└── blog └── Meta-Learning.ipynb /blog/Meta-Learning.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "# Learning to Learn by Gradient Descent by Gradient Descent\n", 8 | "## As simple as possible in TensorFlow" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "When I first came across DeepMind’s paper “Learning to learn by gradient descent by gradient descent”, my reaction was “Wow, how on earth does that work?”. Unfortunately, my first read-through of the paper was not that illuminating, and looking at the code was quite daunitng.\n", 16 | "Thankfully, I was intrigued enough to force myself to re-read the paper and it actually turned out to be surprisingly simple in the end. Personally, what really helps me when I’m trying to understand something is to create the simplest non-trivial version of the problem and then scale up from there. So here it is, the simplest version of the idea I could create, also no maths equations! I hope you find it illuminating.\n", 17 | "I suggest skimming the paper first but this should all be understandable without. Code was ran on TF v1.0.0-rc1.\n", 18 | "\n", 19 | "\n", 20 | "---\n", 21 | "\n", 22 | "So let’s get started. Time to learn about learning to learn by gradient descent by gradient descent by reading my article." 23 | ] 24 | }, 25 | { 26 | "cell_type": "code", 27 | "execution_count": 1, 28 | "metadata": { 29 | "collapsed": true 30 | }, 31 | "outputs": [], 32 | "source": [ 33 | "import tensorflow as tf" 34 | ] 35 | }, 36 | { 37 | "cell_type": "code", 38 | "execution_count": 2, 39 | "metadata": { 40 | "collapsed": false 41 | }, 42 | "outputs": [ 43 | { 44 | "data": { 45 | "text/plain": [ 46 | "'v1.0.0-rc1-0-g114a462-dirty'" 47 | ] 48 | }, 49 | "execution_count": 2, 50 | "metadata": {}, 51 | "output_type": "execute_result" 52 | } 53 | ], 54 | "source": [ 55 | "tf.GIT_VERSION" 56 | ] 57 | }, 58 | { 59 | "cell_type": "markdown", 60 | "metadata": {}, 61 | "source": [ 62 | "First of all we need a problem for our meta-learning optimizer to solve. Let’s take the simplest experiment from the paper; finding the minimum of a multi-dimensional quadratic function. We are going to randomly scale the parabolas and start at random locations, the solution is always at (0, 0)." 63 | ] 64 | }, 65 | { 66 | "cell_type": "code", 67 | "execution_count": 3, 68 | "metadata": { 69 | "collapsed": true 70 | }, 71 | "outputs": [], 72 | "source": [ 73 | "DIMS = 10 # Dimensions of the parabola\n", 74 | "scale = tf.random_uniform([DIMS], 0.5, 1.5)\n", 75 | "# This represents the network we are trying to optimize,\n", 76 | "# the `optimizee' as it's called in the paper.\n", 77 | "# Actually, it's more accurate to think of this as the error\n", 78 | "# landscape.\n", 79 | "def f(x):\n", 80 | " x = scale*x\n", 81 | " return tf.reduce_sum(x*x)" 82 | ] 83 | }, 84 | { 85 | "cell_type": "markdown", 86 | "metadata": {}, 87 | "source": [ 88 | "We can’t easily use TensorFlow’s built in optimizers here since the technique requires us to unroll the training loop inside the computation graph, as we’ll see in a bit. So let’s define a couple of simple hand crafted optimizers to test against our learned optimizer. As discussed in the paper, an optimizer is a function g that takes the gradient of a parameter at a given step and returns back the step you should take in parameter space. Here’s vanilla gradient descent: (Some optimizers need to keep track of state, here I just pass the param through)" 89 | ] 90 | }, 91 | { 92 | "cell_type": "code", 93 | "execution_count": 4, 94 | "metadata": { 95 | "collapsed": false 96 | }, 97 | "outputs": [], 98 | "source": [ 99 | "def g_sgd(gradients, state, learning_rate=0.1):\n", 100 | " return -learning_rate*gradients, state" 101 | ] 102 | }, 103 | { 104 | "cell_type": "markdown", 105 | "metadata": {}, 106 | "source": [ 107 | "For a stronger baseline let’s use RMSProp:" 108 | ] 109 | }, 110 | { 111 | "cell_type": "code", 112 | "execution_count": 5, 113 | "metadata": { 114 | "collapsed": true 115 | }, 116 | "outputs": [], 117 | "source": [ 118 | "def g_rms(gradients, state, learning_rate=0.1, decay_rate=0.99):\n", 119 | " if state is None:\n", 120 | " state = tf.zeros(DIMS)\n", 121 | " state = decay_rate*state + (1-decay_rate)*tf.pow(gradients, 2)\n", 122 | " update = -learning_rate*gradients / (tf.sqrt(state)+1e-5)\n", 123 | " return update, state" 124 | ] 125 | }, 126 | { 127 | "cell_type": "markdown", 128 | "metadata": {}, 129 | "source": [ 130 | "Great, now let’s unroll all the training steps, here learn is a function which takes one of these optimizers and applies it in a loop for number of steps and collects the value of the function f at each point, which we can think of as our loss." 131 | ] 132 | }, 133 | { 134 | "cell_type": "code", 135 | "execution_count": 6, 136 | "metadata": { 137 | "collapsed": false 138 | }, 139 | "outputs": [], 140 | "source": [ 141 | "TRAINING_STEPS = 20 # This is 100 in the paper\n", 142 | "\n", 143 | "initial_pos = tf.random_uniform([DIMS], -1., 1.)\n", 144 | "\n", 145 | "def learn(optimizer):\n", 146 | " losses = []\n", 147 | " x = initial_pos\n", 148 | " state = None\n", 149 | " for _ in range(TRAINING_STEPS):\n", 150 | " loss = f(x)\n", 151 | " losses.append(loss)\n", 152 | " grads, = tf.gradients(loss, x)\n", 153 | " \n", 154 | " update, state = optimizer(grads, state)\n", 155 | " x += update\n", 156 | " return losses" 157 | ] 158 | }, 159 | { 160 | "cell_type": "markdown", 161 | "metadata": {}, 162 | "source": [ 163 | "OK, now let’s test it out." 164 | ] 165 | }, 166 | { 167 | "cell_type": "code", 168 | "execution_count": 7, 169 | "metadata": { 170 | "collapsed": true 171 | }, 172 | "outputs": [], 173 | "source": [ 174 | "sgd_losses = learn(g_sgd)\n", 175 | "rms_losses = learn(g_rms)" 176 | ] 177 | }, 178 | { 179 | "cell_type": "markdown", 180 | "metadata": {}, 181 | "source": [ 182 | "And see what the losses look like." 183 | ] 184 | }, 185 | { 186 | "cell_type": "code", 187 | "execution_count": 8, 188 | "metadata": { 189 | "collapsed": false 190 | }, 191 | "outputs": [ 192 | { 193 | "data": { 194 | "image/png": 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FMXnyZFauXNlk20mTJrF8+XLuu+8+3njjDVasWMH9999Pjx49+NOf/sSll17qt8/SXkEP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\nAShMREQkDPh6hX8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XEZFclfLAd86lfNGdKG2gIyIiuSrlgb+lYQt7W/amJfDVwhcRkVyV8sAPhb1F\nd9LRpR/0B6lrqMM5l/KyRURE0inlgZ+ORXeigiVBmlub2dG4I+Vli4iIpFNaAr8ov2j/yneppNX2\nREQkV6W+S7/em5JnZqkuusMGOiIiIrkkLS38dNy/B7XwRUQkd6Ul8NNx/x6gwl8BaMc8ERHJPTkV\n+Pm+fIYVD1OXvoiI5JyUBn5TSxMbd21MW5c+aC6+iIjkppQG/vr69Thc2lr4oNX2REQkN6U08NM5\nBz9KLXwREclFKQ38UH1klb3y9HXpa4tcERHJRSlv4VcUV+Af5E9lsR1oi1wREclFKQ/8dHbng7r0\nRUQkN6W8Sz/dgR/0B9nVtIvG5sa01kNERCSVUt7CT+eUPNBqeyIikptyrks/WBJZT18D90REJIek\nLPDDjWHq99anP/C1gY6IiOSglAV+JkzJA3Xpi4hIbkpZ4GfCojsAJQUlFOcXq0tfRERySkoDP8/y\nGFk6MlVFdktT80REJNekrks/HGJ02WjyfHmpKrJbWnxHRERyTepa+PW1ab9/H6UNdEREJNektEs/\n3ffvo9SlLyIiuSalXfpjyzIj8LWBjoiI5JqUBH5Lawsf1n+YMV36auGLiEiuSUngb9uzjX2t+zKm\nSz9YEmTrnq20utZ0V0VERCQlUhL4G3dtBNI/Bz8q6A/S6lrZtmdbuqsiIiKSEikN/HRvnBOl1fZE\nRCTXpCzwSwtKGVI0JBXFHZA20BERkVyTssAfWz4WM0tFcQekFr6IiOSalAT+pt2bMub+PcCw4mH4\nzKfFd0REJGekrIWfKffvAXzmo6K4Ql36IiKSM1IS+B/t/CijWvigufgiIpJbUhL4Oxp3ZFzgawMd\nERHJJXEFvpl9x8xeN7N6M9tkZk+b2eG9eW0mdemDWvgiIpJb4m3hnwz8J/ApYBowCHjJzIoP9MKM\na+FrxzwREckh+fGc7Jz7XPufzWw2sBmoAl7t6bWjy0bHW7ek0gY6IiKSS/p7D38I4IAe16it8FdQ\nmF/Yz6ISS136IiKSS/oc+OatonMX8Kpz7u89nTuiZERfi0maYEmQPc172N20O91VERERSbq4uvQ7\nuQ/4OHDigU7c/F+bOfdv53Y4Vl1dTXV1dT+K75/2q+2VFJSkrR4iIiI1NTXU1NR0OBYOhxNaRp8C\n38zuAT4HnOyc++hA50//1+k8PufxvhSVNEF/ZD39hi2MGzIuzbUREZFcFqsRvHLlSqqqqhJWRtyB\nHwn7LwCu4ZMSAAAV+ElEQVRTnXO1vXlNZWllvMUknTbQERGRXBJX4JvZfUA1cC6w28yiN+fDzrnG\n7l6XiYGvDXRERCSXxDto7+tAGfAysKHd48KeXjTcn3mBX5RfRGlBqebii4hIToh3Hn6fRvX/bekI\n745/htHUPBERyRUpWUv/kV8EaGhIRUnx0eI7IiKSK1Kzec4OuOuuVJQUH22gIyIiuSIlgX/hhXDr\nrbAlw7JVXfoiIpIrUhL4X/4y+Hxw882pKK33tIGOiIjkipQE/pAhcP318LOfwTvvpKLE3tE9fBER\nyRUpCXyAb34TKivhu99NVYkHFvAH2N64nebW5nRXRUREJKlSFvjFxV6X/sKF8Je/pKrUnkVX29va\nsDXNNREREUmulAU+wJe+BEcfDdddB86lsuTYtNqeiIjkipQGfl4e3HYbvPIK/Pa3qSw5tvYb6IiI\niAxkKQ18gDPOgNNPh29/G5rTfOtcG+iIiEiuSHngm3mt/LVrYf78VJfeUXlhOfm+fHXpi4jIgJfy\nwAeYPBkuvhhuvBF2705HDTxmRsAfUJe+iIgMeGkJfIB/+zfYtg3uvDNdNfBotT0REckFaQv88eNh\nzhyve3/z5nTVQqvtiYhIbkhb4APccAPk58NNN6WvDsESrbYnIiIDX1oDf9gwb+W9X/wC3n47PXUI\nFKtLX0REBr60Bj7AVVfBqFHpW3JXW+SKiEguSHvgFxV5S+4+9RS89lrqy48O2nOZsPSfiIhIkqQ9\n8AFmzoRjjoFrr039krtBf5CmliZ2Nu1MbcEiIiIplBGBH11yd8kSeOaZ1Jat1fZERCQXZETgA0yf\nDp/9LFx/fWqX3NUGOiIikgsyJvAB/v3fvdH6Dz2UujK1gY6IiOSCjAr8Y4+FSy6BH/wAdu1KTZkV\n/gpALXwRERnYMirwwRuxv2MH3HFHasoryCugvLBc9/BFRGRAy7jAHzfOm5t/++2wcWNqytRcfBER\nGegyLvDBW4SnoAB+9KPUlKcNdEREZKDLyMAfOtRbZ/+BB+Ctt5JfnjbQERGRgS4jAx/gyith9Gj4\nzneSX5Za+CIiMtBlbOAXFcEtt8B//7e3IE8yBf3aMU9ERAa2jA18gOpqb6pespfc1aA9EREZ6DI6\n8H0+b7T+a6/B008nr5yAP0D93nqaWpqSV4iIiEgaZXTgA5x+Opxxhrfk7r59ySkjutqe7uOLiMhA\nlfGBD96Su++8443aTwatpy8iIgNdVgT+McfArFnwwx/CziTsYqsd80REZKDLisAHb8nd+nrvnn6i\naQMdEREZ6LIm8MeMgauv9tbY/+ijxF67tKCUgrwCdemLiMiAlTWBD97AvaIir2s/kcxMc/FFRGRA\ny6rAHzIEvv99ePBBWLs2sdfWansiIjKQZVXgA/zLv8DYsV5rP5G0+I6IiAxkWRf4hYXw4x/Ds8/C\nK68k7rraQEdERAayuAPfzE42s2fNbL2ZtZrZucmoWE/++Z+hqiqxS+6qS19ERAayvrTwS4BVwJVA\nEle47150yd3XX4fbbkvMNTVoT0REBrL8eF/gnPsd8DsAM7OE16iXTj0Vvvtd717+5s3eBwBfP25Q\nRFv4zjnS+GuJiIgkRdyBn0luuQVGjoRvfMObmz9/vnePvy+CJUFaXAs7GncwtHhoYisqIiKSZlkd\n+ABz5kBlJcycCZs2ebvqlZXFf532q+0p8EVEZKDJulH6scyYAS+9BCtWwGc+Axs2xH8NbaAjIiID\nWUpa+HPnzqW8vLzDserqaqqrqxNWxtSp8OqrcOaZcMIJ8LvfwYQJvX+9NtAREZF0qampoaampsOx\ncDic0DJSEvjz5s1j8uTJSS9n4kR47TU46yw48UT47W/h+ON799phxcMAtfBFRCT1YjWCV65cSVVV\nVcLK6Ms8/BIzO8bMJkUOHRL5eUzCatUPY8bAn/8MRx0Fp53mLdDTG/m+fIYVD9PiOyIiMiD15R7+\nFOCvwAq8efh3ACuBHyWwXv0ydKh3T//zn4fzz4f77+/d6zQXX0REBqq+zMP/E1kw2K+oCH79a29L\n3a99Ddav93bZ62mKfcAfoG6PuvRFRGTgyfppeT3Jy4O774bRo70Fetavh5//HPK7+a2DJWrhi4jI\nwDSgAx+8Fv23vw2jRsHll8PGjV7Lv6Sk67mB4gCrN61OfSVFRESSLOO75hPlS1/yRu2//DKcfjps\nidGQ1xa5IiIyUOVM4AOccQb86U+wbp03bW/duo7Pa9CeiIgMVDkV+OBtq/vaa962uscfDytXtj0X\n8AfYvW83e/btSV8FRUREkiDnAh/gkENg6VIYO9ZboW/xYu94dLU9Lb4jIiIDTU4GPkAwCH/8o7f2\n/uc+B489pvX0RURk4MrZwAdvpP4zz8CsWd6gvqceadsxT0REZCAZ8NPyDiQ/Hx580Ju29283BuEG\n2LRLgS8iIgNLTrfwo8zg5pvhZ3f7YV8xd/6sjsbGdNdKREQkcRT47Xz9697UvDXvbeHMM2HHjnTX\nSEREJDEU+J2MCQQ4+8I6/vY3OOww+MlPIMFbEouIiKScAr+ToD9IXtkWVq+GCy/0NtwZNw5uvBG2\nbk137URERPpGgd9JdAOdMWPg3nu91fi+/GW44w4v+K+7zluPX0REJJso8DsJFAc6zMMfNcoL+/ff\nh29+E37xCxg/Hq66CkKh9NVTREQkHgr8TrrbQCcYhFtugQ8+gBtugAUL4NBD4atfhXffTUNFRURE\n4qDA7yTgD7BtzzZaWltiPj9kCHzve17w//jH8NxzcPjh3sI9f/97iisrIiLSSwr8ToL+IK2ule2N\n23s8r7QUvvUt7x7/3Xd7u/BNnAgzZsBf/5qiyoqIiPSSAr+T6AY6vd0mt7gYrrwS3nkHHngAVq2C\nyZPh7LO9XflEREQygQK/k75uoFNQ4I3mf+stbyOedevghBNg2jR4+WVvO14REZF0UeB3EvT3bwOd\n/HyYORPWrIGnnoJt2+DUU+Gkk2DRIgW/iIikhwK/k6HFQ/GZr99b5Pp8cMEFsGIFPP+8F/Sf+xxM\nmQJPPw2trQmqsIiISC8o8DvxmY+K4ope38M/EDMv6JcsgT/8wRvlf8EF3sj+uXPhpZfQRj0iIpJ0\nCvwYupuL3x9mXtf+//yPF/7TpsGTT8IZZ0BFBZx7Lvz85950PxERkUTLT3cFMlHAH+h3l35PTjjB\nezgHb74JL7zgPebMgZYWOOoor1fgc5+DE0+EQYOSVhUREckRauHHEPQnvoUfi5k3d/+667yR/HV1\nsHAhHHccPPqo1yNQUQH/9E/w0EOwYUPSqyQiIgOUWvgxBPwB1u1Yl/JyhwzxFu6ZMcMb1Ld6dVvr\n/4orvGOTJrW1/j/1KW9WgIiIyIGohR9D0B9M2KC9vvL54NhjvXX7lyyBzZu99fsnToT77/em+Q0f\nDtXVXm/A5s1pra6IiGQ4tQ9jiA7ac85hZumuDuB17VdXe4+WFli+3Gv5L1oEs2Z5twemTPFa/mec\n4X1YKCpKd61FRCRTKPBjCPgDNDY30rCvgZKCknRXp4u8PK87/1Ofgh/9CDZtghdf9D4A/Md/eMfy\n8mDCBDjmGO82wKRJ3vfDh6e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ChPrGej5Y+UGnz0cICRQFNNwgIiJZLy2ChE/WfMKm+k0JCxLUkyAiIpImQUIo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\nuTLZLRMREYmdgoQYhHoSAAY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215 | "text/plain": [ 216 | "" 217 | ] 218 | }, 219 | "metadata": {}, 220 | "output_type": "display_data" 221 | } 222 | ], 223 | "source": [ 224 | "sess = tf.InteractiveSession()\n", 225 | "sess.run(tf.global_variables_initializer())\n", 226 | "\n", 227 | "import matplotlib\n", 228 | "import matplotlib.pyplot as plt\n", 229 | "%matplotlib inline\n", 230 | "import numpy as np\n", 231 | "\n", 232 | "x = np.arange(TRAINING_STEPS)\n", 233 | "for _ in range(3): \n", 234 | " sgd_l, rms_l = sess.run([sgd_losses, rms_losses])\n", 235 | " p1, = plt.plot(x, sgd_l, label='SGD')\n", 236 | " p2, = plt.plot(x, rms_l, label='RMS')\n", 237 | " plt.legend(handles=[p1, p2])\n", 238 | " plt.title('Losses')\n", 239 | " plt.show()" 240 | ] 241 | }, 242 | { 243 | "cell_type": "markdown", 244 | "metadata": {}, 245 | "source": [ 246 | "## Meta-Learning\n", 247 | "Time to put together our meta-learning optimizer, just like in the paper this is an LSTM with 2 layers and 20 hidden units." 248 | ] 249 | }, 250 | { 251 | "cell_type": "code", 252 | "execution_count": 9, 253 | "metadata": { 254 | "collapsed": true 255 | }, 256 | "outputs": [], 257 | "source": [ 258 | "LAYERS = 2\n", 259 | "STATE_SIZE = 20\n", 260 | "\n", 261 | "cell = tf.contrib.rnn.MultiRNNCell(\n", 262 | " [tf.contrib.rnn.LSTMCell(STATE_SIZE) for _ in range(LAYERS)])\n", 263 | "cell = tf.contrib.rnn.InputProjectionWrapper(cell, STATE_SIZE)\n", 264 | "cell = tf.contrib.rnn.OutputProjectionWrapper(cell, 1)\n", 265 | "cell = tf.make_template('cell', cell)\n", 266 | "\n", 267 | "def g_rnn(gradients, state):\n", 268 | " # Make a `batch' of single gradients to create a \n", 269 | " # \"coordinate-wise\" RNN as the paper describes. \n", 270 | " gradients = tf.expand_dims(gradients, axis=1)\n", 271 | " \n", 272 | " if state is None:\n", 273 | " state = [[tf.zeros([DIMS, STATE_SIZE])] * 2] * LAYERS\n", 274 | " update, state = cell(gradients, state)\n", 275 | " # Squeeze to make it a single batch again.\n", 276 | " return tf.squeeze(update, axis=[1]), state" 277 | ] 278 | }, 279 | { 280 | "cell_type": "markdown", 281 | "metadata": {}, 282 | "source": [ 283 | "And *that’s it*, that’s our meta learner. We can use it in exactly the same way:" 284 | ] 285 | }, 286 | { 287 | "cell_type": "code", 288 | "execution_count": 10, 289 | "metadata": { 290 | "collapsed": true 291 | }, 292 | "outputs": [], 293 | "source": [ 294 | "rnn_losses = learn(g_rnn)\n", 295 | "sum_losses = tf.reduce_sum(rnn_losses)" 296 | ] 297 | }, 298 | { 299 | "cell_type": "markdown", 300 | "metadata": {}, 301 | "source": [ 302 | "Now here’s the magic bit, we want sum_losses to be low, since the lower the losses the better the optimizer right? And because the entire training loop is in the graph we can use Back-Propagation Through Time (BPTT) and a meta-optimizer to minimize this value!" 303 | ] 304 | }, 305 | { 306 | "cell_type": "markdown", 307 | "metadata": {}, 308 | "source": [ 309 | "And this is the main point: *sum_losses is differentiable*, gradients flow through the graph we’ve defined just fine! TensorFlow is able to work out the gradients of the parameters in our LSTM with respect to this sum of losses. So let’s optimize:" 310 | ] 311 | }, 312 | { 313 | "cell_type": "code", 314 | "execution_count": 11, 315 | "metadata": { 316 | "collapsed": false 317 | }, 318 | "outputs": [], 319 | "source": [ 320 | "def optimize(loss):\n", 321 | " optimizer = tf.train.AdamOptimizer(0.0001)\n", 322 | " gradients, v = zip(*optimizer.compute_gradients(loss))\n", 323 | " gradients, _ = tf.clip_by_global_norm(gradients, 1.)\n", 324 | " return optimizer.apply_gradients(zip(gradients, v))\n", 325 | "\n", 326 | "apply_update = optimize(sum_losses)" 327 | ] 328 | }, 329 | { 330 | "cell_type": "markdown", 331 | "metadata": {}, 332 | "source": [ 333 | "I found gradient clipping to be *critical* here since the values that go into our meta-learner can be very large at the start of training." 334 | ] 335 | }, 336 | { 337 | "cell_type": "code", 338 | "execution_count": 12, 339 | "metadata": { 340 | "collapsed": false 341 | }, 342 | "outputs": [ 343 | { 344 | "name": "stdout", 345 | "output_type": "stream", 346 | "text": [ 347 | "53.7043800354\n", 348 | "9.93897572911\n", 349 | "4.20905622232\n", 350 | "3.9845823524\n", 351 | "3.92957963991\n" 352 | ] 353 | } 354 | ], 355 | "source": [ 356 | "sess.run(tf.global_variables_initializer())\n", 357 | "\n", 358 | "ave = 0\n", 359 | "for i in range(4000):\n", 360 | " err, _ = sess.run([sum_losses, apply_update])\n", 361 | " ave += err\n", 362 | " if i % 1000 == 0:\n", 363 | " print(ave / 1000 if i!=0 else ave)\n", 364 | " ave = 0\n", 365 | "print(ave / 1000)" 366 | ] 367 | }, 368 | { 369 | "cell_type": "markdown", 370 | "metadata": {}, 371 | "source": [ 372 | "And see how it does:" 373 | ] 374 | }, 375 | { 376 | "cell_type": "code", 377 | "execution_count": 13, 378 | "metadata": { 379 | "collapsed": false 380 | }, 381 | "outputs": [ 382 | { 383 | "data": { 384 | "image/png": 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5rhLoFXb0j/G+e0Qxk5CZCQccANWfK3lRREQkXumxNHbOfTv8vZldAHwNlAFv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\nr7LjmWd6E0Nvvgn/+Y93/OxnUF0NXbv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7EXgxyn5FrTM1EkAhQUREpKWUWbuhsyGhoEcBOZk5CgkiIiIBKRUSevboSVF2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\noDjfm+NQubmynZaSrnr39rbW/hfbts0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JPzvbzbcrLSU/w1ttr5GBe0lJbnqeEr6IiEhwop/wk5Nd0i8tpVvHbhhMo3Px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\nT7n4pIsZ1XsUA3IGYHTTVgJISXF3ipq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405 | "text/plain": [ 406 | "" 407 | ] 408 | }, 409 | "metadata": {}, 410 | "output_type": "display_data" 411 | } 412 | ], 413 | "source": [ 414 | "for _ in range(3): \n", 415 | " sgd_l, rms_l, rnn_l = sess.run(\n", 416 | " [sgd_losses, rms_losses, rnn_losses])\n", 417 | " p1, = plt.plot(x, sgd_l, label='SGD')\n", 418 | " p2, = plt.plot(x, rms_l, label='RMS')\n", 419 | " p3, = plt.plot(x, rnn_l, label='RNN')\n", 420 | " plt.legend(handles=[p1, p2, p3])\n", 421 | " plt.title('Losses')\n", 422 | " plt.show()" 423 | ] 424 | }, 425 | { 426 | "cell_type": "markdown", 427 | "metadata": {}, 428 | "source": [ 429 | "Success! Looks like it’s doing even better than RMS on this problem. Actually, these graphs are slightly misleading, log scale shows something slightly different:" 430 | ] 431 | }, 432 | { 433 | "cell_type": "code", 434 | "execution_count": 14, 435 | "metadata": { 436 | "collapsed": false, 437 | "scrolled": true 438 | }, 439 | "outputs": [ 440 | { 441 | "data": { 442 | "image/png": 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27tzJiiSmLycnJ3x9ffH19aVs2bL06dOHpUuX8n//939W/TxPS4KFPSpTBpYs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\niwbQbkY70vekex3tjFKxEBEROYMantOQV25/hTV3ruFY3jG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NixdCiJRzd3G3aW+CPTg5OfHBBx/QsGFDvvjiC1566SWr13Xr1o2+ffuSN29e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\nnb379oYdr0RULEREREJyXLXjGNd1HBuGbSC1fiqD5g0ieWo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st/nzO+Y1iOzpxws/EvSRNatA3k3k0EhqFrFulWalFDNmzKBcuXJcvnyZefPm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\nKVAhpALxbePZk7iHvhF9GbViFNfPup6Psj7yOprkU4GLhXN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463 | "text/plain": [ 464 | "" 465 | ] 466 | }, 467 | "metadata": {}, 468 | "output_type": "display_data" 469 | } 470 | ], 471 | "source": [ 472 | "for _ in range(3): \n", 473 | " sgd_l, rms_l, rnn_l = sess.run(\n", 474 | " [sgd_losses, rms_losses, rnn_losses])\n", 475 | " p1, = plt.semilogy(x, sgd_l, label='SGD')\n", 476 | " p2, = plt.semilogy(x, rms_l, label='RMS')\n", 477 | " p3, = plt.semilogy(x, rnn_l, label='RNN')\n", 478 | " plt.legend(handles=[p1, p2, p3])\n", 479 | " plt.title('Losses')\n", 480 | " plt.show()" 481 | ] 482 | }, 483 | { 484 | "cell_type": "markdown", 485 | "metadata": {}, 486 | "source": [ 487 | "I think the reason for this, again as discussed in the paper, is that the magnitude of the values being fed into the LSTM can vary wildly and neural networks generally do not perform well when that happens. Here the gradients get so small that it isn’t able to compute sensible updates. The paper uses a solution to this for the bigger experiments; feed in the log gradient and the direction instead. See the paper for details.\n", 488 | "Hopefully, now that you understand how learn to learn by gradient descent by gradient descent you can see the limitations. It doesn’t seem very scalable. I think it is quite telling that the experiments in the paper are very small. It takes 4000 steps for even our toy problem to converge, we had to train a network completely just for one step of optimization for the meta-learner. We would have to optimize a large problem many more times and would take a very long time. Also unrolling the entire training loop in the graph is not feasible for larger problems, although in the paper they only unroll the BPTT to 20 steps. There is also evidence in the paper that the RNN optimizer can generalize from smaller problem to larger problems.\n", 489 | "I expect meta-learning to become increasingly more important, for more inspiration I suggest watching these NIPS presentations. https://www.youtube.com/watch?v=0YLpp_TVhLY&list=PLPwzH56Rdmq4hcuEMtvBGxUrcQ4cAkoSc" 490 | ] 491 | }, 492 | { 493 | "cell_type": "code", 494 | "execution_count": null, 495 | "metadata": { 496 | "collapsed": true 497 | }, 498 | "outputs": [], 499 | "source": [] 500 | } 501 | ], 502 | "metadata": { 503 | "kernelspec": { 504 | "display_name": "Python 2", 505 | "language": "python", 506 | "name": "python2" 507 | }, 508 | "language_info": { 509 | "codemirror_mode": { 510 | "name": "ipython", 511 | "version": 2 512 | }, 513 | "file_extension": ".py", 514 | "mimetype": "text/x-python", 515 | "name": "python", 516 | "nbconvert_exporter": "python", 517 | "pygments_lexer": "ipython2", 518 | "version": "2.7.12" 519 | } 520 | }, 521 | "nbformat": 4, 522 | "nbformat_minor": 1 523 | } 524 | --------------------------------------------------------------------------------