variations_of_adam_optimizer.ipynb

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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/amitkp57/simplified-adam-optimizer/blob/main/variations_of_adam_optimizer.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bRBKd9lhywA1"
      },
      "source": [
        "# Experiment with Adam optimizer\n",
        "\n",
        "Variations of adam optimizer are used for image classfication on CIFAR-10 dataset. Resnet is used for the classification task and implemented in pytorch."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TRW6ofcZz5h9"
      },
      "source": [
        "# Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1j41K_HOzKqP"
      },
      "source": [
        "import os\n",
        "import pickle\n",
        "import warnings\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "from datetime import datetime\n",
        "\n",
        "import torch\n",
        "from torchvision import models\n",
        "import torchvision\n",
        "import torchvision.transforms as transforms\n",
        "from torch.autograd import Function\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch.utils.data import Dataset\n",
        "\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "plt.ion()"
      ],
      "execution_count": null,
      "outputs": []
    },
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        "id": "h2wKUyAzMh3Q",
        "outputId": "e0d24231-643d-4301-e75c-f3ffeb2345f1"
      },
      "source": [
        "from torchvision import transforms\n",
        "BATCH_SIZE = 32\n",
        "\n",
        "## transformations\n",
        "transform_train = transforms.Compose([transforms.Resize((32,32)),  #resises the image so it can be perfect for our model.\n",
        "                                      transforms.RandomHorizontalFlip(), # FLips the image w.r.t horizontal axis\n",
        "                                      transforms.RandomRotation(10),     #Rotates the image to a specified angel\n",
        "                                      transforms.ColorJitter(brightness=0.2, contrast=0.2, saturation=0.2), # Set the color params\n",
        "                                      transforms.ToTensor(), # comvert the image to tensor so that it can work with torch\n",
        "                                      transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5)) #Normalize all the images\n",
        "                                      ])\n",
        " \n",
        "transform_test = transforms.Compose([transforms.Resize((32,32)),\n",
        "                               transforms.ToTensor(),\n",
        "                               transforms.Normalize((0.5, 0.5, 0.5), (0.5, 0.5, 0.5))\n",
        "                               ])\n",
        "\n",
        "train_dset = torchvision.datasets.CIFAR10('cifar10_pytorch', train=True,\n",
        "                                                  transform=transform_train, download=True)\n",
        "train_loader = torch.utils.data.DataLoader(train_dset, batch_size=BATCH_SIZE, shuffle=False, num_workers=0)\n",
        "\n",
        "test_dset = torchvision.datasets.CIFAR10('cifar10_pytorch', train=False,\n",
        "                                                  transform=transform_test, download=True)\n",
        "test_loader = torch.utils.data.DataLoader(test_dset, batch_size=BATCH_SIZE, shuffle=False, num_workers=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Downloading https://www.cs.toronto.edu/~kriz/cifar-10-python.tar.gz to cifar10_pytorch/cifar-10-python.tar.gz\n"
          ]
        },
        {
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              "  0%|          | 0/170498071 [00:00<?, ?it/s]"
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          "name": "stdout",
          "text": [
            "Extracting cifar10_pytorch/cifar-10-python.tar.gz to cifar10_pytorch\n",
            "Files already downloaded and verified\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "24TEyOu00Bk8"
      },
      "source": [
        "# Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aznt08VN-iFp",
        "outputId": "16caaedd-0bbb-46d0-dd44-6561d42c04a2"
      },
      "source": [
        "from torchsummary import summary\n",
        "\n",
        "class ResNet(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.conv1 = nn.Conv2d(in_channels=3, out_channels=64, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn1 = nn.BatchNorm2d(64)\n",
        "        self.conv2 = nn.Conv2d(in_channels=64, out_channels=64, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn2 = nn.BatchNorm2d(64)\n",
        "        self.conv3 = nn.Conv2d(in_channels=64, out_channels=64, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn3 = nn.BatchNorm2d(64)\n",
        "        self.pool1 = nn.MaxPool2d(2, 2)\n",
        "\n",
        "        self.conv4 = nn.Conv2d(in_channels=64, out_channels=128, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn4 = nn.BatchNorm2d(128)\n",
        "        self.conv5 = nn.Conv2d(in_channels=128, out_channels=128, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn5 = nn.BatchNorm2d(128)\n",
        "        self.conv6 = nn.Conv2d(in_channels=128, out_channels=128, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn6 = nn.BatchNorm2d(128)\n",
        "        self.pool2 = nn.MaxPool2d(2, 2)\n",
        "\n",
        "        self.conv7 = nn.Conv2d(in_channels=128, out_channels=256, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn7 = nn.BatchNorm2d(256)\n",
        "        self.conv8 = nn.Conv2d(in_channels=256, out_channels=256, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn8 = nn.BatchNorm2d(256)\n",
        "        self.conv9 = nn.Conv2d(in_channels=256, out_channels=256, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn9 = nn.BatchNorm2d(256)\n",
        "        self.pool3 = nn.MaxPool2d(2, 2)\n",
        "\n",
        "        self.conv10 = nn.Conv2d(in_channels=256, out_channels=512, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn10 = nn.BatchNorm2d(512)\n",
        "        self.conv11 = nn.Conv2d(in_channels=512, out_channels=512, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn11 = nn.BatchNorm2d(512)\n",
        "        self.conv12 = nn.Conv2d(in_channels=512, out_channels=512, kernel_size=3, stride=1, padding=1)\n",
        "        self.bn12 = nn.BatchNorm2d(512)\n",
        "        self.pool4 = nn.MaxPool2d(2, 2)\n",
        "\n",
        "        self.fc1 = nn.Linear(2 * 2 * 512, 200)\n",
        "        self.fc2 = nn.Linear(200, 10)\n",
        "        \n",
        "\n",
        "    def forward(self, x):\n",
        "        x = F.relu(self.bn1(self.conv1(x)))\n",
        "        x = F.relu(self.bn2(self.conv2(x)))\n",
        "        res = x\n",
        "        x = F.relu(self.bn3(self.conv3(x)))\n",
        "        x = res + x\n",
        "        x = self.pool1(x)\n",
        "\n",
        "        x = F.relu(self.bn4(self.conv4(x)))\n",
        "        x = F.relu(self.bn5(self.conv5(x)))\n",
        "        res = x\n",
        "        x = F.relu(self.bn6(self.conv6(x)))\n",
        "        x = res + x\n",
        "        x = self.pool2(x)\n",
        "\n",
        "        x = F.relu(self.bn7(self.conv7(x)))\n",
        "        x = F.relu(self.bn8(self.conv8(x)))\n",
        "        res = x\n",
        "        x = F.relu(self.bn9(self.conv9(x)))\n",
        "        x = res + x\n",
        "        x = self.pool3(x)\n",
        "\n",
        "        x = F.relu(self.bn10(self.conv10(x)))\n",
        "        x = F.relu(self.bn11(self.conv11(x)))\n",
        "        res = x\n",
        "        x = F.relu(self.bn12(self.conv12(x)))\n",
        "        x = res + x\n",
        "        x = self.pool4(x)\n",
        "        \n",
        "        x = torch.flatten(x, 1) # flatten all dimensions except batch\n",
        "        x = F.relu(self.fc1(x))\n",
        "        x = self.fc2(x)\n",
        "        return x\n",
        "\n",
        "summary(ResNet().cuda(), (3, 32, 32))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "----------------------------------------------------------------\n",
            "        Layer (type)               Output Shape         Param #\n",
            "================================================================\n",
            "            Conv2d-1           [-1, 64, 32, 32]           1,792\n",
            "       BatchNorm2d-2           [-1, 64, 32, 32]             128\n",
            "            Conv2d-3           [-1, 64, 32, 32]          36,928\n",
            "       BatchNorm2d-4           [-1, 64, 32, 32]             128\n",
            "            Conv2d-5           [-1, 64, 32, 32]          36,928\n",
            "       BatchNorm2d-6           [-1, 64, 32, 32]             128\n",
            "         MaxPool2d-7           [-1, 64, 16, 16]               0\n",
            "            Conv2d-8          [-1, 128, 16, 16]          73,856\n",
            "       BatchNorm2d-9          [-1, 128, 16, 16]             256\n",
            "           Conv2d-10          [-1, 128, 16, 16]         147,584\n",
            "      BatchNorm2d-11          [-1, 128, 16, 16]             256\n",
            "           Conv2d-12          [-1, 128, 16, 16]         147,584\n",
            "      BatchNorm2d-13          [-1, 128, 16, 16]             256\n",
            "        MaxPool2d-14            [-1, 128, 8, 8]               0\n",
            "           Conv2d-15            [-1, 256, 8, 8]         295,168\n",
            "      BatchNorm2d-16            [-1, 256, 8, 8]             512\n",
            "           Conv2d-17            [-1, 256, 8, 8]         590,080\n",
            "      BatchNorm2d-18            [-1, 256, 8, 8]             512\n",
            "           Conv2d-19            [-1, 256, 8, 8]         590,080\n",
            "      BatchNorm2d-20            [-1, 256, 8, 8]             512\n",
            "        MaxPool2d-21            [-1, 256, 4, 4]               0\n",
            "           Conv2d-22            [-1, 512, 4, 4]       1,180,160\n",
            "      BatchNorm2d-23            [-1, 512, 4, 4]           1,024\n",
            "           Conv2d-24            [-1, 512, 4, 4]       2,359,808\n",
            "      BatchNorm2d-25            [-1, 512, 4, 4]           1,024\n",
            "           Conv2d-26            [-1, 512, 4, 4]       2,359,808\n",
            "      BatchNorm2d-27            [-1, 512, 4, 4]           1,024\n",
            "        MaxPool2d-28            [-1, 512, 2, 2]               0\n",
            "           Linear-29                  [-1, 200]         409,800\n",
            "           Linear-30                   [-1, 10]           2,010\n",
            "================================================================\n",
            "Total params: 8,237,346\n",
            "Trainable params: 8,237,346\n",
            "Non-trainable params: 0\n",
            "----------------------------------------------------------------\n",
            "Input size (MB): 0.01\n",
            "Forward/backward pass size (MB): 5.86\n",
            "Params size (MB): 31.42\n",
            "Estimated Total Size (MB): 37.30\n",
            "----------------------------------------------------------------\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bjDp9Jb_KZlr"
      },
      "source": [
        "def train(epochs, model, criterion, optimizer, train_loader, test_loader):\n",
        "    train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = [], [], [], []\n",
        "    for epoch in range(epochs):\n",
        "        train_acc, train_loss = train_epoch(model, criterion, optimizer, train_loader)\n",
        "        test_acc, test_loss = test(model, criterion, test_loader)\n",
        "        train_epoch_acc.append(train_acc)\n",
        "        test_epoch_acc.append(test_acc)\n",
        "        train_epoch_loss.append(train_loss)\n",
        "        test_epoch_loss.append(test_loss)\n",
        "        print('Epoch {:03d}/{:03d}, Train Accuracy {:.2f}% || Test Accuracy {:.2f}% || Train Loss {:.2f} || Test Loss {:.2f}'.format(epoch, epochs, train_acc*100, test_acc*100, train_loss, test_loss))\n",
        "    return train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc\n",
        "    \n",
        "def train_epoch(model, criterion, optimizer, loader):\n",
        "    total_correct = 0.\n",
        "    total_samples = 0.\n",
        "    total_loss = 0.\n",
        "    \n",
        "    for batch_idx, (data, target) in enumerate(loader):\n",
        "        if torch.cuda.is_available():\n",
        "          data, target = data.cuda(), target.cuda()            \n",
        "        output = model(data)\n",
        "        loss = criterion(output, target)\n",
        "        total_correct += (torch.max(output, 1)[1].view(target.size()).data == target.data).sum()\n",
        "        total_samples += target.shape[0]\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        total_loss += loss.item()\n",
        "    total_loss /= (batch_idx + 1)\n",
        "    return total_correct/total_samples, total_loss\n",
        "    \n",
        "def test(model, criterion, loader):\n",
        "    total_correct = 0.\n",
        "    total_samples = 0.\n",
        "    total_loss = 0.0\n",
        "    model.eval()\n",
        "    \n",
        "    with torch.no_grad():\n",
        "        for batch_idx, (data, target) in enumerate(loader):\n",
        "            if torch.cuda.is_available():\n",
        "              data, target = data.cuda(), target.cuda()            \n",
        "            output = model(data)\n",
        "            loss = criterion(output, target)\n",
        "            total_correct += torch.eq(torch.max(output, 1)[1].view(target.size()).data, target.data).sum()\n",
        "            total_samples += target.shape[0]\n",
        "            total_loss += loss.item()\n",
        "        total_loss /= (batch_idx + 1)\n",
        "    return total_correct/total_samples, total_loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f1dHuyL5Nf6u"
      },
      "source": [
        "# Optimizers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aGiUfcfoyW1v"
      },
      "source": [
        "### Adam\n",
        "Standard Adam algorithm is described below: \\\n",
        "$\\eta$: Step size \\\n",
        "$\\beta_1, \\beta_2 \\in [0, 1)$: Exponential decay rates for the moment estimates \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to parameters $\\phi$)\\\n",
        "$m_t \\gets \\frac{\\beta_1 m_{t−1} + (1 − \\beta_1) g_t}{1-\\beta_1^t}$ (first moment)\\\n",
        "$v_t \\gets \\frac{\\beta_2 v_{t−1} + (1 − \\beta_2) g_t^2}{1 - \\beta_2^t}$ (second moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bEzpZUUJ0LVJ"
      },
      "source": [
        "# Adam optimizer\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class Adam(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0):\n",
        "        defaults = dict(lr=lr, betas=betas, epsilon=epsilon,\n",
        "                weight_decay=weight_decay)\n",
        "        super(Adam, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of squared gradient values\n",
        "                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']\n",
        "                beta1, beta2 = group['betas']\n",
        "\n",
        "                state['step'] += 1\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(beta1).add_(1 - beta1, grad)\n",
        "                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)\n",
        "\n",
        "                denom = exp_avg_sq.sqrt().add_(group['epsilon'])\n",
        "\n",
        "                bias_correction1 = 1 - beta1 ** state['step']\n",
        "                bias_correction2 = 1 - beta2 ** state['step']\n",
        "                step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1\n",
        "\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NtRdHvBQLC62",
        "outputId": "3634338f-cd66-4ab6-d89b-51874b2eedca"
      },
      "source": [
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 37.09% || Test Accuracy 52.79% || Train Loss 1.66 || Test Loss 1.31\n",
            "Epoch 001/020, Train Accuracy 54.33% || Test Accuracy 62.09% || Train Loss 1.25 || Test Loss 1.06\n",
            "Epoch 002/020, Train Accuracy 63.25% || Test Accuracy 69.79% || Train Loss 1.03 || Test Loss 0.85\n",
            "Epoch 003/020, Train Accuracy 69.62% || Test Accuracy 73.66% || Train Loss 0.86 || Test Loss 0.75\n",
            "Epoch 004/020, Train Accuracy 74.22% || Test Accuracy 76.17% || Train Loss 0.74 || Test Loss 0.70\n",
            "Epoch 005/020, Train Accuracy 77.52% || Test Accuracy 78.88% || Train Loss 0.65 || Test Loss 0.62\n",
            "Epoch 006/020, Train Accuracy 80.26% || Test Accuracy 80.51% || Train Loss 0.57 || Test Loss 0.57\n",
            "Epoch 007/020, Train Accuracy 82.39% || Test Accuracy 81.73% || Train Loss 0.51 || Test Loss 0.55\n",
            "Epoch 008/020, Train Accuracy 83.89% || Test Accuracy 82.89% || Train Loss 0.46 || Test Loss 0.51\n",
            "Epoch 009/020, Train Accuracy 85.72% || Test Accuracy 83.25% || Train Loss 0.42 || Test Loss 0.52\n",
            "Epoch 010/020, Train Accuracy 87.03% || Test Accuracy 81.75% || Train Loss 0.37 || Test Loss 0.55\n",
            "Epoch 011/020, Train Accuracy 87.89% || Test Accuracy 83.38% || Train Loss 0.35 || Test Loss 0.53\n",
            "Epoch 012/020, Train Accuracy 89.22% || Test Accuracy 83.39% || Train Loss 0.31 || Test Loss 0.53\n",
            "Epoch 013/020, Train Accuracy 89.85% || Test Accuracy 84.27% || Train Loss 0.29 || Test Loss 0.51\n",
            "Epoch 014/020, Train Accuracy 90.83% || Test Accuracy 85.06% || Train Loss 0.27 || Test Loss 0.48\n",
            "Epoch 015/020, Train Accuracy 91.32% || Test Accuracy 85.46% || Train Loss 0.25 || Test Loss 0.48\n",
            "Epoch 016/020, Train Accuracy 92.16% || Test Accuracy 84.92% || Train Loss 0.23 || Test Loss 0.50\n",
            "Epoch 017/020, Train Accuracy 92.67% || Test Accuracy 85.41% || Train Loss 0.21 || Test Loss 0.51\n",
            "Epoch 018/020, Train Accuracy 93.17% || Test Accuracy 85.16% || Train Loss 0.20 || Test Loss 0.54\n",
            "Epoch 019/020, Train Accuracy 93.46% || Test Accuracy 85.77% || Train Loss 0.19 || Test Loss 0.51\n",
            "time taken:  1147.5543022155762\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "FlWfTj-Vd3KT",
        "outputId": "0f8158f5-f152-41cc-a4fa-ca1bac6f0c72"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uZ-Qcooq-xwb"
      },
      "source": [
        "### Simplified Adam\n",
        "A simplified Adam algorithm is described below (discussed in the lecture): \\\n",
        "$\\eta$: Step size \\\n",
        "$N_1, N_2$ are typically 100 and 1000 \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to parameters $\\phi$)\\\n",
        "$m_t \\gets (1-\\frac{1}{min(t, N_1)}) m_{t−1} + \\frac{1}{min(t, N_1)} g_t$ (first moment)\\\n",
        "$v_t \\gets (1 - \\frac{1}{min(t, N_2)}) v_{t-1} + \\frac{1}{min(t, N_1)} g_t^2$ (second moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "znsVz8l05d2y"
      },
      "source": [
        "# A simplified adam (taken from lecture notes)\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class AdamSimplified(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0):\n",
        "        ns = (1/(1-betas[0]), 1/(1-betas[1]))\n",
        "        defaults = dict(lr=lr, ns=ns, epsilon=epsilon,\n",
        "                weight_decay=weight_decay)\n",
        "        super(AdamSimplified, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of squared gradient values\n",
        "                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']\n",
        "                ns1, ns2 = group['ns']\n",
        "\n",
        "                state['step'] += 1\n",
        "                t = state['step']\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(1 - 1 / min(t, ns1)).add_(1 / min(t, ns1), grad)\n",
        "                exp_avg_sq.mul_(1 - 1 / min(t, ns2)).addcmul_(1 / min(t, ns2), grad, grad)\n",
        "\n",
        "                denom = exp_avg_sq.sqrt().add_(group['epsilon'])              \n",
        "                step_size = group['lr']\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BrdJTiCR77Ty",
        "outputId": "0a8a5e4d-9d91-4ecc-c9c4-e428ded58290"
      },
      "source": [
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = AdamSimplified(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 29.76% || Test Accuracy 46.17% || Train Loss 1.82 || Test Loss 1.42\n",
            "Epoch 001/020, Train Accuracy 47.44% || Test Accuracy 56.77% || Train Loss 1.41 || Test Loss 1.21\n",
            "Epoch 002/020, Train Accuracy 59.23% || Test Accuracy 65.47% || Train Loss 1.13 || Test Loss 0.99\n",
            "Epoch 003/020, Train Accuracy 66.14% || Test Accuracy 71.31% || Train Loss 0.96 || Test Loss 0.82\n",
            "Epoch 004/020, Train Accuracy 70.90% || Test Accuracy 74.88% || Train Loss 0.84 || Test Loss 0.74\n",
            "Epoch 005/020, Train Accuracy 74.71% || Test Accuracy 76.70% || Train Loss 0.73 || Test Loss 0.69\n",
            "Epoch 006/020, Train Accuracy 77.92% || Test Accuracy 78.79% || Train Loss 0.65 || Test Loss 0.62\n",
            "Epoch 007/020, Train Accuracy 80.13% || Test Accuracy 80.61% || Train Loss 0.58 || Test Loss 0.57\n",
            "Epoch 008/020, Train Accuracy 81.99% || Test Accuracy 80.51% || Train Loss 0.53 || Test Loss 0.58\n",
            "Epoch 009/020, Train Accuracy 83.46% || Test Accuracy 80.96% || Train Loss 0.48 || Test Loss 0.58\n",
            "Epoch 010/020, Train Accuracy 84.63% || Test Accuracy 82.91% || Train Loss 0.44 || Test Loss 0.52\n",
            "Epoch 011/020, Train Accuracy 86.28% || Test Accuracy 83.39% || Train Loss 0.40 || Test Loss 0.53\n",
            "Epoch 012/020, Train Accuracy 87.27% || Test Accuracy 83.32% || Train Loss 0.37 || Test Loss 0.51\n",
            "Epoch 013/020, Train Accuracy 88.32% || Test Accuracy 84.31% || Train Loss 0.34 || Test Loss 0.51\n",
            "Epoch 014/020, Train Accuracy 89.21% || Test Accuracy 84.00% || Train Loss 0.32 || Test Loss 0.52\n",
            "Epoch 015/020, Train Accuracy 89.96% || Test Accuracy 84.16% || Train Loss 0.29 || Test Loss 0.53\n",
            "Epoch 016/020, Train Accuracy 90.62% || Test Accuracy 84.25% || Train Loss 0.27 || Test Loss 0.53\n",
            "Epoch 017/020, Train Accuracy 91.33% || Test Accuracy 85.04% || Train Loss 0.25 || Test Loss 0.54\n",
            "Epoch 018/020, Train Accuracy 91.76% || Test Accuracy 83.70% || Train Loss 0.24 || Test Loss 0.53\n",
            "Epoch 019/020, Train Accuracy 92.54% || Test Accuracy 85.52% || Train Loss 0.22 || Test Loss 0.53\n",
            "time taken:  1154.2092010974884\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "ZS779w8B8ASU",
        "outputId": "73f0dec6-23f6-4bcc-cc41-a69fab9df091"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xxs+Kiop4++23uemmmxrc9/HHH2fy5MlER7fYP75zgE41Xqd63vuR5+bv8wBEpBVwvqoW+S1CY8zPqCqb80tZsq2QldnFrMgpZu3OvVR4VsKIjQxlQMd4rj6+MwM7JjCgYzydWkc1qzLWpjpuB1UC7QoRBqclsNg2VDEmKBUVFfHss88e8UB8+eWXt+QEehHQQ0S64CTOFwOX1mwgIsnAHlV1A/firMhhjPGTareyLncvC3/Y8+OjoLQCgFYRofTvGMeVo9IZkJrAwI7xpLU+/Mxyc9JUx+2gSqABMtJb8/jsDewtqyQuMizQ4Rhj/Oiee+5h8+bNDB48mFNPPZW2bdvy/vvvU15ezrnnnstDDz1EaWkpF154IdnZ2VRXV3P//feza9cuduzYwUknnURycjJffvlloL9Ko1PVKhG5BZiBs4zdK6q6WkQeBjJVdSrO2v5/FRHFKeG4OWABGxMEKqvdrMwp/jFZXrR1DyVlVQCkJkZxYq82jOzSmmHpremaHNPsk+XDaarjdtAl0MPSE1GFpduKOLFnm0CHY4zxo0ceeYRVq1axbNkyZs6cyQcffMDChQtRVc466yzmzp1Lfn4+KSkpfPrppwAUFxcTHx/PP//5T7788kuSk5MD/C18R1WnA9MPee+BGs8/AD7wd1zGBIuyymqWbityEuatBSzJKuJApXObQbc2MUwYmMLILq0Z3qU1HROiAhytfzTVcTvoEujBaQmECCzOKrQE2phA+uweyF3ZuJ/ZfgCc/kj97YCZM2cyc+ZMhgwZAsC+ffvYuHEjo0eP5o477uDuu+9mwoQJjB5tC8cbY3zD7VZW7Sjmq/X5fLMxn2Xbi6isVkSgT/s4Lhre6ceEOblVRGCDDfCYDU1r3A66BLpVRCh9OsSxOGtPoEMxxgSQqnLvvfdy/fXX/+LYkiVLmD59Ovfddx+nnHIKDzzwwGE+wRhjGq5gXznfbNzN1xvymbshn4LSCkRgQMd4rjm+y48lGfFRVmZ6qKY0bgddAg1OGccHi7OpqnYH3c45xjQZDZh1aCyxsbGUlJQAcNppp3H//fdz2WWX0apVK3JycggLC6OqqorWrVtz+eWXk5CQwEsvvfSzvi25hMMY0/iq3cqy7UV8vSGfr9fnsSKnGFVIignnhJ5tOLFnG0b3SCYp0DPM9QnAmA1Nd9wO2gT69flZrMstoX/H+ECHY4zxk6SkJI477jj69+/P6aefzqWXXsqoUaMAaNWqFW+++SabNm3irrvuIiQkhLCwMJ577jkAJk+ezPjx40lJSWmRNxEaYxpPXkkZX6/P5+sN+XyzcTfFByoJERjcKYHfjO3JiT3bMKBjfIu86a+xNdVxWw7ubd5cZGRkaGZm5lF9Rk7RAY57ZA4PndWPK4/t3DiBGWPqtXbtWvr06RPoMPzmcN9XRBarakaAQvK7xhizjWnqyiqrWZxVyLebdvP1+nzW7NwLQJvYCE6sMcucEB0e4Egbxsbs2sfsoJyB7pgQRYf4SDKzCi2BNsYYY0yDVLuVNTv28u2m3Xy3aTeLtu6hvMpNaIgwNC2Ru07rxYk929C3Q5zNMrdQQZlAAwxNT2TxVruR0BhjjDF1U1W27dn/Y8I8b3MBRfsrAejVLpbLRqZzfI8kRnRJolVE0KZWQSVo/ytnpCfy6Yqd7Cg6QEqQrKVojDHGGO/sKa3gO0/C/O2m3WQXHgCgfVwkY/u04/juyRzbLYm2cZEBjtQEQhAn0K0BZz1oS6CN8R9VRaTlX9JsbveXGGPgQEU1HyzJ5r1F21iV49Qxx0aEcky3JCaN7srxPZLpmhwTFGPYQTZmH17QJtC9O8QSFeZicVYhEwelBDocY4JCZGQkBQUFJCUltegBWVUpKCggMtJmpoxpDvL2lvH6/Cze/D6Lov2V9O8Yxx2n9uS4HskM7BgftEve2phdu6BNoMNcIQzulECmbahijN+kpqaSnZ1Nfn5+oEPxucjISFJTUwMdhjGmDmt37uWlb35g6vIcqtzKuL7tuG50VzLSE1t0wugtG7NrF7QJNEBG50Se/WozpeVVxFjRvzE+FxYWRpcuXQIdhjEmiLndytcb83n5mx/4dtNuosJcXDoijauP60Ln5JhAh9ektIgxu2AzfPNPiE6EcX9utI8N6qxxWHoi1W5l+fYiju1uu4sZY4wxLVVZZTWfLM3hpW9/YFPePtrFRfC78b24dERas1uf2Xhh90aY+xisfB9c4XDMTY368UGdQA9JS0QEMrMKLYE2xhhjWqDd+8p5Y34Wby7IoqC0gr4d4vjXRYM4c0AK4aHBWdvsV+5qyF8H2ZmQsxh2LoP4TjDoYugxDkIbeQvzvLVO4rzqQwiLglE3w6hbIbZdo57GZwm0iLwCTADyVLV/LW3GAI8DYcBuVT3RV/EcTnxUGD3bxrI4q9CfpzXGGGOMD6kqa3eW8Pr8rXy0NIeKKjen9G7LtaO7MKpry74hLuCKc5xEOScTshfDjqVQWeoci0yADoNg+0JYN8153e9cJ5nuNBKO5r9L7iqY+3dYMxXCY+D422HULRDjmwlSX85AvwY8Dbx+uIMikgA8C4xX1W0i0taHsdRqWOdE/rd8B2632m5BxhhjTDPlditLtxcyY/UuZqzOJatgPxGhIVwwLJVrjutC97atAh1iy1Ne4iTIB2eXcxZDyU7nWEgYdBgIQy6DjhnQcRgkdXOS5Ooq2PIVrHgXlr8Li1+FhHQYeJHzSO7ufQw7lsHcR52EPCIOTrjTKdeIbu2Tr3yQzxJoVZ0rIp3raHIp8JGqbvO0z/NVLHUZlpbI299vY0NeCb3bxwUiBGOMMcYcgYoqNwu2FDBjdS5frNlFXkk5YS7h2G7JXH9CN8b3b0/rmCZa3+yuhp3LnURyy1fOrGxoBMS0cWZNY5IhOrn211GtwVVHGueuhopSqNz/858/Pt/v/Kwqh+oKz6OyxvMa7/3Ypsbx0nzIXw941k9u3Q06j4ZUT7LcfkDt5RmuUOgx1nmUl8DaaU4yPfdRZxa54zAYeDH0P6/2GeTsxU7bDZ9DZDyMuRdGXg9RiUfxH8V7gayB7gmEichXQCzwhKoedrbalzI6O//QmVsLLYE2xhhjmrj9FVV8vT6fGatzmb0uj5KyKqLDXYzp1YbT+rXnpN5tiYsMC3SYh1e4FTZ/CVu+hB/mwgFPCWnbfjD0ClA3lO52Hrs3Quk82L+HH5PUnxEnWYxp49T6/pgUlzo/q8uPLMaQMOemu9Bw56crHFxh4Irw/PS8l9jFKb/omAEdhx75jG9ELAy+xHns3QErP4AV78Nnd8GMe6H7WGdWutfpzvfc9r2TOG+a5Xz/k++DEZOdJNqPAplAhwLDgFOAKGC+iCxQ1Q2HNhSRycBkgLS0tEYNIq11NMmtIliSVcjlx6Q36mcbY4wx5ugV7a9g1to8ZqzOZe6GfMqr3CRGhzG+X3tO69ee43skExnmCnSYv7R/j5Mob/nKSZoLtzrvx6ZArzOg6xjocmLdN7i5q51EuzTfk1znw/6CGs93Q+UBCIt2an/DoiE8GsJiPD9re9/zMzTy5wlyIOvD41LguNucx67VTnnHyv84s8wRcZDUHXYsgegkGPsgDL/OScADIJAJdDZQoKqlQKmIzAUGAb9IoFV1CjAFICMjo1H3xxURMtITybQbCY0xxpgm40BFNZ+u3MnHS7NZsGUP1W6lQ3wkl4xIY1y/dozo3LpxdwisroTibCjKgpJcQJxSg5AwJ7EMCXUerjDPe55jP77n+Vmw+aeEeccyQCE8FrqMdmpzu54EyT28T1RDXD+VcASTdv1g3J+cRHnrN7D8PafkZdyfIeMa54+CAApkAv1f4GkRCQXCgZHAvwIRyLD0RD5fnUteSRltY23rXWOMMSZQ1u7cy7sLt/HR0hxKyqrokhzD9Sd05bR+7RmYGn/kK2iowr48J0EuzHJmg4u2Os+LspzVI7S6cb5ESCikDocx9zgJc8ehTnJtGi7E5czUdx0T2DgO4ctl7N4BxgDJIpIN/BFnuTpU9XlVXSsinwMrADfwkqqu8lU8dRnmqYNeklXI+P4dAhGCMcYYE7T2V1QxbflO3l64jWXbiwgPDeGM/u25ZEQaI7q0bnjS7K6GVR9B9sKfEuTCLKg68PN2rdo5qz90GgkD0iGxMySmQ1xH53h1JbirwF3prBzhrqzxXpXneY1j7iqIaQudjwtYaYHxD1+uwnGJF20eBR71VQze6p8ST3hoCJlbLYE2xhhj/GX1jmLeWbiNT5buYF95Fd3btuL+CX05b0hHEo9k9QxVWDsV5vwFdq936mYT053a2e5jnWQ50ZMoJ6Q5N6UZcwSCeifCg8JDQxiUGm910MYYY4yP7Suv4n/Ld/DOwm2syC4mIjSEMwd04JKRaWSkJx5ZiYaqU3M8+2FnXeLkXnDhG9BnYmBvijMtliXQHsPSW/Pyt1soq6xumnfyGmOMMc3Yyuxi3l64janLciitqKZnu1Y8OLEv5w5JJT76KOqDty+C2Q85N5rFd4JznnOWPQux3+XGdyyB9shIT+T5r5UV2cWM6OLb3WuMMcaYYKCqzFqbx1NzNrIiu5jIsBAmDEzhkhFpDE1LOLottXetgTl/hvWfOmshn/53GHZV7Zt3GNOILIH2GJru2VAla48l0MYYY8xROJg4Pz5rA6t37CWtdTQPndWPc4Z0JD7qKFejKNwKX/4VVrzn3Kh38n0w8kaIsK26jf9YAu3ROiacrm1iWLzV6qCNMcaYI6GqzF6bx+OzN7Aqx0mcH71gIOcM6UjY0a7ZXJILcx+Dxa855RnH3QbH3X7kO+AZcxQsga4hIz2RmWt2oapHd1nJGGOMCSKqypx1eTw+ayMrc4pJax3N3y8YyLmNkTgfKITvnoAFzztLxQ39FZzwO4izVbNM4FgCXUNGemvez8xmc34p3dvapSBjjDGmLocmzp1aRx1Z4uyuhpKdULQdirdD0TbPz+2QnQnle2HABTDmXkjq5rsvZIyXLIGu4WAd9OKsPZZAG2OCjoiMB54AXDibWz1yyPE04N9AgqfNPao63e+BmsDIXQVZ88AVirrCWZNXztRVu9lYUEH32Bh+M6YLJ/RtQ2hYIezZD65w54Y+V4Sz7XXp7p+S4p/93AZ7c5xNSGqKTnJW1eh1Ohx7K7TvH5jvbcxhWAJdQ7c2MSRGh5G5tZCLhqcFOhxjjPEbEXEBzwCnAtnAIhGZqqprajS7D3hfVZ8Tkb7AdKCz34M1/rVjGcx9FNZN+/EtAfp5HoQD5cACz8MrArEdIKETdBrhJMoJnSA+zfMzFcJjGvd7GNOILIGuQUQYlp7I4m12I6ExJuiMADap6hYAEXkXOBuomUArEOd5Hg/s8GuExr+yF8Pcv8OGzyEinu0Db+PB7UNZubOU9HgXVx+Twqm9EgnTSqiqgOryGj/LobrCeRx8L6q1Jznu5GyVHXoEOw0a00RYAn2IoemJzFqbx57SClofyTaixhjTPHUEttd4nQ2MPKTNg8BMEbkViAHG+ic041fbF8LXf4NNsyAqkZJj7+HBXcfx4cISOiZEccf5wzhvaOrR3xxoTDNmCfQhMtKd5XAWZxVyat92AY7GGGOalEuA11T1HyIyCnhDRPqrqrtmIxGZDEwGSEuzcrhmI2uekzhv+Qqik6g6+Y+8VjGWf87dQbW7lN+M7cn1J3a13XqNwRLoXxiYGk+YSyyBNsYEmxygU43XqZ73aroWGA+gqvNFJBJIBvJqNlLVKcAUgIyMDPVVwKYRqDpbYH/9d+dnTFsY92e+TTiLB6b/wJbd2xnXtx33T+hLp9bRgY7WmCbDEuhDRIa56N8xnsVZewIdijHG+NMioIeIdMFJnC8GLj2kzTbgFOA1EekDRAL5fo3SNA5V2PKlkzhvmw+t2sP4R9jR7UIe/nwrn69eReekaF67ejhjerUNdLTGNDmWQB/GsLREXl+QRXlVNRGhdqnKGNPyqWqViNwCzMBZou4VVV0tIg8Dmao6FbgDeFFEfoNzQ+FVqmozzM2JqlPb/PXfIHuRczPfGY9RPvBSXpy3g6efXAjAXaf14rrRXex3oDG1sAT6MDI6J/LStz+wKmcvwzxrQxtjTEvnWdN5+tyZ7E0AACAASURBVCHvPVDj+RrgOH/HZRpJ7kqY8Xv4Ya6zXNyEx2HwpXy5qZiHnlrI1oL9nDGgPX84sy8dE6ICHa0xTZol0IdxcEOVJVmFlkAbY4xp3kp2wZw/wdI3ISoBTn8Uhl3FtuIqHn5rBbPW5tG1TQxvXDuC0T3aBDpaY5oFS6APo21sJGmto8nM2sMkugY6HGOMMabhKg/A/Kfhm3856zGPuhlOuJOy0Die+3Izz329mdAQ4d7Te3P1cV0ID7Vl6YzxliXQtchIT2TuxnxUFREJdDjGGGOMd1Rh5Qcw60HYmw29J8CpD0NSN9bl7mXy63PZtmc/Ewel8Icz+tA+PjLQERvT7FgCXYthnRP5aGkO2/bsJz3JthM1xhjTDGxfCJ/fCzmZ0H4gnPs8dBkNwLcbd3Pjm4uJjnDx9qSRHNstOcDBGtN8WQJdi4MbqmRuLbQE2hhjTNNWmOXMOK/+yFmS7uxnYdDFEOKsovGfzO3c+9FKurVpxatXDyfFbhI05qgERwK99C0o3wvH3Oh1lx5tWxEbGUpmViHnD0v1YXDGGGPMESrbC9/+E+Y/CxICJ94Nx94GEa0AUFX+NWsjT87eyPHdk3n28qHERYYFOGhjmj+fJdAi8gowAchT1f51tBsOzAcuVtUPfBLM5tmw8QsYfBlExnnVJSREGJqWyJKsQp+EZIwxxhwxdzUseR2+/AuU5sPAi+CUByD+pwmfiio393y4go+W5vB/w1L5f+cNIMxlNwoa0xh8+f+k1/Bs+VobEXEBfwNm+jAOGHWLMwO99I0GdctIT2RDXgnFByp9FJgxxhjTANVVsOJ9ePYYmHY7tO4Gk+bAeVN+ljwXH6jkylcW8tHSHO44tSd/v2CgJc/GNCKf/b9JVecC9e2HfSvwIZDnqzgA6DgU0o6FBc87g4+XhqUnoopt622MMSawqith2dvwzAj4aBKEhMKFr8M1n0PHYT9rml24nwuem0dm1h7+ddEgbj2lh60mZUwjC9ifoyLSETgXeM4vJzz2FijeBmv/63WXoemJxIS7mLl6lw8DM8YYY2pRVeGUajydAZ/cCOHRcNGbcMN30PdsOCQxXpFdxLnPziN3bxn/vmYE5w6xe3iM8YVAXs95HLhbVd31NRSRySKSKSKZ+fn5R3a2nqc7l7rmPe2skemFyDAXp/Ztx+erc6msrjdMY4wxpnFUlUPmK/DUMJh6K0QlwiXvwvXfQJ+JEPLLX9+z1+7iohcWEO4K4aMbj7Vl6ozxoUAm0BnAuyKyFbgAeFZEzjlcQ1WdoqoZqprRps0RbjMaEgKjboIdS2DbfK+7nTkwhaL9lXy7afeRndcYY4zxVmUZLHwRnhwC034Dse3gsg9g0pfQ6/RfzDgf9Mb8rUx6PZPubVvx8c3H0qNdrH/jNibIBGwZO1XtcvC5iLwGTFPVT3x60kGXwpy/OLPQ6cd61eWEnsnERoby6YqdnNSrrU/DM8YYE6Qq9sPi1+C7J2BfLqSNgrOfga5jak2aAdxu5ZHP1zFl7hbG9mnLk5cMITo8OFaoNSaQfLmM3TvAGCBZRLKBPwJhAKr6vK/OW6fwaBh+Lcx9DAo2Q1K3ertEhLoY17c9M1bn8pdz+xMR6vJDoMYYY4JCRSksehnmPeksR9d5NJz/EnQ+vs7EGaCssprfvr+M6StzuXJUOg9M7IcrxG4WNMYffJZAq+olDWh7la/i+IXhk5y/8Bc8C2f+w6suEwZ24MMl2Xy7cTen9Gnn4wCNMcYEhax58N4VsH83dD0JTvyd11dHC/aVM+n1TJZuL+K+M/tw7fFdbKUNY/wo+BaFjG0HAy90difc793ydMd1TyY+KoxpK3b6ODhjjDFBYctX8Ob5zs2B134Bv/qkQcnzxVMWsHrHXp69dCjXje5qybMxfhZ8CTQ4G6tUHYDMl71qHh4awvh+7flizS7KKqt9HJwxxpgWbcNMeOtCSOwCV0+HTiO87lq0v4LLX17I9sL9vHb1CE4f0MGHgRpjahOcCXTbPtB9rHOnc1W5V13OHNiBfeVVfL3hCJfRM8YYY9b+D9691Pk9dNU0aOX9zenFByq54uWFbM7fx4u/ymBUtyQfBmqMqUtwJtDgzELv2wUr/+NV82O7JZEYbWUcxhhjjtDKD+D9KyFlCPzqvxDd2uuu+8qruOrVhazL3cvzlw9ldI8jXNLVGNMogjeB7joG2vWH+c94tbFKqCuE8f07MHvtLg5UWBmHMcaYBlj6Fnx4HaQdA1d8BFEJXnfdX1HFNa8uYkV2MU9dMpSTe9vN7MYEWvAm0CIw6mbIWwObZ3vVZeLADuyvqObL9Xk+Ds4YY0yLsegl+O9NzsTNZR9AhPebnJRVVnPdvzPJzNrD4xcNZnz/9j4L0xjjveBNoAH6XwCt2jsbq3hhZNckkluFM23FDh8HZowxpkWY/wx8egf0PN3Zijs82uuu5VXVXP/GYuZvKeCx/xvExEEpPgzUGNMQwZ1Ah4bDyMmw5UvIXVVvc1eIcHr/DsxZl0dpeZUfAjTGGNNszX0MZvwe+pwFF74OYZFed62ocnPzW0v5ekM+j5w3gPOGpvowUGNMQwV3Ag0w7GoIi3ZmCbwwYWAHyirdzF5nZRzGGGMOQxXm/Bnm/AkGXAgXvOpM2HipqtrNr99dyqy1u/jT2f24aHiaD4M1xhwJS6CjW8OQy53VOPbWv8LG8M6taRsbwbTlVsZhjDHmEKow8z6Y+ygMuQLOfR5c3m/6W+1W7vjPcj5blct9Z/bhilGdfRerMeaIWQINcMyN4K6CRS/W2zQkRDhjQAe+2pBPSVmlH4IzxhjTLLjdMP0umP80DJ8EE5+EEFcDuit3f7iC/y7bwe/G9+K60V19GKwx5mhYAg3Quiv0mQCLXoaK0nqbTxzUgYoqN7PW7vJDcMYYY5o8dzX87zZnIubYW+GMRyHE+1+xqsp9/13FB4uzuX1sD24a092HwRpjjpYl0AeNuhXKimDZ2/U2HdIpkZT4SKYtt01VjDEm6FVXwcfXw9I34ITfwal/cpZK9ZKq8tD/1vD299u4cUw3fn1KDx8Ga4xpDJZAH5Q2ElKHOzcTuuveKOVgGcfcjfkUH7AyDmOMCWpTb3HuoznlATj5Dw1Onh/5bB2vzdvKtcd34Xen9UIa0N8YExiWQNc06hYo/AHWT6+36YRBKVRWKzNX5/ohMGOMMU3Suumw/B044S4YfUeDu//ziw28MHcLVxyTzn1n9rHk2ZhmwhLomnpPgIQ0rzZWGZQaT2piFNNWWBmHMaZlEJHxIrJeRDaJyD2HOf4vEVnmeWwQkaJAxNlklJfA9DuhbV+ndKOB3lm4jafmbOLi4Z146Kx+ljwb04xYAl2TKxSOuQm2L4DszDqbighnDuzAd5t2U1ha4acAjTHGN0TEBTwDnA70BS4Rkb4126jqb1R1sKoOBp4CPvJ/pE3I7D/B3h0w8YkGrfMMsHx7EX/872pG90jmL+cOICTEkmdjmhNLoA815HKIiId5T9XbdOLAFKrcygwr4zDGNH8jgE2qukVVK4B3gbPraH8J8I5fImuKsjNh4RQYfh10GtGgrntKK7jprSW0iY3gyYuH4LLk2ZhmxxLoQ0XEQsZVsHYqFG6ts2m/lDjSk6KtjMMY0xJ0BLbXeJ3tee8XRCQd6ALM8UNcTU91JUy9DWI7ODcONqSrW/n1u0vJLynn2cuGkhjTsJlrY0zTYAn04Yy4HiQEFjxfZzMRYcLADszbvJuCfeV+Cs4YYwLuYuADVT3skkUiMllEMkUkMz8/38+h+cG8pyBvNZz5GETGNajrE7M28M3G3Tx4Vj8GdUrwUYDGGF+zBPpw4jtC//OdNT0P1H2PzISBKbgVPltlZRzGmGYtB+hU43Wq573DuZg6yjdUdYqqZqhqRps2bRoxxCagYDN8/TfoMxF6n9mgrnPW7eLJOZu4YFgql4zoVH8HY0yTZQl0bUbdAhX7YPFrdTbr3T6Wrm1i+NTKOIwxzdsioIeIdBGRcJwkeeqhjUSkN5AIzPdzfIGnCtN+A65wOP3vDeq6rWA/t7+7jL4d4vjzOf1txQ1jmjmfJdAi8oqI5InIqlqOXyYiK0RkpYjME5FBvorliHQYCF1OgO9fcOrdauGUcaTw/Q8F5JWU+TFAY4xpPKpaBdwCzADWAu+r6moReVhEzqrR9GLgXVXVQMQZUMvfgR++hrF/hLgUr7uVVVZzw5uLAXj+8mFEhrl8FaExxk98OQP9GjC+juM/ACeq6gDgT8AUH8ZyZEbdCiU7YPUndTabMLCDU8ax0so4jDHNl6pOV9WeqtpNVf/iee8BVZ1ao82DqvqLNaJbvNLdMOP30GkkDLvG626qyv2frGLNzr3866LBpCVF+zBIY4y/+CyBVtW5wJ46js9T1ULPywU49XZNS/ex0Lqbs1RRHXq2i6Vnu1ZWxmGMMS3VjN9D+T5nzecQ7391vrtoO/9ZnM1tJ3fnlD7tfBigMcafmkoN9LXAZ4EO4hdCQmDEJMheCDuW1tl0wsAUFmXtIbfYyjiMMaZF2TQbVrwHx/8G2vbxutuK7J82S/n12J4+DNAY428BT6BF5CScBPruOtoEbkmkwZdCWAwsfKnOZmcO7IAqfLrSZqGNMabFqCh1bhxM6gGj7/C6W2FpBTe+aZulGNNSBTSBFpGBwEvA2apaUFu7gC6JFBkPgy6Glf+B/bVWpNCtTSv6dIjj0xU7/BicMcYYn/rqESjKgomPQ1ikV12q3cqv31tmm6UY04IFLIEWkTTgI+AKVd0QqDi8MmISVJfDktfrbDZhYAeWbCsip+iAnwIzxhjjMzuXw/xnYOivoPPxXnd7YvZG5m7It81SjGnBfLmM3Ts464T2EpFsEblWRG4QkRs8TR4AkoBnRWSZiGT6Kpaj1rYPdB4Ni14G92E33gKcBBqwWWhjjGnu3NXOdt3RSXDqw153m7NuF0/O3mibpRjTwoX66oNV9ZJ6jl8HXOer8ze6EZPh/Stgw+e17j6VnhTDgI7xfLpiJ5NP6ObnAI0xxjSa71+AncvgglcgKtGrLrZZijHBI+A3ETYbvc6AuI71Lmk3YWAHlmcXs61gv58CM8YY06iKtsGcP0OP06DfeV51sc1SjAkulkB7yxUKGdfAlq8gf32tzc4Y4CnjsNU4jDGm+VGFab91np/5GHgxi2ybpRgTfCyBboihV4IrHBbVvqRdp9bRDO6UwDSrgzbGmOZn9Uew6Qs4+T5ISPOqy3uezVJutc1SjAkalkA3RKs2zuW8ZW9D2d5am00Y2IHVO/byw+5SPwZnjDEOEflIRM4UERvjG+JAIXx2N6QMgZHXe9VlT2kFf/50Lcd1T+J22yzFmKBhg2tDjZgMFfucXalq8WMZh81CG2MC41ngUmCjiDwiIr0CHVCz8MUDznr/E5+EEO9qmJ/5chP7K6p4cGI/2yzFmCBiCXRDpQ6DlKHOzYSqh22SkhBFRnoinyzbgdt9+DbGGOMrqjpLVS8DhgJbgVkiMk9ErhaRsMBG10RtX+is9X/sLdBhoFddsgv388b8LM4fmkqPdrE+DtAY05RYAn0kRl4Puzc4NxTW4vJj0tmUt4+py20W2hjjfyKSBFyFs1zoUuAJnIT6iwCG1XTNe9JZru7Eu73u8q8vNoLAb0610g1jgo0l0Eei7zkQnQwLX6y1yVmDUujfMY5HZ6ynrLL2zVeMMaaxicjHwDdANDBRVc9S1fdU9VagVWCja4KKtsO6T50bxcNjvOqyPreEj5Zmc+WodFISonwcoDGmqbEE+kiERcKwK2HDZ1CYddgmISHC78/oQ07RAV6bt9W/8Rljgt2TqtpXVf+qqj9bU1NVMwIVVJOV+bLzc/i1Xnd5dMY6WoWHctOY7j4KyhjTlFkCfaQyrnF+Zr5Sa5NjuyVzSu+2PDNnE3tKK/wUmDHG0FdEEg6+EJFEEbkpkAE1WZUHYPG/nc2yvFy2btHWPcxam8cNY7qRGBPu4wCNMU2RJdBHKj7V2dJ7yevOAFyLe07vTWlFFU/O3ujH4IwxQW6SqhYdfKGqhcCkAMbTdK36EA7s8XrZOlXlb5+to01sBFcf19m3sRljmixLoI/GiMnOwLvqo1qb9GgXy8Uj0nhzQZatC22M8ReXyE9b6ImIC7Cp0kOpwvcvQJs+0Hm0V11mr80jM6uQX5/Sg+jwUB8HaIxpqiyBPhqdR0Ob3rDwhVqXtAO4fWwPwkND+Pvn6/wYnDEmiH0OvCcip4jIKcA7nvdMTdsXQu4KGDHJqy27q93K32eso0tyDBcN7+SHAI0xTZUl0EdDxBl4dy6H7Mxam7WNjeSGE7vx2apcMrfu8WOAxpggdTfwJXCj5zEb+F1AI2qKFr4AEfEw8CKvmn+8NIcNu/Zxx7iehLns16cxwcxGgKM18GKIiHM2VqnDdaO70DY2gr9MX4vWMVttjDFHS1Xdqvqcql7gebygqraeZk17d8Ka/8KQyyGi/pX9yiqr+dcXGxjQMZ4z+nfwQ4DGmKbMEuijFdEKBl8Gqz+Gkl21NosOD+XOcb1Yuq2I6Stz/RigMSbYiEgPEflARNaIyJaDj0DH1aQsfhXc1TDiOq+av7kgi5yiA9w9vjchtmW3MUHPqwRaRH4tInHieFlElojIOF8H12wMvw7clbDk33U2O39YKr3bx/K3z9dRUeX2U3DGmCD0KvAcUAWcBLwOvBnQiJqSqgrIfBV6jIPWXettvreskme+3MTx3ZM5vkeyHwI0xjR13s5AX6Oqe4FxQCJwBfCIz6JqbpK7Q7dTnDWhqytrbeYKEe49ow/b9uznjQWH34DFGGMaQZSqzgZEVbNU9UHgzADH1HSs+QRK82DkZK+avzh3C4X7K7l7fG8fB2aMaS68TaAPXq86A3hDVVfXeM+As6RdyU5YN63OZif2bMPoHsk8NWcjxftrT7aNMeYolItICLBRRG4RkXOxLbx/8v0LkNQdup5cb9O8kjJe+uYHJgzswIDUeD8EZ4xpDrxNoBeLyEycBHqGiMQCVoNQU49TISEdFr5Yb9N7T+9D8YFKnvlqkx8CM8YEoV8D0cBtwDDgcuDKgEbUVOQshpxMGD4JQur/FfjU7E1UVru5c1wvPwRnjGkuvE2grwXuAYar6n4gDLjaZ1E1RyEupxY66zvIXVVn074pcZw/NJXXvtvK9j37/RSgMSYYeDZNuUhV96lqtqperarnq+qCQMfWJCx8EcJbweBL6226dXcp7yzcxsUjOtE5OcYPwRljmgtvE+hRwHpVLRKRy4H7gGLfhdVMDbkcQiNhUf2z0HeM60lICDw6Y70fAjPGBAvPcnXHBzqOJmlfvrN196BLIDKu3uaPzVxPmCuE207p4YfgjDHNibcJ9HPAfhEZBNwBbMa5q7tWIvKKiOSJyGGnYz0rejwpIptEZIWIDG1Q5E1RdGsY8H+w4n04UFhn0w7xUVx3fFemLt/B8u1FfgrQGBMklorIVBG5QkTOO/gIdFABt+Q1qK5w7lmpx8rsYqat2Mm1x3ehbWyk72MzxjQr3ibQVers/nE28LSqPgPE1tPnNWB8HcdPB3p4HpNxkvTmb8QkqNwPS9+qt+kNY7qR3CrcNlcxxjS2SKAAOBmY6HlMCGhEgVZdCYtega4nQZue9Tb/+4x1JEaHMfnE+pe5M8YEH28T6BIRuRdn+bpPPXd3h9XVQVXnAnXtW3028Lo6FgAJItL8t3fqMAg6HeOUcbjrvs+yVUQovx7bk4U/7GHW2jw/BWiMaek8dc+HPq6pr5+IjBeR9Z4rg/fU0uZCzwYtq0Xk7caP3kfWTYOSHTDy+nqbfrdpN99s3M3NJ3UnLrLOX3XGmCDlbQJ9EVCOsx50LpAKPHqU5+4IbK/xOtvzXvM3cjIUboVNs+ptevHwTnRrE8NfP1tLZbUtbGKMOXoi8qqnjO5nj3r6uIBncK4O9gUuEZG+h7TpAdwLHKeq/YDbffQVGt/3U5yVknrUvQeYqvK3z9eREh/J5cek+yk4Y0xz41UC7Uma3wLiRWQCUKaqddZANyYRmSwimSKSmZ+f76/THrneE6FVe1j4Qr1Nw1wh3HN6H7bkl/Luou31tjfGGC9MAz71PGYDccC+evqMADap6hZVrQDexblSWNMk4BlVLQRQ1eZx6Sx3JWyb56yUFOKqs+n0lbmsyC7mN6f2JDKs7rbGmODl7VbeFwILgf8DLgS+F5ELjvLcOUCnGq9TPe/9gqpOUdUMVc1o06bNUZ7WD0LDnVroTbNgW/0rR43t05aRXVrz+BcbKCmzzVWMMUdHVT+s8XgLZ9zOqKebN1cFewI9ReQ7EVkgIoe9z6XJTXp8/wKERjkrJdWhstrNYzPX07NdK84bmuqn4IwxzZG3JRx/wFkD+kpV/RXOTMX9R3nuqcCvPKtxHAMUq+rOo/zMpuOYG51Z6Jn3QT03CIoIfzizDwWlFbzw9RY/BWiMCSI9gLaN8Dmhns8aA1wCvCgiCYc2alKTHvv3wMr/wMALnZWS6vB+5nZ+2F3KXaf1xhVim+0aY2rnbQIdcsiluoL6+orIO8B8oJeIZIvItSJyg4jc4GkyHdgCbAJeBG5qWOhNXHgMnHwfZC+CNZ/U23xgagJnD07hxW+2sLP4gB8CNMa0VCJSIiJ7Dz6A/wF319PNm6uC2cBUVa1U1R+ADTgJddO15HWoKqv35sEDFdU8MWsjGemJjO3TGH9rGGNaslAv230uIjOAdzyvL8JJgGulqpfUc1yBm708f/M0+FJY8BzMehB6nemUdtThznG9+GxVLv+YuYHH/m+Qf2I0xrQ4qlrfMqOHswjoISJdcBLni4FDt+v7BGfm+VURScYp6Wi6l83c1bDoZUg/Htr1q7Ppx0tzyCsp56lLhiBis8/GmLp5exPhXcAUYKDnMUVV65vNMCEuGPewsyLHopfqbd6pdTRXH9uZD5dksyrHNno0xhwZETlXROJrvE4QkXPq6qOqVcAtwAxgLfC+qq4WkYdF5CxPsxlAgYisAb4E7lLVAt98i0aw4XMo3uasjFSPGatzSU+KZkSXuss8jDEGvC/hOHhTym89j499GVSL0n2ss3D/3L/XuzshwE0ndScpJpzb31tGaXmVHwI0xrRAf1TVH/8KV9Ui4I/1dVLV6araU1W7qepfPO89oKpTPc/V8zugr6oOUNV3ffYNGsP3L0BcR+cKYB32llUyb/NuxvVtZ7PPxhiv1FfH/LM6uhqPEk9dnfHGuD/BgSL45h/1No2PCuOJi4ewJX8ff/h4pe1QaIw5Eocb270t2WsZ8tbBD19DxjXgqvurf7U+n8pq5bR+7f0UnDGmuaszgVbVWFWNO8wjVlXj/BVks9d+gFMP/f0LTjlHPY7rnsxvT+3JJ8t28Nb323wfnzGmpckUkX+KSDfP45/A4kAH5VcLp4ArAoZdVW/TmatzSW4VzpC0RN/HZYxpEbwu4TBH6aQ/gLhg9p+8an7TmO6M6dWGh/+3hhXZRT4OzhjTwtwKVADv4WyIUkZLv2m7prJiWP4u9D8fYpLrbFpeVc1X6/M5tW87W7rOGOM1S6D9Jb4jjLoZVn0AOfVPBIWECP+6cDBtYiO48c0lFO2v8EOQxpiWQFVLVfUez1rMw1X196paGui4/GbpW1BZ6tXNg/M2F7CvvIpxfa18wxjjPUug/en42yGmDcy8v97NVQASY8J59rKh5JWU8dv3l+N2Wz20MaZ+IvJFzQ1ORCTRsxRpy+d2w6IXIXUEpAypt/nM1bnEhLsY1S3JD8EZY1oKS6D9KSIWxtwDWd/B+jqX0f7RoE4JPDChL3PW5fHc15t9HKAxpoVI9qy8AYCqFtI4OxE2fZtmwZ4t9W6cAlDtVr5Ys4sxvdsSGebyQ3DGmJbCEmh/G3olJPeEL/4I1ZVedbn8mHTOGpTCP2auZ97m3T4O0BjTArhFJO3gCxHpDATHJayFU6BVO+hzVr1Nl20vZPe+Csb1beeHwIwxLYkl0P7mCoOxD0HBRlj8mlddRIS/njeArm1acds7S9m1t8y3MRpjmrs/AN+KyBsi8ibwNXBvgGPyvb07nRnoob+qd+dXgBmrdxHmEk7qHRyT88aYxmMJdCD0Ot3ZWvarR6DMu+W0YyJCee6yoeyvqOaWt5dQWe32cZDGmOZKVT8HMoD1wDvAHcCBgAblD6s/BhQGXFhvU1VlxupcRnVLJi4yzPexmf/f3p3HR1We/R//XNnJvpAAIQkQVtnBiIgK4oK41LXWte5Sqv7ULo9tn1br06etXZ7aWku1brV1F6yKFgUUwV1BJYEgu2hCIIQlgbAkJLl/f5wBYhpkAjmZSfJ9v17nNWfOuc/MlZnJnStn7nNfIh2KEuhQMPOKq+zaDO/+KejD+ndL4u4LhrFw3Tb+b/YKHwMUkfbMzK4H3sBLnH8IPA7cFcqY2sSS6dB9OGQOOGTTleXVfLFll4ZviMhhUQIdKj1Hw7CL4P1pULU+6MPOHdmTb4/txd/eWsvs4o0+Bigi7ditwDHAF865icAooGNPKL9lDZR9AsO+GVTzOYH+Uwm0iBwOJdChdHJgOrt5v2zRYT87+yiG56Tww+cK+WJL55naVUSCtsc5twfAzGKdc8uBgSGOyV9L/+XdDrkgqOZzlpUzKi+VrOQ4H4MSkY5KCXQopfXyploqfBo2FAV9WGxUJNMuG01EhPHdJz5hz956H4MUkXaoNDAP9IvAXDN7CfgixDH5xzlv+EbeOEjNPWTz9ZW7WbK+itOHqHiKiBweJdChduIPoEsqzA2uuMo+uenx/OnikSzbsJ27Zhb7GKCItDfOufOdc5XOubuAO4BHgPNCG5WPypfC5hUw7MKgms/V8A0ROUJKoEOtSypM+BGsnQ+r32jRoRMHZXHzxH48s7CE6YtK/IlPRNo159wC59xM51xtqGPxzZIZEBEFg88Pqvns4nL6x+/HIAAAIABJREFUZyWSn5noc2Ai0lEpgQ4HBddBWh/vLHRDy4ZjfO+0AYzrm8HPXlzKsrLgpsQTEekwGhpg6fOQPxESDl2Oe9vOWj5at5VJQ3T2WUQOnxLocBAVA6feBZuWweInW3RoZIRx7yWjSOkSzY1Pfsz2PcFVNxQR6RBKP4KqkqBn35i3fBP1DY5JgzX+WUQOnxLocDH4XMgZA/N+BTXVLTo0MymWaZePpmTbbm6fXkRDQ+eo2CsiwpLpEBUHg84Kqvns4o10T45jeE6Kz4GJSEemBDpcmMGkX0L1Rnj/Ly0+/Jje6fzkjEG8VryRu1/9zIcARUTCTH0dFL8IAyZDbNIhm++ureetVRVMGtINM2uDAEWko1ICHU7yjvXORL/7Z9jR8iIp153Qh6vH9eahtz/nbwvW+BCgiEgY+Xy+V9E1yOEbb6+qYM/eBk1fJyJHzNcE2swmm9kKM1ttZj9uZn+emb1pZp+aWZGZnelnPO3CKT+Hhr3w1MWwc3OLDjUz7jx7MGcP78Hdry5nxselPgUpIhIGlsyA2BTod1pQzWcXl5McF8WYPuk+ByYiHZ1vCbSZRQLTgDOAwcClZja4SbOfAc8550YBlwB/9SuediOjL1z8BFSsgEcmwbaW1T6IiDD+8K0RnNCvKz96voh5y8t9ClREJIT27obPXoGjvgHRh64mWFffwBvLyznlqG5ER+rLVxE5Mn72ImOA1c65tYH5R58Bzm3SxgHJgfUUoMzHeNqPAafDlS95X00+MgnKW1YoJTYqkge+fTRDspO58clP+PiLrT4FKiISIqvmQO2OoIdvfLRuK5W79nK6pq8TkVbgZwLdE2hc3aM0sK2xu4ArzKwUmAX8Px/jaV/yjoVrXvMuLvz7GfDF+y06PDE2ikevPoYeKV249rFFrCzf4VOgIiIhsGQ6JGRBn/FBNZ9TXE5sVATjB2T6HJiIdAah/h7rUuAx51wOcCbwuJn9R0xmNsXMFpnZooqKijYPMmS6DYbr5kBCJjx+Hqx4tUWHd02M5Z/XjiEmKoIrH/mI9ZW7fQpURKQN7amClXNgyPkQEXnI5s455i4r58T+mcTHRLVBgCLS0fmZQK8Hchvdzwlsa+w64DkA59z7QBzQtekDOecedM4VOOcKMjM72dmD1Dy4djZkHQXPXA6ftqzQSm56PP+8dgw7a+u48pEP2baz41bzFZFOYvm/ob4Ghl0UVPPisu2sr9yt6oMi0mr8TKAXAv3NrI+ZxeBdJDizSZsvgVMAzOwovAS6E51iDlJCV7jqZehzIrx0I7x7b4sOP6pHMg9fWUDJtt1c89hCdtXW+RSoiEgbWDIdUntBTkFQzecUbyTC4JRBWT4HJiKdhW8JtHOuDrgZmA18hjfbRrGZ/cLMzgk0+wFwg5kVAk8DVzvnVEavObFJcNlzMOQCmHsnzPkZNDQEffix+Rncd+koikorufHJT9hbH/yxIiJho7oC1i7wLh4MshjK7OJyjumdTkZirM/BiUhn4etgMOfcLLyLAxtvu7PR+jLgeD9j6FCiYuHCR7wz0u/dBzu3wDl/hsjooA4/fUh3fn3+MH78ryXcPqOIP1w0gogIVeMSkXZk2Yvg6mFocLNvrNu8kxXlO7jj7KazqIqIHD5dTdHeRETAGb/zLix881ewawtc9BjExAd1+CVj8thcXcP/zVlJ18QYfnqW/qiISDuyZDpkDfYusg7C3GXeXPiTBmv8s4i0nlDPwiGHwwwm3A5n3ePNhfr4ebB7W9CH3zSxn0p+i8h/CKJ67NVmVmFmiwPL9W0a4LYvoOTDoOd+BphdvJHBPZLJTQ/uJIOISDCUQLdnx1znnX0u+xQePQO2B1eHRiW/RaSpIKvHAjzrnBsZWB5u0yCXPu/dDr0wqOYVO2r4+Mttmn1DRFqdEuj2bsh5cPkMqCr1qhZuXhXUYSr5LSJNBFM9NrSWPg85x0Ba76Cav/5ZOc5513+IiLQmJdAdQf4EuPoV2LsbHjoF5v8mqCEdTUt+L1ynkt8inVgw1WMBLjSzIjObYWa5zez3x6bPoHxp0HM/gzd9XW56FwZ1T/IxMBHpjJRAdxTZI+H6udD7BJh/N/xxGLz+P7Bz89celhgbxd+vPobslC5c+chHzF+xqY0CFpF26GWgt3NuODAX+EdzjXypHrtkBliEV30wCNU1dby7egunD+6OBTndnYhIsJRAdyTp+XDpUzD1Xeh/GrzzR/jjUHjtv2H7hoMelpEYy7PfOY78zASu/8ciXlrctGCkiHQCh6we65zb4pyrCdx9GDi6uQdq9eqxzsHSGdBnAiQGVwxl/opN1NY3MEnDN0TEB0qgO6LuQ+Giv8PNC72zNR8+APcOh1e+713F3ozMpFiemTKWY3qnc+szi3n0nc/bOGgRCbFDVo81sx6N7p6DVyTLf+s/gW3rWjT7xpzicjISYji6V5p/cYlIp6UEuiPr2h/Ovx9u+QRGXg6fPg73jYYXb4LNq/+jeVJcNH+/5hgmD+nOL15Zxu9nL0eFIUU6hyCrx95iZsWB6rG3AFe3SXBLpkNkDAw6O6jmtXUNvLl8E6ce1Y1IFYsSER+okEpnkNYbvvEnGP9fXgXDj/8OhU95ZcFP/MFXChLERUcy7fLR/OzFpUx7cw1bqmv55XlDiYrU/1oiHV0Q1WN/AvykTYNqqIfif0H/SdAlNahD3l+7hR01dZq+TkR8o6yoM0npCWf8Bm5bAuNugZWvwf3HwTOXe3NJB0RGGL8+fyj/7+R+PLOwhJue+oQ9e+tDGLiIdFrr3oHq8hYO39hIfEwkx/fr6mNgItKZKYHujBKz4LT/8RLpCT+GdW/DgyfB8zfAnirAK7byg0kD+fk3BjO7uJyrHv2I7Xv2hjZuEel8lkyHmEQYMDmo5g0NjrnLyjlpYCZx0ZE+BycinZUS6M4sPh0m/gRuWwoTfuQVKXjgBCj5aH+Ta47vw72XjOTjL7Zxyd8+oGJHzdc8oIhIK6qrgc9memOfo7sEdcji0ko27ahh0mDNviEi/lECLRCXDBP/G66dDRg8OhkW/M4bewicO7InD19VwOebd/LNB97jyy27QhuviHQOq9/wvhVrwfCN2cUbiYowJg4Kbro7EZHDoQRaDsg9Bqa+A0MvhDd/BY+dDZVeYbKTBmbx1A3HUrV7Lxc+8B7LyraHOFgR6fCWTIf4DMg/KehDXl9WznF9M0jpEu1bWCIiSqDlq+KS4cKH4PwHYeMSeOB4KH4BgFF5acyYehxREcbFf3ufD9duCXGwItJh1VTDildh8HkQGVwyvG1nLWsqduriQRHxnRJoad6Ii2HqW5DRH6ZfDS/dBDXV9MtKYsZ3x5GVHMu3H/2IOcUbQx2piHREK16Fut0tGr5RWFoJwIic4Ka7ExE5XEqg5eDS8+Ha1+DEH8KnT8KDE6DsU3qmdmH61HEc1SOZqU98zHMLS0IdqYh0NEumQ3IO5I4N+pCi0irMYFhOio+BiYgogZZDiYyGU+6Aq1+Bvbvh4dPg3T+T3iWKp64/luP7deX254v46QtL2F2ruaJFpBXs2gpr3oChF0BE8H+mCksq6ZeZSGKsaoSJiL+UQEtwep/gXWA4cDLMvQOeuICE2s08ctUxTBmfz5MffsnZ973N0vVVoY5URNq7ZS9CQx0MuyjoQ5xzFJZWMVzDN0SkDSiBluDFp8O3Hodv3AtffgD3jyNmzRz++8yjeOK6Y6muqeP8v77Lg2+toaHBhTpaEWmvUnJh5BXQfVjQh5RV7WFzdQ0jczV8Q0T8pwRaWsYMjr4avvMWJGfD0xfDv3/ACTmRvHbreE4elMWvZy3nikc+ZGPVnlBHKyLtUf/T4LxpXn8TpKKSwAWEuToDLSL+8zWBNrPJZrbCzFab2Y8P0uZbZrbMzIrN7Ck/45FWlDkArn8Dxt4ICx+GPw0nbeE9PPDNfvzmgmF8+mUlk+99i9eWbgh1pCLSCSwurSQmMoJB3ZNDHYqIdAK+JdBmFglMA84ABgOXmtngJm36Az8BjnfODQFu8yse8UFULEy+2xsb3Wc8zL8bu3cEl+x5jllTR5KbFs/UJz7hRzOK2FlTF+poRaQDKyyp5KjsZGKi9MWqiPjPz55mDLDaObfWOVcLPAOc26TNDcA059w2AOfcJh/jEb90HwaXPAlT5kPeWJj3v/R54jheGLGQW0/M5rmPSzj7vncoDHzFKiLSmuobHEvXb2eEpq8TkTbiZwLdE2g8QXBpYFtjA4ABZvaumX1gZpN9jEf8lj0KLnsWrp8HPUcTNe8uvlf8Td48finU7uLC+99j2purqdcFhiLSitZWVFNdU6cCKiLSZkL9XVcU0B84CbgUeMjM/qMHNLMpZrbIzBZVVFS0cYjSYjlHwxXPw7VzoPtQei/6NW9E38rdPd/lz7OXcOlDH7C+cneooxSRDqKw1Js+c4Rm4BCRNuJnAr0eyG10PyewrbFSYKZzbq9z7nNgJV5C/RXOuQedcwXOuYLMzEzfApZWlncsXPkSXD2LiK4DuKjiL3ya+iOGrX+Ob/zpDV4uLAt1hCLSARSWVJIYG0V+18RQhyIinYSf5ZoWAv3NrA9e4nwJcFmTNi/inXn+u5l1xRvSsdbHmCQUeh/vVTL8/C3i3/w1d5Q8ytSIl7nnuXN4r/BMbhmfQ48uDV6lw707vdvawO3eXd5Su+vA+r7t9Xu9pWHfbd2B2/3re6G+rlGbvZDe17v4MS/4EsEiEr6KSisZ1jOFiIjgp70TETkSviXQzrk6M7sZmA1EAo8654rN7BfAIufczMC+SWa2DKgH/ss5t8WvmCSEzCB/gjdbx5p5ZLz5a+5e/wisfST4f5mi4iA6PrB0gcgYiIyCiGiv5HhElNcmMjqwrcm+fbfLZ8Gjp8PIy+HU/4FEfash0l7V1NWzbMN2rjshP9ShiEgn4ucZaJxzs4BZTbbd2WjdAd8PLNIZmEG/U4joezKsmUfl+uW8unw773yxi6i4BM46uh8nD+tFVFyilyRHJwRu4yGilUYcnXoXLPgdvP8XWP4KnHInHH0NRES2zuOLSJv5bMMO9tY7VSAUkTYV6osIpbMKJNKpE27i0u/8hKk3/pCN3SYw5e0uTJ6xi3lb03Gpvbyzw7GJrZc8A8QkwGn/A999D7oPh3//AB4+BdZ/3HrPISJtoqjUmx5zuGbgEJE2pARawsKwnBSemTKWB799NPUNjmsfW8QVj3zIsrLt/j1p5kC46mW48BHYvgEeOgVevg12bfXvOUWkVS0uqSQzKZYeKXGhDkVEOhEl0BI2zIxJQ7oz+7bx/Pwbgyku285Z973N7TMKKd++x68nhWHfhJsXwtjvwif/hL8UwCePQ0ODP88pIq2mqLSKETkpmOkCQhFpO76OgRY5HDFREVxzfB8uGJXDX95cxWPvrePlwg18Z0I+U8bnEx/jw8c2LtmbmWPk5d6Qjpk3e8n0WX+AHsNb//nk0BoaoLbaW2qqoWYH1O5otF4NNdu9GVpikyChK8RnfHWJS/H+SZIOaceevaypqObcEdmhDkVEOhkl0BK2UuKj+elZg7libC9++9py/vT6Kp7+6Et+MGkgF47OIdKPKau6D4VrXoXCp2HunfDgBDjmBjj5p14yJoenfi/srPCW6sDtzk1QvQl2bvbWd2/zkuPaRglyUAw4SHXLiCjoku4l0wldIT6wHh9Itrukef88xSYHbpO89dhkbxYXCWtL1lfhHAzP1fhnEWlb+gshYa9XRgJ/vfxoFq3byi///Rm3zyjisXfX8b3TBnDKoKzWn/s1IgJGXQ6DzoR5v4SPHoTiF2DS/0L2aKivhfqawDzUtVBX+9VtdTWB+3sD22q96fW6DYFuw9rntHnOeT9X4+S2ptqbr3vfWeF9+3ZWfDUx3lnhJcfNiYqDhCzvNYnPgLTeEJMYSGITvYQ2JnC7f33f9sC2qFgvjl1bYNdmbwz7ri3esnPzgfVdW2HT8gNtDpZ07xOd4D3+VxLsQJIdlwL9J3lTM0rIFJYEKhDm6J9bEWlbSqCl3Sjonc4LN47j5aIN/N/sFdzwz0UM6p7EjRP7cdawHq1/RrpLmjeEY9QV3rCOF77TOo+b2B26D2u0DIf0PqGZRq+hAXaUwZY1sGU1bF3rre+saJQkB5aGuuAeMy7FS4oTMiHrKEiY4K0nZnq3CVne2eDELC8hbo0hFrGBxDqtV3DtG+phT5WXSNds95Y9gduaHQfW91R59/ftryo9sD8hUwl0iBWWVNIrI57U+JhQhyIinYwSaGlXzIxzRmRz5tDuvFxUxrQ313DL05/yp7krmXpSX84f1ZPoyFa+NjZ7FFz3Oqye6yVPkTHeEhVzYL3x0tz22mooXwoblxxY1r55ICmNjvfOUDdOqrOO8qbcO1LOeQnxljWwNZAob1kTuL8W6nYfaBvVBdLzIakbJGcfOOO7/zbpwP2YhK+eFd53pjgy+shj9ltEZGA4R/rhP4Y7xBls8V1RaSUFvY/gPRQROUxKoKVdioqM4PxROZw7oiezizdy37zV3D6jiHtfX8XUCflcVJBLXHQrntGNiIABpx9BwOleFcY+4w9sq6uBiuWBhDqQXC95HhY9GmhgkNHXG9pgkWARXhwW6SWA+7c1ud23v67GS5C3rvXOoO7/WaIgrY/32H0neglzRj/vflJ268653ZHp4sSQ2rRjD2VVexih8c8iEgJKoKVdi4gwzhjWg8lDuzN/RQX3zVvFHS8V8+d5q5lyYj6XHZtHQmyYfsyjYqHHCG/Zxzmo/PLAWerypd5Zb9fgLXW14Oq9IQiuIbAeuHUNge2BbZFR3pji3DGQ3jeQJOdDSp4ukJNmmdlk4F4gEnjYOfebg7S7EJgBHOOcW9SGIe5XpPHPIhJC+isqHYKZMXFQFicNzOT9tVuY9uZqfjXrM6bNX821x/fhqnG9SenSDoYWmHnjeNN6wVFnhzoa6UTMLBKYBpwGlAILzWymc25Zk3ZJwK3Ah20f5QGFpZVERhhDspVAi0jb03e10qGYGeP6duXJ68fyrxvHcXReGvfMXckJv5nH715bzpbqmlCHKBKuxgCrnXNrnXO1wDPAuc20+1/gt4BP1Y2CU1haxYBuSXSJCcHFtyLS6SmBlg5rdF4aj1x9DP++5QTGD8jk/gVrOP6387jzpaX+lggXaZ96AiWN7pcGtu1nZqOBXOfcv9sysKaccxSWVDIyV2efRSQ0NIRDOrwh2SlMu3w0qzdV89f5q3nmoxL++f4XDOuZwreOyeWcEdntY3iHSAiZWQRwD3B1EG2nAFMA8vLyWj2WL7bsomr3Xobn6AJCEQkNnYGWTqNfViL3fGskH/73Kfz8G4PZW9/AHS8uZcyvXud7zy7m/TVbcJqaTDqv9UBuo/s5gW37JAFDgflmtg4YC8w0s4KmD+Sce9A5V+CcK8jMbP3CQYWllQCMUAItIiGiM9DS6aQlxHDN8X24elxvlqyv4tmFJcxcXMYLn66nV0Y83yrI5cLROXRPiQt1qCJtaSHQ38z64CXOlwCX7dvpnKsCuu67b2bzgR+GYhaOwpIq4qIjGNAtsa2fWkQEUAItnZiZMTwnleE5qfzsrMG8VryBZxeW8PvZK/jDnBWcNDCLbxXkcspRWa1fnEUkzDjn6szsZmA23jR2jzrnis3sF8Ai59zM0EZ4QFFpJUOzU4jS76WIhIgSaBGgS0wk54/K4fxROazbvJPpH5cw4+NSpj6xia6JMZw/qicXH5NLv6ykUIcq4hvn3CxgVpNtdx6k7UltEVNTdfUNLC2r4vJjgyzbLiLiAyXQIk307prAf50+iO+dOoC3V23m2YUl/P3ddTz09udMHJjJ904boIuXREJkZXk1e/Y2MFwFVEQkhJRAixxEVGQEEwdlMXFQFpura3h2YQkPvb2Wc/7yLqce1Y3bTu3P0J76Iy7SlvZdQDhSJbxFJIQ0gEwkCF0TY7lpYj/evn0iP5w0gI8+38LZ973D1Mc/ZvlGzSkt0lYKSypJjY8mLz0+1KGISCemM9AiLZAUF83NJ/fnynG9efSdz3nk7c95rXgjZw3rwa2n9mdAN42RFvFTYWkVw3NSMbNQhyIinZivZ6DNbLKZrTCz1Wb2469pd6GZuebmExUJR8lx0dx26gDe+dHJ3HJyPxasrOD0P73FLU9/yupN1aEOT6RD2l1bz8ryHYzQ+GcRCTHfEmgziwSmAWcAg4FLzWxwM+2SgFuBD/2KRcQvKfHRfH/SQN6+fSLfndCX1z8rZ9IfF/C9Zxfz+eadoQ5PpEMpLquivsGpgIqIhJyfZ6DHAKudc2udc7XAM8C5zbT7X+C3wB4fYxHxVVpCDLdPHsTbt0/khhPzeXXpBk69ZwE/nF7Il1t2hTo8kQ5hcYl3AeHwXJ2BFpHQ8jOB7gmUNLpfGti2n5mNBnKdc//2MQ6RNpORGMtPzjyKt28/mavH9eblwjJO/sN8bnvmU174tJSNVfo/UeRwFZVWkZ0SR1aSqoSKSGiF7CJCM4sA7gGuDqLtFGAKQF5enr+BibSCzKRY7jh7MFPG53P//DX865NSXlxcBkCfrgmMzU9nbH4Gx+VnkJWsZEAkGIWllYzQ9HUiEgb8TKDXA7mN7ucEtu2TBAwF5geupu4OzDSzc5xzixo/kHPuQeBBgIKCAudjzCKtqltyHHedM4Q7zh7MZxu288HaLXywdguvFG3g6Y+8L2jyMxM4Lj+DsYElMyk2xFGLhJ9tO2v5YssuLjlGJ1FEJPT8TKAXAv3NrA9e4nwJcNm+nc65KqDrvvtmNh/4YdPkWaQjiIwwhvZMYWjPFK4/MZ/6Bseysu28v3Yz76/ZwkuLy3jywy8B6JeVyHH5GRzXN4Nj+6STkaiEWqRofRUAIzT+WUTCgG8JtHOuzsxuBmYDkcCjzrliM/sFsMg5N9Ov5xYJd5ERxrCcFIblpDBlfF/q6htYWuadoX5/zRae/6SUxz/4AoARuamcObQ7ZwztQV6GikdI51RYUokZDFP1TxEJA76OgXbOzQJmNdl250HanuRnLCLhLCoygpG5qYzMTWXqhL7srW9gyfoq3lu9mTnLyrn71eXc/epyhvZM5oyhPThzWA/6dE0IddgibaaotJK+mYkkxUWHOhQREVUiFAlH0ZERjM5LY3ReGjef3J+Srbt4belGZi3dwO9nr+D3s1cwqHsSZw7rwZnDutMvSxUQpeNyzrG4pIrxA7oeurGISBtQAi3SDuSmx3PD+HxuGJ9PWeVuXlu6kVeXbuCPr6/knrkr6Z+VyBnDenDWsB4M6JaoMsfSoWyo2sPm6hpGagYOEQkTSqBF2pns1C5ce0Ifrj2hD+Xb9zC7eCP/LtrAffNW8ec3VpGfmcCZQ3sweWh3hmQnK5mWdq8wUEBFFQhFJFwogRZpx7olx3Hlcb258rjeVOyoYXaxd2b6/gVr+Mubq8lMimXCgExOGpjJCf26khofE+qQRVpscWkl0ZHGoB4aqiQi4UEJtEgHkZkUyxVje3HF2F5s3VnLG5+Vs2BlBXOXlTPj41IiDEbmpnLSwCwmDMhkWM8UIiJ0dlrCX1FJFYN7JBMbFRnqUEREACXQIh1SekIMFxXkclFBLvUNjsUllSxYWcGCFZv2j5tOT4hhfP+uTBiYyfj+mZpvWsJSQ4Njyfoqzh/VM9ShiIjspwRapIOLjDCO7pXG0b3S+P5pA9hSXcPbqzazYGUFb62s4MXFZfvn1z1pQCYTBmYyIieVqMiIUIcuwtrN1VTX1KmEt4iEFSXQIp1MRmIs543qyXmjetLQ4FhaVsX8FRUsWFnBX95czZ/nrSYpNopj89MZm5/BuL5dGdQ9ScM9JCQWlwQqEOaogIqIhA8l0CKdWESEMTwnleE5qdxySn8qd9XyzurNvLt6C++v2czrn20CIC0+mrGB8uLj+mbQN1NT5UnbKCqtJDE2ivzMxFCHIiKynxJoEdkvNT6Gs4dnc/bwbADKKnfz/potvB8oMf7q0o2Ad8HicfleMn1c3wzy0uOVUIsvCksqGdozmUh9AyIiYUQJtIgcVHZqFy48OocLj87BOceXW3fx/potvBdIqmcWlgHQM7ULx/XNYGx+BsNzUsjvmqAx1HLEaurqWbZhO9ee0CfUoYiIfIUSaBEJipnRKyOBXhkJXDImD+ccayqq9yfUr3/mTZcHEBsVwaAeyQzJ3rekMKh7EnHRmoZMgrd8ww721jtGqoCKiIQZJdAicljMjH5ZSfTLSuLbx/WmocGxalM1xWVVFJdtp7isipcLy3jqwy8BbzaQvpkJDMlOYUh2MoOzkxnSI4WU+OgQ/yQSrgpLvQqEwzUDh4iEGSXQItIqIiKMgd2TGNg9iQtGe9ucc5Ru290oqd7Oe2s288Kn6/cf1zO1C0OykxnWM4WRed4FjSldlFQLFJZU0TUxluyUuFCHIiLyFUqgRcQ3ZkZuejy56fFMHtpj//bN1TX7z1IXl21nWdl25iwr378/PzOBkbmp+5dB3ZOJidKY6s6msLSSETkpukBVRMKOEmgRaXNdE2OZMCCTCQMy92+r2r2XotJKCksqWVxSyVsrK/jXJ96Z6pioCIZkJ38lqdbMHx3bjj17WVNRzTkjskMdiojIf1ACLSJhIaVLNCf2z+TE/l5S7ZxjfeVuCkuqWFyyjcUllTz90Zf8/d11gDc39YjcVEbkpNKnawLZqV3ITo2jW3Ic0ZoBpN1bsr4K52C4CqiISBhSAi0iYcnMyEmLJyctnrOGe8M/6uobWFG+Y39SXVhSxYKVq3DuwHERBllJcWSnxpGd2oWeqV0CybWXYPdM7UJKl2idvQ5zhfsrEOoCQhEJP0qgRaTdiIqMCMzikcJlx+YBsLu2nrKq3ZRVesv6yj3715eur2JOcTm19Q1feZz4mEiyU7vQp2sCBb3SKOidzrCeKZ1+nLWZTQbuBSKBh51zv2mCTYSVAAALRUlEQVSyfypwE1APVANTnHPL/IilqLSSvPR40hJi/Hh4EZEjogRaRNq1LjGR9M1MpO9BSj03NDi27KxtlGDvpqxyDxuqdrNi4w7mBi5ejI2KYGRuKmP6pFPQO53ReakkxXWe2UDMLBKYBpwGlAILzWxmkwT5KefcA4H25wD3AJP9iKewpJKje6f78dAiIkdMCbSIdGgREUZmUiyZSbGMaGY+4YodNXz8xVY++nwbi77Yyl/nr6G+YTURBoOzkynolR5IqtPISurQ06mNAVY759YCmNkzwLnA/gTaObe9UfsEwOGDTTv2UFa1h2s1/llEwpQSaBHp1DKTYpk8tMf+afaqa+r49MttLFy3jYWfb+WZhV/y2HvrAOidEU9B73TG9E5nXL8MctLiQxh5q+sJlDS6Xwoc27SRmd0EfB+IAU72I5CifeOfVUBFRMKUrwl0EOPpvg9cD9QBFcC1zrkv/IxJROTrJMZGfWU2kL31DSxdX8XCdVtZuG4bbwRKln//tAHcckr/EEfb9pxz04BpZnYZ8DPgqqZtzGwKMAUgLy+vxc9RVFpJZIQxJDv5CKMVEfGHbwl0kOPpPgUKnHO7zOy7wO+Ai/2KSUSkpaIjIxiVl8aovDSmjPfGVK/dXE1ibIcbH70eyG10Pyew7WCeAe5vbodz7kHgQYCCgoIWD/O4fnw+Jw3KIj5GX5KKSHjy85Lz/ePpnHO1eJ3tuY0bOOfedM7tCtz9AK/DFhEJWxERRr+sJLp3vPLSC4H+ZtbHzGKAS4CZjRuYWeNT7mcBq/wIJDkumtF5aX48tIhIq/Dz3/ugxtM1ch3wqo/xiIjIQTjn6szsZmA23rC7R51zxWb2C2CRc24mcLOZnQrsBbbRzPANEZHOICy+HzOzK4ACYMJB9h/ReDoRETk059wsYFaTbXc2Wr+1zYMSEQlDfg7hCGo8XeBsxk+Bc5xzNc09kHPuQedcgXOuIDMz05dgRURERESC4WcCHcx4ulHA3/CS500+xiIiIiIi0ip8S6Cdc3XAvvF0nwHP7RtPF6hgBfB7IBGYbmaLzWzmQR5ORERERCQs+DoGOojxdKf6+fwiIiIiIq3NzyEcIiIiIiIdjhJoEREREZEWUAItIiIiItICSqBFRERERFrAnHOhjqFFzKwC+CLUcTTSFdgc6iAaCbd4IPxiCrd4IPxiUjyHdrgx9XLOdZoJ7dVnByXcYlI8hxZuMYVbPBB+MbVqn93uEuhwY2aLnHMFoY5jn3CLB8IvpnCLB8IvJsVzaOEYkxxaOL5v4RaT4jm0cIsp3OKB8IuptePREA4RERERkRZQAi0iIiIi0gJKoI/cg6EOoIlwiwfCL6ZwiwfCLybFc2jhGJMcWji+b+EWk+I5tHCLKdzigfCLqVXj0RhoEREREZEW0BloEREREZEWUAIdBDPLNbM3zWyZmRWb2a3NtDnJzKrMbHFgudPnmNaZ2ZLAcy1qZr+Z2Z/NbLWZFZnZaJ/jGdjoZ19sZtvN7LYmbXx9jczsUTPbZGZLG21LN7O5ZrYqcJt2kGOvCrRZZWZX+RjP781seeA9ecHMUg9y7Ne+v60c011mtr7R+3LmQY6dbGYrAp+pH/sYz7ONYllnZosPcmyrv0YH+10P5edIWk59dlDxqM8OPqaQ9dvqs4OKKTT9tnNOyyEWoAcwOrCeBKwEBjdpcxLwShvGtA7o+jX7zwReBQwYC3zYhrFFAhvx5k5ss9cIGA+MBpY22vY74MeB9R8Dv23muHRgbeA2LbCe5lM8k4CowPpvm4snmPe3lWO6C/hhEO/pGiAfiAEKm/4OtFY8Tfb/AbizrV6jg/2uh/JzpKX13scmbdRnH3hu9dlfH1PI+m312UHFFJJ+W2egg+Cc2+Cc+ySwvgP4DOgZ2qgO6Vzgn87zAZBqZj3a6LlPAdY459q0eIJz7i1ga5PN5wL/CKz/AzivmUNPB+Y657Y657YBc4HJfsTjnJvjnKsL3P0AyDnS5znSmII0BljtnFvrnKsFnsF7bX2Lx8wM+Bbw9JE+TwviOdjvesg+R9Jy6rNbTH3218QUyn5bfXZQMYWk31YC3UJm1hsYBXzYzO7jzKzQzF41syE+h+KAOWb2sZlNaWZ/T6Ck0f1S2u4PyCUc/BeoLV8jgG7OuQ2B9Y1At2bahOq1uhbvjFNzDvX+trabA19PPnqQr7lC8RqdCJQ751YdZL+vr1GT3/Vw/hzJ11CfHRT12cELl35bfXYz2rLfVgLdAmaWCDwP3Oac295k9yd4X3+NAO4DXvQ5nBOcc6OBM4CbzGy8z88XFDOLAc4Bpjezu61fo69w3vc1YTHtjJn9FKgDnjxIk7Z8f+8H+gIjgQ14X8GFg0v5+jMZvr1GX/e7Hk6fI/l66rMPTX128MKo31af3Yy27reVQAfJzKLx3pgnnXP/arrfObfdOVcdWJ8FRJtZV7/icc6tD9xuAl7A+7qmsfVAbqP7OYFtfjsD+MQ5V950R1u/RgHl+74GDdxuaqZNm75WZnY1cDZweeCX+j8E8f62GudcuXOu3jnXADx0kOdq69coCrgAePZgbfx6jQ7yux52nyP5euqzg6Y+Owjh1G+rz272+du831YCHYTAuJ5HgM+cc/ccpE33QDvMbAzea7vFp3gSzCxp3zreBQ5LmzSbCVxpnrFAVaOvMvx00P9A2/I1amQmsO+q2quAl5ppMxuYZGZpga/CJgW2tTozmwzcDpzjnNt1kDbBvL+tGVPjcZbnH+S5FgL9zaxP4IzVJXivrV9OBZY750qb2+nXa/Q1v+th9TmSr6c+u0XUZx9CuPXb6rP/47FD02+7Vr4asiMuwAl4p/6LgMWB5UxgKjA10OZmoBjvStcPgHE+xpMfeJ7CwHP+NLC9cTwGTMO7CncJUNAGr1MCXuea0mhbm71GeH8ENgB78cYxXQdkAG8Aq4DXgfRA2wLg4UbHXgusDizX+BjParzxVvs+Rw8E2mYDs77u/fUxpscDn5EivA6nR9OYAvfPxLu6eU1rxdRcPIHtj+373DRq6/tr9DW/6yH7HGlp1fdRffZX41KfHVxMIeu3DxKP+uyvPk9I+m1VIhQRERERaQEN4RARERERaQEl0CIiIiIiLaAEWkRERESkBZRAi4iIiIi0gBJoEREREZEWUAIt0kJmdpKZvRLqOERE5NDUZ4sflECLiIiIiLSAEmjpsMzsCjP7yMwWm9nfzCzSzKrN7I9mVmxmb5hZZqDtSDP7wMyKzOyFQEUizKyfmb1uZoVm9omZ9Q08fKKZzTCz5Wb25L5qXSIicnjUZ0t7ogRaOiQzOwq4GDjeOTcSqAcux6u8tcg5NwRYAPw8cMg/gR8554bjVXjat/1JYJpzbgQwDq8CE8Ao4DZgMF6FpeN9/6FERDoo9dnS3kSFOgARn5wCHA0sDJxo6AJsAhqAZwNtngD+ZWYpQKpzbkFg+z+A6WaWBPR0zr0A4JzbAxB4vI+cc6WB+4uB3sA7/v9YIiIdkvpsaVeUQEtHZcA/nHM/+cpGszuatDvcWvY1jdbr0e+SiMiRUJ8t7YqGcEhH9QbwTTPLAjCzdDPrhfeZ/2agzWXAO865KmCbmZ0Y2P5tYIFzbgdQambnBR4j1szi2/SnEBHpHNRnS7ui/8CkQ3LOLTOznwFzzCwC2AvcBOwExgT2bcIbcwdwFfBAoLNdC1wT2P5t4G9m9ovAY1zUhj+GiEinoD5b2htz7nC/DRFpf8ys2jmXGOo4RETk0NRnS7jSEA4RERERkRbQGWgRERERkRbQGWgRERERkRZQAi0iIiIi0gJKoEVEREREWkAJtIiIiIhICyiBFhERERFpASXQIiIiIiIt8P8BT9a+59ArCdgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iXm4LSg4wp3Y"
      },
      "source": [
        "### Adam with higher order moment\n",
        "Adam with higher order moment is described below: \\\n",
        "$\\eta$: Step size \\\n",
        "$\\beta_1, \\beta_2 \\in [0, 1)$: Exponential decay rates for the moment estimates \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to parameters $\\phi$)\\\n",
        "$m_t \\gets \\frac{\\beta_1 m_{t−1} + (1 − \\beta_1) g_t}{1-\\beta_1^t}$ (first moment)\\\n",
        "$v_t \\gets \\frac{\\beta_2 v_{t−1} + (1 − \\beta_2) g_t^3}{1 - \\beta_2^k}$ (third moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt[k]{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hgx9O8wkwpSM"
      },
      "source": [
        "# Adam optimizer\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class Adam_HigherOrderMoment(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0, order=3):\n",
        "        defaults = dict(lr=lr, betas=betas, epsilon=epsilon,\n",
        "                weight_decay=weight_decay, order=order)\n",
        "        super(Adam_HigherOrderMoment, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of higher order gradient values\n",
        "                    state['exp_avg_hi'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_hi = state['exp_avg'], state['exp_avg_hi']\n",
        "                beta1, beta2 = group['betas']\n",
        "                order = group['order']\n",
        "                state['step'] += 1\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(beta1).add_(1 - beta1, grad)\n",
        "                \n",
        "                # take power of grad\n",
        "                grad_pow = grad\n",
        "                for _ in range(order - 1):\n",
        "                  grad_pow = grad_pow.mul(grad)\n",
        "                  \n",
        "\n",
        "                exp_avg_hi.mul_(beta2).add_(1 - beta2, grad_pow)\n",
        "\n",
        "                denom = exp_avg_hi.pow(1/order).add_(group['epsilon'])\n",
        "\n",
        "                bias_correction1 = 1 - beta1 ** state['step']\n",
        "                bias_correction2 = 1 - beta2 ** state['step']\n",
        "                step_size = group['lr'] * math.pow(bias_correction2, 1/order) / bias_correction1\n",
        "\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MT8YrCPMzlEN",
        "outputId": "101920a4-758b-458a-a789-31cfc407b431"
      },
      "source": [
        "# order 3\n",
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_HigherOrderMoment(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 30.60% || Test Accuracy 47.91% || Train Loss 1.89 || Test Loss 1.41\n",
            "Epoch 001/020, Train Accuracy 49.94% || Test Accuracy 59.56% || Train Loss 1.37 || Test Loss 1.12\n",
            "Epoch 002/020, Train Accuracy 60.61% || Test Accuracy 66.67% || Train Loss 1.10 || Test Loss 0.94\n",
            "Epoch 003/020, Train Accuracy 67.76% || Test Accuracy 73.22% || Train Loss 0.92 || Test Loss 0.79\n",
            "Epoch 004/020, Train Accuracy 72.37% || Test Accuracy 76.58% || Train Loss 0.79 || Test Loss 0.68\n",
            "Epoch 005/020, Train Accuracy 75.86% || Test Accuracy 78.56% || Train Loss 0.70 || Test Loss 0.62\n",
            "Epoch 006/020, Train Accuracy 78.14% || Test Accuracy 80.48% || Train Loss 0.63 || Test Loss 0.59\n",
            "Epoch 007/020, Train Accuracy 80.14% || Test Accuracy 81.27% || Train Loss 0.58 || Test Loss 0.57\n",
            "Epoch 008/020, Train Accuracy 81.53% || Test Accuracy 82.52% || Train Loss 0.54 || Test Loss 0.53\n",
            "Epoch 009/020, Train Accuracy 83.05% || Test Accuracy 81.83% || Train Loss 0.50 || Test Loss 0.54\n",
            "Epoch 010/020, Train Accuracy 83.75% || Test Accuracy 83.16% || Train Loss 0.47 || Test Loss 0.52\n",
            "Epoch 011/020, Train Accuracy 84.77% || Test Accuracy 83.59% || Train Loss 0.44 || Test Loss 0.49\n",
            "Epoch 012/020, Train Accuracy 85.92% || Test Accuracy 83.47% || Train Loss 0.41 || Test Loss 0.49\n",
            "Epoch 013/020, Train Accuracy 86.57% || Test Accuracy 84.37% || Train Loss 0.39 || Test Loss 0.48\n",
            "Epoch 014/020, Train Accuracy 87.35% || Test Accuracy 83.54% || Train Loss 0.37 || Test Loss 0.54\n",
            "Epoch 015/020, Train Accuracy 87.92% || Test Accuracy 84.80% || Train Loss 0.35 || Test Loss 0.49\n",
            "Epoch 016/020, Train Accuracy 88.82% || Test Accuracy 84.79% || Train Loss 0.33 || Test Loss 0.48\n",
            "Epoch 017/020, Train Accuracy 89.16% || Test Accuracy 84.89% || Train Loss 0.32 || Test Loss 0.48\n",
            "Epoch 018/020, Train Accuracy 89.69% || Test Accuracy 85.24% || Train Loss 0.30 || Test Loss 0.47\n",
            "Epoch 019/020, Train Accuracy 90.28% || Test Accuracy 85.42% || Train Loss 0.28 || Test Loss 0.49\n",
            "time taken:  1171.1034009456635\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "G0P2enwR1pzB",
        "outputId": "243c173c-2324-466a-870b-dd58eeff9efd"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DMPafJpQ7mtG",
        "outputId": "08af1e4e-0d0b-4e4e-f715-8a05489b934f"
      },
      "source": [
        "# order 4\n",
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_HigherOrderMoment(model.parameters(), lr=lr, order=4)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 38.47% || Test Accuracy 56.14% || Train Loss 1.65 || Test Loss 1.20\n",
            "Epoch 001/020, Train Accuracy 58.08% || Test Accuracy 67.10% || Train Loss 1.16 || Test Loss 0.93\n",
            "Epoch 002/020, Train Accuracy 67.25% || Test Accuracy 73.35% || Train Loss 0.92 || Test Loss 0.76\n",
            "Epoch 003/020, Train Accuracy 73.05% || Test Accuracy 76.98% || Train Loss 0.78 || Test Loss 0.67\n",
            "Epoch 004/020, Train Accuracy 77.12% || Test Accuracy 80.63% || Train Loss 0.66 || Test Loss 0.57\n",
            "Epoch 005/020, Train Accuracy 79.94% || Test Accuracy 81.33% || Train Loss 0.58 || Test Loss 0.55\n",
            "Epoch 006/020, Train Accuracy 82.34% || Test Accuracy 82.38% || Train Loss 0.51 || Test Loss 0.52\n",
            "Epoch 007/020, Train Accuracy 84.26% || Test Accuracy 84.06% || Train Loss 0.46 || Test Loss 0.49\n",
            "Epoch 008/020, Train Accuracy 85.69% || Test Accuracy 84.63% || Train Loss 0.41 || Test Loss 0.47\n",
            "Epoch 009/020, Train Accuracy 87.18% || Test Accuracy 84.23% || Train Loss 0.37 || Test Loss 0.48\n",
            "Epoch 010/020, Train Accuracy 88.62% || Test Accuracy 85.04% || Train Loss 0.33 || Test Loss 0.47\n",
            "Epoch 011/020, Train Accuracy 89.67% || Test Accuracy 85.41% || Train Loss 0.30 || Test Loss 0.46\n",
            "Epoch 012/020, Train Accuracy 90.55% || Test Accuracy 85.72% || Train Loss 0.27 || Test Loss 0.47\n",
            "Epoch 013/020, Train Accuracy 91.39% || Test Accuracy 85.12% || Train Loss 0.25 || Test Loss 0.50\n",
            "Epoch 014/020, Train Accuracy 92.28% || Test Accuracy 85.71% || Train Loss 0.22 || Test Loss 0.51\n",
            "Epoch 015/020, Train Accuracy 92.82% || Test Accuracy 85.51% || Train Loss 0.21 || Test Loss 0.49\n",
            "Epoch 016/020, Train Accuracy 93.43% || Test Accuracy 84.76% || Train Loss 0.19 || Test Loss 0.58\n",
            "Epoch 017/020, Train Accuracy 93.97% || Test Accuracy 86.54% || Train Loss 0.18 || Test Loss 0.49\n",
            "Epoch 018/020, Train Accuracy 94.51% || Test Accuracy 86.33% || Train Loss 0.16 || Test Loss 0.49\n",
            "Epoch 019/020, Train Accuracy 94.84% || Test Accuracy 86.14% || Train Loss 0.15 || Test Loss 0.52\n",
            "time taken:  1187.406508922577\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "AzM8LW_68J49",
        "outputId": "ddb0b65b-0e5f-4875-b4d7-d6a06bedae8d"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UE8_Obe6LBOV",
        "outputId": "9b86959b-2db9-43d4-d55b-819e9b56a63c"
      },
      "source": [
        "# order 5\n",
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_HigherOrderMoment(model.parameters(), lr=lr, order=5)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 001/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 002/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 003/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 004/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 005/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 006/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 007/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 008/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 009/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 010/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 011/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 012/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 013/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 014/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 015/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 016/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 017/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 018/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "Epoch 019/020, Train Accuracy 10.00% || Test Accuracy 10.00% || Train Loss nan || Test Loss nan\n",
            "time taken:  1199.6783862113953\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "2HAOUNEfLELu",
        "outputId": "b0d877c5-935b-4446-b761-856ae60edf68"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ILT2p_rIWqx"
      },
      "source": [
        "### Adam without first moment correction\n",
        "A modified Adam algorithm without first moment correction is described below: \\\n",
        "$\\eta$: Step size \\\n",
        "$\\beta_1, \\beta_2 \\in [0, 1)$: Exponential decay rates for the moment estimates \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to parameters $\\phi$)\\\n",
        "$m_t \\gets \\beta_1 m_{t−1} + (1 − \\beta_1) g_t$ (first moment)\\\n",
        "$v_t \\gets \\frac{\\beta_2 v_{t−1} + (1 − \\beta_2) g_t^2}{1 - \\beta_2^t}$ (second moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5ZZ2I0nfIepu"
      },
      "source": [
        "# Adam optimizer without first moment correction\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class Adam_WithoutFirstCorrection(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0):\n",
        "        defaults = dict(lr=lr, betas=betas, epsilon=epsilon,\n",
        "                weight_decay=weight_decay)\n",
        "        super(Adam_WithoutFirstCorrection, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of squared gradient values\n",
        "                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']\n",
        "                beta1, beta2 = group['betas']\n",
        "\n",
        "                state['step'] += 1\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(beta1).add_(1 - beta1, grad)\n",
        "                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)\n",
        "\n",
        "                denom = exp_avg_sq.sqrt().add_(group['epsilon'])\n",
        "\n",
        "                # bias_correction1 = 1 - beta1 ** state['step']\n",
        "                bias_correction2 = 1 - beta2 ** state['step']\n",
        "                step_size = group['lr'] * math.sqrt(bias_correction2)\n",
        "\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Au38VwOBI1VO",
        "outputId": "17a3e259-d7ef-40f1-e93c-50c0c330de68"
      },
      "source": [
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_WithoutFirstCorrection(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 42.80% || Test Accuracy 57.13% || Train Loss 1.53 || Test Loss 1.20\n",
            "Epoch 001/020, Train Accuracy 57.47% || Test Accuracy 66.53% || Train Loss 1.18 || Test Loss 0.94\n",
            "Epoch 002/020, Train Accuracy 67.31% || Test Accuracy 72.97% || Train Loss 0.92 || Test Loss 0.77\n",
            "Epoch 003/020, Train Accuracy 73.13% || Test Accuracy 76.72% || Train Loss 0.77 || Test Loss 0.68\n",
            "Epoch 004/020, Train Accuracy 77.25% || Test Accuracy 79.18% || Train Loss 0.66 || Test Loss 0.60\n",
            "Epoch 005/020, Train Accuracy 79.80% || Test Accuracy 81.06% || Train Loss 0.58 || Test Loss 0.56\n",
            "Epoch 006/020, Train Accuracy 82.22% || Test Accuracy 82.46% || Train Loss 0.51 || Test Loss 0.53\n",
            "Epoch 007/020, Train Accuracy 84.28% || Test Accuracy 83.20% || Train Loss 0.46 || Test Loss 0.50\n",
            "Epoch 008/020, Train Accuracy 85.85% || Test Accuracy 83.11% || Train Loss 0.41 || Test Loss 0.52\n",
            "Epoch 009/020, Train Accuracy 87.13% || Test Accuracy 83.31% || Train Loss 0.38 || Test Loss 0.50\n",
            "Epoch 010/020, Train Accuracy 88.12% || Test Accuracy 84.80% || Train Loss 0.34 || Test Loss 0.48\n",
            "Epoch 011/020, Train Accuracy 89.13% || Test Accuracy 84.32% || Train Loss 0.32 || Test Loss 0.51\n",
            "Epoch 012/020, Train Accuracy 89.92% || Test Accuracy 85.77% || Train Loss 0.29 || Test Loss 0.46\n",
            "Epoch 013/020, Train Accuracy 90.66% || Test Accuracy 84.59% || Train Loss 0.27 || Test Loss 0.52\n",
            "Epoch 014/020, Train Accuracy 91.44% || Test Accuracy 85.29% || Train Loss 0.25 || Test Loss 0.49\n",
            "Epoch 015/020, Train Accuracy 91.86% || Test Accuracy 86.04% || Train Loss 0.23 || Test Loss 0.48\n",
            "Epoch 016/020, Train Accuracy 92.59% || Test Accuracy 84.46% || Train Loss 0.22 || Test Loss 0.50\n",
            "Epoch 017/020, Train Accuracy 93.11% || Test Accuracy 85.56% || Train Loss 0.20 || Test Loss 0.51\n",
            "Epoch 018/020, Train Accuracy 93.59% || Test Accuracy 84.81% || Train Loss 0.19 || Test Loss 0.56\n",
            "Epoch 019/020, Train Accuracy 93.78% || Test Accuracy 86.07% || Train Loss 0.18 || Test Loss 0.49\n",
            "time taken:  1147.1447339057922\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "yfD9tJCgJ1D3",
        "outputId": "2cec4df6-bf8f-49c4-ee68-6ca16582fb70"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wCcS3N0yHajB"
      },
      "source": [
        "### Adam without second moment correction\n",
        "$\\eta$: Step size \\\n",
        "$\\beta_1, \\beta_2 \\in [0, 1)$: Exponential decay rates for the moment estimates \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to paramters $\\phi$)\\\n",
        "$m_t \\gets \\frac{\\beta_1 m_{t−1} + (1 − \\beta_1) g_t}{1-\\beta_1^t}$ (first moment)\\\n",
        "$v_t \\gets \\beta_2 v_{t−1} + (1 − \\beta_2) g_t^2$ (second moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V7jKNvdkBi4a"
      },
      "source": [
        "# Adam optimizer without second moment correction\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class Adam_WithoutSecondCorrection(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0):\n",
        "        defaults = dict(lr=lr, betas=betas, epsilon=epsilon,\n",
        "                weight_decay=weight_decay)\n",
        "        super(Adam_WithoutSecondCorrection, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of squared gradient values\n",
        "                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']\n",
        "                beta1, beta2 = group['betas']\n",
        "\n",
        "                state['step'] += 1\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(beta1).add_(1 - beta1, grad)\n",
        "                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)\n",
        "\n",
        "                denom = exp_avg_sq.sqrt().add_(group['epsilon'])\n",
        "\n",
        "                bias_correction1 = 1 - beta1 ** state['step']\n",
        "                # bias_correction2 = 1 - beta2 ** state['step']\n",
        "                step_size = group['lr'] / bias_correction1 # second correction does not change value by much\n",
        "\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AI74zQ3yDk1o",
        "outputId": "a2b0b840-f67b-45eb-dcac-5802304402bc"
      },
      "source": [
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_WithoutSecondCorrection(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 11.62% || Test Accuracy 17.46% || Train Loss 2.66 || Test Loss 2.13\n",
            "Epoch 001/020, Train Accuracy 21.17% || Test Accuracy 24.15% || Train Loss 2.01 || Test Loss 1.92\n",
            "Epoch 002/020, Train Accuracy 25.88% || Test Accuracy 27.44% || Train Loss 1.87 || Test Loss 1.81\n",
            "Epoch 003/020, Train Accuracy 31.35% || Test Accuracy 33.95% || Train Loss 1.78 || Test Loss 1.71\n",
            "Epoch 004/020, Train Accuracy 37.22% || Test Accuracy 41.79% || Train Loss 1.65 || Test Loss 1.52\n",
            "Epoch 005/020, Train Accuracy 42.94% || Test Accuracy 46.42% || Train Loss 1.51 || Test Loss 1.42\n",
            "Epoch 006/020, Train Accuracy 47.83% || Test Accuracy 51.85% || Train Loss 1.40 || Test Loss 1.29\n",
            "Epoch 007/020, Train Accuracy 52.46% || Test Accuracy 56.95% || Train Loss 1.29 || Test Loss 1.17\n",
            "Epoch 008/020, Train Accuracy 56.82% || Test Accuracy 60.66% || Train Loss 1.18 || Test Loss 1.09\n",
            "Epoch 009/020, Train Accuracy 60.57% || Test Accuracy 63.63% || Train Loss 1.10 || Test Loss 1.02\n",
            "Epoch 010/020, Train Accuracy 63.39% || Test Accuracy 65.88% || Train Loss 1.02 || Test Loss 0.96\n",
            "Epoch 011/020, Train Accuracy 65.79% || Test Accuracy 67.80% || Train Loss 0.96 || Test Loss 0.91\n",
            "Epoch 012/020, Train Accuracy 68.04% || Test Accuracy 69.65% || Train Loss 0.90 || Test Loss 0.86\n",
            "Epoch 013/020, Train Accuracy 69.80% || Test Accuracy 71.09% || Train Loss 0.85 || Test Loss 0.82\n",
            "Epoch 014/020, Train Accuracy 71.81% || Test Accuracy 71.96% || Train Loss 0.80 || Test Loss 0.80\n",
            "Epoch 015/020, Train Accuracy 73.62% || Test Accuracy 72.57% || Train Loss 0.76 || Test Loss 0.77\n",
            "Epoch 016/020, Train Accuracy 75.10% || Test Accuracy 74.24% || Train Loss 0.71 || Test Loss 0.74\n",
            "Epoch 017/020, Train Accuracy 76.60% || Test Accuracy 75.47% || Train Loss 0.67 || Test Loss 0.71\n",
            "Epoch 018/020, Train Accuracy 77.88% || Test Accuracy 75.88% || Train Loss 0.63 || Test Loss 0.70\n",
            "Epoch 019/020, Train Accuracy 79.26% || Test Accuracy 77.08% || Train Loss 0.60 || Test Loss 0.69\n",
            "time taken:  1148.8427574634552\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "vlhBR-91D26H",
        "outputId": "361f29f4-b5d2-474b-ab0d-fbf0aa416d45"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gUW0Y-i_JN6k"
      },
      "source": [
        "### Adam without correction\n",
        "$\\eta$: Step size \\\n",
        "$\\beta_1, \\beta_2 \\in [0, 1)$: Exponential decay rates for the moment estimates \\\n",
        "$L(\\phi)$: Loss function with parameters $\\phi$ \\\n",
        "$t$: Current step \\\n",
        "$g_t \\gets \\nabla_{\\phi}f_t(\\phi_{t-1})$  (gradients with respect to parameters $\\phi$)\\\n",
        "$m_t \\gets \\beta_1 m_{t−1} + (1 − \\beta_1) g_t$ (first moment)\\\n",
        "$v_t \\gets \\beta_2 v_{t−1} + (1 − \\beta_2) g_t^2$ (second moment) \\\n",
        "\n",
        "$\\phi_{t+1} \\gets \\phi_t - \\frac{\\eta m_t}{\\sqrt{v_t} + ϵ} $ \\\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O1Emp_WDJcvP"
      },
      "source": [
        "# Adam optimizer without correction\n",
        "import math\n",
        "from torch.optim import Optimizer\n",
        "\n",
        "class Adam_WithoutCorrection(Optimizer):\n",
        "\n",
        "    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), epsilon=1e-8,\n",
        "            weight_decay=0):\n",
        "        defaults = dict(lr=lr, betas=betas, epsilon=epsilon,\n",
        "                weight_decay=weight_decay)\n",
        "        super(Adam_WithoutCorrection, self).__init__(params, defaults)\n",
        "\n",
        "    def step(self, forward_closure=None):\n",
        "        loss = None\n",
        "        if forward_closure is not None:\n",
        "            loss = self._forward_backward(forward_closure)\n",
        "\n",
        "        for group in self.param_groups:\n",
        "            for p in group['params']:\n",
        "                grad = p.grad\n",
        "                state = self.state[id(p)]\n",
        "\n",
        "                # State initialization\n",
        "                if len(state) == 0:\n",
        "                    state['step'] = 0\n",
        "                    # Exponential moving average of gradient values\n",
        "                    state['exp_avg'] = grad.new().resize_as_(grad).zero_()\n",
        "                    # Exponential moving average of squared gradient values\n",
        "                    state['exp_avg_sq'] = grad.new().resize_as_(grad).zero_()\n",
        "\n",
        "                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']\n",
        "                beta1, beta2 = group['betas']\n",
        "\n",
        "                state['step'] += 1\n",
        "\n",
        "                if group['weight_decay'] != 0:\n",
        "                    grad = grad.add(group['weight_decay'], p.data)\n",
        "\n",
        "                # Decay the first and second moment running average coefficient\n",
        "                exp_avg.mul_(beta1).add_(1 - beta1, grad)\n",
        "                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)\n",
        "\n",
        "                denom = exp_avg_sq.sqrt().add_(group['epsilon'])\n",
        "\n",
        "                # bias_correction1 = 1 - beta1 ** state['step']\n",
        "                # bias_correction2 = 1 - beta2 ** state['step']\n",
        "                step_size = group['lr']\n",
        "\n",
        "                p.data.addcdiv_(-step_size, exp_avg, denom)\n",
        "\n",
        "        return loss\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3G04eRggJnWa",
        "outputId": "6678bbdb-1531-4beb-c354-0029e0b69037"
      },
      "source": [
        "import time\n",
        "\n",
        "EPOCHS = 20\n",
        "start = time.time()\n",
        "criterion = torch.nn.CrossEntropyLoss()\n",
        "model = ResNet().cuda()\n",
        "lr = 1e-3\n",
        "optimizer = Adam_WithoutCorrection(model.parameters(), lr=lr)\n",
        "train_epoch_loss, test_epoch_loss, train_epoch_acc, test_epoch_acc = train(EPOCHS, model, criterion, optimizer, train_loader, test_loader)\n",
        "print('time taken: ',time.time() - start)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 000/020, Train Accuracy 15.25% || Test Accuracy 20.29% || Train Loss 2.18 || Test Loss 1.97\n",
            "Epoch 001/020, Train Accuracy 19.96% || Test Accuracy 20.84% || Train Loss 1.95 || Test Loss 1.89\n",
            "Epoch 002/020, Train Accuracy 20.82% || Test Accuracy 22.17% || Train Loss 1.89 || Test Loss 1.86\n",
            "Epoch 003/020, Train Accuracy 21.85% || Test Accuracy 22.40% || Train Loss 1.86 || Test Loss 1.83\n",
            "Epoch 004/020, Train Accuracy 22.63% || Test Accuracy 23.30% || Train Loss 1.83 || Test Loss 1.79\n",
            "Epoch 005/020, Train Accuracy 24.16% || Test Accuracy 25.07% || Train Loss 1.80 || Test Loss 1.77\n",
            "Epoch 006/020, Train Accuracy 26.03% || Test Accuracy 27.18% || Train Loss 1.78 || Test Loss 1.74\n",
            "Epoch 007/020, Train Accuracy 28.30% || Test Accuracy 29.86% || Train Loss 1.74 || Test Loss 1.71\n",
            "Epoch 008/020, Train Accuracy 30.11% || Test Accuracy 31.15% || Train Loss 1.72 || Test Loss 1.69\n",
            "Epoch 009/020, Train Accuracy 32.38% || Test Accuracy 31.11% || Train Loss 1.69 || Test Loss 1.72\n",
            "Epoch 010/020, Train Accuracy 39.89% || Test Accuracy 48.90% || Train Loss 1.55 || Test Loss 1.33\n",
            "Epoch 011/020, Train Accuracy 52.81% || Test Accuracy 57.69% || Train Loss 1.29 || Test Loss 1.17\n",
            "Epoch 012/020, Train Accuracy 58.91% || Test Accuracy 62.02% || Train Loss 1.16 || Test Loss 1.10\n",
            "Epoch 013/020, Train Accuracy 63.06% || Test Accuracy 66.09% || Train Loss 1.06 || Test Loss 1.02\n",
            "Epoch 014/020, Train Accuracy 66.00% || Test Accuracy 67.60% || Train Loss 0.99 || Test Loss 0.96\n",
            "Epoch 015/020, Train Accuracy 68.24% || Test Accuracy 68.82% || Train Loss 0.93 || Test Loss 0.96\n",
            "Epoch 016/020, Train Accuracy 69.93% || Test Accuracy 70.29% || Train Loss 0.88 || Test Loss 0.92\n",
            "Epoch 017/020, Train Accuracy 72.10% || Test Accuracy 70.85% || Train Loss 0.83 || Test Loss 0.90\n",
            "Epoch 018/020, Train Accuracy 73.65% || Test Accuracy 74.15% || Train Loss 0.79 || Test Loss 0.85\n",
            "Epoch 019/020, Train Accuracy 74.94% || Test Accuracy 75.23% || Train Loss 0.76 || Test Loss 0.83\n",
            "time taken:  1144.8133356571198\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "wI1Knp--OQDE",
        "outputId": "2c1546cd-df9b-46ce-e987-ef34053f79b1"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12,5))\n",
        "\n",
        "epochs = range(1, EPOCHS + 1)\n",
        "ax1.plot(epochs, train_epoch_loss)\n",
        "ax1.plot(epochs, test_epoch_loss)\n",
        "ax2.plot(epochs, train_epoch_acc)\n",
        "ax2.plot(epochs, test_epoch_acc)\n",
        "ax1.set_title('model loss')\n",
        "ax2.set_title('model accuracy')\n",
        "ax1.set_ylabel('loss')\n",
        "ax1.set_xlabel('epoch')\n",
        "ax2.set_ylabel('accuracy')\n",
        "ax2.set_xlabel('epoch')\n",
        "ax1.legend(['train', 'test'], loc=\"upper right\")\n",
        "ax2.legend(['train', 'test'], loc=\"upper right\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}