notebooks/4.batch-normalization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Layer activation normalization (Batch normalization)\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/parrt/fundamentals-of-deep-learning/blob/main/notebooks/4.batch-normalization.ipynb)\n",
    "\n",
    "By [Terence Parr](https://explained.ai).\n",
    "\n",
    "*In progress...can't get a good example that uses a toy data set* (I also decided this is not the right time to introduce the complexity of batch normalization.)\n",
    "\n",
    "Just as we normalize or standardize the input variables, networks train better if we normalize the output of each layer's activation. It is called batch normalization because we normally train with batches of records not the entire data set, but it's really just allowing the model to shift and scale each neurons activation. Batch normalization does not use the joint distribution. Each neuron activation is \"whitened\" independently by subtracting the mean and dividing by the standard deviation. Then, we scale and shift that data using two new model parameters to support layer activation distributions that are useful for training purposes.\n",
    "\n",
    "At test time, we use mean/var estimated during training for activations to whiten the activations as the test instance sails through the network. The learned parameters scale and shift the layer activations but do not change the shape of the distribution. This technique helps move gradients through the network during training without exploding or vanishing.\n",
    "\n",
    "As with normalizing the input layer, batch normalization is believed to support faster learning rates for faster training. It also has a mild regularization effect per Andrew Ng, improving model generality. The model could also be less sensitive to the initialization procedure.  See [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://arxiv.org/abs/1502.03167) for more information and video [Why Does Batch Norm Work?](https://www.youtube.com/watch?v=nUUqwaxLnWs)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "import torch\n",
    "import copy\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import load_diabetes\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import colors \n",
    "import colour\n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "import tsensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_history(history, ax=None, maxy=None, file=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots(1,1, figsize=(3.5,3))\n",
    "    ax.set_ylabel(\"Loss\")\n",
    "    ax.set_xlabel(\"Epochs\")\n",
    "    loss = history[:,0]\n",
    "    val_loss = history[:,1]\n",
    "    if maxy:\n",
    "        ax.set_ylim(0,maxy)\n",
    "    else:\n",
    "        ax.set_ylim(0,torch.max(val_loss))\n",
    "    ax.plot(loss, label='train_loss')\n",
    "    ax.plot(val_loss, label='val_loss')\n",
    "    ax.legend(loc='upper right')\n",
    "    plt.tight_layout()\n",
    "    if file:\n",
    "        plt.savefig(f\"/Users/{os.environ['USER']}/Desktop/{file}.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(model, X_train, X_test, y_train, y_test,\n",
    "          learning_rate = .5, nepochs=2000, weight_decay=0):\n",
    "    optimizer = torch.optim.Adam(model.parameters(),\n",
    "                                 lr=learning_rate, weight_decay=weight_decay)\n",
    "    history = [] # track training and validation loss\n",
    "    best_loss = 1e10\n",
    "    best_model = None\n",
    "    for epoch in range(nepochs+1):\n",
    "        y_pred = model(X_train)\n",
    "        loss = torch.mean((y_pred - y_train)**2)\n",
    "\n",
    "        y_pred_test = model(X_test)\n",
    "        loss_test = torch.mean((y_pred_test - y_test)**2)\n",
    "        history.append((loss, loss_test))\n",
    "        if loss_test < best_loss:\n",
    "            best_loss = loss_test\n",
    "            best_model = copy.deepcopy(model)\n",
    "            best_epoch = epoch\n",
    "        if epoch % (nepochs//10) == 0:\n",
    "            print(f\"Epoch {epoch:4d} MSE train loss {loss:12.3f}   test loss {loss_test:12.3f}\")\n",
    "            \n",
    "        optimizer.zero_grad()\n",
    "        loss.backward() # autograd computes w1.grad, b1.grad, ...\n",
    "        optimizer.step()\n",
    "    print(f\"BEST MSE test loss {best_loss:.3f} at epoch {best_epoch}\")\n",
    "    return torch.tensor(history), best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "442"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = load_diabetes()\n",
    "len(d.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>bp</th>\n",
       "      <th>s1</th>\n",
       "      <th>s2</th>\n",
       "      <th>s3</th>\n",
       "      <th>s4</th>\n",
       "      <th>s5</th>\n",
       "      <th>s6</th>\n",
       "      <th>disease</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.038076</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.061696</td>\n",
       "      <td>0.021872</td>\n",
       "      <td>-0.044223</td>\n",
       "      <td>-0.034821</td>\n",
       "      <td>-0.043401</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.019908</td>\n",
       "      <td>-0.017646</td>\n",
       "      <td>151.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.001882</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.051474</td>\n",
       "      <td>-0.026328</td>\n",
       "      <td>-0.008449</td>\n",
       "      <td>-0.019163</td>\n",
       "      <td>0.074412</td>\n",
       "      <td>-0.039493</td>\n",
       "      <td>-0.068330</td>\n",
       "      <td>-0.092204</td>\n",
       "      <td>75.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.085299</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.044451</td>\n",
       "      <td>-0.005671</td>\n",
       "      <td>-0.045599</td>\n",
       "      <td>-0.034194</td>\n",
       "      <td>-0.032356</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.002864</td>\n",
       "      <td>-0.025930</td>\n",
       "      <td>141.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        age       sex       bmi        bp        s1        s2        s3  \\\n",
       "0  0.038076  0.050680  0.061696  0.021872 -0.044223 -0.034821 -0.043401   \n",
       "1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163  0.074412   \n",
       "2  0.085299  0.050680  0.044451 -0.005671 -0.045599 -0.034194 -0.032356   \n",
       "\n",
       "         s4        s5        s6  disease  \n",
       "0 -0.002592  0.019908 -0.017646    151.0  \n",
       "1 -0.039493 -0.068330 -0.092204     75.0  \n",
       "2 -0.002592  0.002864 -0.025930    141.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(d.data, columns=d.feature_names)\n",
    "df['disease'] = d.target # \"quantitative measure of disease progression one year after baseline\"\n",
    "df.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Split data into train, validation sets\n",
    "\n",
    "We'll use \"test\" as shorthand for \"validation\" but technically they are not the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1) # set a random seed for consistency across runs\n",
    "n = len(df)\n",
    "n_test = int(n*0.20) # 20% held out as validation set\n",
    "n_train = n - n_test\n",
    "X = df.drop('disease',axis=1).values\n",
    "y = df['disease'].values\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=n_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = np.mean(X_train,axis=0)\n",
    "std = np.std(X_train,axis=0)\n",
    "X_train = (X_train-m)/std\n",
    "X_test = (X_test-m)/std       # use training data only when prepping test sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Baseline with random forest\n",
    "\n",
    "As we did in the previous notebook, let's get a baseline (although it's the same as before)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training MSE 455.43 validation MSE 3405.60\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestRegressor(n_estimators=500)#, min_samples_leaf=2, max_features=1)\n",
    "rf.fit(X_train, y_train.reshape(-1))\n",
    "y_pred = rf.predict(X_train)\n",
    "mse = np.mean((y_pred - y_train.reshape(-1))**2)\n",
    "\n",
    "y_pred = rf.predict(X_test)\n",
    "mse_test = np.mean((y_pred - y_test.reshape(-1))**2)\n",
    "\n",
    "print(f\"Training MSE {mse:.2f} validation MSE {mse_test:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No batch normalization\n",
    "\n",
    "We know how to train a vanilla neural network on this data, so let's do that again to reinforce our understanding and get the results into this notebook as well for comparison purposes. (We'll see how batch normalization performs after this.) Let's start by converting the numpy arrays into pytorch tensors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = torch.tensor(X_train).float()\n",
    "X_test = torch.tensor(X_test).float()\n",
    "y_train = torch.tensor(y_train).float().reshape(-1,1) # column vector\n",
    "y_test = torch.tensor(y_test).float().reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0 MSE train loss    29824.736   test loss    25906.725\n",
      "Epoch  100 MSE train loss     2498.819   test loss     3001.228\n",
      "Epoch  200 MSE train loss     2362.622   test loss     2951.789\n",
      "Epoch  300 MSE train loss     2170.585   test loss     3284.207\n",
      "Epoch  400 MSE train loss     2080.921   test loss     3272.910\n",
      "Epoch  500 MSE train loss     1989.582   test loss     3354.512\n",
      "Epoch  600 MSE train loss     1976.366   test loss     3439.697\n",
      "Epoch  700 MSE train loss     1960.431   test loss     3484.861\n",
      "Epoch  800 MSE train loss     1954.916   test loss     3476.629\n",
      "Epoch  900 MSE train loss     1933.969   test loss     3574.152\n",
      "Epoch 1000 MSE train loss     1970.010   test loss     3607.064\n",
      "BEST MSE test loss 2925.281 at epoch 182\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 245
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ncols = X.shape[1]\n",
    "n_neurons = 10\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(ncols, n_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(n_neurons, n_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(n_neurons, 1)\n",
    ")\n",
    "\n",
    "history, best_model = train(model, X_train, X_test, y_train, y_test,\n",
    "                            learning_rate=.3, nepochs=1000,\n",
    "                            weight_decay=0)\n",
    "\n",
    "# verify we got the best model out\n",
    "y_pred = best_model(X_test)\n",
    "loss_test = torch.mean((y_pred - y_test)**2)\n",
    "\n",
    "plot_history(torch.clamp(history, 0, 12000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batch normalization prior to nonlinearity\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0 MSE train loss    29855.828   test loss    25954.975\n",
      "Epoch  100 MSE train loss     2341.888   test loss     3284.765\n",
      "Epoch  200 MSE train loss     2190.471   test loss     3271.307\n",
      "Epoch  300 MSE train loss     2124.554   test loss     3266.053\n",
      "Epoch  400 MSE train loss     2086.827   test loss     3269.585\n",
      "Epoch  500 MSE train loss     2059.068   test loss     3292.539\n",
      "Epoch  600 MSE train loss     2033.019   test loss     3312.165\n",
      "Epoch  700 MSE train loss     2008.856   test loss     3340.174\n",
      "Epoch  800 MSE train loss     1984.274   test loss     3380.038\n",
      "Epoch  900 MSE train loss     1960.679   test loss     3420.923\n",
      "Epoch 1000 MSE train loss     1939.954   test loss     3465.430\n",
      "BEST MSE test loss 3126.286 at epoch 58\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 245
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ncols = X.shape[1]\n",
    "n_neurons = 300\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(ncols, n_neurons),\n",
    "    nn.BatchNorm1d(n_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(n_neurons, 1)\n",
    ")\n",
    "\n",
    "history, best_model = train(model, X_train, X_test, y_train, y_test,\n",
    "                            learning_rate=.02, nepochs=1000,\n",
    "                            weight_decay=0)\n",
    "\n",
    "# verify we got the best model out\n",
    "y_pred = best_model(X_test)\n",
    "loss_test = torch.mean((y_pred - y_test)**2)\n",
    "\n",
    "plot_history(torch.clamp(history, 0, 12000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Batch normalization after nonlinearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch    0 MSE train loss    29825.834   test loss    25912.461\n",
      "Epoch  100 MSE train loss     1580.148   test loss     4041.223\n",
      "Epoch  200 MSE train loss      599.812   test loss     5057.402\n",
      "Epoch  300 MSE train loss      192.489   test loss     5665.648\n",
      "Epoch  400 MSE train loss       83.200   test loss     6629.621\n",
      "Epoch  500 MSE train loss       32.758   test loss     7357.072\n",
      "Epoch  600 MSE train loss       26.932   test loss     7657.275\n",
      "Epoch  700 MSE train loss       20.176   test loss     7938.530\n",
      "Epoch  800 MSE train loss       16.955   test loss     8132.025\n",
      "Epoch  900 MSE train loss       12.196   test loss     8320.524\n",
      "Epoch 1000 MSE train loss        8.558   test loss     8386.548\n",
      "BEST MSE test loss 3331.539 at epoch 35\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 252x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 207,
       "width": 245
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ncols = X.shape[1]\n",
    "n_neurons = 300\n",
    "model = nn.Sequential(\n",
    "    nn.Linear(ncols, n_neurons),\n",
    "    nn.ReLU(),\n",
    "    nn.BatchNorm1d(n_neurons),\n",
    "#     nn.Linear(n_neurons, n_neurons),\n",
    "#     nn.ReLU(),\n",
    "#     nn.BatchNorm1d(n_neurons),\n",
    "    nn.Linear(n_neurons, 1)\n",
    ")\n",
    "\n",
    "history, best_model = train(model, X_train, X_test, y_train, y_test,\n",
    "                            learning_rate=.02, nepochs=1000,\n",
    "                            weight_decay=0)\n",
    "\n",
    "# verify we got the best model out\n",
    "y_pred = best_model(X_test)\n",
    "loss_test = torch.mean((y_pred - y_test)**2)\n",
    "\n",
    "plot_history(torch.clamp(history, 0, 12000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At least for this data set and a random train/test set, batch normalization gives us much faster convergence to the best validation loss and also we get a lower test loss:\n",
    "\n",
    "1. No normalization: BEST MSE test loss 3073.239 at epoch 47\n",
    "1. Prior to ReLU: BEST MSE test loss 2997.867 at epoch 30\n",
    "1. Post ReLU: BEST MSE test loss 3073.734 at epoch 19\n",
    "\n",
    "In the end, this data set is pretty small and perhaps not the most impressive demonstration of batch normalization, but it serves our purposes to demonstrate the technique.\n",
    "\n",
    "See [Batch Normalization before or after ReLU?](https://www.reddit.com/r/MachineLearning/comments/67gonq/d_batch_normalization_before_or_after_relu/)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}