Dropout.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Dropout\n",
    "Dropout [1] is a technique for regularizing neural networks by randomly setting some features to zero during the forward pass. In this exercise you will implement a dropout layer and modify your fully-connected network to optionally use dropout.\n",
    "\n",
    "[1] Geoffrey E. Hinton et al, \"Improving neural networks by preventing co-adaptation of feature detectors\", arXiv 2012"
   ]
  },
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   "source": [
    "# As usual, a bit of setup\n",
    "\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from cs231n.classifiers.fc_net import *\n",
    "from cs231n.data_utils import get_CIFAR10_data\n",
    "from cs231n.gradient_check import eval_numerical_gradient, eval_numerical_gradient_array\n",
    "from cs231n.solver import Solver\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'\n",
    "\n",
    "# for auto-reloading external modules\n",
    "# see http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "def rel_error(x, y):\n",
    "  \"\"\" returns relative error \"\"\"\n",
    "  return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_val:  (1000, 3, 32, 32)\n",
      "X_train:  (49000, 3, 32, 32)\n",
      "X_test:  (1000, 3, 32, 32)\n",
      "y_val:  (1000,)\n",
      "y_train:  (49000,)\n",
      "y_test:  (1000,)\n"
     ]
    }
   ],
   "source": [
    "# Load the (preprocessed) CIFAR10 data.\n",
    "\n",
    "data = get_CIFAR10_data()\n",
    "for k, v in data.iteritems():\n",
    "  print '%s: ' % k, v.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dropout forward pass\n",
    "In the file `cs231n/layers.py`, implement the forward pass for dropout. Since dropout behaves differently during training and testing, make sure to implement the operation for both modes.\n",
    "\n",
    "Once you have done so, run the cell below to test your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running tests with p =  0.3\n",
      "Mean of input:  9.99947812133\n",
      "Mean of train-time output:  9.99860913229\n",
      "Mean of test-time output:  9.99947812133\n",
      "Fraction of train-time output set to zero:  0.300048\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n",
      "Running tests with p =  0.6\n",
      "Mean of input:  9.99947812133\n",
      "Mean of train-time output:  9.99926194399\n",
      "Mean of test-time output:  9.99947812133\n",
      "Fraction of train-time output set to zero:  0.600112\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n",
      "Running tests with p =  0.75\n",
      "Mean of input:  9.99947812133\n",
      "Mean of train-time output:  10.0095091761\n",
      "Mean of test-time output:  9.99947812133\n",
      "Fraction of train-time output set to zero:  0.749792\n",
      "Fraction of test-time output set to zero:  0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = np.random.randn(500, 500) + 10\n",
    "\n",
    "for p in [0.3, 0.6, 0.75]:\n",
    "  out, _ = dropout_forward(x, {'mode': 'train', 'p': p})\n",
    "  out_test, _ = dropout_forward(x, {'mode': 'test', 'p': p})\n",
    "\n",
    "  print 'Running tests with p = ', p\n",
    "  print 'Mean of input: ', x.mean()\n",
    "  print 'Mean of train-time output: ', out.mean()\n",
    "  print 'Mean of test-time output: ', out_test.mean()\n",
    "  print 'Fraction of train-time output set to zero: ', (out == 0).mean()\n",
    "  print 'Fraction of test-time output set to zero: ', (out_test == 0).mean()\n",
    "  print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Dropout backward pass\n",
    "In the file `cs231n/layers.py`, implement the backward pass for dropout. After doing so, run the following cell to numerically gradient-check your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dx relative error:  1.89290708557e-11\n"
     ]
    }
   ],
   "source": [
    "x = np.random.randn(10, 10) + 10\n",
    "dout = np.random.randn(*x.shape)\n",
    "\n",
    "dropout_param = {'mode': 'train', 'p': 0.8, 'seed': 123}\n",
    "out, cache = dropout_forward(x, dropout_param)\n",
    "dx = dropout_backward(dout, cache)\n",
    "dx_num = eval_numerical_gradient_array(lambda xx: dropout_forward(xx, dropout_param)[0], x, dout)\n",
    "\n",
    "print 'dx relative error: ', rel_error(dx, dx_num)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Fully-connected nets with Dropout\n",
    "In the file `cs231n/classifiers/fc_net.py`, modify your implementation to use dropout. Specificially, if the constructor the the net receives a nonzero value for the `dropout` parameter, then the net should add dropout immediately after every ReLU nonlinearity. After doing so, run the following to numerically gradient-check your implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running check with dropout =  0\n",
      "Initial loss:  2.30782978974\n",
      "W1 relative error: 1.24e-07\n",
      "W2 relative error: 1.11e-06\n",
      "W3 relative error: 5.92e-08\n",
      "b1 relative error: 9.69e-09\n",
      "b2 relative error: 2.54e-08\n",
      "b3 relative error: 1.11e-10\n",
      "\n",
      "Running check with dropout =  0.25\n",
      "Initial loss:  2.30770805241\n",
      "W1 relative error: 3.49e-07\n",
      "W2 relative error: 2.86e-07\n",
      "W3 relative error: 3.60e-08\n",
      "b1 relative error: 1.47e-08\n",
      "b2 relative error: 4.83e-09\n",
      "b3 relative error: 1.44e-10\n",
      "\n",
      "Running check with dropout =  0.5\n",
      "Initial loss:  2.3109013384\n",
      "W1 relative error: 3.22e-08\n",
      "W2 relative error: 5.88e-08\n",
      "W3 relative error: 2.79e-08\n",
      "b1 relative error: 1.02e-08\n",
      "b2 relative error: 2.87e-09\n",
      "b3 relative error: 1.37e-10\n",
      "\n"
     ]
    }
   ],
   "source": [
    "N, D, H1, H2, C = 2, 15, 20, 30, 10\n",
    "X = np.random.randn(N, D)\n",
    "y = np.random.randint(C, size=(N,))\n",
    "\n",
    "for dropout in [0, 0.25, 0.5]:\n",
    "  print 'Running check with dropout = ', dropout\n",
    "  model = FullyConnectedNet([H1, H2], input_dim=D, num_classes=C,\n",
    "                            weight_scale=5e-2, dtype=np.float64,\n",
    "                            dropout=dropout, seed=123)\n",
    "\n",
    "  loss, grads = model.loss(X, y)\n",
    "  print 'Initial loss: ', loss\n",
    "\n",
    "  for name in sorted(grads):\n",
    "    f = lambda _: model.loss(X, y)[0]\n",
    "    grad_num = eval_numerical_gradient(f, model.params[name], verbose=False, h=1e-5)\n",
    "    print '%s relative error: %.2e' % (name, rel_error(grad_num, grads[name]))\n",
    "  print"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Regularization experiment\n",
    "As an experiment, we will train a pair of two-layer networks on 500 training examples: one will use no dropout, and one will use a dropout probability of 0.75. We will then visualize the training and validation accuracies of the two networks over time."
   ]
  },
  {
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   "execution_count": 10,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "(Iteration 1 / 125) loss: 8.596245\n",
      "(Epoch 0 / 25) train acc: 0.252000; val_acc: 0.177000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "cs231n/layers.py:574: RuntimeWarning: divide by zero encountered in log\n",
      "  loss = -np.sum(np.log(probs[np.arange(N), y])) / N\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(Epoch 1 / 25) train acc: 0.284000; val_acc: 0.184000\n",
      "(Epoch 2 / 25) train acc: 0.348000; val_acc: 0.215000\n",
      "(Epoch 3 / 25) train acc: 0.424000; val_acc: 0.216000\n",
      "(Epoch 4 / 25) train acc: 0.456000; val_acc: 0.240000\n",
      "(Epoch 5 / 25) train acc: 0.544000; val_acc: 0.239000\n",
      "(Epoch 6 / 25) train acc: 0.622000; val_acc: 0.266000\n",
      "(Epoch 7 / 25) train acc: 0.660000; val_acc: 0.261000\n",
      "(Epoch 8 / 25) train acc: 0.738000; val_acc: 0.301000\n",
      "(Epoch 9 / 25) train acc: 0.782000; val_acc: 0.259000\n",
      "(Epoch 10 / 25) train acc: 0.832000; val_acc: 0.287000\n",
      "(Epoch 11 / 25) train acc: 0.878000; val_acc: 0.287000\n",
      "(Epoch 12 / 25) train acc: 0.864000; val_acc: 0.280000\n",
      "(Epoch 13 / 25) train acc: 0.904000; val_acc: 0.308000\n",
      "(Epoch 14 / 25) train acc: 0.916000; val_acc: 0.310000\n",
      "(Epoch 15 / 25) train acc: 0.954000; val_acc: 0.293000\n",
      "(Epoch 16 / 25) train acc: 0.950000; val_acc: 0.294000\n",
      "(Epoch 17 / 25) train acc: 0.974000; val_acc: 0.312000\n",
      "(Epoch 18 / 25) train acc: 0.992000; val_acc: 0.315000\n",
      "(Epoch 19 / 25) train acc: 0.974000; val_acc: 0.289000\n",
      "(Epoch 20 / 25) train acc: 0.978000; val_acc: 0.304000\n",
      "(Iteration 101 / 125) loss: 0.065032\n",
      "(Epoch 21 / 25) train acc: 0.982000; val_acc: 0.290000\n",
      "(Epoch 22 / 25) train acc: 0.976000; val_acc: 0.309000\n",
      "(Epoch 23 / 25) train acc: 0.980000; val_acc: 0.309000\n",
      "(Epoch 24 / 25) train acc: 0.990000; val_acc: 0.319000\n",
      "(Epoch 25 / 25) train acc: 0.992000; val_acc: 0.301000\n",
      "0.75\n",
      "(Iteration 1 / 125) loss: 15.993098\n",
      "(Epoch 0 / 25) train acc: 0.200000; val_acc: 0.180000\n",
      "(Epoch 1 / 25) train acc: 0.330000; val_acc: 0.232000\n",
      "(Epoch 2 / 25) train acc: 0.338000; val_acc: 0.237000\n",
      "(Epoch 3 / 25) train acc: 0.410000; val_acc: 0.252000\n",
      "(Epoch 4 / 25) train acc: 0.448000; val_acc: 0.270000\n",
      "(Epoch 5 / 25) train acc: 0.476000; val_acc: 0.274000\n",
      "(Epoch 6 / 25) train acc: 0.576000; val_acc: 0.278000\n",
      "(Epoch 7 / 25) train acc: 0.590000; val_acc: 0.307000\n",
      "(Epoch 8 / 25) train acc: 0.562000; val_acc: 0.297000\n",
      "(Epoch 9 / 25) train acc: 0.604000; val_acc: 0.289000\n",
      "(Epoch 10 / 25) train acc: 0.620000; val_acc: 0.266000\n",
      "(Epoch 11 / 25) train acc: 0.694000; val_acc: 0.284000\n",
      "(Epoch 12 / 25) train acc: 0.730000; val_acc: 0.301000\n",
      "(Epoch 13 / 25) train acc: 0.682000; val_acc: 0.303000\n",
      "(Epoch 14 / 25) train acc: 0.726000; val_acc: 0.305000\n",
      "(Epoch 15 / 25) train acc: 0.774000; val_acc: 0.307000\n",
      "(Epoch 16 / 25) train acc: 0.772000; val_acc: 0.287000\n",
      "(Epoch 17 / 25) train acc: 0.792000; val_acc: 0.304000\n",
      "(Epoch 18 / 25) train acc: 0.792000; val_acc: 0.342000\n",
      "(Epoch 19 / 25) train acc: 0.796000; val_acc: 0.298000\n",
      "(Epoch 20 / 25) train acc: 0.824000; val_acc: 0.313000\n",
      "(Iteration 101 / 125) loss: 58.441788\n",
      "(Epoch 21 / 25) train acc: 0.816000; val_acc: 0.311000\n",
      "(Epoch 22 / 25) train acc: 0.836000; val_acc: 0.330000\n",
      "(Epoch 23 / 25) train acc: 0.834000; val_acc: 0.304000\n",
      "(Epoch 24 / 25) train acc: 0.888000; val_acc: 0.299000\n",
      "(Epoch 25 / 25) train acc: 0.920000; val_acc: 0.317000\n"
     ]
    }
   ],
   "source": [
    "# Train two identical nets, one with dropout and one without\n",
    "\n",
    "num_train = 500\n",
    "small_data = {\n",
    "  'X_train': data['X_train'][:num_train],\n",
    "  'y_train': data['y_train'][:num_train],\n",
    "  'X_val': data['X_val'],\n",
    "  'y_val': data['y_val'],\n",
    "}\n",
    "\n",
    "solvers = {}\n",
    "dropout_choices = [0, 0.75]\n",
    "for dropout in dropout_choices:\n",
    "  model = FullyConnectedNet([500], dropout=dropout)\n",
    "  print dropout\n",
    "\n",
    "  solver = Solver(model, small_data,\n",
    "                  num_epochs=25, batch_size=100,\n",
    "                  update_rule='adam',\n",
    "                  optim_config={\n",
    "                    'learning_rate': 5e-4,\n",
    "                  },\n",
    "                  verbose=True, print_every=100)\n",
    "  solver.train()\n",
    "  solvers[dropout] = solver"
   ]
  },
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   "execution_count": 11,
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   "outputs": [
    {
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Vde3BJmZxwhapZtRUQMzMncClwErgXkqzld4dEYsiYk75sD8D/jAifgx8Fbg4m2ExR0kq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\nlymmkiRJkiTAAFGSJEmSVGWAWK4byu6A6prXl4rk9aUieX2paF5jKlJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118c1d450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot train and validation accuracies of the two models\n",
    "\n",
    "train_accs = []\n",
    "val_accs = []\n",
    "for dropout in dropout_choices:\n",
    "  solver = solvers[dropout]\n",
    "  train_accs.append(solver.train_acc_history[-1])\n",
    "  val_accs.append(solver.val_acc_history[-1])\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "for dropout in dropout_choices:\n",
    "  plt.plot(solvers[dropout].train_acc_history, 'o', label='%.2f dropout' % dropout)\n",
    "plt.title('Train accuracy')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(ncol=2, loc='lower right')\n",
    "  \n",
    "plt.subplot(3, 1, 2)\n",
    "for dropout in dropout_choices:\n",
    "  plt.plot(solvers[dropout].val_acc_history, 'o', label='%.2f dropout' % dropout)\n",
    "plt.title('Val accuracy')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(ncol=2, loc='lower right')\n",
    "\n",
    "plt.gcf().set_size_inches(15, 15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Question\n",
    "Explain what you see in this experiment. What does it suggest about dropout?\n",
    "** dropout prevents overfitting i.e. pulls down the training accuracy from going up too fast**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Answer\n"
   ]
  }
 ],
 "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}