zduey/lstm_exploration.ipynb

## lstm_exploration.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Understanding LSTM Parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import numpy as np\n",
    "import random\n",
    "import string\n",
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "import zipfile\n",
    "import itertools\n",
    "from six.moves import range\n",
    "from six.moves.urllib.request import urlretrieve\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from matplotlib import cm\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found and verified text8.zip\n"
     ]
    }
   ],
   "source": [
    "url = 'http://mattmahoney.net/dc/'\n",
    "\n",
    "def maybe_download(filename, expected_bytes):\n",
    "    \"\"\"Download a file if not present, and make sure it's the right size.\"\"\"\n",
    "    if not os.path.exists(filename):\n",
    "        filename, _ = urlretrieve(url + filename, filename)\n",
    "    statinfo = os.stat(filename)\n",
    "    if statinfo.st_size == expected_bytes:\n",
    "        print('Found and verified %s' % filename)\n",
    "    else:\n",
    "        print(statinfo.st_size)\n",
    "        raise Exception(\n",
    "            'Failed to verify ' + filename + '. Can you get to it with a browser?')\n",
    "    return filename\n",
    "\n",
    "filename = maybe_download('text8.zip', 31344016)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data size 100000000\n"
     ]
    }
   ],
   "source": [
    "def read_data(filename):\n",
    "    f = zipfile.ZipFile(filename)\n",
    "    for name in f.namelist():\n",
    "        return tf.compat.as_str(f.read(name))\n",
    "    f.close()\n",
    "    \n",
    "text = read_data(filename)\n",
    "print('Data size %d' % len(text))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "valid_size = 1000\n",
    "valid_text = text[:valid_size]\n",
    "train_text = text[valid_size:]\n",
    "train_size = len(train_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vocabulary_size = len(string.ascii_lowercase) + 1 # [a-z] + ' '\n",
    "first_letter = ord(string.ascii_lowercase[0])\n",
    "\n",
    "def char2id(char):\n",
    "    if char in string.ascii_lowercase:\n",
    "        return ord(char) - first_letter + 1\n",
    "    elif char == ' ':\n",
    "        return 0\n",
    "    else:\n",
    "        print('Unexpected character: %s' % char)\n",
    "        return 0\n",
    "    \n",
    "def id2char(dictid):\n",
    "    if dictid > 0:\n",
    "        return chr(dictid + first_letter - 1)\n",
    "    else:\n",
    "        return ' '"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def logprob(predictions, labels):\n",
    "    \"\"\"Log-probability of the true labels in a predicted batch.\"\"\"\n",
    "    predictions[predictions < 1e-10] = 1e-10\n",
    "    return np.sum(np.multiply(labels, -np.log(predictions))) / labels.shape[0]\n",
    "\n",
    "def sample_distribution(distribution):\n",
    "    \"\"\"Sample one element from a distribution assumed to be an array of normalized\n",
    "    probabilities.\n",
    "    \"\"\"\n",
    "    r = random.uniform(0, 1)\n",
    "    s = 0\n",
    "    for i in range(len(distribution)):\n",
    "        s += distribution[i]\n",
    "        if s >= r:\n",
    "            return i\n",
    "    return len(distribution) - 1\n",
    "\n",
    "def sample(prediction):\n",
    "    \"\"\"Turn a (column) prediction into 1-hot encoded samples.\"\"\"\n",
    "    p = np.zeros(shape=[1, vocabulary_size], dtype=np.float)\n",
    "    p[0, sample_distribution(prediction[0])] = 1.0\n",
    "    return p\n",
    "\n",
    "def random_distribution():\n",
    "    \"\"\"Generate a random column of probabilities.\"\"\"\n",
    "    b = np.random.uniform(0.0, 1.0, size=[1, vocabulary_size])\n",
    "    return b/np.sum(b, 1)[:,None]\n",
    "\n",
    "def characters(probabilities):\n",
    "    \"\"\"Turn a 1-hot encoding or a probability distribution over the possible\n",
    "    characters back into its (most likely) character representation.\"\"\"\n",
    "    return [id2char(c) for c in np.argmax(probabilities, 1)]\n",
    "\n",
    "def batches2string(batches):\n",
    "    \"\"\"Convert a sequence of batches back into their (most likely) string\n",
    "    representation.\"\"\"\n",
    "    s = [''] * batches[0].shape[0]\n",
    "    for b in batches:\n",
    "        s = [''.join(x) for x in zip(s, characters(b))]\n",
    "    return s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameter-Dependent Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def lstm_model_test(batch_size, num_nodes, num_unrollings, num_steps, summary_frequency):\n",
    "    class BatchGenerator(object):\n",
    "        def __init__(self, text, batch_size, num_unrollings):\n",
    "            self._text = text\n",
    "            self._text_size = len(text)\n",
    "            self._batch_size = batch_size\n",
    "            self._num_unrollings = num_unrollings\n",
    "            segment = self._text_size // batch_size # length of the word\n",
    "            self._cursor = [ offset * segment for offset in range(batch_size)]\n",
    "            self._last_batch = self._next_batch()\n",
    "\n",
    "        def _next_batch(self):\n",
    "            \"\"\"Generate a single batch from the current cursor position in the data.\"\"\"\n",
    "            batch = np.zeros(shape=(self._batch_size, vocabulary_size), dtype=np.float)\n",
    "            for b in range(self._batch_size):\n",
    "                batch[b, char2id(self._text[self._cursor[b]])] = 1.0\n",
    "                self._cursor[b] = (self._cursor[b] + 1) % self._text_size\n",
    "            return batch\n",
    "\n",
    "        def next(self):\n",
    "            \"\"\"Generate the next array of batches from the data. The array consists of\n",
    "            the last batch of the previous array, followed by num_unrollings new ones.\n",
    "            \"\"\"\n",
    "            batches = [self._last_batch]\n",
    "            for step in range(self._num_unrollings):\n",
    "                batches.append(self._next_batch())\n",
    "            self._last_batch = batches[-1]\n",
    "            return batches\n",
    "\n",
    "    train_batches = BatchGenerator(train_text, batch_size, num_unrollings)\n",
    "    valid_batches = BatchGenerator(valid_text, 1, 1)\n",
    "    graph = tf.Graph()\n",
    "    with graph.as_default():\n",
    "\n",
    "            # Parameters:\n",
    "            # Input gate: input, previous output, and bias.\n",
    "            ix = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))\n",
    "            im = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))\n",
    "            ib = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            # Forget gate: input, previous output, and bias.\n",
    "            fx = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))\n",
    "            fm = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))\n",
    "            fb = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            # Memory cell: input, state and bias.                                                         \n",
    "            cx = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))\n",
    "            cm = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))\n",
    "            cb = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            # Output gate: input, previous output, and bias.\n",
    "            ox = tf.Variable(tf.truncated_normal([vocabulary_size, num_nodes], -0.1, 0.1))\n",
    "            om = tf.Variable(tf.truncated_normal([num_nodes, num_nodes], -0.1, 0.1))\n",
    "            ob = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            # Variables saving state across unrollings.\n",
    "            saved_output = tf.Variable(tf.zeros([batch_size, num_nodes]), trainable=False)\n",
    "            saved_state = tf.Variable(tf.zeros([batch_size, num_nodes]), trainable=False)\n",
    "            # Classifier weights and biases.\n",
    "            w = tf.Variable(tf.truncated_normal([num_nodes, vocabulary_size], -0.1, 0.1))\n",
    "            b = tf.Variable(tf.zeros([vocabulary_size]))\n",
    "\n",
    "            # Definition of the cell computation.\n",
    "            def lstm_cell(i, o, state):\n",
    "                \"\"\"Create a LSTM cell. See e.g.: http://arxiv.org/pdf/1402.1128v1.pdf\n",
    "                Note that in this formulation, we omit the various connections between the\n",
    "                previous state and the gates.\"\"\"\n",
    "                input_gate = tf.sigmoid(tf.matmul(i, ix) + tf.matmul(o, im) + ib)\n",
    "                forget_gate = tf.sigmoid(tf.matmul(i, fx) + tf.matmul(o, fm) + fb)\n",
    "                update = tf.matmul(i, cx) + tf.matmul(o, cm) + cb\n",
    "                state = forget_gate * state + input_gate * tf.tanh(update)\n",
    "                output_gate = tf.sigmoid(tf.matmul(i, ox) + tf.matmul(o, om) + ob)\n",
    "                return output_gate * tf.tanh(state), state\n",
    "\n",
    "            # Input data.\n",
    "            train_data = list()\n",
    "            for _ in range(num_unrollings + 1):\n",
    "                    train_data.append(\n",
    "                        tf.placeholder(tf.float32, shape=[batch_size,vocabulary_size]))\n",
    "                    train_inputs = train_data[:num_unrollings]\n",
    "                    train_labels = train_data[1:]    # labels are inputs shifted by one time step.\n",
    "\n",
    "            # Unrolled LSTM loop.\n",
    "            outputs = list()\n",
    "            output = saved_output\n",
    "            state = saved_state\n",
    "            for i in train_inputs:\n",
    "                    output, state = lstm_cell(i, output, state)\n",
    "                    outputs.append(output)\n",
    "\n",
    "            # State saving across unrollings.\n",
    "            with tf.control_dependencies([saved_output.assign(output),saved_state.assign(state)]):\n",
    "                # Classifier.\n",
    "                logits = tf.nn.xw_plus_b(tf.concat(0, outputs), w, b)\n",
    "                loss = tf.reduce_mean(\n",
    "                    tf.nn.softmax_cross_entropy_with_logits(\n",
    "                        logits, tf.concat(0, train_labels)))\n",
    "\n",
    "            # Optimizer.\n",
    "            global_step = tf.Variable(0)\n",
    "            learning_rate = tf.train.exponential_decay(\n",
    "            10.0, global_step, 5000, 0.1, staircase=True)\n",
    "            optimizer = tf.train.GradientDescentOptimizer(learning_rate)\n",
    "            gradients, v = zip(*optimizer.compute_gradients(loss))\n",
    "            gradients, _ = tf.clip_by_global_norm(gradients, 1.25)\n",
    "            optimizer = optimizer.apply_gradients(\n",
    "            zip(gradients, v), global_step=global_step)\n",
    "\n",
    "            # Predictions.\n",
    "            train_prediction = tf.nn.softmax(logits)\n",
    "\n",
    "            # Sampling and validation eval: batch 1, no unrolling.\n",
    "            sample_input = tf.placeholder(tf.float32, shape=[1, vocabulary_size])\n",
    "            saved_sample_output = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            saved_sample_state = tf.Variable(tf.zeros([1, num_nodes]))\n",
    "            reset_sample_state = tf.group(\n",
    "            saved_sample_output.assign(tf.zeros([1, num_nodes])),\n",
    "            saved_sample_state.assign(tf.zeros([1, num_nodes])))\n",
    "            sample_output, sample_state = lstm_cell(sample_input, saved_sample_output, saved_sample_state)\n",
    "            with tf.control_dependencies([saved_sample_output.assign(sample_output),\n",
    "                                         saved_sample_state.assign(sample_state)]):\n",
    "                    sample_prediction = tf.nn.softmax(tf.nn.xw_plus_b(sample_output, w, b))\n",
    "\n",
    "    # Training the model\n",
    "    with tf.Session(graph=graph) as session:\n",
    "        tf.initialize_all_variables().run()\n",
    "        mean_loss = 0\n",
    "        for step in range(num_steps):\n",
    "            batches = train_batches.next()\n",
    "            feed_dict = dict()\n",
    "            for i in range(num_unrollings + 1):\n",
    "                feed_dict[train_data[i]] = batches[i]\n",
    "\n",
    "            _, l, predictions, lr = session.run([optimizer, loss, train_prediction, learning_rate], feed_dict=feed_dict)\n",
    "            mean_loss += l\n",
    "        reset_sample_state.run()\n",
    "        valid_logprob = 0\n",
    "        for _ in range(valid_size):\n",
    "            b = valid_batches.next()\n",
    "            predictions = sample_prediction.eval({sample_input: b[0]})\n",
    "            valid_logprob = valid_logprob + logprob(predictions, b[1])\n",
    "\n",
    "        perplexity = float(np.exp(valid_logprob / valid_size))\n",
    "    return perplexity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.675105314113517"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(64, 64, 10, 3001, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hypothesis**: The number nodes must be equal to the batch size\n",
    "\n",
    "**Result**: The number of nodes and the batch size can be different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.913481800643745"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(32, 64, 10, 3001, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.748203599403953"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(64, 32, 10, 3001, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Question ** Can you have more unrollings than number of epochs?\n",
    "\n",
    "** Result ** Yes, however, it is not completely clear if it is different (aside from some randomness) than  if you had just 1 unrolling. Note: You cannot have 0 unrollings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.477824989981638"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(64, 64, 100, 65, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.85651774565771"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(64, 64, 1, 65, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Question ** Can you have more unrollings than nodes?\n",
    "\n",
    "** Result ** Yes, and it seems like the number of nodes places a significant role in reducing validation set perplexity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.328228938264665"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstm_model_test(64, 12, 15, 3001, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Hypothesis ** Increasing the num_nodes/batch_size will not reduce the perplexity.\n",
    "\n",
    "Given the above, this rests on the hidden assumption that the number of nodes and the bath size must be equal. Let's test them independently since I've already proven that hidden assumption to be incorrect.\n",
    "\n",
    "** Result **  Increasing the number of nodes or the batch size (holding everything else constant) results in lower perplexity. In fact, the validation set perplexity is a monotonically decreassing function of these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing batch size  2\n",
      "Testing batch size  4\n",
      "Testing batch size  8\n",
      "Testing batch size  16\n",
      "Testing batch size  32\n",
      "Testing batch size  64\n",
      "Testing batch size  128\n",
      "Testing batch size  256\n"
     ]
    }
   ],
   "source": [
    "batch_sizes = [2, 4, 8, 16, 32, 64, 128, 256]\n",
    "batch_size_results = []\n",
    "for batch_size in batch_sizes:\n",
    "    print(\"Testing batch size \", batch_size)\n",
    "    result = lstm_model_test(batch_size, 64, 10, 3001, 10000)\n",
    "    batch_size_results.append(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f40dd950a50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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P5J13oKMDll4633jMzMyaQbUPvdsOmAV8CVgGeH/2+qls22LHI2fMzMzqr9qZ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\nmJmZWW6ciJiZmVlu/j8TeJVnK12+YAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f409399a890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(batch_sizes, batch_size_results, label='', linewidth=2)\n",
    "plt.xlabel('Batch Size')\n",
    "plt.ylabel('Perplexity')\n",
    "plt.title(\"Batch Size and Perplexity\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing number of nodes:  2\n",
      "Testing number of nodes:  4\n",
      "Testing number of nodes:  8\n",
      "Testing number of nodes:  16\n",
      "Testing number of nodes:  32\n",
      "Testing number of nodes:  64\n",
      "Testing number of nodes:  128\n",
      "Testing number of nodes:  256\n"
     ]
    }
   ],
   "source": [
    "num_nodes = [2, 4, 8, 16, 32, 64, 128, 256]\n",
    "num_nodes_results = []\n",
    "for nodes in num_nodes:\n",
    "    print(\"Testing number of nodes: \", nodes)\n",
    "    result = lstm_model_test(64, nodes, 10, 3001, 10000)\n",
    "    num_nodes_results.append(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f40d95f2a10>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xMDMz661u9/GQtF53lxLEeSJwFfBb4AnipZffAd8twblWa+tgCu7nYWZmVgw9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\njRMPMzMzKxsnHmZmZlY2TjzMzMysbP4fEmRATFfHKWUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40a12a5990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_nodes, num_nodes_results, linewidth=2)\n",
    "plt.xlabel('Number of Nodes')\n",
    "plt.ylabel('Perplexity')\n",
    "plt.title(\"Number of Nodes and Perplexity\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Hypothesis ** Increasing the number of unrollings will reduce the validation set perplexity.\n",
    "\n",
    "** Result ** Correct: Like the number of nodes and batch size, increasing the number of unrollings reduces the validation set perplexity. However, it seems like after a certain point, this effect disapears, and may actually result in an increasing validation set perplexity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing number of unrollings 1\n",
      "Testing number of unrollings 2\n",
      "Testing number of unrollings 3\n",
      "Testing number of unrollings 4\n",
      "Testing number of unrollings 5\n",
      "Testing number of unrollings 10\n",
      "Testing number of unrollings 15\n",
      "Testing number of unrollings 20\n",
      "Testing number of unrollings 25\n",
      "Testing number of unrollings 30\n",
      "Testing number of unrollings 50\n"
     ]
    }
   ],
   "source": [
    "num_unrollings = [1,2,3,4,5,10,15,20,25,30,50]\n",
    "num_unrollings_results = []\n",
    "for unrollings in num_unrollings:\n",
    "    print(\"Testing number of unrollings\", unrollings)\n",
    "    result = lstm_model_test(64, 64, unrollings, 3001, 10000)\n",
    "    num_unrollings_results.append(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f409b68db50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZmZl1ppY4dNJo2Q1+diddd6D0Es1mZmbWvzHABqSLAr5U78o6MmiQQobv4mdmZla7/Ul3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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40d949ead0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(num_unrollings, num_unrollings_results, linewidth=2)\n",
    "plt.xlabel('Number of Unrollings')\n",
    "plt.ylabel('Perplexity')\n",
    "plt.title(\"Number of Unrollings and Perplexity\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Hypothesis ** Increasing the number of epochs will reduce the perplexity\n",
    "\n",
    "** Result ** Correct: Increasing the number of epochs does result in a generally decreasing perplexity, however it is not a monotonically decreasing function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing number of epochs 1001\n",
      "Testing number of epochs 2001\n",
      "Testing number of epochs 3001\n",
      "Testing number of epochs 4001\n",
      "Testing number of epochs 5001\n",
      "Testing number of epochs 6001\n",
      "Testing number of epochs 7001\n",
      "Testing number of epochs 8001\n",
      "Testing number of epochs 9001\n",
      "Testing number of epochs 10001\n"
     ]
    }
   ],
   "source": [
    "epochs = [1001, 2001, 3001, 4001, 5001, 6001, 7001, 8001, 9001, 10001]\n",
    "epoch_results = []\n",
    "for epoch in epochs:\n",
    "    print(\"Testing number of epochs\", epoch)\n",
    "    result = lstm_model_test(64, 64, 10, epoch, 10000)\n",
    "    epoch_results.append(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f40debc0290>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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aQWPHJheHiIiUnnyHLt8L7Ai0Bt4CpgLPAH1DCC83XXhSLHbbDTbf3LefeAIW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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f409b6824d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(epochs, epoch_results, linewidth=2)\n",
    "plt.xlabel('Number of Epochs')\n",
    "plt.ylabel('Perplexity')\n",
    "plt.title(\"Number of Epochs and Perplexity\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Question ** How is the model accuracy (validation set perplexity) affected by the joint changing of num_nodes and num_unrollings?\n",
    "\n",
    "** Result ** Correct: The resulting surfacie is a \"ski slope.\" As you increase both the number of nodes and the number of unrollings, the perplexity decreases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing paramters:  (64, 2, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 2, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 4, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 8, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 16, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 32, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 64, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 128, 50, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 1, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 2, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 3, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 4, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 5, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 10, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 15, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 20, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 25, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 30, 3001, 10000)\n",
      "Testing paramters:  (64, 256, 50, 3001, 10000)\n"
     ]
    }
   ],
   "source": [
    "num_unrollings = [1,2,3,4,5,10,15,20,25,30,50]\n",
    "num_nodes = [2, 4, 8, 16, 32, 64, 128, 256]\n",
    "num_epochs = [3001]\n",
    "batch_sizes = [64]\n",
    "summary = [10000]\n",
    "\n",
    "params = list(itertools.product(batch_sizes, num_nodes, num_unrollings, num_epochs, summary))\n",
    "params_results = []\n",
    "for params in params:\n",
    "    print(\"Testing paramters: \", params)\n",
    "    result = lstm_model_test(*params)\n",
    "    params_results.append(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_unrollings = [1,2,3,4,5,10,15,20,25,30,50]\n",
    "num_nodes = [2, 4, 8, 16, 32, 64, 128, 256]\n",
    "params = list(itertools.product(num_nodes, num_unrollings))\n",
    "\n",
    "x = [t[0] for t in params]\n",
    "y = [t[1] for t in params]\n",
    "z = params_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7f40a1849310>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kJz+Jtra2ko1DLeQ5gtrdp7aIiQCSfVVFUWCz2WC322GxWEy3IGVDzyLWE+Fia0lTzEm6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LC9o1XVYNUqEVWH2bNH5ehRnWDQ7FLqSodMRG3/ud1uMl0deqCjVX2BvXnMwNIMn5DnY1qQZRg+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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40a18997d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.set_xlabel('Nodes')\n",
    "ax.set_ylabel('Unrollings')\n",
    "ax.plot_trisurf(x, y, z, linewidth=0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}