feed-forward-nn-experiments.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "from torch import autograd\n",
    "import torch.nn.functional as F\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "images1 = np.load(\"cs475_project_data/images.npy\")\n",
    "num_images, height, width = images1.shape\n",
    "images1 = images1.reshape(num_images, height*width) #reshape\n",
    "labels1 = np.load(\"cs475_project_data/labels.npy\")\n",
    "\n",
    "images = torch.from_numpy(images1)\n",
    "labels = torch.from_numpy(labels1).type(torch.IntTensor) # make sure int values\n",
    "\n",
    "images = images.type(torch.DoubleTensor)\n",
    "images = (images - torch.mean(images))/torch.std(images)\n",
    "# the above normalizes the data based on z score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# split data\n",
    "train_data = images[:40000]\n",
    "dev_data = images[40000:45000]\n",
    "test_data = images[45000:]\n",
    "\n",
    "train_labels = labels[:40000]\n",
    "dev_labels = labels[40000:45000]\n",
    "test_labels = labels[45000:]\n",
    "\n",
    "HEIGHT = 26\n",
    "WIDTH = 26\n",
    "NUM_CLASSES = 5\n",
    "NUM_OPT_STEPS = 1500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FeedForwardNN(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.linear1 = torch.nn.Linear(HEIGHT*WIDTH, 300)\n",
    "        self.linear2 = torch.nn.Linear(300, 100)\n",
    "        self.linear3 = torch.nn.Linear(100, NUM_CLASSES)\n",
    "    def forward(self, x):\n",
    "        first = F.relu(self.linear1(x)).clamp(min=0)\n",
    "        #first = F.dropout(first, training=True)\n",
    "        second = F.relu(self.linear2(first)).clamp(min=0)\n",
    "        y_pred = F.relu(self.linear3(second)).clamp(min=0)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FeedForwardNN()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(batch_size):\n",
    "    # model.train() puts our model in train mode, which can require different\n",
    "    # behavior than eval mode (for example in the case of dropout).\n",
    "    model.train()\n",
    "    # i is is a 1-D array with shape [batch_size]\n",
    "    i = np.random.choice(train_data.shape[0], size=batch_size, replace=False)\n",
    "    temp = train_data.numpy()\n",
    "    temp1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(temp[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(temp1[i].astype(np.int)))\n",
    "    optimizer.zero_grad()\n",
    "    y_hat_ = model(x)\n",
    "    loss = F.cross_entropy(y_hat_, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    return loss.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_train_accuracy():\n",
    "    #model.eval()\n",
    "    i = np.random.choice(train_data.shape[0], size=1000, replace=False)\n",
    "    tempy = train_data.numpy()\n",
    "    tempy1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy1[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()\n",
    "\n",
    "def val_accuracy():\n",
    "    #model.eval()\n",
    "    i = np.random.choice(dev_data.shape[0], size=5000, replace=False)\n",
    "    tempy2 = dev_data.numpy()\n",
    "    tempy3 = dev_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy2[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy3[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 3 layer NN with parameters described in code above.\n",
      "     0  0.43  0.43\n",
      "   100  0.87  0.83\n",
      "   200  0.89  0.85\n",
      "   300  0.92  0.87\n",
      "   400  0.95  0.87\n",
      "   500  0.95  0.87\n",
      "   600  0.97  0.87\n",
      "   700  0.98  0.87\n",
      "   800  0.99  0.87\n",
      "   900  0.99  0.87\n",
      "  1000  1.00  0.87\n",
      "  1100  1.00  0.87\n",
      "  1200  0.99  0.87\n",
      "  1300  0.99  0.87\n",
      "  1400  0.99  0.87\n"
     ]
    }
   ],
   "source": [
    "train_accs, val_accs = [], []\n",
    "iterations = []\n",
    "print(\"Using 3 layer NN with parameters described in code above.\")\n",
    "for i in range(NUM_OPT_STEPS):\n",
    "    train(1000)\n",
    "    if i % 100 == 0:\n",
    "        iterations.append(i)\n",
    "        train_accs.append(approx_train_accuracy())\n",
    "        val_accs.append(val_accuracy())\n",
    "        print(\"%6d %5.2f %5.2f\" % (i, train_accs[-1], val_accs[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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pe1HSR4mGrChPbVjZx+dlds7lgzhJ4XKiYa0/QVS3MA74UCqDykbeR8E5lw8G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\nXK//DzsCYua4hu/HAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b2c940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jhk0KEXF3RFwYEfsC7wAWAX+QdLOks8sWYYW4pGBmtSjP00dExB8i4nzgdKAF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\nBTMzG+CkYGZmA/5/NvGDz4Ja2E0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105f71ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(iterations, train_accs)\n",
    "plt.title(\"Accuracy on Training Set (3 layers)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over 1000 Training examples\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(iterations, val_accs)\n",
    "plt.title(\"Accuracy on Validation Set (3 layers)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over all Validation examples\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FeedForwardNN(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.linear1 = torch.nn.Linear(HEIGHT*WIDTH, 300)\n",
    "        self.linear2 = torch.nn.Linear(300, 150)\n",
    "        self.linear3 = torch.nn.Linear(150, 50)\n",
    "        self.linear4 = torch.nn.Linear(50, NUM_CLASSES)\n",
    "    def forward(self, x):\n",
    "        first = F.relu(self.linear1(x)).clamp(min=0)\n",
    "        #first = F.dropout(first, training=True)\n",
    "        second = F.relu(self.linear2(first)).clamp(min=0) # MAYBE CLAMP THE RELU INSTEAD OF THE LINEAR??\n",
    "        third = F.relu(self.linear3(second)).clamp(min=0)\n",
    "        y_pred = F.relu(self.linear4(third)).clamp(min=0)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FeedForwardNN()\n",
    "\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(batch_size):\n",
    "    # model.train() puts our model in train mode, which can require different\n",
    "    # behavior than eval mode (for example in the case of dropout).\n",
    "    model.train()\n",
    "    # i is is a 1-D array with shape [batch_size]\n",
    "    i = np.random.choice(train_data.shape[0], size=batch_size, replace=False)\n",
    "    temp = train_data.numpy()\n",
    "    temp1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(temp[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(temp1[i].astype(np.int)))\n",
    "    optimizer.zero_grad()\n",
    "    y_hat_ = model(x)\n",
    "    loss = F.cross_entropy(y_hat_, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    return loss.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_train_accuracy():\n",
    "    #model.eval()\n",
    "    i = np.random.choice(train_data.shape[0], size=1000, replace=False)\n",
    "    tempy = train_data.numpy()\n",
    "    tempy1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy1[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()\n",
    "\n",
    "def val_accuracy():\n",
    "    #model.eval()\n",
    "    i = np.random.choice(dev_data.shape[0], size=5000, replace=False)\n",
    "    tempy2 = dev_data.numpy()\n",
    "    tempy3 = dev_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy2[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy3[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 4 layer NN with parameters described above\n",
      "     0  0.43  0.43\n",
      "   100  0.84  0.83\n",
      "   200  0.90  0.86\n",
      "   300  0.92  0.87\n",
      "   400  0.93  0.86\n",
      "   500  0.97  0.87\n",
      "   600  0.97  0.87\n",
      "   700  0.98  0.87\n",
      "   800  0.99  0.87\n",
      "   900  0.99  0.87\n",
      "  1000  0.99  0.87\n",
      "  1100  0.98  0.87\n",
      "  1200  0.99  0.87\n",
      "  1300  0.99  0.86\n",
      "  1400  0.99  0.87\n"
     ]
    }
   ],
   "source": [
    "train_accs, val_accs = [], []\n",
    "iterations = []\n",
    "print(\"Using 4 layer NN with parameters described above\")\n",
    "for i in range(NUM_OPT_STEPS):\n",
    "    train(1000)\n",
    "    if i % 100 == 0:\n",
    "        iterations.append(i)\n",
    "        train_accs.append(approx_train_accuracy())\n",
    "        val_accs.append(val_accuracy())\n",
    "        print(\"%6d %5.2f %5.2f\" % (i, train_accs[-1], val_accs[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9PJdBFStPCs65wa7HpBCH1HyfmT0EbAE+mpeoilRtfaOPy+ycG9R6rFOIYym8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b49710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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W33HNOVdC+iw+krRc0qWS9sjMM7MXSyEhQGiOOra6gvGjvI+Cc6509FencDow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\nc85leVJwzjmX5UnBOedclicF55xzWf8fmIsMRJ1F+2wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b663c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(iterations, train_accs)\n",
    "plt.title(\"Accuracy on Training Set (4 layers)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over 1000 Training examples\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(iterations, val_accs)\n",
    "plt.title(\"Accuracy on Validation Set (4 layers)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over all Validation examples\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FeedForwardNN(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.linear1 = torch.nn.Linear(HEIGHT*WIDTH, 300)\n",
    "        self.linear2 = torch.nn.Linear(300, 100)\n",
    "        self.linear3 = torch.nn.Linear(100, NUM_CLASSES)\n",
    "    def forward(self, x):\n",
    "        first = F.relu(self.linear1(x)).clamp(min=0)\n",
    "        first = F.dropout(first, training=True)\n",
    "        second = F.relu(self.linear2(first)).clamp(min=0)\n",
    "        y_pred = F.relu(self.linear3(second)).clamp(min=0)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FeedForwardNN()\n",
    "\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(batch_size):\n",
    "    # model.train() puts our model in train mode, which can require different\n",
    "    # behavior than eval mode (for example in the case of dropout).\n",
    "    model.train()\n",
    "    # i is is a 1-D array with shape [batch_size]\n",
    "    i = np.random.choice(train_data.shape[0], size=batch_size, replace=False)\n",
    "    temp = train_data.numpy()\n",
    "    temp1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(temp[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(temp1[i].astype(np.int)))\n",
    "    optimizer.zero_grad()\n",
    "    y_hat_ = model(x)\n",
    "    loss = F.cross_entropy(y_hat_, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    return loss.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_train_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(train_data.shape[0], size=1000, replace=False)\n",
    "    tempy = train_data.numpy()\n",
    "    tempy1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy1[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()\n",
    "\n",
    "def val_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(dev_data.shape[0], size=5000, replace=False)\n",
    "    tempy2 = dev_data.numpy()\n",
    "    tempy3 = dev_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy2[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy3[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 3 layer NN with dropout\n",
      "     0  0.37  0.39\n",
      "   100  0.82  0.81\n",
      "   200  0.87  0.84\n",
      "   300  0.85  0.85\n",
      "   400  0.90  0.85\n",
      "   500  0.90  0.85\n",
      "   600  0.92  0.85\n",
      "   700  0.93  0.86\n",
      "   800  0.91  0.86\n",
      "   900  0.93  0.85\n",
      "  1000  0.94  0.87\n",
      "  1100  0.94  0.86\n",
      "  1200  0.93  0.86\n",
      "  1300  0.94  0.86\n",
      "  1400  0.94  0.86\n"
     ]
    }
   ],
   "source": [
    "train_accs, val_accs = [], []\n",
    "iterations = []\n",
    "print(\"Using 3 layer NN with dropout\")\n",
    "for i in range(NUM_OPT_STEPS):\n",
    "    train(1000)\n",
    "    if i % 100 == 0:\n",
    "        iterations.append(i)\n",
    "        train_accs.append(approx_train_accuracy())\n",
    "        val_accs.append(val_accuracy())\n",
    "        print(\"%6d %5.2f %5.2f\" % (i, train_accs[-1], val_accs[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wOeAaSZ8hnHS+yMx6tnQquIbmFEfMnlDoMJxzLueSNEm9nlBKeALojJMNyJoU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\nzXcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107bdd208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p6hQelPRBQlFSodjIzN6TWVSDbEdS8Ipm51xlSdPNxfXADOCNwN2E9gbNWQY1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\nV+BJwTnnXIEnBeeccwWeFJxzzhX8f1c/+cN2kNEsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108298d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(iterations, train_accs)\n",
    "plt.title(\"Accuracy on Training Set (3 layers with Dropout)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over 1000 Training examples\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(iterations, val_accs)\n",
    "plt.title(\"Accuracy on Validation Set (3 layers with Dropout)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over all Validation examples\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "class FeedForwardNN(torch.nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.linear1 = torch.nn.Linear(HEIGHT*WIDTH, 300)\n",
    "        self.linear2 = torch.nn.Linear(300, 100)\n",
    "        self.linear3 = torch.nn.Linear(100, NUM_CLASSES)\n",
    "    def forward(self, x):\n",
    "        first = F.relu(self.linear1(x)).clamp(min=0)\n",
    "        first = F.dropout(first, training=True)\n",
    "        second = F.relu(self.linear2(first)).clamp(min=0)\n",
    "        y_pred = F.relu(self.linear3(second)).clamp(min=0)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = FeedForwardNN()\n",
    "NUM_OPT_STEPS = 2000\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(batch_size):\n",
    "    # model.train() puts our model in train mode, which can require different\n",
    "    # behavior than eval mode (for example in the case of dropout).\n",
    "    model.train()\n",
    "    # i is is a 1-D array with shape [batch_size]\n",
    "    i = np.random.choice(train_data.shape[0], size=batch_size, replace=False)\n",
    "    temp = train_data.numpy()\n",
    "    temp1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(temp[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(temp1[i].astype(np.int)))\n",
    "    optimizer.zero_grad()\n",
    "    y_hat_ = model(x)\n",
    "    #loss = nn.MultiLabelMarginLoss()\n",
    "    loss = F.multi_margin_loss(y_hat_, y)\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    return loss.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_train_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(train_data.shape[0], size=1000, replace=False)\n",
    "    tempy = train_data.numpy()\n",
    "    tempy1 = train_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy1[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()\n",
    "\n",
    "def val_accuracy():\n",
    "    model.eval()\n",
    "    i = np.random.choice(dev_data.shape[0], size=5000, replace=False)\n",
    "    tempy2 = dev_data.numpy()\n",
    "    tempy3 = dev_labels.numpy()\n",
    "    x = autograd.Variable(torch.from_numpy(tempy2[i].astype(np.float32)))\n",
    "    y = autograd.Variable(torch.from_numpy(tempy3[i].astype(np.int)))\n",
    "    y_hat_ = model(x)\n",
    "    #print(y)\n",
    "    y = y.data.numpy()\n",
    "    y_hat_ = y_hat_.data.numpy()\n",
    "    y_hat_ = np.argmax(y_hat_, axis=1)\n",
    "    #print(y_hat_)\n",
    "    return (y == y_hat_).astype(np.float).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 3 layer NN with dropout\n",
      "     0  0.40  0.39\n",
      "   100  0.82  0.81\n",
      "   200  0.86  0.83\n",
      "   300  0.86  0.84\n",
      "   400  0.88  0.85\n",
      "   500  0.91  0.85\n",
      "   600  0.92  0.85\n",
      "   700  0.92  0.86\n",
      "   800  0.92  0.86\n",
      "   900  0.92  0.86\n",
      "  1000  0.92  0.85\n",
      "  1100  0.92  0.86\n",
      "  1200  0.92  0.85\n",
      "  1300  0.93  0.85\n",
      "  1400  0.94  0.85\n",
      "  1500  0.95  0.85\n",
      "  1600  0.94  0.86\n",
      "  1700  0.95  0.86\n",
      "  1800  0.96  0.85\n",
      "  1900  0.96  0.85\n"
     ]
    }
   ],
   "source": [
    "train_accs, val_accs = [], []\n",
    "iterations = []\n",
    "print(\"Using 3 layer NN with dropout\")\n",
    "for i in range(NUM_OPT_STEPS):\n",
    "    train(1000)\n",
    "    if i % 100 == 0:\n",
    "        iterations.append(i)\n",
    "        train_accs.append(approx_train_accuracy())\n",
    "        val_accs.append(val_accuracy())\n",
    "        print(\"%6d %5.2f %5.2f\" % (i, train_accs[-1], val_accs[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2x3Jtmbd8Ays2bGNAaUn8U+uvy0oYULLzNcADL6zm5ide5clYCj15/0mcc+R0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\nFkq6UtLpcbR7gPWSFgEPAp8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3xtjh77S7jvHm4ovDrwM+2mTcJNvQ/9r/590JOueccwXy\nal7nnHOuQJ5MnXPOuQJ5MnXOOecK5MnUOeecK5AnU+ecc65Ankxd0ZJkkn6Qef9ZSVd00byvk/Te\nrphXG8v5N0kvSHqwyfDdJP0uvj4k+/STLljmKEkfa25ZzrnmeTJ1xawGOFPSuNSBZMUebtrrw8BH\nzOz47EAze83M8sn8EMK9kF0VwyhgRzJtsiznXDM8mbpiVg9cDXy66QdNS5aStsT/x8WOxP8kaZmk\n70h6v6Qn4zMj98rM5gRJ8yW9JOkdcfpShed6zoudqf9HZr5/lzQXWNRMPOfE+T8v6btx2FcJHXL8\nStJ/NRl/Rhy3HLgSeJ/Ccy7fF3uc+nWM+Z+SzojTnC9prqS/Ag9IGibpAUlPx2Xnn4byHWCvOL//\nyi8rzmOQpGvj+P+UdHxm3n+QdLfCc1O/l9ke18VYn5P0uu/CuWLQkV/IzvVFVwHP5k/u7XQwsB/h\n8VjLgGvM7EiFh65/HPhUHG8GoW/XvYAHJc0kdOdWZWZHSBoIPCrp3jj+YcABFh7xtYOk3QjP/zwc\n2Eh4us67zOxKSW8lPH9zfnOBmlltTLpzzOySOL9vAX81swsUHtD9pKT7MzEcZGYbYun03WZWHUvv\nj8dkf1mM85A4vxmZRV4cFmsHSto3xjorfnYI4YlFNcBiST8FJgBTzOyAOK9RbWx75/okL5m6ombh\n6Tk3AJ/owGTzLDwjtobQRVs+GT5HSKB5t5tZo4XHZC0D9iX0fXuepAWEx+CNJfSjCvBk00QaHQE8\nZGZrLTwP9GbCg6M76yTgshjDQ8AgYHr87D4zyz9DU8C3JD1L6JpwCjsf6daSY4GbAMzsReAVQofr\nAA+YWZWZ5Qil790J22VPST9V6Lu3uoD1cq7X8pKp6w9+TOjP9NrMsHrij0lJJUB55rOazOvGzPtG\ndj1mmvbFaYQE9XEz26UzeUnHAVs7F36HCXiPmS1uEsNRTWJ4PzAeONzM6iQtJyTezsputwagzMw2\nSjqY8JDyjxIeeH1BActwrlfykqkrerEkdjuhMU/eckK1KoRnmA7oxKz/TVJJvI66J6GD9HuA/6fw\nSDwkzVJ4Uk5rngTeImlcfDLIOcDDHYhjMzA88/4e4OPxKSJIOrSF6UYCa2IiPZ5Qkmxufll/JyRh\nYvXudMJ6NytWH5eY2e+BLxOqmZ0rOp5MXX/xAyDbqveXhAT2DHA0nSs1vkpIhHcRnvKRA64hVHE+\nHRvt/C9t1ABZeIzWZcCDhCfrPGVmHXmM1oPA7HwDJODrhB8Hz0paGN8352ZgjqTnCNd6X4zxrCdc\n632+acMn4H+AkjjNbcD5sTq8JVOAh2KV803AFzuwXs71Gf7UGOecc65AXjJ1zjnnCuTJ1DnnnCuQ\nJ1PnnHOuQJ5MnXPOuQJ5MnXOOecK5MnUOeecK5AnU+ecc65A/x/ndmdPTQO32QAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107d05128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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OerIRABFx00ATRUSXpNNIT0FqBL4bEXdIOhu4ISIWAR8EviXp/aSbr06OiH7b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\nP/B+29GLkUW7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10867de48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(iterations, train_accs)\n",
    "plt.title(\"Accuracy on Training Set (3 layers with Dropout and Multiclass Hinge Loss)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over 1000 Training examples\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(iterations, val_accs)\n",
    "plt.title(\"Accuracy on Validation Set (3 layers with Dropout and Multiclass Hinge Loss)\")\n",
    "plt.xlabel(\"Number of iterations\")\n",
    "plt.ylabel(\"Accuracy over all Validation examples\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best validation accuracy achieved was 87% with multiple models. The 3 layer NN, 4 layer NN, 3 layer NN with dropout all resulted in this accuracy. The batch size was 1000 and the learning rate was .001 in all cases. I needed 1500 steps to reach this accuracy, and training took about 2 minutes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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