"input\", \"hidden3\")\n", "net.connect(\"input\", \"output\")\n", "net.connect(\"hidden1\", \"hidden2\")\n", "net.connect(\"hidden1\", \"hidden3\")\n", "net.connect(\"hidden1\", \"output\")\n", "net.connect(\"hidden2\", \"hidden3\")\n", "net.connect(\"hidden2\", \"output\")\n", "net.connect(\"hidden3\", \"output\")\n", "net.build_model()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "__________________________________________________________________________________________________\n", "Layer (type) Output Shape Param # Connected to \n", "==================================================================================================\n", "input (InputLayer) (None, 2) 0 \n", "__________________________________________________________________________________________________\n", "hidden1 (Dense) (None, 5) 15 input[0][0] \n", "__________________________________________________________________________________________________\n", "concatenate_1 (Concatenate) (None, 7) 0 input[0][0] \n", " hidden1[0][0] \n", "__________________________________________________________________________________________________\n", "hidden2 (Dense) (None, 5) 40 concatenate_1[0][0] \n", "__________________________________________________________________________________________________\n", "concatenate_2 (Concatenate) (None, 12) 0 input[0][0] \n", " hidden1[0][0] \n", " hidden2[0][0] \n", "__________________________________________________________________________________________________\n", "hidden3 (Dense) (None, 5) 65 concatenate_2[0][0] \n", "__________________________________________________________________________________________________\n", "concatenate_3 (Concatenate) (None, 17) 0 input[0][0] \n", " hidden1[0][0] \n", " hidden2[0][0] \n", " hidden3[0][0] \n", "__________________________________________________________________________________________________\n", "output (Dense) (None, 2) 36 concatenate_3[0][0] \n", "==================================================================================================\n", "Total params: 156\n", "Trainable params: 156\n", "Non-trainable params: 0\n", "__________________________________________________________________________________________________\n" ] } ], "source": [ "net.summary()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fcac3f85edfb4086a6823f130de4c5d6", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Dashboard(children=(Accordion(children=(HBox(children=(VBox(children=(Select(description='Dataset:', index=1, …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "net.dashboard()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "net.dataset.load([(xy, [1, 0]) for xy in spiral(1)] +\n", " [(xy, [0, 1]) for xy in spiral(-1)])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def schedule(start, end, num_steps):\n", " step = (end - start) / (num_steps - 1)\n", " current = start\n", " values = []\n", " for i in range(num_steps):\n", " values.append(current)\n", " current += step\n", " return values" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.001,\n", " 0.0011111111111111111,\n", " 0.0012222222222222222,\n", " 0.0013333333333333333,\n", " 0.0014444444444444444,\n", " 0.0015555555555555555,\n", " 0.0016666666666666666,\n", " 0.0017777777777777776,\n", " 0.0018888888888888887,\n", " 0.002]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "schedule(0.001, 0.002, 10)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ 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Cleaning up...\n", "========================================================\n", " | Training | Training | Validate | Validate \n", "Epochs | Error | Accuracy | Error | Accuracy \n", "------ | --------- | --------- | --------- | --------- \n", "# 1510 | 0.69089 | 0.50515 | 0.68765 | 0.56186 \n" ] }, { "ename": "KeyboardInterrupt", "evalue": "", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnet\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m20000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreport_rate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m16\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maccuracy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtolerance\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m~/.local/lib/python3.6/site-packages/conx/network.py\u001b[0m in \u001b[0;36mtrain\u001b[0;34m(self, epochs, accuracy, error, batch_size, report_rate, verbose, kverbose, shuffle, tolerance, class_weight, sample_weight, use_validation_to_stop, plot, record, callbacks, save)\u001b[0m\n\u001b[1;32m 1468\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Saved!\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1469\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0minterrupted\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1470\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1471\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mverbose\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1472\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mepoch_count\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhistory\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mKeyboardInterrupt\u001b[0m: " ] } ], "source": [ "net.train(20000, report_rate=10, batch_size=16, accuracy=1.0, tolerance=0.4)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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Z9XQ6KA4i6VkR8ZsyM2Nmk29igyLwfWDPsjJiZjNHZ4OipC9MtQvYrvzsjE+CrbbYuOn1xoYWAJr0dsk8LwBho+p6SfEE4FRgXZ99i8vPjplNuq4vMrscuD4irsjvkHR6JTkys4nW9ZLi64E/99sREXuXnx0zmwk6GxQj4g91ZcTMZoZOlxQlLYmIE6d7TC0iNmt9L6WbpaFvbquKTttU51MV2vJH5Q6f0XU6KAKvkdS3+pwS8OIS82NmE67rHS3vL5DGj8vIiJnNHJ0tKUbEVwEkvSciPp/d129bUZIWAJ8nWe7n7Ig4I7f/eOBTPL5g5Bcj4uxxzmVm7dL16nPPm0iCWNbxfbYNVeQOXKnzI+Kkwgnn2hRLUUZ6Lfr2a2lRbNH11qGq9t86NNXG3OmgKGkxyUq2e0taltm1LTBuz3SRO3CZ2YTqdFAErgDuAuYCn85sfxC4dsxzFrkDF8DrJL0QuAk4OSLuyB8g6UTgRIA999gjv9vMWqjTQTEibgNuAw6vJzubXAwsjYh1kt4GfBV4whJl6a0OlwDMP/jgqDeLZjaWCGatf7TpXEypULyW9CDQCzpbAVsCf4qIp45xzqF34MrdQ+Fs4JNDU924Ef48aPQQzfx7qmogW1v/1TY1cK+tn0eLNTZqtYr2/xIV+k2KiG17zyWJpA3wsDHPOfQOXJJ2iYi70pcLgV+PeS4za5uWB8WR/1lE4iLgleOcMCLWA707cP0auKB3By5JC9PD3i3pBknXAO8m6ek2s0nQC4pFHg0oWn1+beblLGA+UywUUUSBO3B9APjAuOmbWcu1uKRYtCHm1Znn64FbSarQ7REBjz02+Jhh+8ex5Zblp1lEHb9UXWqnc1tmd7S8+ly0TfGEqjNiZjNEkU7RBhVqU5S0j6SLJd0r6R5J35G0T9WZM7MJ1PI2xaIdLd8CLgB2AXYFvg0srSpTZjbhJiAoPjkivh4R69PHN4AWL/5jZq3V8pJi0Vbi70o6DTiPZBD30cAlknaAlqzQHQHrMvfXqqsBfMOG8tOcPbv8NMdRRccUNNc5VYUWdxi0thNoEjpagDekP9+W276IJEi6fdHMiml5R0vR3mffpMrMyjMBJUUkPQ+Yl31PRHytgjyZ2SSbhOqzpK8DTweuBnqNaAG0JyjmP+guLxA76YtIVNEOW0Rb2mrrUlWb8HRNQlAkmda3f0R4eS4zm54JCYrXAzuTLDhrZja+CQmKc4GVkn4ObBr3EhELp36LmVkfEd3vfQZOrzITpWjrjav6mbS2yqy2tFv240Uj2qHEv9VhdwbNHPc64ELgbyJixaA0iw7J+eGIeTUz66+koFj0zqCStgXeA/ysSLoDp/lJ+kn680FJf8w8HpT0x3EuxMxmuPKm+W26M2hEPEoy467fkoYfAz5BwTVgh9246m/Tn9sOOs7MrLDRSopzJWWru0vSG9ZBgTuDSjoY2CMi/k3S+4uc0I0dZla/4kFxbUTMH+cUkmYBn2HE25lMTlAso0errgbxKhr829KYX1dnRluut4i2Dj9p6jMsb+7zsDuDbgs8G7g8ud8eOwPLJC0c1NnSod8sM5sI5fU+D7wzaEQ8QDKcEABJlwPvK6X32cysNCUFxYhYL6l3Z9DZwDm9O4MCKyJi2TjpOiiaWf1KalIYdmfQ3PYjiqQ5OUGxjP8+XkRic21ut3Pb5fQ11dY5IdP8zMzKMQmLzJqZlcYlRTOzHAfFGhQpktexyOgk3ezJ7XZeRKIKLimamWU4KJqZZTgompllTMgis90w7L9Pl8fy1XGzp6Zu7FTXDZaaaJcdVxMlqbp+l11SNDPLcFA0M8twUDQzy3BQNDPLcEdLTfKDt71g7Ogm7e6FeZPcWVWGujq8XFI0M8twUDQzy3BQNDPLcFCsSf6D7nL7WJfz3k8dfwBtabf0AhLFOCiamaW8yKyZWYarz2ZmGQ6KNanrg+7yuMRJbtub6QvitjjI9NXi/M6qMnFJCyTdKGmVpNP67D9F0kpJ10r6d0l7ZfZtkHR1+hjr/q1m1kK9AkyRRwMq+7cnaTZwJvByYDWwXNKyiFiZOexXwPyIeFjSO4BPAken+x6JiAOryp+ZNWQGV58PAVZFxC0Aks4DjgI2BcWI+EHm+KuAYyvMj5m1wQzufd4NuCPzejVw6IDj3wx8N/N6jqQVwHrgjIi4KP8GSScCJwLsOXcuPPLItDO9mboWJe1yO2XepI2xzJuk76pJM7SkWJikY4H5wIsym/eKiDWS9gEuk3RdRNycfV9ELAGWAMx/+tOjtgyb2fhmcPV5DbBH5vXu6bbNSHoZ8EHgRRGxrrc9ItakP2+RdDlwEHBz/v1m1j0R7S3DVNn7vBzYV9LekrYCFgGb9SJLOgj4CrAwIu7JbN9e0tbp87nA88m0RZpZt20s+GhCZSXFiFgv6STgUmA2cE5E3CDpo8CKiFgGfArYBvi2JIDbI2IhsB/wFUkbSQL3GbleazPrqCDpKGirStsUI+IS4JLctg9nnr9sivddARww4snKX0S0qkVJ61iItKoFQ5u6I94kd3DMsIHnQXOlwCLa8SmZ2YxSwxroY3NQNLPatbebxUHRzGrm6nNdyhgl3+WFGerKexXtrE3d7KmuGzU11Q6b16KxgWUFRUkLgM+TdOaeHRFn5PafAryFpG/nXuDvI+K2QWlWuiCEmVler/e5yGOQzPoKrwL2BxZL2j93WG99hb8GLiRZX2EgB0Uzq1Wv+lzCOMVN6ytExKNAb32Fx88V8YOIeDh9eRXJJJKBHBTNrHYjBMW5klZkHidmkum3vsJuA06bX1+hr8lpUyxjPmWX2/qc9821ZEweMFntsCUIRhqSszYi5k/3nFOsr9BXi35zzGymKGlIzrTWV5iKq89mVruS2hTHXl9hEJcUzaxWZc19nub6ClNyUDSz2pU1TnHc9RUGmZygGDH64O06GuPL6kRoouPAeX+itnTgdLhzyjNazMxyHBTNzFIjDsmpnYOimdXOQbEO4wzeLqNdxgOch+ty3vMm6Vryalowwm2KZmY5DopmZimXFM3MchwU65BfZLauCfNVLFRa16KkXW4f63Le8yZ9TGUfDopmZqkZfYtTM7M8tymameU4KNYl2zbT5XaaMhYl7fLNoJq60VOXf2f6afE4XAdFM7OUq89mZjkOimZmqQBquuP2WBwUzax2Jd2jpRKTExTLuJtfES1uvN5MlzsNqrj7HbjzaRwV/B65TdHMLMdB0cws5ZKimVmOp/nVIb8gRBEeVDs65336aYyjywP6c1xSNDPL8e0IzMxSgYfkmJltxtXnOjR146o8L7I6XJfb9mZ63kvgNkUzs5x2hOf+HBTNrFYuKZqZ5Tgo1iECHnnk8dddniva5TYnt0sO1+W8lyDwkBwzs814SI6ZWYarz2Zmqbbf4nRWEyeVtEDSjZJWSTqtz/6tJZ2f7v+ZpHn159LMqtDrfS7yaELtJUVJs4EzgZcDq4HlkpZFxMrMYW8G7ouIZ0haBHwCOHpgwhGbT5rv8gT6mb4oqTtrhhsn7y3qnGlz9bmJkuIhwKqIuCUiHgXOA47KHXMU8NX0+YXASyWpxjyaWYXKKilWUetsIijuBtyReb063db3mIhYDzwA7JhPSNKJklZIWnHvqMuGmVkjyqo+Z2qdrwL2BxZL2j932KZaJ/BZklrnQI20KZYlIpZExPyImL/TnDlNZ8fMCuh1tBR5DFFJrbOJRoY1wB6Z17un2/ods1rSFsDTgN8PSvQXa9eu1Vln3Za+nAusLSe7reFr6oZJvCZ4/Lr2mm5Cd8GlpyfpFTFH0orM6yURsSR93q/WeWju/ZvVOiX1ap1TfkdNBMXlwL6S9iYJfouAY3LHLAPeBFwJvB64LCIGjveMiJ16zyWtiIj5pea6Yb6mbpjEa4JyrysiFpSRTlVqrz6nbYQnAZcCvwYuiIgbJH1U0sL0sP8N7ChpFXAK8IQGVDOb8UapdVK01tlIH31EXAJcktv24czzPwP/pe58mVmnVFLrbM/ApXItGX5I5/iaumESrwlaeF1pG2Gv1jkbOKdX6wRWRMQyklrn19Na5x9IAudAGhI0zcxmlE4PyTEzK5uDoplZRmeD4qQsKlHgOk6RtFLStZL+XdJemX0bJF2dPpbVm/PiClzj8ZLuzVzLW5rI5zAFruOzmWu4SdL9mX2t/64knSPpHknXT7Ffkr6QXv+1kg6uO4+1iIjOPUgaVW8G9gG2Aq4B9s8d8w/Al9Pni4Dzm873mNfxYuDJ6fN3ZK8DeKjpayjpGo8Hvth0Xqd7Hbnj30XS8N+l7+qFwMHA9VPsPxL4LiDgMOBnTee5ikdXS4qTsqjE0OuIiB9ExMPpy6tIxmJ1SZHvqgtGvY7FwNJaclaSiPgRSQ/tVI4CvhaJq4DtJO1ST+7q09WgWNqiEg0rch1Zbyb5T90zJ10Q4ypJr6kigyUoeo2vS6tkF0rao8/+phX+rtImjr2ByzKbu/BdDTPq72snTeo4xYkj6VhgPvCizOa9ImKNpH2AyyRdFxE3N5PDabkYWBoR6yS9jaSE/5KG8zQdi4ALIyK7qOekfFcTr6slxUqm9zSgyHUg6WXAB4GFEbGutz0i1qQ/bwEuBw6qMrNjGnqNEfH7zHWdDTy3pryNotB3lVpErurcke9qmFE+g87qalDcNL1H0lYkv4T5Hr3e9B4oOL2nAUOvQ9JBwFdIAuI9me3bS9o6fT4XeD6QXb28LYpcY7ZdaiHJnPi2KfI7h6RnAduTTCvrbevKdzXMMuC4tBf6MOCBiLir6UyVrZPV56hoek/dCl7Hp4BtgG+n/US3R8RCYD/gK5I2kvxzOyM2v6VDKxS8xneni4GsJ/mujm8sw1MoeB2Q/J6dl/sH3InvStJS4AhgrqTVwEeALQEi4ssk6xUcCawCHgZOaCan1fI0PzOzjK5Wn83MKuGgaGaW4aBoZpbhoGhmluGgaGaW4aBoI5F0RQVpzpN0TOZ1b9WcszPbPpCuznKjpFem256UrjrzaDr+z2zaHBRtJBHxvAqSnccT761xfkS8BUDJDc4XAX8FLAD+RdLsiHgkIg4E7qwgTzZDOSjaSCQ9lP48QtLl6QIOv5H0zd4qRJJulfRJSddJ+rmkZ6Tbz5X0+nxawBnAC9JS38l9TnsUyYDodRHxHySDhw+p8jpt5nJQtOk4CHgvsD/JOoPPz+x7ICIOAL4IfG5IOqcBP46IAyPis332z4jVWawdHBRtOn4eEasjYiNwNUk1uGdp5ufhdWfMbFwOijYd6zLPN7D5XPro83w96e+cpFkkK1gXMSNWZ7F2cFC0qhyd+dlbMeZWHl8WbCHpYgPAg8C2A9JaBixSct+dvYF9gZ+XmluzVCdXybFO2F7StSSlycXptrOA70i6Bvge8Kd0+7XAhnT7ucB92YTS1WguIFluaz3wztwCrmal8So5VjpJtwLzI2LtmO8/Pn3/SXWczyzL1Wdro0eAV2UHb/fTG7xNUg3fWEvObOK5pGhmluGSoplZhoOimVmGg6KZWYaDoplZhoOimVnG/wddkYFFxuyS4AAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "net.plot_activation_map()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, I could never learn to do the task. Perhaps you can find some parameters that will work.\n", "\n", "Or, perhaps we can just make this much easier for the neural network." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Picture-based Approach\n", "\n", "In this formulation, we create \"images\" for each input and use a Convolutional layer." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import conx as cx\n", "import copy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need to pick a resolution for the images. We chop up the input space into a 50 x 50 images." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "RESOLUTION = 50" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def make_picture(res):\n", " matrix = [[0.0 for i in range(res)]\n", " for j in range(res)]\n", " for x,y in spiral(1):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " matrix[1 - y][x] = 0.5\n", " for x,y in spiral(-1):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " matrix[1 - y][x] = 0.5\n", " return matrix" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "matrix = make_picture(RESOLUTION)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cx.array_to_image(matrix, shape=(RESOLUTION,RESOLUTION,1)).resize((400,400))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we have three values:\n", "\n", "* background - 0.0\n", "* other data - 0.5\n", "* the target - 1.0\n", "\n", "We could might be able to leave out the other data, but that seemed to make it more difficult. We want to let the network \"see\" the pattern." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def make_data(res):\n", " data = []\n", " for x,y in spiral(1):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " inputs = copy.deepcopy(matrix)\n", " inputs[1 - y][x] = 1.0\n", " inputs = cx.reshape(inputs,(50,50,1))\n", " data.append([inputs, [0, 1]])\n", " for x,y in spiral(-1):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " inputs = copy.deepcopy(matrix)\n", " inputs[1 - y][x] = 1.0\n", " inputs = cx.reshape(inputs,(50,50,1))\n", " data.append([inputs, [1, 0]])\n", " return data" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "data = make_data(RESOLUTION)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create the simplest form of a Conv2DLayer network:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "net = cx.Network(\"Two-Spirals using Pictures\")\n", "net.add(\n", " cx.ImageLayer(\"input\", (RESOLUTION, RESOLUTION), 1),\n", " cx.Conv2DLayer(\"conv2d\", 2, 4),\n", " cx.FlattenLayer(\"flatten\"),\n", " cx.Layer(\"output\", 2, activation=\"softmax\")\n", ")\n", "net.connect()\n", "net.compile(error=\"categorical_crossentropy\", optimizer=\"rmsprop\")" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "net.dataset.load(data)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "afd2f53e28cc4d9fa3f55a92fbd6fdad", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Dashboard(children=(Accordion(children=(HBox(children=(VBox(children=(Select(description='Dataset:', index=1, …" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "\n", "require(['base/js/namespace'], function(Jupyter) {\n", " Jupyter.notebook.kernel.comm_manager.register_target('conx_svg_control', function(comm, msg) {\n", " comm.on_msg(function(msg) {\n", " console.log(\"received!\")\n", " console.log(msg)\n", " var data = msg[\"content\"][\"data\"];\n", " var images = document.getElementsByClassName(data[\"class\"]);\n", " for (var i = 0; i < images.length; i++) {\n", " if (data[\"xlink:href\"]) {\n", " var xlinkns=\"http://www.w3.org/1999/xlink\";\n", " images[i].setAttributeNS(xlinkns, \"href\", data[\"xlink:href\"]);\n", " }\n", " if (data[\"src\"]) {\n", " images[i].setAttributeNS(null, \"src\", data[\"src\"]);\n", " }\n", " }\n", " });\n", " });\n", "});\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "net.dashboard()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And try training it:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "net.reset()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "No training required: accuracy already to desired value\n", "Training dataset status:\n", " | Training | Training \n", "Epochs | Error | Accuracy \n", "------ | --------- | --------- \n", "# 386 | 0.24732 | 1.00000 \n" ] } ], "source": [ "net.train(1000, accuracy=1.0, report_rate=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It worked! This makes the task easy. \n", "\n", "Let's take a look at the generalization capability of the network by creating images that it wasn't trained on over the 50 x 50 space:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def test0(x, y, res=RESOLUTION):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " inputs = copy.deepcopy(matrix)\n", " inputs[1 - y][x] = 1.0\n", " inputs = cx.reshape(inputs,(50,50,1))\n", " return net.propagate(inputs)[0]\n", "\n", "def test1(x, y, res=RESOLUTION):\n", " x = min(int(round(x * res)), res - 1)\n", " y = min(int(round(y * res)), res - 1)\n", " inputs = copy.deepcopy(matrix)\n", " inputs[1 - y][x] = 1.0\n", " inputs = cx.reshape(inputs,(50,50,1))\n", " return net.propagate(inputs)[1]\n", "\n", "cx.view([cx.heatmap(test0, format=\"image\"), cx.heatmap(test1, format=\"image\")], \n", " labels=[\"output[0]\",\"output[1]\"], scale=7.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sometimes it creates fairly smooth spirals. However, other times, it may just \"memorize\" the problem, with no particular pattern. Which do you get?" ] } ], "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": "3.6.5" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": { "00012df0c16c4324abe48dce6775fe2a": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.0.0", "model_name": "LayoutModel", "state": {} }, "00064d0ecaa24c4ca05d4a5d058d2ea4": { "model_module": "@jupyter-widgets/base", "model_module_version": "1.0.0", "model_name": "LayoutModel", "state": { "width": "100%" } }, "00070b4a49a347108a038d33321c0b8f": { "model_module": "@jupyter-widgets/controls", "model_module_version": "1.1.0", "model_name": "AccordionModel", "state": { "_titles": { "0": "Two-Spirals" }, "children": [ 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\n \n \n \n \n \n \n Layer: output (output)\n output range: (0, 1)\n shape = (2,)\n Keras class = Dense\n activation = softmaxtargetsLayer: output (output)\n output range: (0, 1)\n shape = (2,)\n Keras class = Dense\n activation = softmaxoutputWeights from flatten to output\n output_14/kernel:0 has shape (4418, 2)\n output_14/bias:0 has shape (2,)Layer: flatten (hidden)\n output range: (-Infinity, +Infinity)\n Keras class = FlattenflattenWeights from conv2d to flattenLayer: conv2d (hidden)\n output range: (-Infinity, +Infinity)\n Keras class = Conv2Dconv2d20Weights from input to conv2d\n conv2d/kernel:0 has shape (4, 4, 1, 2)\n conv2d/bias:0 has shape (2,)Layer: input (input)\n output range: (0.0, 1.0)\n shape = (50, 50, 1)\n Keras class = InputinputTwo-Spirals using Pictures

conv2d features


Feature 0

Feature 1
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conv2d features


Feature 0

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conv2d features


Feature 0

Feature 1
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conv2d features


Feature 0

Feature 1

Feature 2

Feature 3

Feature 4

Feature 5

Feature 6

Feature 7
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conv2d features


Feature 0

Feature 1
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