Fizz Buzz in Tensorflow.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fizz Buzz in Tensorflow \n",
    "## [@joelgrus](http://twitter.com/joelgrus)\n",
    "### http://github.com/joelgrus\n",
    "\n",
    "------------------------\n",
    "\n",
    "\n",
    "**interviewer:** Welcome, can I get you coffee or anything? Do you need a break?\n",
    "\n",
    "**me:** No, I've probably had too much coffee already!\n",
    "\n",
    "**interviewer:** Great, great. And are you OK with writing code on the whiteboard?\n",
    "\n",
    "**me:** It's the only way I code!\n",
    "\n",
    "**interviewer:** ...\n",
    "\n",
    "**me:** That was a joke.\n",
    "\n",
    "**interviewer:** OK, so are you familiar with \"fizz buzz\"?\n",
    "\n",
    "**me:** ...\n",
    "\n",
    "**interviewer:** Is that a yes or a no?\n",
    "\n",
    "**me:** It's more of a \"I can't believe you're asking me that.\"\n",
    "\n",
    "**interviewer:** OK, so I need you to print the numbers from 1 to 100, except that if the number is divisible by 3 print \"fizz\", if it's divisible by 5 print \"buzz\", and if it's divisible by 15 print \"fizzbuzz\".\n",
    "\n",
    "**me:** I'm familiar with it.\n",
    "\n",
    "**interviewer:** Great, we find that candidates who can't get this right don't do well here.\n",
    "\n",
    "**me:** ...\n",
    "\n",
    "**interviewer:** Here's a marker and an eraser.\n",
    "\n",
    "**me:** [thinks for a couple of minutes]\n",
    "\n",
    "**interviewer:** Do you need help getting started?\n",
    "\n",
    "**me:** No, no, I'm good. So let's start with some standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer**: Um, you understand the problem is *fizzbuzz*, right?\n",
    "\n",
    "**me:** Do I ever. So, now let's talk models. I'm thinking a simple multi-layer-perceptron with one hidden layer.\n",
    "\n",
    "**interviewer:** Perceptron?\n",
    "\n",
    "**me:** Or neural network, whatever you want to call it. We want the input to be a number, and the output to be the correct \"fizzbuzz\" representation of that number. In particular, we need to turn each input into a vector of \"activations\". One simple way would be to convert it to binary.\n",
    "\n",
    "**interviewer:** Binary?\n",
    "\n",
    "**me:** Yeah, you know, 0's and 1's? Something like:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def binary_encode(i, num_digits):\n",
    "    return np.array([i >> d & 1 for d in range(num_digits)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** [stares at whiteboard for a minute]\n",
    "\n",
    "**me:** And our output will be a one-hot encoding of the fizzbuzz representation of the number, where the first position indicates \"print as-is\", the second indicates \"fizz\", and so on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fizz_buzz_encode(i):\n",
    "    if   i % 15 == 0: return np.array([0, 0, 0, 1])\n",
    "    elif i % 5  == 0: return np.array([0, 0, 1, 0])\n",
    "    elif i % 3  == 0: return np.array([0, 1, 0, 0])\n",
    "    else:             return np.array([1, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** OK, that's probably enough.\n",
    "\n",
    "**me:** That's enough setup, you're exactly right. Now we need to generate some training data. It would be cheating to use the numbers 1 to 100 in our training data, so let's train it on all the remaining numbers up to 1024:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NUM_DIGITS = 10\n",
    "trX = np.array([binary_encode(i, NUM_DIGITS) for i in range(101, 2 ** NUM_DIGITS)])\n",
    "trY = np.array([fizz_buzz_encode(i)          for i in range(101, 2 ** NUM_DIGITS)])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** ...\n",
    "\n",
    "**me:** Now we need to set up our model in tensorflow. Off the top of my head I'm not sure how many hidden units to use, maybe 10?\n",
    "\n",
    "**interviewer:** ...\n",
    "\n",
    "**me:** Yeah, possibly 100 is better. We can always change it later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NUM_HIDDEN = 100\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need an input variable with width NUM_DIGITS, and an output variable with width 4:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = tf.placeholder(\"float\", [None, NUM_DIGITS])\n",
    "Y = tf.placeholder(\"float\", [None, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** How far are you intending to take this?\n",
    "\n",
    "**me:** Oh, just two layers deep -- one hidden layer and one output layer. Let's use randomly-initialized weights for our neurons:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def init_weights(shape):\n",
    "    return tf.Variable(tf.random_normal(shape, stddev=0.01))\n",
    "\n",
    "w_h = init_weights([NUM_DIGITS, NUM_HIDDEN])\n",
    "w_o = init_weights([NUM_HIDDEN, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we're ready to define the model. As I said before, one hidden layer, and let's use, I don't know, ReLU activation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, w_h, w_o):\n",
    "    h = tf.nn.relu(tf.matmul(X, w_h))\n",
    "    return tf.matmul(h, w_o)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use softmax cross-entropy as our cost function and try to minimize it:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "py_x = model(X, w_h, w_o)\n",
    "\n",
    "cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=py_x, labels=Y))\n",
    "train_op = tf.train.GradientDescentOptimizer(0.05).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** ...\n",
    "\n",
    "**me:** And, of course, the prediction will just be the largest output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predict_op = tf.argmax(py_x, 1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** Before you get too far astray, the problem you're supposed to be solving is to generate fizz buzz for the numbers from 1 to 100.\n",
    "\n",
    "**me:** Oh, great point, the predict_op function will output a number from 0 to 3, but we want a \"fizz buzz\" output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fizz_buzz(i, prediction):\n",
    "    return [str(i), \"fizz\", \"buzz\", \"fizzbuzz\"][prediction]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** ...\n",
    "\n",
    "**me:** So now we're ready to train the model. Let's grab a tensorflow session and initialize the variables:"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "sess = tf.Session()\n",
    "with sess.as_default():\n",
    "    tf.initialize_all_variables().run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's run, say, 1000 epochs of training?\n",
    "\n",
    "**interviewer:** ...\n",
    "\n",
    "**me:** Yeah, maybe that's not enough -- so let's do 10000 just to be safe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NUM_EPOCHS = 10000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And our training data are sequential, which I don't like, so let's shuffle them each iteration:\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "    for epoch in range(NUM_EPOCHS):\n",
    "        p = np.random.permutation(range(len(trX)))\n",
    "        trX, trY = trX[p], trY[p]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And each epoch we'll train in batches of, I don't know, 128 inputs?\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "BATCH_SIZE = 128\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So each training pass looks like\n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "        for start in range(0, len(trX), BATCH_SIZE):\n",
    "            end = start + BATCH_SIZE\n",
    "            sess.run(train_op, feed_dict={X: trX[start:end], Y: trY[start:end]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then we can print the accuracy on the training data, since why not?\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "        print(epoch, np.mean(np.argmax(trY, axis=1) ==\n",
    "                             sess.run(predict_op, feed_dict={X: trX, Y: trY})))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "interviewer: Are you serious?\n",
    "\n",
    "me: Yeah, I find it helpful to see how the training accuracy evolves.\n",
    "\n",
    "interviewer: ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "\n",
    "with sess.as_default():\n",
    "    tf.global_variables_initializer().run()\n",
    "    \n",
    "    for epoch in range(NUM_EPOCHS):\n",
    "        p = np.random.permutation(range(len(trX)))\n",
    "        trX, trY = trX[p], trY[p]\n",
    "        \n",
    "        for start in range(0, len(trX), BATCH_SIZE):\n",
    "            end = start + BATCH_SIZE\n",
    "            sess.run(train_op, feed_dict={X: trX[start:end], Y: trY[start:end]})\n",
    "            \n",
    "        accuracy = np.mean(np.argmax(trY, axis=1) ==\n",
    "                           sess.run(predict_op, feed_dict={X: trX, Y: trY}))\n",
    "        print(epoch, accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**me:** So, once the model has been trained, it's fizz buzz time. Our input should just be the binary encoding of the numbers 1 to 100:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numbers = np.arange(1, 101)\n",
    "teX = np.transpose(binary_encode(numbers, NUM_DIGITS))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then our output is just our `fizz_buzz` function applied to the model output:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "teY = sess.run(predict_op, feed_dict={X: teX})\n",
    "output = np.vectorize(fizz_buzz)(numbers, teY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**interviewer:** ...\n",
    "\n",
    "**me:** And that should be your fizz buzz!\n",
    "\n",
    "**interviewer:** Really, that's enough. We'll be in touch.\n",
    "\n",
    "**me:** In touch, that sounds promising.\n",
    "\n",
    "**interviewer: ...**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Postscript\n",
    "\n",
    "I didn't get the job. It turns out it got some of the outputs wrong! Thanks a lot, machine learning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 fizz 4\n",
      "23 fizz 23\n",
      "49 fizz 49\n",
      "53 fizz 53\n"
     ]
    }
   ],
   "source": [
    "actuals = [fizz_buzz(i, fizz_buzz_encode(i).argmax()) for i in numbers]\n",
    "\n",
    "for i, (predicted, actual) in enumerate(zip(output, actuals)):\n",
    "    if predicted != actual:\n",
    "        print(\"{0} {1} {2}\".format(i+1, predicted, actual))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I guess maybe I should have used a deeper network."
   ]
  }
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