{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "825c742f-0ae7-4e3f-99b7-e8420c9c5152",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "fb702cab-f44c-4821-8dbf-9d9c24e01df5",
          "isComponent": false,
          "name": "",
          "parents": []
        },
        "tags": []
      },
      "source": [
        "# MNIST Image Generation with VAE (Variational AutoEncoder)\n",
        "\n",
        "Adapted from: https://github.com/Atcold/pytorch-Deep-Learning/blob/master/11-VAE.ipynb"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8889f014-a2b2-4aac-ac93-ba019a58e02b",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "de9083c7-d0c6-40ff-9359-e65cb47f0abc",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": [
        "## Cell color\n",
        "- Red: Related to model definition and training\n",
        "- Skyblue: Related to visualization"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "dc111be4-7758-4bd7-a3ca-81665e18615d",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "28c1ae75-be87-4fdb-a424-ef1b6e70cdf5",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": [
        "### Required Python Packages\n",
        "- `torch`\n",
        "- `torchvision`\n",
        "- `matplotlib`\n",
        "\n",
        "Run the following cell to install the packages."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "37d085b7-4640-49e5-8c96-290c23631e84",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "a9224a40-e3ac-4804-8e91-6527c0c23206",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "outputs": [],
      "source": [
        "#\n",
        "# Required Packages\n",
        "#   Run this cell to install required packages.\n",
        "#\n",
        "%pip install \"matplotlib>=2.0\" \"torch>=1.9\" \"torchvision>=0.10\""
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0fc9bc91-150f-4753-a15e-9178fe1fea54",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "341de75f-bacb-4af8-9269-f974f4547ca8",
          "isComponent": true,
          "name": "Import packages",
          "parents": []
        },
        "tags": []
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "from torch.utils.data import DataLoader\n",
        "from torchvision import datasets, transforms"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "798532a2-3909-41ec-a2ff-f1ccc070870c",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "f0e2a43a-d5bd-4f6c-bb5b-8bfa3fae2dd9",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Load the Dataset (MNIST)"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9de0ed7d-df92-4ed5-9edc-1cb789eec6d5",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "c1c9d3af-d77f-40cd-b145-3976174d3032",
          "isComponent": true,
          "name": "Load MNIST dataset",
          "parents": [
            {
              "id": "341de75f-bacb-4af8-9269-f974f4547ca8",
              "name": "Import packages"
            }
          ]
        },
        "tags": []
      },
      "outputs": [],
      "source": [
        "# Define data loading step\n",
        "kwargs = {\"num_workers\": 4, \"pin_memory\": True}\n",
        "train_loader = DataLoader(\n",
        "    datasets.MNIST(\"mnist\", train=True, download=True, transform=transforms.ToTensor()),\n",
        "    batch_size=batch_size,\n",
        "    shuffle=True,\n",
        "    **kwargs,\n",
        ")\n",
        "test_loader = DataLoader(\n",
        "    datasets.MNIST(\"mnist\", train=False, transform=transforms.ToTensor()),\n",
        "    batch_size=batch_size,\n",
        "    shuffle=True,\n",
        "    **kwargs,\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f0fdb60f-e4c3-4446-a472-b95d4d11bf9b",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#00E3FF",
          "id": "ee9b8b42-0765-4acc-af7e-fccc4a70491f",
          "isComponent": true,
          "name": "Show some images",
          "parents": [
            {
              "id": "c1c9d3af-d77f-40cd-b145-3976174d3032",
              "name": "Load MNIST dataset"
            }
          ]
        },
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 1152x432 with 10 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# show some images\n",
        "plt.figure(figsize=(16, 6))\n",
        "for i in range(10):\n",
        "    plt.subplot(2, 5, i + 1)\n",
        "    image, _ = train_loader.dataset.__getitem__(i)\n",
        "    plt.imshow(image.squeeze().numpy())\n",
        "    plt.axis(\"off\");"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f62a44cf-6cbe-41c9-8d0e-e4ed17c91a7f",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "a298fe26-4ff8-4c03-89c6-a1351a6253d2",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Vanilla VAE"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "abe73dae-f8a5-4d36-9fbc-c6cb5e51295e",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#FF004F",
          "id": "e9f3371a-e347-4564-80c1-f4e1a17da0d3",
          "isComponent": true,
          "name": "Define VAE",
          "parents": [
            {
              "id": "c1c9d3af-d77f-40cd-b145-3976174d3032",
              "name": "Load MNIST dataset"
            }
          ]
        },
        "tags": []
      },
      "outputs": [],
      "source": [
        "# Defining the model\n",
        "\n",
        "d = 20\n",
        "\n",
        "\n",
        "class VAE(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "\n",
        "        self.encoder = nn.Sequential(nn.Linear(784, d**2), nn.ReLU(), nn.Linear(d**2, d * 2))\n",
        "\n",
        "        self.decoder = nn.Sequential(\n",
        "            nn.Linear(d, d**2),\n",
        "            nn.ReLU(),\n",
        "            nn.Linear(d**2, 784),\n",
        "            nn.Sigmoid(),\n",
        "        )\n",
        "\n",
        "    def reparameterise(self, mu, logvar):\n",
        "        if self.training:\n",
        "            std = logvar.mul(0.5).exp_()\n",
        "            eps = std.new_empty(std.size()).normal_().detach()\n",
        "            return eps.mul_(std).add_(mu)\n",
        "        else:\n",
        "            return mu\n",
        "\n",
        "    def forward(self, x):\n",
        "        mu_logvar = self.encoder(x.view(-1, 784)).view(-1, 2, d)\n",
        "        mu = mu_logvar[:, 0, :]\n",
        "        logvar = mu_logvar[:, 1, :]\n",
        "        z = self.reparameterise(mu, logvar)\n",
        "        return self.decoder(z), mu, logvar"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c0cfdabf-bd6d-4332-94d7-83fe12695584",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "67675843-5e88-41dd-b3e4-0fd8a69f0abb",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Define loss function"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e2ba2545-1905-40be-bc8d-18ef0ca782e6",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#FF004F",
          "id": "e93082b9-135f-4c0c-9ddf-a8b788599667",
          "isComponent": true,
          "name": "Define loss function",
          "parents": [
            {
              "id": "e9f3371a-e347-4564-80c1-f4e1a17da0d3",
              "name": "Define VAE"
            }
          ]
        },
        "tags": []
      },
      "outputs": [],
      "source": [
        "# Reconstruction + β * KL divergence losses summed over all elements and batch\n",
        "\n",
        "\n",
        "def loss_function(x_hat, x, mu, logvar, beta=1):\n",
        "    BCE = nn.functional.binary_cross_entropy(x_hat, x.view(-1, 784), reduction=\"sum\")\n",
        "    KLD = 0.5 * torch.sum(logvar.exp() - logvar - 1 + mu.pow(2))\n",
        "\n",
        "    return BCE + beta * KLD"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "07b2c753-d3ce-4f09-adcd-257c5a515c0b",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "3810673c-b19b-4c9c-a3b5-3462a02080a7",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Visualization function"]
    },
    {
      "cell_type": "markdown",
      "id": "85c5dbbb-532a-47f0-846d-7b7aef911881",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "a2e18508-101e-4f6c-927b-a1175e5b0244",
          "isComponent": false,
          "name": "",
          "parents": []
        },
        "tags": []
      },
      "source": ["### Training process"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "81c54f25-8b86-4aeb-9d9b-0982452bdd7b",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#00E3FF",
          "id": "64bafb82-5b64-4894-a09d-9a4e35202f04",
          "isComponent": true,
          "name": "Define image display function",
          "parents": [
            {
              "id": "341de75f-bacb-4af8-9269-f974f4547ca8",
              "name": "Import packages"
            }
          ]
        },
        "tags": []
      },
      "outputs": [],
      "source": [
        "def display_images(in_, out, n=1, label=None, count=False):\n",
        "    for N in range(n):\n",
        "        if in_ is not None:\n",
        "            in_pic = in_.data.cpu().view(-1, 28, 28)\n",
        "            plt.figure(figsize=(9, 2))\n",
        "            plt.suptitle(label + \" – real test data / reconstructions\", color=\"b\", fontsize=16)\n",
        "            for i in range(4):\n",
        "                plt.subplot(1, 4, i + 1)\n",
        "                plt.imshow(in_pic[i + 4 * N])\n",
        "                plt.axis(\"off\")\n",
        "        out_pic = out.data.cpu().view(-1, 28, 28)\n",
        "        plt.figure(figsize=(9, 3))\n",
        "        for i in range(4):\n",
        "            plt.subplot(1, 4, i + 1)\n",
        "            plt.imshow(out_pic[i + 4 * N])\n",
        "            plt.axis(\"off\")\n",
        "            if count:\n",
        "                plt.title(str(4 * N + i), color=\"w\")\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3b1bc35f-3ea6-43a3-a0ec-5247ed17afce",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#FF004F",
          "id": "73fb295b-17e9-4ca6-a42f-02720231688c",
          "isComponent": true,
          "name": "Train VAE",
          "parents": [
            {
              "id": "e93082b9-135f-4c0c-9ddf-a8b788599667",
              "name": "Define loss function"
            },
            {
              "id": "64bafb82-5b64-4894-a09d-9a4e35202f04",
              "name": "Define image display function"
            }
          ]
        },
        "tags": []
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": ["====> Test set loss: 543.7519\n"]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 1 Average loss: 190.0560\n",
            "====> Test set loss: 137.4955\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 2 Average loss: 133.8396\n",
            "====> Test set loss: 116.5032\n"
          ]
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAACJCAYAAABTsyC5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAbhUlEQVR4nO3deZgU1bnH8e87w4AssgdFUSEoanDBKLgliDvihkaNa9yu+xq3+ERjMGrQuCeK+xUXvBK9Eb0GESWiKCKg4MomsimgLCIgMDIz5/5RNTP9Fj093TA90+jv8zzzTL9dp+qcqq7uPn3OqVMWQkBERER+2ooaugAiIiLS8FQhEBEREVUIRERERBUCERERQRUCERERQRUCERERQRWCvDHjDDNCDX/LGrhsg834cj3X3cOMh82YasYqM+aaMcSMLnVdzvpmxmgzRteSprMZA8z4eR7LcbkZx27gNgabMXs91usR71/bDck/w/YfMuO1fGy7UOX7mG5I/vHn0YAGKJYUIFUI8u94YO/E30ENWqINcyLQHfg7cBhwLfBLYKIZWzVkwepJZ+DPkL8KAXA5bFiFYAP0INq/Ov/yMsOAI4Fhdb3tAteDPB3TOsh/b+DRei2NFKxGDV2An4DJIfB5QxeiDt0WAotSnzDjHWAWcA5wQ74LEH+xlITAD/nOS+rUXkBH4MVcVjKjSQiU5qdIhcWMYsBCoKw+8guBcfWRj2wc1ELQwFK6FnqbMcyMlWYsMeN+M5om0nY040kzFptRasZHZpyaZptdzHjKjIVxui/MuDdNut3MGBM3/c8w4/zaypusDMTPzQEWAVvmtvfZMWO2GU+bcZYZU4EfgMPjZbua8ZIZ35qx2ox3zPh1Yv2eZjxvxpdxmmlm/DV5fLMoRx/gjTh8LaULqE9KmnPM+NCMNfHr9FiyqdaMy8yYEpflWzMmmnFM5b4C2wCnpGx/cC3lOtCMD+I8Z5pxXg3pbozTfReX7T9m7JWy/Azg8TickZJ/53j5xWa8a8ZSM5aZMc4seh2y1B+YGELN3VVx03YwYyczXjVjJfDPeFkzM24zY5YZP8T/rzPzn2Nm/MyMQWbMi8//efH7oUlKmr7xvqyOj8cwM7ZPbGe0GW+bcVB83FaZ8YkZ/RPpupnxghnfxK/BXDOeM6NRFsc0mHGLGdeaMYvo3N7Zqj8XOqc7PonnGpnxBzM+i/NfZMYIM3bIMv8Bie3Vy7FBCo5elPwrTnPyV4RAReK5p4k++AYBvYh+aTcHzgAwoznwJtAG+CMwDzgVeMqMZiHwcJyuCzAeWEXUTDgD2Ao4JJFfS+AZ4B7gL8CZwANmTAuh6ksvK2bsCHQApuSyXo72J2r6vBH4Bphtxi+BMcAkotaJVcD5wOtm7BMC78frbg1MBgYDK4i6PG4gavY/MYcyfABcBNwPXApMiJ//DMCMW4EribpTriaqIN0M7BSXp9yMU4A7iY75GKApsAvVzbnHAMOBD6Hqg3qdSlil+NgPBybG+9IkXq8FUJ5IviVwN/Al0bl1KvCWGXuEwEfAv+PyXk/U1VX5xb0g/t+ZqHl5NtFnx5HAy2b0C4FXaipjiqOBp7JIB1ErwmPAbUBF/B56FfgFcBPwMVGLw5+Ijt2VAGa0AcbGz90MfER0bh4NNAZKzegb7+t/gN8SHau/AG+b0SMEvkopR1fgXmAgsDjO53kzdkhp+XsZWAZcEKfZEuhH9IOrtmMK0Xv8C+Aq4HtgPrBrlscJ4FmiytY9wOvAJkBvotaYbPKvUs/HRgpNCEF/efiDcAaEUMPfy2nSPZhY/zoI5RC6xfHFcbo+iXSvQ/gGQnEcPwlhJYQtMpRtcLyt/VOeawJhMYSHc9zPRhDejMvQJk/HcjaEVRA2Tzw/CsIUCI1TniuOnxtWw7YsLvOpECogtEtZNhrC6FrK0ic+dgclnu8cv143JJ7fN07fP47vg/BBFvv7dJbHZkj8ujVPeW4rCD9AmJ1hveL4OEyDcG+a83HbWvItitcfCeHFLMq5Q7zd7rWkGxCnuyzx/Gnx873TvE9+gNAhjv8Svw67ZchjIoQZEBqlPNcFwloIdyXOh7UQtkt5rkO8/T/Gcfu4XEdlyK/GYxo/Px9C0xrW6Zzu+KTEB8TpLt2A/Ac01LHRX2H9qZaWf8cAPRN/l6dJ989E/CxRLbpXHPcGvgphnVHwTwM/I/rlBFFLwMshML+Wcq0KKS0BIeqjnUH0azoX9wH7AKeGwLeZEppFrSVp/oqzyGdcCCxM2VZTYD/gOeJfkPGvSCP6ldQ7JW3LuKl5JlAKrCX6pWrAdrntbo0OJnq9hqTuG/AesDylPBOAHmb8I25ubbaB+e4NDA+B7yufCIF5wDvJhHF+b5ixBCgjOg7dwDcH18SM3c142YyvU9Y/OMv1jwE+D4FPs8kLeCER9wXmAGMTx3ckUAJVXR+HABNCYFIN+9CcaBDs0JDSTx8Cs4iO2X6JVWaEwIyUdN8QtVBVvk+WEP26v9Wi7qL1OZ9GhMDq9VgPov0NwCPruX6VAj02Uo9UIci/T0JgYuIv3SDDr2uIK/vl25K+mW9hynKAdpDVJYXpvrxLiZobs2LGQOBc4KwQGJnFKqOIvkSSf6OyWDe5722BYqIm4+T2LgbaWHXf8uNEXQl/J/oC60nU9A857G8tOsT/P09TnpZErwvAk0TNp3sSNYEvNeNfyb7iHHRk3XOH5HNx98pwYCVwNtEXaE+irolaj4FFV5CMIjrulxBVAnsCI7JZn6hJe1gW6SolX+8ORGMrksd2fLy8Xcr/TOd/G6KKYE3vpeRI/KVp0lW9T0IgEJ1TE4mazqdbNGbnggxlSErbfJ+ldsDSDahQpCrEYyP1SGMICsdm4H49bRb/r+yzW0r6X2Kbx/+XxP8r++nyyozriC45vDSErPuFzwM2TfP8iizWTd6nexlQQdSf/2TaFQIVZmxC1H88IITqgZVm7JxNgXNQefwPIX1la0lcpgA8BDwU93cfQjSmYChRJSFXC6g+V1Iln/sN0a/6Y0NgbeWTcRmWZZFPX6AVcEJIGRSYTQuHGR2JKg9XZJFPpeTrvYToSpYTakg/O/5f2/n/bbztzdMs25zq1zFrIfAF8DuLrn7ZlahCOsiM2SG7sRXp7kG/Jv7fOPF8u0S8GGhrRtM6qBQU4rGReqQWgsKR/KA7kegLr/IX0JtAJzP2TaQ7maiZrnJA30jgiPhDOC/MuJRooNJ1IfCPbNcLgWlpWksmhsC0XMsQN5GPIfqQ+SDdduOkTYhaEtYmNnFGrnnGKi9/S16h8BrR67V1Dfs4K80+fBsCQ4m6i3ZK5JHtFRDvAv3i5l6g6td88jxpRjTIMKSkO4B1u4hq2r/KL/7UykS3NPmk059oYOS7WaStyQiiwbErazi+i+N0I4FeZukH5cXnzfvA8aldVWZsQ9Tq8eb6FjDuhp1MdcWn8jWt6ZhmMiexDeIukuTg4JFEv+r/K8O2ssq/gY6NFBC1EORfDzPap3l+YvDXGvcz43biDzSiKwSeDIHp8fLBwGXAv+Jf518CpxA1yZ0XQtWI8j8TXZI31oy/EjVhbwn0DWHdSxRzZcaJRKOZR4C/bA1YHkI04r6eXAG8BbxqxmNEv5bbE/WDFofAtSHwnRnjgCvNWED0i+os1r8VZTrRL+2zzFhK9GE7LQRmmnEbcF98idabRL/ytiJ6jR4NgTfMeJioReRdoopcN+A0cF0unwG/NuMIoqbaxSHUOOvgzUSjx0fG509joisxkt0II4jGrgw24/E43z+BGzVemTfARWY8QVQB+IhoXEYZ8KQZdxJ1VdwIzKX2Hxb9gZfCulfW5GII0ZUwo+L8PyTa167AUUD/EFhFdBXFyURXmtxMdDVCe6JWovNDYAXRfv+b6AqJQUQj6W8EviNqrcmaGbsQjbQfSvReKyaqbJYRjdSHGo5pyDyPxgRgJnB73PVVClwI1ZdOAsTn1P8Cd8UVwf8QjanoDfw7HnOUS/71fWykkDT0qMYf6x+ZrzIIENon0vWG8CLRFQJLIdyfZuRxRwhPxaPKSyF8BOHUNHl3hfA/Kem+gHB3yvLBEL5Ms95oah9lPzjDPmVcdwOO5WxqGHUPYUcIzxJd5VAK4UsIL0Hol5KmM4RXIKyI090H4fC4zH1y2f843XnxMS1Ls43TIIyD8H38Wk6J8+sULz89zqeyvLMg3A2hZco2doAwhujKigBhcC3lOQjCpJTX+rz4dZqdSHdJnN9qCBPi9dbZZwh/hvAV0YjxqpHuEE6AMBXCGgifQjgxXT6JbbWMy3V4lq/1gDjPRmmWbRIvnxpvc2m8HwPwo+I7QHgYwgKiKxDmQXgCQpOUNH0hvBsfi+/i9972ad4Pb9dwPg5OyesJCNPj12sp0VU3h2Z5TAOEm2s4Ft3jMqyEMBfCFSSuMojTNSK62mJ6vL+LIAxP3Z9a8h+Q2F69Hhv9Fc6fRS+cNBSrnjhku/DjmtFQpLJF6RGgffiJzDYosrHSGAIRyZsQeDYENlVlQKTwZWwhOLjoeDUf5Nn80IfPuIh9uIRmtrD2FWrxWsVzVgfFWofOhY2PzgWppHNBKmU6FzSosIFtYaPZIvMdd0VERPJOXQYiIiKiCoGIiIioQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiLo9sci8iMS9u3h4u//tNzFb+38vIvPnde76vGC323mlpVPn1m3hRMpcGohEBEREVUIRERERF0GWVl0/t4uXr5tyJi+vEWFi2cd9bCLd3zoQhdvfePYDSidyE/XnBv3cfG7Z93h4hZFTVzs35nw4FZvVj1eOarULTvwlitd/LMH313PUopsHNRCICIiIqoQiIiIiCoEIiIiwkY0hqDiVz1cPKdf05zWH3jckKrHV487zi0z82MCPth/kIub2fsuLsJyyrs8OeQg8xAEqWPFm3Vw8ZRbtq56fPiuH7tl1202ysX9brvGxR3u9+M9irff1sXl0z5f73JK7Yp/0c3FL51xu4vXJtJ3H3Omi0s+bOHiRnt+W/V40C5D3LJR193p4pPeO8fFYdKntZZXGk6jrTq5eNrlPn7tOD/epHVR9e/j/d4/2y1LfuI3frG1i9tN9pe3bqznhloIRERERBUCERERUYVARERE2IjGECzcq5mLp5x+33pvq/+Bj9aSokktyzdMp/3m5XX7P3Vrjuzl4mNuHeni4W187Pk+5knX+fEku/c9wcWrx7d3cbtP2rm42QvvZSqq5KiiuX9vFicG5Ow9+hIXb3vapKy3/dfND3PxJW+PdvHnV5e4uOvJWW9a8sBKGrv4i5t2d/GrJ/nxJVs38t8hkIyrTerpx5MUm//tXN7Tz2jxTfkqFx/w3gUu7nxLuYsrJn9WY94NSS0EIiIiogqBiIiIqEIgIiIibERjCK49Z2hDFyFrXyX6k377h6tc3Polf+17cn51yc3cG/x89pPPu9fFTcz3/c4tW1n1eL9Xfu+WNV7s3xLTznzAxe2b+dd2ndEguU1RITmyj2e4+Ljb/TwR2963/vcFKVv4tYtvvfR3Lv6/Qf68+q/j/bnT4jmNF6lP0x7YxcWfH3Z/IoUfI7CkYrWLj/7Ev76b3NOm+vHX/n1em1nHtnLxkUeMc3GbJ/323j7Az4lQvnhJTvnli1oIRERERBUCERERUYVAREREKOQxBL12duEvmyT7Bjdx0XMr/fXfj53b38WN51XPWT7tos3dsk6j/DWizacuyqGgaVT4UQEtZ/v+JI0Z2DC2e3cXDz/7by5uYn4ugT9+7fsaPzy2S9XjbrMmuGXTH+mZMe/5y1tmXU6pexVr1ri4wwaMGajNwj392JNtS/wcCPP7+s+Nbs/lrSjCuvcN+c/B9yRS1DyvAMC+Yy5y8c9Pnlxj2lw/o7dJbOrjm/wcCZ8P9uOc9v/3dBd/dbj//mqoMQVqIRARERFVCEREREQVAhEREaGAxxAUz/zKxUsrNqkhZeSuzw9ycZs3/RzmZSmPu145O+O2yjIulYY2+yh/zW+XEj9m4KXvfV/i+N/v4eLiWR9UPW7UZRu37MWD/5HIzZ93I3d/2MX7LLvMJ/+0YN9SUovvTt3LxQ+fNqiGlJEmX5VkXC51q6KZH8Ox7r0JvH0/9Pcd6XrmFBf7u2DUrbD2B5/3Kf776Pt32rh4ysCfu7jbORpDICIiIg1EFQIRERFRhUBEREQKeAzBgt/u4OJdGw9PpGiM/DSsOaKXi68+4V8Z018x7HQXdx39bo1pV3bfzMW7NM48VuWLMt9vud0jfsRJ8QefulhzThQWK/GfG9Pu7VH1+H/6+rnwd/dd1qysKHVx6+n57IWWpAV9WmVcPmq1f8HaXOO/3ipK/evXkD5d5OfCef4gf+79Yf/zXVz8xgfUB7UQiIiIiCoEIiIiogqBiIiIUMBjCH5IdBc1NY0Z+Kkqb2IuPrvVwozpNxufued+3nXV84qPOO9viaUtyGRN8Nee29gPXawxA/Vr6Vl7u7i0tT9XfthrhYtLSvz9B6b3eqDqcRF+3dXBX0vec+gVLu76tL9HieTXyq0zv7uu+uQ4F3f8ZEoNKRteyyf8PVG2/4fft1lH+u+7bd/Ie5EAtRCIiIgIqhCIiIgIqhCIiIgIBTyGYFXXH2pPlOLR7k+5+NlJvWpIua63vvb32S5/ooOL247191UomzMvp7JJ/Wpz0VwXN77kZy6e+PN7qh43K8o8ZiDp7nmHJJ5ZkNP6UreW7r/GxVMPeLTOtr3bM793cddrap7PQvKg184u/Nvhz7i4NPg5QJo9n3megkLS7IX3XHzMxce7+KQD3nHxBIrzXiZQC4GIiIigCoGIiIhQQF0Gxdv7ZvvXD74nkSLzrS67J6YkvanD5OwzT6a9w4cPfudvkfvgfx/p4i3uGJt9XpKzTUd+5uI+n/R38eidhrn45W6v1LLF9b+Ede5LXVzcUV0GDWr7y+e4+J9jfXffiS0WZb2tYvO/j5p/6S9DLO7W1cXl02dmvW3J3XfbNXdx/+bLXHzJ/N4ubrURXwYabvLdmjs+5L9TxvU5uupx8ej8TWOsFgIRERFRhUBERERUIRAREREKaAzBrJN831/nRpnHDNSn81v5fsqjL/XT3fYL17i4450aU1CXKlb46WebHef7dvv86hwXN1rlp6ctb+Lrvcu6Vo8hmHT9oIx5j17t193ykY992TKuLflWvmSpix+99BgXL7rrdRdf1DpDv3/wr+bYa+5xcenV/jK3Xw26ysWdBup9X5eaLi7LuPyVj3dycTcm5rM4ebV0R3/r5uTYl+t/V/051G10/sqhFgIRERFRhUBERERUIRAREREKaAxBxY4rXTzs+9YunrJmCxc/+Zmfmrj9sOzHHHzXxdeDLjzt/1ycHDOQ1LHY5/XqZX5MwaHJMQV3qW+xLpUvX+7iJsMnZEyfnPSz1WE9s85recUmLk6OZ5DC0vhV34/8ak//uTHkxMNcvGqz6vEovY7240Pu7zTKxS2KfD/v2IvudPGBi/3tkds9oqmO88pCQ5egzizbM/NU/W3Gl2RcXlfUQiAiIiKqEIiIiIgqBCIiIkIBjSHo/NuPXPxYd9/XF2Z/6eIu3/v0udg0EQ8f3N3Fzzzu+5gf39HfWrlro6Yu7pAYU3DHhY+4+M67/PalYc35TfZ9j7fN7OviFnxR18WRPKpYtcrFbf/b9+u3TXk8f6Bfd78zL3Pxkj38PAXjj7rLxddf4z8nHnn9QBeXzco8Nkly02pSk9oTbSRCLR9Jrb9YWy/lUAuBiIiIqEIgIiIiqhCIiIgIBTSGIKn802n1llfZgoUubuG7jTn5bD9n+dAbbndxId13QdZVtImfS+C23s/VmHb62u9d3OpSf98Ef5cE+TFr+3hivMHjfvmAXge4+O4t/HwjgzZv7WLTGIKczDkiOYOI13Zq5mv3Nya/3mGGi5dXrHFx8er6+eRRC4GIiIioQiAiIiKqEIiIiAgFPIagkLR7zPclnvKbM1z8zq7/rMfSSK7K9tzRxSe0GFdj2g/WdHJx+fSZeSmTbIT22sWFl3Z4wMXjS/38JCULvnVxWX5K9aMVWvx4j9iKE/dy8WNb3uHiE6af5OKiMZPyXiZQC4GIiIigCoGIiIigCoGIiIigMQRpNdrS30N9xkXbuPjmbZ+pz+LIBlq6/Sa1J4otKmuZx5LIhirerIOLi4b6a9Wnje/s4uZf+nkk1rT3k8a3mFf9eMXWPi9LzC+/X9/JLu7SyJ9Xh444z8XdZk9A1l+TeY0bugh1pminHVx80y3+fjfzy/19Gb59xo9lasc86oNaCEREREQVAhEREVGFQERERCjgMQRFm27q41a+b7d84dcuDmWZr1lNnc++tPdObtnc0/080Xf1Guriw5utzLjtssQM9+e9ebqLuzEx4/qSX0t7Zn89892j/Y0stuO9ui6ObIDyr79x8f7tV7j4hVNeXu9tF+HHG1RQy03qExotK9iP043SNjf4+V926X6ai1v+3s/zUDIy70XKWvL+KVOvaOHi1kWrXXztaee6uN3bft/ri1oIRERERBUCERERUYVAREREKOAxBHMv3tnFH118n4t3Guv76des8NdxJm3TaXHV41HdH96gsiXHDOww4gIXdztbYwYKyW376V4TP1Yv3HSwi389cLqLd8/8sZBRaVibcfnRU09w8bZDfJ92xfpnLWl0vmK5i09/7S0XX3/ryS7ucm399cMXNW/u4kUn+vtePNT7URcnxwwUvT05L+XKlVoIRERERBUCERERUYVAREREKOAxBLX5ZJ8n6i2vEaubufjaB89ycbc7xtZbWaR2jTpt6eLOJck55UvqrzCSV5sOHefia0r9eJ41rfy9Dhbt58cF9PnFtKrHoyfv6JZt86Kfh6Co3MclI/1YIY0ZyK+yOX4+/7tuPMnFj970gItvveNAF5cvXpKfggHzz93Vxf+6/G8uPmzI1S7u0kDzDNRGLQQiIiKiCoGIiIhsxF0GdekXb5/h4oo5/hKSrkP95S5bvK8ugkJW0dZPe715cWkiRc1dBh3GWo3LpPA1HTbex4nlbRI9jfNTHnfDryuFrdUQ3110wdYXunib52a7eO4b+7i4JDEjfdup1d1JX++RW7fiwNOedPGhz13l4m73znSxv3C9cKiFQERERFQhEBEREVUIREREhAIeQ9BpoO+n7zfwl3nLqzMfZVye201QpaFVfDTVxX1eutLFXxz7UNXjUav9ZWltR24cfX0i4iW/M9a+vZuLS670U0snrTqw+jbpn/QY6pbtNuEUv+1JbVz80PFHubjrZD++YWP5HFELgYiIiKhCICIiIqoQiIiICAU8hkCkrmx38XsuPvTiHhlSL8prWUSkfhSNmeTijmOyX7cffsxaR6ZkTP9jmbZaLQQiIiKiCoGIiIioQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKoQiAiIiKAhaCZ+kVERH7q1EIgIiIiqhCIiIiIKgQiIiKCKgQiIiKCKgQiIiKCKgQiIiIC/D+RywCOIG5QJgAAAABJRU5ErkJggg==\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 3 Average loss: 121.7237\n",
            "====> Test set loss: 109.5354\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAB7CAYAAAAL6ZirAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAZ/0lEQVR4nO2daZAcZ33Gu3uOnd2dve+V9pB1C1uSZRvZDsbGskKIbYxTOJVgF5XEECBFVah8SFWqEqCSD0lIJZWiSKWKSuUAAsSIJOYGW7bwBbZlo8Oybmm1Ova+d2d35+jOl+Ce33/QjlaWV3s8v0/7qGe6e6bffudVP//DDYLAEUIIIcTKxrveJyCEEEKI648WBEIIIYTQgkAIIYQQWhAIIYQQwtGCQAghhBCOFgRCCCGEcBwnOtfG3d4jyklcgjzlf8u91vvUWFiaaCyIX6KxIH7J5caCnhAIIYQQQgsCIYQQQhSxDIQQQogliVvEIVGV3gL0hEAIIYQQWhAIIYQQQgsCIYQQQjhLKYagmB/kFlnbBP783m9e70Yi3G51Lse3G82N8q6EEOJtYX8TiszhmneLoycEQgghhNCCQAghhBBaEAghhBDCWUwxBEX8oAIP3749xo/iRs1H8+aOQXBLS/kPxm8KrJ6covatPzVHDIEQQoii5M/jdk5343G+uDTB7YkSszPzGzAzCxnMzFCnM3y9z5iEIJultr8BSzCGQU8IhBBCCKEFgRBCCCG0IBBCCCGEc71jCIrVFshjzrx+xymIESjwm2qqodOra6FHNtB/mljD3ZdfpG750SXo3HnzgiXgFy0bzDiy8SbWa3RL6C0Gs8ZLTKep7djTtRXi2mDu3Ugd52WnIdTDO+qwafBmvtQvNXFeZfT4nayJSysx9/VYjNuzPLfEAN/fcIAxBmVnR7m//iGez1SKOhfGGARZE69gWaA5R08IhBBCCKEFgRBCCCG0IBBCCCGEc71jCObyRQLj7xSrU2B95Npq6EwL9anH+NEfv+NZ6A2JHuiXJ9ZCHzy6HTp6ga8X1xCPMQGeyS/2mhqgR3a2QPfcRy8xVk6/LjvM+JGqIzxey7MD0MHZ89C+yV8W14+C2CETL+KaXHWnupI6Th851VkF7aWZWx5NmbF1cRg6GJ+knp4O/87ZPHWjzRxXEMviL8FaJ2aejq5qhc41VEP37wyvz+Q9rP1yY0sf9B21Z6A74oPQtRFei0aj+3NJ6LjL7/fI7Cro7+zaBn3iwGrolhcYD1FxuB/auRSe/2K5tnpCIIQQQggtCIQQQgihBYEQQgghnOsdQzAfjJ/mGa/P9iLwk2XQAzvKoT9551PQj1cfgK7xuL97Sp+H3vnYDuhNr5nc9gxz2UUR8rxFW0cg0tQIPXEbvbrkH1+A/mzbv0GvjzEfeCbg/gdyHBtdu+qhn3jkVuie/+G1X/UtepfZPsYcLEmvd4ngxlhjIlJP3za1rQ16ZAPnjbHtvE/vv+kw9AM1B6CtD30y3Qz91Yu3Q3fv3QxdczKME6g4PYFt3vg0tDth+qWkuN239TOMXoy4UX7/QYLXL9XBe3H0XeH39bEtL2PbneUnobszvPb/PcD7tHu8BrrvHF/vzfA3pnET7+NNNYwBeLyNvwmJdsYm/dXGB6Bn93Cs1D85+tbfrq19EpiYOdUhEEIIIcRCoQWBEEIIIZaQZWDxTNqhSUVLtVdAj97ExzktsRHoMpePsiLGoqjy+Gjrtk1noaeSfNTlT/BxoDDMUW44Us8SpZc+1An9gY+9AP2Z+p9BN0Z4LWYDjo39s7QMerNMLauOsMTon7b/CPrljzMF9d9rd0Ov+U/aVf7Z7rf+ti1TxfywFoHXwVSwC/cz5TSyi3bRR294FbrVzAM7ErSfas1/mWJmXmiOnOMLeDrOkx9gSuqrnTe89XdiM8ddWQ9TIEuHmYaY7KKF4J015dPNY+dFUWLbpovbEvNTtEFmqkyb+8rQBnlzktd2b/9G6Isv8ctv28vvvq6LaYh1WV5r297YNymQB+66CbrqD3jun2t8Dvoz6/dCf3brI9ANe/PmqUleWye4PvOEnhAIIYQQQgsCIYQQQmhBIIQQQghnKccQmNQ0q90c/bPIOGMEnh+j//RgeTd0mUOv0lIRZYrPVCRxmVeK+eLXMz1o+m7GY/xOzSvQSRP/0Z+jH/flkVugv/L990GXjNDXzL17HPrvtu+B/mDFQejUwxwrPzj3Xuj6/BKliiGYH7Zs9RqmEZ76Paakbr3rBPSdNUwJLfN43x6foS89E3As3RBnqlm1R1/6WJq+9XNjG6CHZhjPsnld2CY91cFx0zvKuKfUEeqSEcbClJjvZlHEDFjsOfmmRXHGtBAe4P2RPBTOqz8f3IRt9a9z12v38lrnBhk/kjXHLlYq2hsZhW428RAvfuAG6KmGfdCdMaYt+jX8rH5VXqnkfpOqbGMvlHYohBBCiIVCCwIhhBBCaEEghBBCiMUcQzBHnvqvIphlDm7ZcXp/bW4T9LOr1kP3NrGUcZlHvyflU0/n6DU61hvOP//F6O0tYlyTD5zuY17/T6cY//GdHMtM/+u+u6E3fJV1Bdafp9domXmNpZE//ehj0H+yk2Pl5jLmon/lLo6VxqfDmAg/xXPR2PgV5N07kSrm5vfs5n380G+wBsWD1b+AvpRhPIotZ3t6hDUv6st4fe5tPA79s2H6xkdepq5iNV1nnCUrnHU7w7FyfyvLJB9MMj7i4P4t0LFRxi8EdiwtAQra/KZ5ryT6mdtfXh3O+1VneK9Uvm7qMAyxpkTBsYreayamwNS6yVYzTqwywRiFQfObcDHLseeNmd+MyOXLtQcmnsEJFqb8uZ4QCCGEEEILAiGEEEJoQSCEEEIIZzHHEFhMDWzH+EMFfpppBVrSx5ze0gOsI37wFuYTN0RY5zpl/Kf93e3Q63L0s+QNF8F8P/D7+lhzvO3H1dBfGvtN6Jpj3Nfmp9lnwh8dg84VxHtwXVxykNvXpXmt/zF+L/RjN7EuQm0D6xikO8J2ypGeXmxTXYJfQd718Dtbsan8QX5/j5iaFAmX88J3pzqhD13i/rLdrBMwkqDve+I06xQ076PXu/4XHKtOhtczOs2YhxPtYd2EO+sYy3Kgl3NQ037OYV5XD7Rv/PeliPX5vQnGSZQOhr59ySW2nvaHR+fcl72vbYyA9e29MtODZD1jOk7/Pvf3N+0/hW6K8Hr8Q+826Kpj/A3zJsJ4Cd/ETbnm926h2iHrCYEQQgghtCAQQgghhBYEQgghhHAWUwyBrd1c4P8Y/LlzRq2fFBkYhU4MMr/5fKYWesI/D33S5DPHDtF7fFs5wdepbvVixTe9wZMHGZ+x5iLjPyK9zAe2MQMFXmtBDXN+3/4Evcp4N33i0sP0Fic3s8b82hqeT09DOHaSJXytYgicgvHvlYa+8WRnEtv+sPPH0M0R+uzDJhf89WFeq3SK/QPK+zhvlA5wLFSc5/UpOcexEJh4FzfKKbXiXDV030R4fl8/cSu2efs5JyWOd0H7U5xjguwSiCGwc5vFzNuuuVdL+i8/r7p23MRjl3nl/78+wXvPqeecP3ljA/SFXdz/52//NvRdiYvQb2Y4Lz1/kL0X1r3BGgvBRDjPufG5e+dY3ql5Q08IhBBCCKEFgRBCCCG0IBBCCCGEs6hiCIyXFOOpWW+uwGe3XpWNKaik559q4utjJn95IuDxujL0lyq6jQ9dkAM7Ry+D+fZpWAk+c953FJhcbn+YNcq9NPtW+Cnjzc03BsM3NS2sNZs1283lui3JugfJKH3tszUb3vq7osi1XpHYmhR5PvJsFe/jvix92hmTn91t6sdvrGJPk7PHWVeg9hjHWvlR05fezCPO4DB1xgyWBOvd28/W8mx4/XNx1kap2894BH+IxyqMhVkGsUZ23pzhveNUhrUBXPvaUn7XXgXjTRwTU5Bp5dgY2cAeKIN3cCz87T3/Bf3bScYmXTDT8o/GtvLwA6bOQZrn70bCsRXYeSHGc3ft75lvrr2Ni7rKsaEnBEIIIYTQgkAIIYQQWhAIIYQQwrneMQRe6Jt4JkfUq6Xf40TM2iVnc8lN7ecy+kujW5lzmuqgATTr07MZzrGu9b7hjdClQ8bPsl7jHOdWUEM7aWoaGA99/n29lzjW07feqYkZKPBx3ya2jrjfUA1dcjvrDKyP90H3Gp87MpsXH2HiH8TcxKZ4n7862gm9sYT1/X8+uQ56PMN5oLSZNSZmqpn7X27z4u29WMTrdTK8vvEuxiTEL+ZNuaaWSjAyz/oZS4GCucp8Zju32bdHw+uRrue1ilbw2roZ0w/A7DtdyWuVLeN9Xl7PmgcDWR7vmxMcG/87yJ4mr57pgE4Oc/+Zav7GRUby5v1Kxj+4trfBpKlBYcdl9tqMDT0hEEIIIYQWBEIIIYTQgkAIIYQQznWOIciPG/CamOc/s6YeOjbGPtmu8UwC4/1laukvTbVwe6yansxEzrw+YG3pg73so75qwvh7xlvMjxOwOaNuKfNfbU1tz/pFxksMMivLhy6o2T5t40fm7mNRNEfXxniYfgNjm+gl7m77OXTM5f73j3VCV3aFYzewsS+igPzrXX6R9/2BC6ugt1a2Q0/meO3Wl7MOwUA1vdqTu3jfTzc0Qdce59grO25iDPoZT1JQQ6PP1DWYTxzAUowZKIbtUWPmxsB46Znq8PqYkhNOrpwxAfELozyUqR9S1kUdm+Sxxid4n39pzYPQUdNWwfa9aB03v0mmto2b5etn28I4OVujID92wnEcJ95n6vKMT/D116ivhZ4QCCGEEEILAiGEEEJoQSCEEEIIZ4FjCKw369+49q2/e29lXW/TSsCJzNLTrz1Gb9Gbpnc3U8sdZI1tH43S71mXYC75mzP0KlMDrBXgx3m8mK0lkN97wea1t7Oeuu35Hh/nvuOv2BzUlRVDUFDrvqBvxDzrehepC+G2NEL3PcD66g9XvQadMjUsXummr71uJLx+uSJ518LB9Yqd5X2ZmVoN/cLgWuj31J+G3py4BP3htbx2p9vroP+pjbnlFxK8lquHOE9FbbyP8XbtWCyWd88XL796I7bGh50bg1LO8zN14b2VGKJPHhvhb4Azyu/eTxnT33yf0W4eu+4E5/B6W9vGxP+4Uc4bga0dEOdnyazmWBvdGNa6mWrlsbJlPNdV+7g9MWB6akyb2ixXiZ4QCCGEEEILAiGEEEJoQSCEEEIIZ4FjCLx1ndBHPxbmmLZ19Dhz0ftaM3TtsbmPlYubOtJJejL3dZyC3lJykceLsB59RTP9qalmbvfSPL/8nNkgxnXXyAaT576B5xaZofe07gSP5U8Yn3KlUyxfu0jMQKSJMQNnHmOMx+dufQK6KUK/7pkU6+dH3zB1ycfY515cOYHpU1F6lvfGpu2MMbi17Cz0jhJ6rWUur32FxzoFn2rfB/3ZdzMXvW+SPVZYtcBxohc4pfqDpk5Bft79cqwzYDH3nq1DYH32yTWM0ZitCt8fmzLvneR9GMwwpsCfNjEGxb5v+3qLeb+dRwo/G2OLogl+VmdDGEOQrjRxUu38bEMD7K2z+hjrZ1wr9IRACCGEEFoQCCGEEEILAiGEEEI473QMgUePJdXBWtH3bA0DAR6oPYhtA1l6SX8/tBt6ppY+fHSaH2W6nmudX7v3MPSjdS9BN0eYa57y6SfVltHT6V9LL3G2moUO8utez1bTRxu/iXUEKuunuL3f1PNuZ18Hr6cXOsiybsGyo4gPWfTtMY6NSAud367fZW77Ax/8GfS9ZV3QsyY9/Mn+7dBlfcYPzPc2V4JvfC0xfTxK+/ndJs19W+HxPo05HDszAesA9JreB+fTzBVPxHhvjdzO3PazLcxdv+HbvL7e5CS0m5cLH6RNPZFlWHegAFN3wCunN54tNXPlmvDv2BR/T0rLjY9erIdJMeZZv6SwpsTcNSa8lKmdkwv3n2vmOG+s5rgZT/J7CqpMnFKvqYlQ8F1c2djSEwIhhBBCaEEghBBCCC0IhBBCCOEscB2CiTYe7v01b7z195Y4ffFzHr3B9S3MFz65swM6iNHf2bHzOPSnmp6B7ozSv0sbiyUd0JPJ+Fw7+XG+wTfH96Ph9tla7jtWTr9ocoJemDtt8lt9nuuyjxkwuFHm89r83gI8XivP9JmYehdjCKY30dv7ZN3z0BUmFualFGtOvHGYY3HTi8w998fz/MCV4BNfQwLzfZUO0+c9MMr4jw0J1jM5bWz6F8fXQz/1ylbu/yKvde5m1vy4Y80Z6OdnNkBPdnCsVV0wPnexXPflRpF4n6CSXriXMTVZ0uH7J1dzji3ro6+e6DP9cIyPHmTMvDnP+iVFsXUITOxSUM3zm2oJX7+2jb9vGyupf9DM2JZsJceVZ2si+La/y5X10NATAiGEEEJoQSCEEEIILQiEEEII4SxwDIFrbIzRXOgBVXj0c7bF6cN+vvNJ6KfrboSuijI/+LZSen3VHs3E3hw9l2emNkF/8dVd0I1P07fuOGHyi30bUxDuP5Km1zWRoc/omXiEcrZVcGJ9Y9DLPoLAeHdeqfFhVzEGIIjxWrpZjqWJ9dXQl97LdfAnduyDrjK50n2mD/oXz3BsNLxs1tWXWF8/yDJmRFw5Nlffj/DanB1igM4e91bow6cYY9Cxh+/ffPjCnMcf6m6D7n+cPnDbKs5TfdsZX1L1uokPGg2Pb+MjliOuuZdsrQDX1Jmw9WOCLWEMx1SKvQAuVFE3JRnLkzzK+ARngH0t/BR/MwrqGBjcqPm5NLFKdrtbx1o1g7dwrHbcH/bd+PP272Hb6Qz7q/wwdzN0ZIIxdo6JISiIl7hC9IRACCGEEFoQCCGEEEILAiGEEEI473QMgcnzbHyJftvXPrzzrb93bOzCNttboM7UJbiv4g3oS1n6NV0Z1v//Zu+7oY88xx727U8xP3jzGeMDTzAfOTC+smt977xc+XqTH1txnl5Stoz+T2ycvlowZbyu5Y7N562gFzh8M3Nyx26Yu0ZEdh3r23962z7oB5McSxeyjBf554F7oGefYAxD41OMV8mOM75EtQeuHuuFJrt5LXv6GI9zLM0preUp6vLD56H9Qc5J1heOT66a8/x21HN/T7ZwbGZaOS95l1hvZaUTTLKPS/VJxoyM7gzjBHZveZOv3caxsKeDPnvsDH34pld5bcrPMDbLHTP3ra0jUMq+F34J54nUKo7F0XV8f8fDnCf+sj2MiyvzOM7/7PR7oJNdZk4090Xg2z4MV9czRU8IhBBCCKEFgRBCCCHeccvAPCrtGaD+l7Ds50d+6+PY9NDGQ9Aby/io7cBkO/RPTjJtsOJFpvq1fp/pRWsuvsZTNalhBUkbRUpw2vQaN5uXEmO+h/gRPiaL29QcU5rYHxuf89jLHfuoLtXIa9G5qwv60daXoW8qYR5nc4TpRUM57u/Lg3dDv/IffBTZ+pNz0Dn72Nm/sjKh4gowjz6jQ3ysm+jnY9pcLa2/GdN6PChnm3J3kmPLramGHvoo79W/7vwuj2f+T3VkTQuP59G6zLcWV6SRZOdRM9fFR2kNuyOhXVgX47W4PXkK+tfvYIv7g9uZhvjNW26B7r5YDR0bpJVbUJ4+YdqaJ3if1zaNQt+/+hj0ozWcl7y8EfCJEx/Btr7naFWt2m9s42HaHQUprFdpU+oJgRBCCCG0IBBCCCGEFgRCCCGEcBa4dHFudBS6cu+J8O83G7DtxZuZJvjj1Vy7REwX0XUvMS3QPXIAOmvLVM4X2z7SpBnazcFM6IXZFJHix6JvutLaHVvcqWnzD5Q7apj69f6ybugaj75xT45j4S/OPwR99Adsadv5Pe4/12tLE6/s67Og9A9CNu5nKtn5Ol7riU6+Pf0hpqIFHvXtDzF26WurvgGd9BhzMOLT156Y5fbaIW7PpVd4GWs7t5nvIzLIeKmG18IYgm9U8TfB20Gf/D3JE9DbShnrU7KGxzrTzN+cWZ9phDZurcTj+09OM/14PMsy1YfGGAfwxNFPQbvd4VhtfoXfS/s5xgh43WyHHMyYH8AiZZevFD0hEEIIIYQWBEIIIYTQgkAIIYQQzgLHENjcyNzISChMrn1NF+sG1JbQmwum6Sv7xosK3ulc8KJ5nqEnZOMLirLC89gLWqba7cayPzPFXO++aq5z+3LMbf5i/27o498xMQN7WLcgZ9sZXyO/TlwBds4wZaGTR3htaptbob2HGXPwR2t/Cn1fGcvJNkUYgxBzWc/EMmPOb+gQfenaAebKX21J2aWKja+xLYIL2lubGJHavJLyNYdYJ2Df+juhn1x7F3S6itfGNbftbOPc9/HeOs4LmXOseZEY5DxTfonHqzrFWKUNgybObTr8rIGJccuPQXOcwpoV9nu9VnFMekIghBBCCC0IhBBCCKEFgRBCCCGchY4hmAvjm/u2bsDbrSOw0OR7i/MOIljZWI/eHxmFbv1hD/Spcfax+NAW6vgoYxJaX2D8SfuZLuic8TFtnwu1M76OGA/eHxyGruymh981yNbjOdMqm43HHcd3uP+MbceS49j5Qt8u6LV76BP7+XFSjrPix06x+BsbG+bk6wH2DCln13InaWOPivSfcWz/GVNbxonY0WEw17Lgs/mmF4KtweBffizYOKqFilvSEwIhhBBCaEEghBBCCC0IhBBCCOEsphgCIX6J8eZsjQmvjx5/wz7m4Db8xNSkyFD7Y/R5s4oRWDrYsTHJugQlz9FY3nycMQVfX3s/9BfeF+f+KJ1sHcdG+Sm+oPU59irwDh7l6arPBXk791aRWKy3W+JhMd31QeDaf1iQ4+oJgRBCCCG0IBBCCCGEFgRCCCGEcBRDIJYCtkbFhMn1Nj5yAYoJWL7YmALTJ94/dx46anTnM2Z/Nhfd5rJbo9rmol/+TIW4cq7TnKUnBEIIIYTQgkAIIYQQWhAIIYQQwlEMgVgOKEZAXCvsWFIfEnG12HiUJTBP6QmBEEIIIbQgEEIIIYQWBEIIIYRwHMcNloCvIYQQQoh3Fj0hEEIIIYQWBEIIIYTQgkAIIYQQjhYEQgghhHC0IBBCCCGEowWBEEIIIRzH+T9Q95L2lgYH6AAAAABJRU5ErkJggg==\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 4 Average loss: 116.5905\n",
            "====> Test set loss: 104.9082\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 5 Average loss: 113.7427\n",
            "====> Test set loss: 102.8385\n"
          ]
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAACJCAYAAABTsyC5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAcgklEQVR4nO3dd5xU1d3H8c+PXem9SRFYOoo1llgigiUSG/rEFssTY8wDtmgsyROjEX2ImuRJLFFUjBERo2J5kFiwAsGGggVsCAIKAiId6eye54972Z3fZWZ2dtnZXeT7fr32tfO7c+69Z+69M3PmnHPPsRACIiIisnOrU9MZEBERkZqnAoGIiIioQCAiIiIqEIiIiAgqEIiIiAgqEIiIiAgqEOSNGeeZETL8razhvI00Y8F2rJ/pde1bhdmsdmZMNGNiOWmKzBhqRrc85uNyM/5jO7cx0ox5lVhv3/j1tdye/WfZ/r1mvJSPbddW+T6m27P/+H07tAayJbVQYU1nYCdwGmzz5bulJjJSxUYC9yaWfVYD+ahuRcD1wGvAnDzt4/J4+0/lafvZ7Ev0+kYDy6tyw2YYcCLwh6rc7g5gX/J0TKtg/4ew7eeT7KRUIMi/90Ngdk1nIg++CoG3amLH8RfLLiGwqSb2L5V2MNAeeLoiK5lRLwQ25idLtYsZBYCFUD0/GmrqPSy1k5oMalhK00I/M8aa8a0Zy8y4y4wGibTtzRhlxlIzNpox3Yxz0myzqxkPmbE4TjfHjNvTpNvPjMlmrDNjlhlD8vlaK8uMeWaMNuN8Mz4FNgHHx8/tY8Y4M1aYsd6M1804PLH+gWY8YcaCOM1MM25KHt8c8tEfmBCHL6U0lfRPSfMLMz4wY0N8nu5PVtWacZkZn8R5WWHGVDNO2fpagS7A2SnbH1lOvo4y4914n5+bMThDuhvidKvivL1qxsEpz58HPBCHs1L2XxQ/f4kZb5qx3IyVZrxlFp2HHJ0MTA0h8y/SuGo7mLGnGS+Y8S0wJn6uoRl/NGOuGZvi/78z859jZrQxY7gZ8+Prf378fqiXkmZg/FrWx8djrBm9E9uZaMZrZhwdH7d1ZnxoxsmJdL3M+D8zlsTn4EszHjejMIdjGsz4gxn/bcZcomt7Lyv7XChKd3wSywrN+I0ZH8f7/8aM8Wb0yXH/QxPbq5Zjg9Q6Oin5V5Dm4i8JgZLEstFEH3zDgYOA3wONgPMAzGgETAJaANcA84FzgIfMaBgCI+J0XYG3gXVE1YSzgE7ADxP7awr8E7gNuBH4GXC3GTNDKP3Sy+ZCM64GioG3gOtDYHIO61XWAKKqzxuAJcA8M74HTAbeA35B9JqHAC+bcWgITIvX7Qy8T9TMsQboS3R8uwFnViAP7wIXA3cBvwTeiZd/DGDGLcCVwB3A1UBHYBiwZ5yfYjPOBv5CdMwnAw2AvaG00HAK8BzwAZR+UH+TKUNm7B6nnxq/lnrxeo2Jzk2qjsCtRFXEjYiun3+bcUAITAeejfN7Lb6pa1H8vwj4OzCP6LPjROAZM44Lgecz5THFIOChHNJBVItwP/BHoCR+D70A7AH8DzCDqMbhOqJjdyWAGS2AN+Jlw4DpQNt433WBjWYMjF/rq8AZRMfqRuA1M/YNga9S8tEduB24GVga7+cJM/qk1Pw9A6wELozTdASOI/rBVd4xheg9Pge4ClgLLAT2yfE4ATxKVNi6DXgZqA/0I6qNyWX/par52EhtE0LQXx7+IJwHIWT4eyZNunsS6/8OQjGEXnF8SZyufyLdyxCWQCiI41EQvoXQIUveRsbbGpCyrB6EpRBG5PDaHoJwBoTDIZwD4QMIm5N5q8JjOQ/COgjtEstfgfAJhLopywriZWMzbMsgFMb5LoHQKuW5iRAmlpOX/vGxOzqxvCg+X79PLD8sTn9yHN8J4d0cXu/oHI/Nw/F5a5SyrBOETRDmZVmvID4OMyHcnuZ67FHOfuvE678I4ekc8tkn3m7fctINjdNdllh+bry8X5r3ySYIbeP4xvg87JdlH1MhzIJQmLKsa3wN/zVxPWyG0DNlWdt4+9fEces4Xydl2V/GYxovXwihQYZ1itIdn5T4yDjdL7dj/0Nr6tjor3b9qZSWf6cAByb+Lk+TbkwifpSoFH1QHPcjarefmEg3GmhD9MsJopqAZ0JgYTn5WhdSagJC1EY7i+jXdFYhcG4IPBYCk0NgNPADol81w7KtZxbVlqT5Kyhvn8BbIbA4ZVsNgCOAx4l/Qca/Io3oV1K/lLRN46rmz4GNwGaiX6oG9Mxh37k4huh8PZz62oApwOqU/LwD7GvG3+Lq1obbud9DgOdCYO3WBSEwH3g9mTDe3wQzlhF1bN0M9AJfHZyJGfub8YwZX6esf0yO658CzA6Bj3LZF/B/iXgg8AXwRuL4vgjsAqVNHz8E3gmB9zK8hkbA94DHQko7fQjMJTpmRyRWmRUCs1LSLSGqodr6PllG9Ov+FouaiypzPY0PgfWVWA+i1xuA+yq5fqlaemykGqlAkH8fhsDUxF+6ToZfZ4g7xv9bkr6ab3HK8wCtyK3X8Io0yzYSVTdWSAisIapmPLCcpK8QfYkk/17JYTfJ194SKCCqMk5u7xKghZW1LT9A1JRwB9EX2IFEVf9QidebQdv4/+w0+WlKdF4ARhFVn36fqAp8uRlPJduKK6A92147JJfFzSvPAd8CPyf6Aj2QqGmi3GNgRiei89QSuBQ4NF5/fC7rE1Vpj80h3VbJ892WqG9F8ti+HT/fKuV/tuu/BVFBMNN7KXlrXrq7AkrfJyEQiK6pqURV559Z1Gfnwix5SEpbfZ+jVsDy7ShQpKqNx0aqkfoQ1B67gvv1tGv8f2ub3XLS/xJrF/9fFv/f2k5X3Qx8Z6c0BgNN0ixfk8P2k9teCZQQteePSrtCoMSM+kTtx0NDKOtYacZeOeyzIrYe/x+SvrC1LM5TILpd8964vfuHRH0KHiMqJFTUIsqulVTJZT8m+lX/HyGweevCOA8rc9jPQKAZcHpI6RSYSw2HGe2JCg9X5LCfrZLnexkwFzg9Q/p58f/yrv8V8bbbpXmuHWXnMWchMAf4T4vuftmHqEA63Ix5Ibe+FeneNxvi/3UTy1sl4qVASzMaVEGhoDYeG6lGqiGoPZIfdGcSfeFt/QU0CdjNjMMS6c4iqqb7JI5fBE6IP4SrhRlNiXr9T8mWLgRmpqktmRoCMyu6z7iKfDLRh8y76bYbJ61HVJOwObGJ8yq6z9jW29+Sdyi8RHS+Omd4jXPTvIYVIfAYUXPRnol95HoHxJvAcXF1L1D6az55nTQk6mQYUtIdybZNRJle39Yv/tTCRK80+0nnZKKOkW/mkDaT8USdY7/NcHyXxuleBA4yS98pL75upgGnpTZVmdGFqNZjUmUzGDfDvk9ZwWfrOc10TLP5IrEN4iaSZOfgF4kK4xdk2VZO+6+hYyO1iGoI8m9fM1qnWT41+HuNjzPjz8QfaER3CIwKoXSwn5HAZcBTZvyOqFr0bKIqucEhlPYov57oy/kNM24iqsLuCAwMYdtbFCvKjKuIaiomEPUb6ELUO7pdnJ/qdAXwb+AFM+4n+rXcmqgdtCAE/jsEVpnxFnClGYuIflGdT+VrUT4j+qV9vhnLiT5sZ4bA52b8EbgzvkVrEtGvvE5E5+jvITDBjBFENSJvEhXkegHnEp33rT4GDjfjBKKq2qUhZBx1cBhR7/EX4+unLtGdGMlmhPFEfVdGmvFAvN/rwPUa37pvgIvNeJCoADCdqF/GFmCUGX8haqq4AfiS8n9YnAyMC9veWVMRDxPdCfNKvP8PiF5rd+Ak4OQQWEd0F8VZRHeaDCO6G6E1US3RkLh56zqiJq5nzBhO1JP+BmAVUW1NzszYm6in/WNE77UCosLmFqKe+pDhmIbs42i8A3wO/Dlu+toIXARlt04CxNfUk8Bf44Lgq0R9KvoBz8Z9jiqy/+o+NlKb1HSvxu/qH9nvMggQWifS9YPwNNEdAssh3JWm53F7oh7+SyFshDAdwjlp9t0dwiMp6eZAuDXl+ZEQFqRZbyLl97I/EcLr8bY3Q1gGYRyEg/J4LOeRodc9hN0hPEp0p8VGCAvi/ByXkqYIwvMQ1sTp7oRwfHzc+1fk9cfpBsfHdEuabZwL4S0Ia+Nz+Um8v93i538a72drfudCuBVC05Rt9IEwmejOigBhZDn5ORrCeynnenB8jucl0l0a7289hHfi9bZ5zRCuh/AVUY/x0p7uEE6H8CmEDRA+gnBmuv0kttU0ztfxOZ7rofE+C9M8Vz9+/tN4m8vj1zEU3yu+LYQREBYR3YEwH8KDEOqlpBkI4c34WKyK33u907wfXstwPY5M2deDED6Lz9dyCJMgHJvjMQ0QhmU4Fn3jPHwL4UsIV5C4yyBOV0h0t8Vn8ev9BsJzqa+nnP0PTWyvWo+N/mrPn0UnTmqKlQ0c0jN8N0c0lJ2YGWcS9YBvHXaS0QZFdlTqQyAieRMCj4ZAExUGRGq/rDUEx9Q5TdUHebYw9OdjLuZQLqWhLS5/hXK8VPK4VUG2tqFrYceja0G20rUgW2W7FtSpsIZ1sIl0yD7jroiISN6pyUBERERUIBAREREVCERERAQVCERERAQVCERERAQVCERERATddigiIkKd+mWzeDd5uZF77p1Purl40rG3uvjnZ13it/Xa+1WbuWqiGgIRERFRgUBERERUIBARERHUh0BERITZQ/crffxp17vccwXd/G/nvm8OdvFuO2ifgSTVEIiIiIgKBCIiIqICgYiIiKA+BCIishMq6NvbxY+ecXvp4482l7jn9q5b38Xh/Wb5y1gNUg2BiIiIqEAgIiIi1dhk0POdei5+dto+Lt79t7NcXLxiRd7zVFUK9ujlF3y91IXFy5ZXY26kKhW0aePieYN7urjzkV+4+F+9x7l4Fytw8esbfFXk/5x2rovDtI8qlU8RqZgzn3zFxfvWLfs63PNePxTxhi6bXNznXytd7N/VOy7VEIiIiIgKBCIiIqICgYiIiFCNfQjm/LSLi6e84KePHPjBVS5uc/ebec9TZa0fdJCLn7rTv5bTPj3LxXWPUR+C2qqwSycXz/mpj3971hgXn9HkuazbS7Ylbg4+PqCeT/H1wf72pbbTsm5earGCVi1dvKaf72+y4Fh/MZx3yGsuHtDkYxdfeN9FpY93u/mNqsjiTq14wPdcfPOMvVy8/4EjSh93vcP35SleucrF35U+A0mqIRAREREVCEREREQFAhEREaEa+xAsObSVi5vVqeviNqfO9yvcne8cVV7Dy75ycbM6fljLge18W+CrNMp7niR3BT26lj4+4MnP3HNjW491cUmitfD3Sw508Ser22XdV+8mX7t42K5vu3hLw6yrSzWq09CfjNC3u4vnDmrs4i1dNrj4DweNdfGPG79Uof2PWFXk4i5PLSl9XFyhLQnApoH+vfrgCN/Xa37izXfBb39V+rjZt1Pzl7FaTDUEIiIiogKBiIiIqEAgIiIiVGMfguX9Nrq4TqIs8qsuvr3tjt4nurh45uz8ZKwS+jT7uvxEUmts/JFvS7z8jkdKH/+ooZ8z4/ol+7t4/L2Hubjd4zNdXLxssYsXX36oi5+8+lkXT9/k70Vv//raTNmWavDVb8rO18k/meyeu77NyAptqw7m4vLuVe87yo+X3/O+RS62dWtKHy9/xs+XsmKV75fU/ez3cszlzmPT5ctc3LHA9xkY8vkJLm7x6pzSx8VbtuQvY7WYaghEREREBQIRERFRgUBERESoxj4Evf+y3sWrBvh7eI9q4NP//hA/D32LGuxDkByjvHO9eVnTT1lRlFjyTZXmRyrmq/7+Mk/2G0j1/oAWLm6z0s+pkbwf/LO7/bwWLxz350QKP0ZFt0LfNnnNQw+5+J7F/Usfrz7e7y05nrqUb9OxB7j4kFv8OBDPtb0z47pHzDjNxd2aLXXxA50nZt33A6v9vBh/u/9kF7ee73sZNBq1xsWPdM08jsEr6+u5+C/0zZqXncHCq3z/nVf6+vfik2s7uNjOK3Dxlq8X5idjOxDVEIiIiIgKBCIiIqICgYiIiFCNfQhKPvjExX9b7tter2093cUHXOzvq537uL/vtmRt/u7frtPI72v1w81dfGmLWVnXnzXOz4PeQX0IqpXV8+2rh/Tzc5unjoHRZ8zF7rkeK9/Kuu3Cdru6+LJ+L7q4a6HvM7CL+XbKxnV83g6rv9nFDxaUxatVXq+wggm+nfjB7re5eEPwYwXs8Y+rSh/3uN/PUVLy/bYuvvZPvr9HSaJ/yJhvffqjGvp5Mo669E8u7lzoO059ucX3s9rjtYtKH7d82t9D3+Klz/H0GdP1xDkunry+vYvHLd3Pr7BxU76ztMPRJ46IiIioQCAiIiIqEIiIiAjV2Icg6aHJP3Dxtaf4PgS3d3jdxYPan+o3MHtuleWl5AjftlQw1M9VMKHX4xXaXp2dcxjsWqP4oD1cfF/nES5Ovfu7z22+3Tj06Ori2Re0c/Gdp/7dxUc0WJdx2wCrSnw75W3L/FwJo184wsW9/poynvpKzZlRnpXnHuLi+7r6Oe+bmP/Nc8QLl7m413Vl40yENn7sk5U9/brzNjd3cddCP5bKmY19O34Jvo/A8+uauPjo589xcceXff+GoiemkElyPIydUcnh/nP70e73unj0miIXz1zu+3i0bpv4PbxY7zfVEIiIiIgKBCIiIqICgYiIiFCDfQg6TEgsOCV7+r5j5rn44+N92+6WRX5e+qQ69cvuGZ59g2976nfEDBff02lS9swkjFvrx79vd9sbFVpfak6LR/z48Se19uNfDGrkx69PmrC+sYuHfzXAxStv7eziBmP9WPrd8HMlqPtJxawZ5M9f313qurjHM4Nd3HOk79Mx+68Hlz4eMeg+91y/+uMrlJd9ppzr4kZjm7q41bMzXdxrmb8WpGK+vWa1ixvW8ee+INmj56lWLiyZ7t97ohoCERERQQUCERERQQUCERERoQb7EDR59gMX9z31fBd/1O8fLr5p16kuvuflbi7+2/T+Lm4+3o/9vezosnuGPz0y8xzolXH1+J+4uCeZ7x+W/Fu6V4PyE8Xu7+LnnK+TKCNP3xRcfPrYX7q49z2+j0HxzNkubkD2vi2yffq09feOFyTGHRjW/ykXn3lC5jH/Z2zy80oc/K7vE9D8Vj+OQOGr01zcET9nRpLGDtg+hZ12c/GFXX1fr+Lg+ww8ufh7Lm75j6rrM1DQwvcbCx39HCczr/Lz4STVm+vnNOlyi7+WwsaN25G7ylMNgYiIiKhAICIiIjXYZFCywQ/72WOYj18ft4uLk9PEDmnup7oc0s/H9PNhHcqGBU0OL7vflP90cZsRvrnhxfvvQWqvgubNXPyjX7xW6W2dOPMkv+2zfUVvj0V+emRVA9es92f4psPi7v7dfXrjJS5eXeKrYn9wd9n0x0X/8FMKt17spy+WmlXc2r/Pz27iz+2Viw9y8cz3/S2/PVhY6X0v/PWhLh501mS/7fq+uejcJhVrKuzRboiL+/zKD+Wf/L7MF9UQiIiIiAoEIiIiogKBiIiIUIN9CJKKP/LDet5yxlkuPv5B32ZzUfOKTX/80eayIUt/c9J57rmO0337T2GRb3vaxQp8XhO3t+BnLZU8S/YZeO5jf/vR5pBs2c9c7u31rwt9PMQPJ6uhhGuW1fO3Z9XpUeTiZrutqtD2vinxt5G2f6OsbXaLpr+t1dZ3zH4r35T/PcDFPR55K0PK9FJva1x4px+SfMaBw128zXfAdpp9ku+ndsK9fmps3v+4SveXiWoIRERERAUCERERUYFAREREqEV9CJLC1A9d/Oy+fmjI0T85rkLb22VdWZtPo+kVG1p42zbphJD9adk+he38uW83dq2Lk+enZJuRJmRHtewsP/zsG8PKG3Y8e4eeroX1Xfz8w2VTHve//CL3XOPHNQR5bfLlIP9Be8+qLtu1vcKufv09n/qi9PG4tu8mUmf/7ZwcA2HSgh4unnrAPyuewRqgGgIRERFRgUBERERUIBARERFqcR+CpJAyjgBA81FVN5Vl0qr92+dt21K+wo4dXNxkjB/He3inCS5eVeKvjcPvu9rFJ53yhotvbPtO6eObBzzunnuA7WuXlKrVeKGfw+STzT7uu0tdF+/9lp+yeN0KPxX24X39/AQPdJ5Y+njA7/x1Mu1ZP91xybp15WdY8qZ+c/85MKTZFy4eXc76hd2KXLzHE379m1L6DZz2+bHuuU+X+H5M4cOmLi4p9P0bOr2cmL744ex52/3fP3Nx98/nZEiZX6ohEBERERUIRERERAUCERERYQfqQ1CdFg6oWPqCDSpXVaUFd/m5Ct4uejpr+qP+1/cZ6Hy7bwueeZRv/6Nt2cP5m1tWPIOSNwuu8fPOj/rFbS6etamti6/86Y9dvNuk97Ju/+0xe7m4pHNZ2+/Dbx/snuu1IXkvuuxIkn0G+jz+pYtv2XVaxnUX39XdxS1+tsTFa1b7PgSF/Ze7uPj7vr9D0jZ9Bv7L9xkoWbMm6/r5om8yERERUYFAREREVCAQERER1IegSvS6a4GLt9RQPnZU4ZB9XPzS/sMTKfy95ru/PNjFPRN9Bgq7dHLxwDaZ24KHv3aUi3vxdrasSp51OGq+i/euW+Di058+y8U9JlVszvtNXzfM+FzrDqv8gpJy5jCRatXtqpUuPqT/xS7euKufx2LdID+eybh2T+W8r1/e+JiLz2yywsXT+/g+AvXNXysnTRni4sOv8PNkdH/uIxfXVJ+BJNUQiIiIiAoEIiIiogKBiIiIoD4EUgOs0F92q65b6+IWdfyc9dcv2c/FfS773MUlie3NGrybi3/ebGwiB2Xl4D1uWeyeUf+PmrVoVdOsz3d7Ivv93UlbjtzfxScdmvne845NfB+C9RXak+Rb2ODnBzjgEj/mxMQverj413u+WOl9ndZ4WWKJ/+186+JjXDx58p4u7n519rl2Siqds/xSDYGIiIioQCAiIiIqEIiIiAjqQ1AlPrvYt1l3+/X8DCkFoKBTRxdP2ucRFyfb156e48efL2q22sUr/9nGxTP2uSPr9o6ccUbp46bffF1ObqU6HbabH9P92XV+Xou6sxe5eEOij8DSveu5ePwVf3Jx2wI/DsEr68v6q3xzZ5F7rjG6NmqT4m98u/7cC3q5eO/hC11803s/cvGwEv/79/y9/Pgl5zQv61/SMXGddB/jxxXo+Rvff6H7xux9BnYUqiEQERERFQhEREREBQIRERFBfQjS6jAhseCU7OmL69fWu0q/G3q38XOR7zXOtxVe23q6i5Nn4/dLDnRxs7NXlj4uXrsWqT1eX9DNxX/q8KqLm7/+kov3rOvHgG9Rp4GLX1rfysWXTTvDxd0vKeuT0PibKRXLrFSvxNwSJR984uIVh/nkXVmedXOTaJCIf5AxbQ/8nBkh65Z3XKohEBERERUIRERERAUCERERQX0I0mo2bVH5iaTaPNL9uXJS+HJt6jgDAE2vquvikmWfVkW2JA/a3OvbdQfveryLh7Sb6OIPNzVx8W8/8x1+WlxuLi6a6fub+FZpkZ2baghEREREBQIRERFRk0GVaDlD5aqKKJ7/lYtPPPUCF58/cpyLT2nsbztM6jPmYhf3unaGi0t0a+EOo+4LU1284gX//M3snXX9pvipsdUkIJI7fZOJiIiICgQiIiKiAoGIiIigPgRpbZn3pYtP6Lh/hpSRVnw3pr6sLmHLFhfbmx+4+IHeXXyMj5OSw4pqIGkRkYpTDYGIiIioQCAiIiIqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAgqEIiIiAhgIYSazoOIiIjUMNUQiIiIiAoEIiIiogKBiIiIoAKBiIiIoAKBiIiIoAKBiIiIAP8PSVhmuR14kCAAAAAASUVORK5CYII=\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 6 Average loss: 111.8959\n",
            "====> Test set loss: 101.6415\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 7 Average loss: 110.5948\n",
            "====> Test set loss: 101.0912\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "====> Epoch: 8 Average loss: 109.5482\n",
            "====> Test set loss: 99.2361\n"
          ]
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x144 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAB7CAYAAAAL6ZirAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAS40lEQVR4nO3da3Bc9XnH8XPOaldarVZaXSzr5qss340Nxg0oEMDEDJhASloyIW3HIX3ZztC8zEzaJG3aznQynekkTEkTCmmcC9hcEpxLG0NJHAzYxjb4fsGWLFmSLcm6X3f3nL7oxNLvUWLFIMna1ffzSj92tV50jtZ/n+c5z98NgsABAABzm3ej3wAAALjxWBAAAAAWBAAAgAUBAABwWBAAAACHBQEAAHAcJ+daD27xHuWexAz0S3+HO9WvybmQmTgX8FucC/it33cucIUAAACwIAAAAJOUDIA5ydWraW4oJDlIpWby3QDAjOAKAQAAYEEAAABYEAAAAIceAmQCT2v4XjRPsltTKbl3bankvhrz/Ul9+dxeX3Li1IA+f3BUcnChRbI/MKgv6KcdAMg0XCEAAAAsCAAAAAsCAADg0EPwhzP3pjuuWUsFvslM9Lwu436+bk5YHgqVFkvurV8suflBrdl/sf4VybdFz0luT8c0pwolv9xxs+RjL62UvHDnkORgyGRzKgBAJuAKAQAAYEEAAABYEAAAAGcu9xCYnoBQ+TzJJ7+0RPI/3LdT8qVkkeQd/3if5KIXD139OhgZ+cBvM2tdoyfDDetpGRRrjT8d0e/N6dSegx0tGyW3liUk10SuSB4O9PtTvq6TBxZpj0K6TN+P06xzCTCHTNJbZPfBsOe28LX5JEhfXzNKkByd/EnANXCFAAAAsCAAAAAsCAAAgDOnewjMWqg0IfETtx+UvDnaKLklEpH8X2X3Sy7ymUPwQQXJlGT3cqfkxBE9dvFzeiz8V8ok/8bT7KT12AzPy5XcXad1X6dGewh6lxVILjoVlRz09TnIUGbfjFCR9ov4y2ok9y7VmRYDlXpu9tXpueMlxur8XpPuyRHu1X6EvA49T/Pbtacgvve85HS7/p6wpwauF1cIAAAACwIAAMCCAAAAOHO4h8DeH9y3Uuflf6pY5w7km9piw7DWpcsPDkoOUskP+xazm93rIUiPe0hrpX5Pr2R3aFiyZ+4Fn7DKTV+7lhqPag9ArFnrxK13xCVfWaXfX3S0Wv/DsVOa2ddi9rDzR0pLJHc+sFxy8lGdWXFP9bFrvnxxWD8HynK0n6Qq3HX16/Lb9bFfDeieGdvPbpKcej0hOXZBZ6e43T2SgxF6CKaSm6u9Rq45l3w7byYDf++5QgAAAFgQAACAuVQyMJd33IiOq21+SG91Wx/pty8g6RsNmyXnH9EtdtMZeLlo1jA/uyClxyYwt3S6nnvNxyfbj9g1rx9q1cvEIwktGVTWX5Tc0VAlueS43RqbS7c3ipujH3Fe7WLJp/9Oj+1z9f8m+aaIlgpHAi0FntNTx2lKJa75fqpDY5f1h4Nrf/wODeol6qJhPa9DbV2S09lwq/Nk28yPN8Vbznv5+ZI7P71ectk2vfX8/ctaNq79qpYy/TMN+vYyYLQ0VwgAAAALAgAAwIIAAAA4c6mHwPDmlUr+Wv3Lkgs8rd91+VofurxH68YL+pum7s3h2sxI1iAwdcfrrCUG5rZEe5tjvFFfr3qL3t61d2OF5NLtWncOGCE7Yyb0DKyolXzqi1onfr7+W5JXaWvRhN/7gyN6m+LbA/r6YVeP9UdiZyV3+mN//oHBpfLYU2/cI7nue1pzDjc3S/Y7tdclE2rUk7G3gzs2j2d+byfrHbKvHVqotxcPfku///VV2k+S6+q59f3Kcsn/uegRydFz+u/tIAPuROcKAQAAYEEAAABYEAAAAGcO9RC4Zrvipk9p/eiRWKvksKvPHzD1qYW/0LGj1IlvoCme+RAM6wjSwgatzfYmddvaIGq2uI3q4+ksqO3OWnYU8Ty9N/z0X2jN/29vfUFynqn5P9Oro4u/e/42ye2tRZILywYkP7hIRxs3JbVX6bWusfHE7/1grTy2+hXtEUi3XpKcMtuCTzZfIxtM6CmQB81smbA2gNh+kv676iR/9p9+Kvkviy5Itn8H2BkUu7tWS85rM+Pr05l3fLhCAAAAWBAAAAAWBAAAwMnmHgJbWyxOSP6zx38pOd/TepH15Zat+h8On/rdT0TmsXsnmPubw73aU+CbuQcl5WZ75niBvn6vPo6p4+Zo3Xh0eaXk8g1ah7d+2P1Hkp/7nzskF76vz8+r1GNft6JBcmVEZ1Qc6Fsi+eRTa65+XbXrpDyWuqJ7E2Ti9rlTzh+rwwfm52F7BNwK3Q760ub5kj//xC7JjxXqjIhkoP0KPWYGxamkbpN+olPnjyQK9e+QHLNfju35kM+ZWXKsuUIAAABYEAAAABYEAADAyeYeAqPnjsWSH0+8aJ4Rk9SV1ntKm76i9ydHkgem6q1hlkvHtBb4sZJzkptjxZIbolrHxvRxTZ22d5HOgMhxtKbfOKJzCl5v03vTczu1R6B3idZ2azZelHxXyRnJJwb12L+x/RbJ1eP6BtL0DEwQpHTWwoT9Ccbx8nVfirZ7tWdg7TadCVEbuSx5p+nveL7lVsm5Ofpe5ufp7JnBET33Uuu0x6CiZ5HkUHe/ZL9z7Pjb2SdBymx8MEPnBlcIAAAACwIAAMCCAAAAOFncQ+BFtZ4z+rjuHV7smXnz5h7RJ7u09hd9W2uF7FxwA5kZE46r61o3bE5rU4ecrD5nv7/xfj1X/qbkiOSne7QO3eDQQ3CjhAf093g0rfeWr8jTPUvya7R2e+hhreuvjbdIro/p58DOK5skv/F90zPwXa1jp7u1pwGTGL9HjN27oCguueejOjdgTYEe6xc6tUfgjZ+slxwx40KSd+ux2rhM9zq4rVrfz967tCfh9NJCyUWnzT4YjWM9D9EW7S9wzzRK9ge1p226cIUAAACwIAAAACwIAACAk009BLa+tGSB5L+ufVWy5+jzu/whyc8/u1lyVf++D/sO8UHZfSlKdY97pyQhMcjPlex1anEw3ab3I9sZ46Fq7QH46D1HJdt9L/b36v3G7vCogxli9p2I9Oi94565lzwe0t/zrbl6bD8Zf09yMtB/Mx0eqZH81n9oz0DVD97Vtzcw8LveNaZCSo99UZHW2ctydG7Am8NLJftm+5rBau0l+vLaX0iuyOmWHIvr7/mmwvOSjy7Wc+XXS/XPb+wam6Ow4GXth4idNX1SM4QrBAAAgAUBAABgQQAAAJws6iFwI1oQOv+npZK35DdI9h2dU7CzT/cqWPCcPj+VZvLAjDE9AznVVZIvPKY1+4EFemwSJ3SdW75fcyipcwiCAp2Jfv4z2kOwtfAdye+MaO3wwK61khd1HHRwY0R69Nicb9bPgVCt1onnhbR/JN/VuQXHk5q/9JtHJK/acVwyPQPTyMwLCfr13v3uJq3ZV6/WmRKfr9oj+a2HdU7BTflNktfn6r4Vvuk7i3v6ueNFGyQP+trLdCxWIbnvUsHVr6Ot2ttyo/a14AoBAABgQQAAAFgQAAAAJ5N7CEyd2Vuscwe+8JmXJZeFtGcgGWj9519e/YTk5R2H9c9jr/LpNe54hsrnyUNn/mqh5GW3NUhuHyiQ3DOodeNInz6eV67nQsdNuq/5Q3+yV/KW2EnJ32y/W/KiH+s+Gf6o2SsB08fTf9N4g9pDEGnTY38xWSx5daRTv9/sUtKeTkguPqDnSrpX69iYOX6/9mtU79bHv7lGZ8lsSDRLzg/pudKW0r0G7MyKmKvP7/P193xX7wbJPzyieyfUPK/nzupDYz0K6fYOecwfvTGzTLhCAAAAWBAAAAAWBAAAwMngHgIvX+8dP/u41p0/Gz8nOezqnvYnzL3oK76te1/7SZ2BjukVio/N8u68r1YeW1mvM8ITEZ1ZfuqQ9hhUv6V14NxOPdYd67SH4OOP6j4Vf1++X/KhET13frpno76/zgbJeme7M6HfRdCbcn3sniURrcsmy/RzwWxF4Bzq1xkW1WG9V31FWHsKKkK6D8ZQufnzPc3BhIOP6RKk9DM6tuuQPr6vTPLB6DLJycqE5It36+fC7Q/qvhZbio9J/tqxrZJLn4lJXnnggmTbJ5BKzb6/Y7hCAAAAWBAAAAAWBAAAwMmkHgJPZ4o7tTp34LEHfi056ureBnbuwLZ3Pye54qzWeygGTi83R089tyRx9esra/S5Czytte3du1ry8u9pndfr1OyXFkrurdMZ43fGT0tuSY1I/sKpbZJLjpi6cUL3Mg8N6f3LwfDY69m6pxXYPTNcs2a35+Uc60Hwolrn9Zfo/PquZdrv4Zof18/2bZD82vw6yU/dsl3yurD2qzhr+/T1zR4qkx1fTJ8gqffupy62XPP5oUY9dpXhdZLjfzws+cSw7qlS8KL+3sf26udI6or2p2TC7ypXCAAAAAsCAADAggAAADgZ1EPgmfuN2+4skfzpogPmO7RO3JzSum7ecwnJQVLnFmCamdp4MO74+nlaazvWVim58Iy5FzypdXe/WOfXt34sIXnNLXqsz47Ml/z197dI7t2jj8dHtTDds87snbBQZ6JHusZ6CHJata4Y2JnlZh8EW5P2B0xN2/TGZIVxswa8Aj2WzqJqiU0P6M96aL4em+glPc/yL2ovUv+AqQNv1ONR6GlPQu08vZc8HTK9TcgYQUp/1/prtKdga9G7ko8Oa99avFF7jXy7r0UG9AxYXCEAAAAsCAAAAAsCAADgZFIPQZnWaXMe0FpeVUjrNSOB1l5/3L9WcvG7Wsv1mTsws8zP2x23d0SkS9ep81frvd+NG/Re9CCk50b3Wj32D23SvQlSgdZ9v/3f90qu3Kvn0rwhrTX2LNV+lt46c+6Ump6GwbE6dOl+U4ds1vea2649AqFO/X93zJwC24OQDffBj581kFqv+1pcuN8c+2Vat3WTemxHktpLlDOo51ZosX5/VUh/nr6jr3fmku6ZsmT0ioMMZfqY+h7W37UNud2Sz4xWSA5f1uenTU9CJuIKAQAAYEEAAABYEAAAAGc29xCYvQu667X2+pWVz+rTzT7pHb7WAn/UeKvk0m6t/wR+5t0zmsnszzsYHJsTkdeuz23uSEi+efV5yUUbdOb4wqjWdcOu1t2fefVuybUv6IyKcHOnZL9I74XvXKMzMJauuyg5mdZzN+SN9RicH9WZCsmY9iPM79Mc8sya3dd+haw4b83vrldRfvXrs5/Tj6hP3qz9IKO+Pn70iv58m/q15t93i34u/OvNL0muzDEzLFLaY1D0c93zfsIcCWQMO9vm44tPSR42cwSePlsvuaK1VV8wA+cOWFwhAAAALAgAAMAsLhnYyzkt9+pl3/URve0w7OjYyQFzKbVnX7nkkhG9PIQZ5ptb87p7rn5d+boe24LWYsnv1S+THFmi5Z9f9S+XnHtObz1b8aNLkoOLbZLTZnywa7Yxrdmt6+imkJazhir0sn6kZ+z5Bbozs1O5V9+71z2g762rR7O9rdDPwtHF426tzCvS8bCbC49LLvS0XHSvKe801Wh5Z3PspORVYf2cSZqrvv98+R7J83brNumpLLhMPFe5efq5EA3p71qfb8ZcH9dzKRhtnJ43dgNxhQAAALAgAAAALAgAAIAzi3sI3Fi+5AWLta4cMbcqJR2tpZ5Lab2n7D0z8rVfa7V2lG423EKSScbfvuW/r7W5eKveh1h4uFC/2d6KZ+ru/pDWmSeMGJ3kWAdJvbXMPXZW8sKLugWvU6zvL8gbq1N77d362LDWyCeMIh4xj6ezsGfAGtf/kz6jPQF9N+no4k25lyXnRcwWtFHtD8n3tGfA+smA9qu8+aS5XblNb3tE9hhIaU9BQ0rPhaLT+vxsGBNucYUAAACwIAAAACwIAACAM4t7COw400v7devJPUt0RGnY1XrOE7v/XPLqfc2SU6PXV0fGNBv387d187TJTpfOBZhptqcg3W5mLXdov8t4EzbZ5ryb8DMYP5Oi9EiNPPbsR3R8bN1S7RGoy9Hf66Sjr/2/Q9qT8J3WOyW3PKkzLkpfOqhvNQvrxnNWrvYMDJn+nL609quMFurfSU5I5xQ4WXBucIUAAACwIAAAACwIAACAM4t7CNIdugXtkq++I/npr98sOUhrdXbFkNb+UllQ30GGoC/gQ/EHBq9+XfzaOXlssHeR5G2bnpA8XKU9BNFGnTtQflgfjx3WravjrTpnIMjGvSLw/+K6lfWGuO5vszKi/Sl9tXouVOXoX5+29ykTcYUAAACwIAAAACwIAACAM4t7CKwJ9353j/6eZwLIaOPq9ulLuldB7s905sPCn1/nv2lMTwCdRXNX2xadbVMV1vkmbWndkyS/2cwd8My5Z2bnZGIvEVcIAAAACwIAAMCCAAAAOBnUQwAAE+qyAXMC8AfytAfAD2vNf0f7rZLfPrlU8urtDZJTfX1T995mCa4QAAAAFgQAAIAFAQAAcOghAADMBWYGxfxvvCm5+99134vl6UOSU3NgXwuuEAAAABYEAACABQEAAHAcxw0ycN4yAACYWlwhAAAALAgAAAALAgAA4LAgAAAADgsCAADgsCAAAACO4/wfYU6v7MCYXZkAAAAASUVORK5CYII=\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Training and testing the VAE\n",
        "codes = dict(mu=list(), logvar=list(), y=list())\n",
        "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
        "model = VAE().to(device)\n",
        "optimizer = torch.optim.Adam(\n",
        "    model.parameters(),\n",
        "    lr=learning_rate,\n",
        ")\n",
        "\n",
        "\n",
        "def train_and_test(model):\n",
        "    for epoch in range(0, epochs + 1):\n",
        "        # Training\n",
        "        if epoch > 0:  # test untrained net first\n",
        "            model.train()\n",
        "            train_loss = 0\n",
        "            for x, _ in train_loader:\n",
        "                x = x.to(device)\n",
        "                # ===================forward=====================\n",
        "                x_hat, mu, logvar = model(x)\n",
        "                loss = loss_function(x_hat, x, mu, logvar, beta)\n",
        "                train_loss += loss.item()\n",
        "                # ===================backward====================\n",
        "                optimizer.zero_grad()\n",
        "                loss.backward()\n",
        "                optimizer.step()\n",
        "            # ===================log========================\n",
        "            print(f\"====> Epoch: {epoch} Average loss: {train_loss / len(train_loader.dataset):.4f}\")\n",
        "\n",
        "        # Testing\n",
        "        means, logvars, labels = list(), list(), list()\n",
        "        with torch.no_grad():\n",
        "            model.eval()\n",
        "            test_loss = 0\n",
        "            for x, y in test_loader:\n",
        "                x = x.to(device)\n",
        "                # ===================forward=====================\n",
        "                x_hat, mu, logvar = model(x)\n",
        "                test_loss += loss_function(x_hat, x, mu, logvar, beta).item()\n",
        "                # =====================log=======================\n",
        "                means.append(mu.detach())\n",
        "                logvars.append(logvar.detach())\n",
        "                labels.append(y.detach())\n",
        "        # ===================log========================\n",
        "        codes[\"mu\"].append(torch.cat(means))\n",
        "        codes[\"logvar\"].append(torch.cat(logvars))\n",
        "        codes[\"y\"].append(torch.cat(labels))\n",
        "        test_loss /= len(test_loader.dataset)\n",
        "        print(f\"====> Test set loss: {test_loss:.4f}\")\n",
        "        display_images(x, x_hat, 1, f\"Epoch {epoch}\")\n",
        "\n",
        "\n",
        "train_and_test(model)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "690c045b-f07c-4e63-a608-58abcab5cb88",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "55c262f8-927b-4fa2-a144-902d93cec844",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Generating few samples with randomly sampled vectors"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "84fb2ab9-1619-4b11-97f8-1bd8dab6d5d2",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#00E3FF",
          "id": "38bb92df-0247-47ce-bc3b-57ffbd90a436",
          "isComponent": true,
          "name": "Generate few samples",
          "parents": [
            {
              "id": "73fb295b-17e9-4ca6-a42f-02720231688c",
              "name": "Train VAE"
            }
          ]
        },
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Generating a few samples\n",
        "N = 16\n",
        "z = torch.randn((N, d)).to(device)\n",
        "sample = model.decoder(z)\n",
        "display_images(None, sample, N // 4, count=True)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cf2ad8fa-ae8c-4d5d-aa2a-fdbe84186eaa",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "none",
          "id": "9609e541-cef9-423a-a362-6ccb80d11989",
          "isComponent": false,
          "name": "",
          "parents": []
        }
      },
      "source": ["### Visualize with interpolation"]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "453833c6-d3a5-4f96-91d7-10aa02c2e6d7",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#00E3FF",
          "id": "1c15b12d-e85a-4342-876e-80103630540d",
          "isComponent": true,
          "name": "Interpolation start-end point",
          "parents": [
            {
              "id": "73fb295b-17e9-4ca6-a42f-02720231688c",
              "name": "Train VAE"
            }
          ]
        },
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Choose starting and ending point for the interpolation -> shows original and reconstructed\n",
        "x, _ = next(iter(train_loader))\n",
        "_, mu, _ = model(x.to(device))\n",
        "mu = mu.detach().requires_grad_(False)\n",
        "\n",
        "A, B = 0, -1\n",
        "sample = model.decoder(torch.stack((mu[A].data, mu[B].data), 0)).detach()\n",
        "display_images(None, torch.stack(((x[A].data.view(-1), x[B].data.view(-1), sample.data[0], sample.data[1])), 0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c5c377d1-936e-4242-87af-d1cbf4284f29",
      "metadata": {
        "canvas": {
          "comments": [],
          "componentType": "CodeCell",
          "copiedOriginId": null,
          "diskcache": false,
          "headerColor": "#00E3FF",
          "id": "c8c3d975-8f3a-4563-aec3-011fef22b19a",
          "isComponent": true,
          "name": "Visualize interpolation",
          "parents": [
            {
              "id": "1c15b12d-e85a-4342-876e-80103630540d",
              "name": "Interpolation start-end point"
            }
          ]
        },
        "tags": []
      },
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": "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\n",
            "text/plain": ["<Figure size 648x216 with 4 Axes>"]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Perform an interpolation between input A and B, in N steps\n",
        "N = 16\n",
        "code = torch.Tensor(N, 20).to(device)\n",
        "sample = torch.Tensor(N, 28, 28).to(device)\n",
        "for i in range(N):\n",
        "    code[i] = i / (N - 1) * mu[B].data + (1 - i / (N - 1)) * mu[A].data\n",
        "sample = model.decoder(code)\n",
        "display_images(None, sample, N // 4, count=True)"
      ]
    }
  ],
  "metadata": {
    "canvas": {
      "parameters": [
        {
          "name": "batch_size",
          "type": "int",
          "value": "256"
        },
        {
          "name": "d",
          "type": "int",
          "value": "20"
        },
        {
          "name": "epochs",
          "type": "int",
          "value": "8"
        },
        {
          "name": "beta",
          "type": "float",
          "value": "1.0"
        },
        {
          "name": "learning_rate",
          "type": "float",
          "value": "1e-3"
        }
      ],
      "version": "1.0"
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.10"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}