From 87040e084e8ac70d8c91745b5fb31206dcdf49de Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Aur=C3=A9lien=20Geron?= <ageron@users.noreply.github.com>
Date: Thu, 18 Jan 2018 17:41:32 +0100
Subject: [PATCH] Replace reduce_sum with reduce_mean: adds an extra .1%
 accuracy :)

---
 extra_capsnets.ipynb | 386 ++++++++++++++++---------------------------
 1 file changed, 138 insertions(+), 248 deletions(-)

diff --git a/extra_capsnets.ipynb b/extra_capsnets.ipynb
index cdfeb2d..20e5dd1 100644
--- a/extra_capsnets.ipynb
+++ b/extra_capsnets.ipynb
@@ -77,10 +77,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 3,
+   "metadata": {},
    "outputs": [],
    "source": [
     "from __future__ import division, print_function, unicode_literals"
@@ -95,10 +93,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 4,
+   "metadata": {},
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -115,10 +111,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 5,
+   "metadata": {},
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -141,10 +135,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 6,
+   "metadata": {},
    "outputs": [],
    "source": [
     "tf.reset_default_graph()"
@@ -159,10 +151,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 7,
+   "metadata": {},
    "outputs": [],
    "source": [
     "np.random.seed(42)\n",
@@ -185,7 +175,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -203,7 +193,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -228,7 +218,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -286,10 +276,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 11,
+   "metadata": {},
    "outputs": [],
    "source": [
     "X = tf.placeholder(shape=[None, 28, 28, 1], dtype=tf.float32, name=\"X\")"
@@ -311,10 +299,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 12,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps1_n_maps = 32\n",
@@ -331,10 +317,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 13,
+   "metadata": {},
    "outputs": [],
    "source": [
     "conv1_params = {\n",
@@ -356,10 +340,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 14,
+   "metadata": {},
    "outputs": [],
    "source": [
     "conv1 = tf.layers.conv2d(X, name=\"conv1\", **conv1_params)\n",
@@ -382,10 +364,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 15,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps1_raw = tf.reshape(conv2, [-1, caps1_n_caps, caps1_n_dims],\n",
@@ -407,10 +387,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 16,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def squash(s, axis=-1, epsilon=1e-7, name=None):\n",
@@ -432,10 +410,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 17,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps1_output = squash(caps1_raw, name=\"caps1_output\")"
@@ -478,10 +454,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 18,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_n_caps = 10\n",
@@ -568,10 +542,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 19,
+   "metadata": {},
    "outputs": [],
    "source": [
     "init_sigma = 0.01\n",
@@ -591,10 +563,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 20,
+   "metadata": {},
    "outputs": [],
    "source": [
     "batch_size = tf.shape(X)[0]\n",
@@ -610,10 +580,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 21,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps1_output_expanded = tf.expand_dims(caps1_output, -1,\n",
@@ -633,7 +601,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -649,7 +617,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -665,10 +633,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 24,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_predicted = tf.matmul(W_tiled, caps1_output_tiled,\n",
@@ -684,7 +650,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -714,10 +680,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 26,
+   "metadata": {},
    "outputs": [],
    "source": [
     "raw_weights = tf.zeros([batch_size, caps1_n_caps, caps2_n_caps, 1, 1],\n",
@@ -747,10 +711,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 27,
+   "metadata": {},
    "outputs": [],
    "source": [
     "routing_weights = tf.nn.softmax(raw_weights, dim=2, name=\"routing_weights\")"
@@ -765,10 +727,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 28,
+   "metadata": {},
    "outputs": [],
    "source": [
     "weighted_predictions = tf.multiply(routing_weights, caps2_predicted,\n",
@@ -797,10 +757,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 29,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_output_round_1 = squash(weighted_sum, axis=-2,\n",
@@ -809,7 +767,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -853,7 +811,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 31,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -869,7 +827,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -885,10 +843,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 33,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_output_round_1_tiled = tf.tile(\n",
@@ -905,10 +861,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 34,
+   "metadata": {},
    "outputs": [],
    "source": [
     "agreement = tf.matmul(caps2_predicted, caps2_output_round_1_tiled,\n",
@@ -924,10 +878,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 35,
+   "metadata": {},
    "outputs": [],
    "source": [
     "raw_weights_round_2 = tf.add(raw_weights, agreement,\n",
@@ -943,10 +895,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 36,
+   "metadata": {},
    "outputs": [],
    "source": [
     "routing_weights_round_2 = tf.nn.softmax(raw_weights_round_2,\n",
@@ -972,10 +922,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 37,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_output = caps2_output_round_2"
@@ -1003,7 +951,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1043,7 +991,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1073,10 +1021,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 40,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def safe_norm(s, axis=-1, epsilon=1e-7, keep_dims=False, name=None):\n",
@@ -1088,10 +1034,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 41,
+   "metadata": {},
    "outputs": [],
    "source": [
     "y_proba = safe_norm(caps2_output, axis=-2, name=\"y_proba\")"
@@ -1106,10 +1050,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 42,
+   "metadata": {},
    "outputs": [],
    "source": [
     "y_proba_argmax = tf.argmax(y_proba, axis=2, name=\"y_proba\")"
@@ -1124,7 +1066,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 43,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1140,10 +1082,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 44,
+   "metadata": {},
    "outputs": [],
    "source": [
     "y_pred = tf.squeeze(y_proba_argmax, axis=[1,2], name=\"y_pred\")"
@@ -1151,7 +1091,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1181,10 +1121,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 46,
+   "metadata": {},
    "outputs": [],
    "source": [
     "y = tf.placeholder(shape=[None], dtype=tf.int64, name=\"y\")"
@@ -1212,10 +1150,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 47,
+   "metadata": {},
    "outputs": [],
    "source": [
     "m_plus = 0.9\n",
@@ -1232,10 +1168,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 48,
+   "metadata": {},
    "outputs": [],
    "source": [
     "T = tf.one_hot(y, depth=caps2_n_caps, name=\"T\")"
@@ -1250,7 +1184,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 48,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1267,7 +1201,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 49,
+   "execution_count": 50,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1283,10 +1217,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 51,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_output_norm = safe_norm(caps2_output, axis=-2, keep_dims=True,\n",
@@ -1302,10 +1234,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 52,
+   "metadata": {},
    "outputs": [],
    "source": [
     "present_error_raw = tf.square(tf.maximum(0., m_plus - caps2_output_norm),\n",
@@ -1323,10 +1253,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 53,
+   "metadata": {},
    "outputs": [],
    "source": [
     "absent_error_raw = tf.square(tf.maximum(0., caps2_output_norm - m_minus),\n",
@@ -1344,10 +1272,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 54,
+   "metadata": {},
    "outputs": [],
    "source": [
     "L = tf.add(T * present_error, lambda_ * (1.0 - T) * absent_error,\n",
@@ -1363,10 +1289,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 55,
+   "metadata": {},
    "outputs": [],
    "source": [
     "margin_loss = tf.reduce_mean(tf.reduce_sum(L, axis=1), name=\"margin_loss\")"
@@ -1409,10 +1333,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 56,
+   "metadata": {},
    "outputs": [],
    "source": [
     "mask_with_labels = tf.placeholder_with_default(False, shape=(),\n",
@@ -1428,10 +1350,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 57,
+   "metadata": {},
    "outputs": [],
    "source": [
     "reconstruction_targets = tf.cond(mask_with_labels, # condition\n",
@@ -1458,10 +1378,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 58,
+   "metadata": {},
    "outputs": [],
    "source": [
     "reconstruction_mask = tf.one_hot(reconstruction_targets,\n",
@@ -1478,7 +1396,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 59,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1494,7 +1412,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 60,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1510,10 +1428,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 61,
+   "metadata": {},
    "outputs": [],
    "source": [
     "reconstruction_mask_reshaped = tf.reshape(\n",
@@ -1530,10 +1446,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 62,
+   "metadata": {},
    "outputs": [],
    "source": [
     "caps2_output_masked = tf.multiply(\n",
@@ -1543,7 +1457,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 63,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1559,10 +1473,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 64,
+   "metadata": {},
    "outputs": [],
    "source": [
     "decoder_input = tf.reshape(caps2_output_masked,\n",
@@ -1579,7 +1491,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 65,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1602,10 +1514,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 65,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 66,
+   "metadata": {},
    "outputs": [],
    "source": [
     "n_hidden1 = 512\n",
@@ -1615,10 +1525,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 67,
+   "metadata": {},
    "outputs": [],
    "source": [
     "with tf.name_scope(\"decoder\"):\n",
@@ -1649,16 +1557,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 68,
+   "metadata": {},
    "outputs": [],
    "source": [
     "X_flat = tf.reshape(X, [-1, n_output], name=\"X_flat\")\n",
     "squared_difference = tf.square(X_flat - decoder_output,\n",
     "                               name=\"squared_difference\")\n",
-    "reconstruction_loss = tf.reduce_sum(squared_difference,\n",
+    "reconstruction_loss = tf.reduce_mean(squared_difference,\n",
     "                                    name=\"reconstruction_loss\")"
    ]
   },
@@ -1678,10 +1584,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 69,
+   "metadata": {},
    "outputs": [],
    "source": [
     "alpha = 0.0005\n",
@@ -1712,10 +1616,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 70,
+   "metadata": {},
    "outputs": [],
    "source": [
     "correct = tf.equal(y, y_pred, name=\"correct\")\n",
@@ -1738,10 +1640,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 71,
+   "metadata": {},
    "outputs": [],
    "source": [
     "optimizer = tf.train.AdamOptimizer()\n",
@@ -1764,10 +1664,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 72,
+   "metadata": {},
    "outputs": [],
    "source": [
     "init = tf.global_variables_initializer()\n",
@@ -1804,7 +1702,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 73,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1870,7 +1768,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Training is finished, we reached over 99.3% accuracy on the validation set after just 5 epochs, things are looking good. Now let's evaluate the model on the test set."
+    "Training is finished, we reached over 99.4% accuracy on the validation set after just 5 epochs, things are looking good. Now let's evaluate the model on the test set."
    ]
   },
   {
@@ -1882,7 +1780,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 74,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1915,7 +1813,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We reach 99.43% accuracy on the test set. Pretty nice. :)"
+    "We reach 99.53% accuracy on the test set. Pretty nice. :)"
    ]
   },
   {
@@ -1934,7 +1832,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 75,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1966,7 +1864,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 76,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2022,7 +1920,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 77,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2038,10 +1936,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 78,
+   "metadata": {},
    "outputs": [],
    "source": [
     "def tweak_pose_parameters(output_vectors, min=-0.5, max=0.5, n_steps=11):\n",
@@ -2062,10 +1958,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 79,
+   "metadata": {},
    "outputs": [],
    "source": [
     "n_steps = 11\n",
@@ -2084,7 +1978,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 80,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2108,10 +2002,8 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {
-    "collapsed": true
-   },
+   "execution_count": 81,
+   "metadata": {},
    "outputs": [],
    "source": [
     "tweak_reconstructions = decoder_output_value.reshape(\n",
@@ -2127,7 +2019,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 82,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2161,9 +2053,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
+   "metadata": {},
    "outputs": [],
    "source": []
   }