pytorch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-05-18T02:51:00.914429Z",
     "start_time": "2024-05-18T02:50:58.639637Z"
    }
   },
   "source": "import torch",
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T02:51:00.930472Z",
     "start_time": "2024-05-18T02:51:00.916432Z"
    }
   },
   "cell_type": "code",
   "source": "torch.__version__",
   "id": "be97bb0e5081b02",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.3.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:05:06.836324Z",
     "start_time": "2024-05-18T03:05:06.827742Z"
    }
   },
   "cell_type": "code",
   "source": "device = 'cuda' if torch.cuda.is_available() else 'cpu'",
   "id": "2ec6e4669082ba4",
   "outputs": [],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:05:10.673766Z",
     "start_time": "2024-05-18T03:05:10.661266Z"
    }
   },
   "cell_type": "code",
   "source": "x = torch.rand(5, 3).to(device)",
   "id": "6d4d2ca8914c9e4b",
   "outputs": [],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:05:17.931581Z",
     "start_time": "2024-05-18T03:05:17.908063Z"
    }
   },
   "cell_type": "code",
   "source": "x",
   "id": "eead2703e2d31727",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.9843, 0.7592, 0.2892],\n",
       "        [0.6643, 0.8915, 0.3509],\n",
       "        [0.1993, 0.0820, 0.1898],\n",
       "        [0.3453, 0.1750, 0.6430],\n",
       "        [0.9031, 0.2291, 0.1446]], device='cuda:0')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# K-Means",
   "id": "df87b33d96829eea"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:14:10.166432Z",
     "start_time": "2024-05-18T03:14:09.500647Z"
    }
   },
   "cell_type": "code",
   "source": "import matplotlib.pyplot as plt",
   "id": "3da87f52095385c1",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:42:00.807482Z",
     "start_time": "2024-05-18T06:42:00.793359Z"
    }
   },
   "cell_type": "code",
   "source": [
    "N = 100\n",
    "x1 = torch.randn(N, 2)\n",
    "x2 = torch.randn(N, 2) + torch.Tensor([3, 3])\n",
    "x3 = torch.randn(N, 2) + torch.Tensor([-3, 3])"
   ],
   "id": "7725c65406bb2966",
   "outputs": [],
   "execution_count": 178
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:42:01.286329Z",
     "start_time": "2024-05-18T06:42:01.270768Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X = torch.cat([x1, x2, x3], dim=0)\n",
    "print(X.shape)"
   ],
   "id": "722661e33f6607e3",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([300, 2])\n"
     ]
    }
   ],
   "execution_count": 179
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:42:05.251091Z",
     "start_time": "2024-05-18T06:42:05.096697Z"
    }
   },
   "cell_type": "code",
   "source": [
    "for i in range(3):\n",
    "    plt.scatter(X[i*N:(i+1)*N, 0], X[i*N:(i+1)*N, 1])\n",
    "plt.show()"
   ],
   "id": "417618b8a69ad095",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 180
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:41:36.062263Z",
     "start_time": "2024-05-18T03:41:34.883192Z"
    }
   },
   "cell_type": "code",
   "source": [
    "K = 3\n",
    "centroids = X[torch.randperm(len(X))[:K]]\n",
    "while True:\n",
    "    D = torch.cdist(X, centroids)\n",
    "    clusters = torch.argmin(D, dim=1)\n",
    "    for i in range(3):\n",
    "        plt.scatter(X[i*N:(i+1)*N, 0], X[i*N:(i+1)*N, 1])\n",
    "    old_centroids = centroids.clone()\n",
    "    for k in range(K):\n",
    "        plt.scatter(centroids[k, 0], centroids[k, 1], marker='x')\n",
    "        centroids[k] = X[clusters == k].mean(dim=0)\n",
    "    change = torch.sum((centroids - old_centroids) ** 2)\n",
    "    if change < 0.1:\n",
    "        break\n",
    "    plt.show()"
   ],
   "id": "82126519ae745d21",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 40
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T03:47:48.200063Z",
     "start_time": "2024-05-18T03:47:47.779541Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import time\n",
    "device = 'cuda'\n",
    "\n",
    "N = 100000\n",
    "x1 = torch.randn(N, 2)\n",
    "x2 = torch.randn(N, 2) + torch.Tensor([3, 3])\n",
    "x3 = torch.randn(N, 2) + torch.Tensor([-3, 3])\n",
    "X = torch.cat([x1, x2, x3], dim=0).to(device)\n",
    "\n",
    "t1 = time.time()\n",
    "K = 3\n",
    "centroids = X[torch.randperm(len(X))[:K]]\n",
    "for _ in range(100):\n",
    "    D = torch.cdist(X, centroids)\n",
    "    clusters = torch.argmin(D, dim=1)\n",
    "    for k in range(K):\n",
    "        centroids[k] = X[clusters == k].mean(dim=0)\n",
    "print(time.time() - t1)"
   ],
   "id": "53ceb59e45191567",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.35938453674316406\n"
     ]
    }
   ],
   "execution_count": 59
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Auto differentiation",
   "id": "665e1d1a31fcd578"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:01:30.179004Z",
     "start_time": "2024-05-18T04:01:30.157015Z"
    }
   },
   "cell_type": "code",
   "source": [
    "x = torch.tensor(3., requires_grad=True)\n",
    "y = x**2 + 2*x + 1 \n",
    "# y' = 2x + 2\n",
    "y.backward()"
   ],
   "id": "1e5c7e5a52542ce6",
   "outputs": [],
   "execution_count": 62
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:01:46.381056Z",
     "start_time": "2024-05-18T04:01:46.361172Z"
    }
   },
   "cell_type": "code",
   "source": "x.grad # 2(3) + 2",
   "id": "3166146d2351ce23",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(8.)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 65
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Regression",
   "id": "ea5ad1d8094dff47"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:06:12.430627Z",
     "start_time": "2024-05-18T04:06:12.279530Z"
    }
   },
   "cell_type": "code",
   "source": [
    "N = 100\n",
    "x = torch.rand(N, 1)\n",
    "y = torch.sin(3 * x + 1) + 0.5 * torch.rand(N, 1)\n",
    "plt.scatter(x, y)"
   ],
   "id": "8edd69794556a53c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x17cb50762b0>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 66
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:11:39.365043Z",
     "start_time": "2024-05-18T04:11:39.352645Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ones = torch.ones(N, 1)\n",
    "X = torch.cat([x, ones], dim=1)"
   ],
   "id": "227b2991ea8bd9bd",
   "outputs": [],
   "execution_count": 68
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:13:12.867982Z",
     "start_time": "2024-05-18T04:13:12.858221Z"
    }
   },
   "cell_type": "code",
   "source": "R = torch.inverse(X.T @ X) @ X.T @ y",
   "id": "6cf9337b3c2f2fb1",
   "outputs": [],
   "execution_count": 74
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:13:57.610104Z",
     "start_time": "2024-05-18T04:13:57.604105Z"
    }
   },
   "cell_type": "code",
   "source": "x_ = torch.linspace(0, 1, 100).reshape(-1, 1)",
   "id": "e13305e1e77863a8",
   "outputs": [],
   "execution_count": 76
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:15:03.330935Z",
     "start_time": "2024-05-18T04:15:03.314421Z"
    }
   },
   "cell_type": "code",
   "source": "y_ = x_ * R[0] + R[1]",
   "id": "a8c85031aa752678",
   "outputs": [],
   "execution_count": 82
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:15:41.594463Z",
     "start_time": "2024-05-18T04:15:41.465377Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.scatter(x, y)\n",
    "plt.scatter(x_, y_, color='r')\n",
    "plt.show()"
   ],
   "id": "2a7804e1e0a6ad01",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 83
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "nonlinear",
   "id": "d315078521de2f9b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:17:30.783470Z",
     "start_time": "2024-05-18T04:17:30.777308Z"
    }
   },
   "cell_type": "code",
   "source": [
    "ones = torch.ones(N, 1)\n",
    "X = torch.cat([x**2, x, ones], dim=1)"
   ],
   "id": "77f555713a9f006",
   "outputs": [],
   "execution_count": 84
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:17:50.331152Z",
     "start_time": "2024-05-18T04:17:50.324571Z"
    }
   },
   "cell_type": "code",
   "source": "R = torch.inverse(X.T @ X) @ X.T @ y",
   "id": "e9b38034a6884f73",
   "outputs": [],
   "execution_count": 86
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:18:45.053175Z",
     "start_time": "2024-05-18T04:18:45.038933Z"
    }
   },
   "cell_type": "code",
   "source": "y_ = x_**2 * R[0] + x_ * R[1] + R[2]",
   "id": "4a3103cd28cab953",
   "outputs": [],
   "execution_count": 88
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:18:51.743594Z",
     "start_time": "2024-05-18T04:18:51.593916Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.scatter(x, y)\n",
    "plt.scatter(x_, y_, color='r')\n",
    "plt.show()"
   ],
   "id": "715bd90e2b22fba5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 89
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T04:31:57.006587Z",
     "start_time": "2024-05-18T04:31:54.194587Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device = 'cpu'\n",
    "\n",
    "N = 100000000\n",
    "x = torch.rand(N, 1).to(device)\n",
    "y = torch.sin(3 * x + 1) + 0.5 * torch.rand(N, 1).to(device)\n",
    "\n",
    "t1 = time.time()\n",
    "degree = 1\n",
    "ones = torch.ones(N, 1).to(device)\n",
    "X = torch.cat([x, ones], dim=1)\n",
    "for i in range(2, degree + 1):\n",
    "    X = torch.cat([x**i, X], dim=1)\n",
    "R = torch.inverse(X.T @ X) @ X.T @ y\n",
    "print(time.time() - t1)"
   ],
   "id": "efc9e188c66e967",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.726722240447998\n"
     ]
    }
   ],
   "execution_count": 134
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# MLP",
   "id": "2203c236fc396e6b"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:02:08.111550Z",
     "start_time": "2024-05-18T06:02:08.102037Z"
    }
   },
   "cell_type": "code",
   "source": "from torch import nn",
   "id": "f7e25fcc705cad8",
   "outputs": [],
   "execution_count": 135
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:10:46.017552Z",
     "start_time": "2024-05-18T06:10:46.003578Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# [1] 32 16 [1]\n",
    "class Regressor(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(1, 32)\n",
    "        self.fc2 = nn.Linear(32, 16)\n",
    "        self.fc3 = nn.Linear(16, 1)\n",
    "    def forward(self, x):\n",
    "        x = torch.sigmoid(self.fc1(x))\n",
    "        x = torch.sigmoid(self.fc2(x))\n",
    "        return self.fc3(x)"
   ],
   "id": "a69b8497563b6694",
   "outputs": [],
   "execution_count": 136
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:14:07.567398Z",
     "start_time": "2024-05-18T06:14:07.556187Z"
    }
   },
   "cell_type": "code",
   "source": "(1*32+32) + (32*16+16) + (16*1+1)",
   "id": "bebebcfd80cc28fb",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "609"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 140
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:14:20.468478Z",
     "start_time": "2024-05-18T06:14:20.448450Z"
    }
   },
   "cell_type": "code",
   "source": "model = Regressor()",
   "id": "2476059a2d85c276",
   "outputs": [],
   "execution_count": 141
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:15:23.443822Z",
     "start_time": "2024-05-18T06:15:23.436664Z"
    }
   },
   "cell_type": "code",
   "source": "gen = iter(model.parameters())",
   "id": "6d596bb872ef5e3",
   "outputs": [],
   "execution_count": 146
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:16:02.718003Z",
     "start_time": "2024-05-18T06:16:02.707772Z"
    }
   },
   "cell_type": "code",
   "source": "next(gen).shape",
   "id": "b8610e63c4074c91",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 152
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:28:52.750879Z",
     "start_time": "2024-05-18T06:28:52.614791Z"
    }
   },
   "cell_type": "code",
   "source": [
    "N = 1000\n",
    "x = torch.rand(N, 1).to(device)\n",
    "y = torch.sin(3 * x + 1) + 0.5 * torch.rand(N, 1).to(device)"
   ],
   "id": "62fed73ddee762e3",
   "outputs": [],
   "execution_count": 155
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:39:24.963513Z",
     "start_time": "2024-05-18T06:39:12.967417Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device = 'cuda' \n",
    "\n",
    "model = model.to(device)\n",
    "\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n",
    "\n",
    "model.train()\n",
    "for epoch in range(5000):\n",
    "    y_ = model(x.to(device))\n",
    "    loss = criterion(y_, y.to(device))\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 100 == 0:\n",
    "        print(f'{epoch}: {loss.item()}')"
   ],
   "id": "71fc4ce868c29a26",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: 0.021910324692726135\n",
      "100: 0.02190151810646057\n",
      "200: 0.021893003955483437\n",
      "300: 0.02188478223979473\n",
      "400: 0.021876834332942963\n",
      "500: 0.021869158372282982\n",
      "600: 0.021861745044589043\n",
      "700: 0.02185457944869995\n",
      "800: 0.02184765413403511\n",
      "900: 0.02184097096323967\n",
      "1000: 0.02183450758457184\n",
      "1100: 0.021828267723321915\n",
      "1200: 0.021822236478328705\n",
      "1300: 0.021816406399011612\n",
      "1400: 0.02181076817214489\n",
      "1500: 0.02180532179772854\n",
      "1600: 0.021800054237246513\n",
      "1700: 0.021794956177473068\n",
      "1800: 0.021790029481053352\n",
      "1900: 0.021785257384181023\n",
      "2000: 0.02178063616156578\n",
      "2100: 0.021776162087917328\n",
      "2200: 0.021771827712655067\n",
      "2300: 0.0217676293104887\n",
      "2400: 0.021763557568192482\n",
      "2500: 0.021759605035185814\n",
      "2600: 0.021755769848823547\n",
      "2700: 0.021752052009105682\n",
      "2800: 0.021748436614871025\n",
      "2900: 0.021744923666119576\n",
      "3000: 0.021741509437561035\n",
      "3100: 0.02173818275332451\n",
      "3200: 0.021734952926635742\n",
      "3300: 0.021731801331043243\n",
      "3400: 0.02172873169183731\n",
      "3500: 0.021725740283727646\n",
      "3600: 0.02172281965613365\n",
      "3700: 0.021719971671700478\n",
      "3800: 0.021717185154557228\n",
      "3900: 0.0217144638299942\n",
      "4000: 0.021711798384785652\n",
      "4100: 0.02170919068157673\n",
      "4200: 0.021706636995077133\n",
      "4300: 0.021704133599996567\n",
      "4400: 0.02170168049633503\n",
      "4500: 0.021699272096157074\n",
      "4600: 0.0216969046741724\n",
      "4700: 0.02169458195567131\n",
      "4800: 0.021692300215363503\n",
      "4900: 0.02169005386531353\n"
     ]
    }
   ],
   "execution_count": 174
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:40:42.269091Z",
     "start_time": "2024-05-18T06:40:42.115146Z"
    }
   },
   "cell_type": "code",
   "source": [
    "x_ = torch.linspace(0, 1, 100).reshape(-1, 1)\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_ = model(x_.to(device))\n",
    "plt.scatter(x, y)\n",
    "plt.scatter(x_, y_.cpu(), color='r')\n",
    "plt.show()"
   ],
   "id": "159cfd4a048dd87",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 177
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Classification",
   "id": "eff0182fc54b2c37"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:42:52.051321Z",
     "start_time": "2024-05-18T06:42:52.034277Z"
    }
   },
   "cell_type": "code",
   "source": "N",
   "id": "6b926bf4bdb01744",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 182
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:42:18.590726Z",
     "start_time": "2024-05-18T06:42:18.573786Z"
    }
   },
   "cell_type": "code",
   "source": "X.shape",
   "id": "1015b382e0345b4e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([300, 2])"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 181
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:43:06.436975Z",
     "start_time": "2024-05-18T06:43:06.423940Z"
    }
   },
   "cell_type": "code",
   "source": "Y = torch.cat([torch.zeros(N), torch.ones(N), torch.ones(N) * 2]).long()",
   "id": "5bfb56eccde99e16",
   "outputs": [],
   "execution_count": 183
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:43:08.043258Z",
     "start_time": "2024-05-18T06:43:08.032764Z"
    }
   },
   "cell_type": "code",
   "source": "Y",
   "id": "3e2ddbae6acc1904",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 184
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:45:06.063783Z",
     "start_time": "2024-05-18T06:45:06.053272Z"
    }
   },
   "cell_type": "code",
   "source": "X.shape[1]",
   "id": "fc110dece76492f6",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 185
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:45:27.248695Z",
     "start_time": "2024-05-18T06:45:27.241177Z"
    }
   },
   "cell_type": "code",
   "source": "len(Y.unique())",
   "id": "48d64afbd1217c79",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 187
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:52:22.870589Z",
     "start_time": "2024-05-18T06:52:22.857533Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# [2] 32 16 [3]\n",
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(2, 32)\n",
    "        self.fc2 = nn.Linear(32, 16)\n",
    "        self.fc3 = nn.Linear(16, 3)\n",
    "    def forward(self, x):\n",
    "        x = torch.sigmoid(self.fc1(x))\n",
    "        x = torch.sigmoid(self.fc2(x))\n",
    "        return torch.sigmoid(self.fc3(x))"
   ],
   "id": "943124dcb7812b70",
   "outputs": [],
   "execution_count": 188
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:54:07.313677Z",
     "start_time": "2024-05-18T06:54:07.299214Z"
    }
   },
   "cell_type": "code",
   "source": "model = Classifier()",
   "id": "b8923d99a94fba40",
   "outputs": [],
   "execution_count": 190
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:54:39.435921Z",
     "start_time": "2024-05-18T06:54:27.233812Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "\n",
    "model = model.to(device)\n",
    "\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)\n",
    "\n",
    "model.train()\n",
    "for epoch in range(5000):\n",
    "    y_ = model(X.to(device))\n",
    "    loss = criterion(y_, Y.to(device))\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 100 == 0:\n",
    "        print(f'{epoch}: {loss.item()}')"
   ],
   "id": "3e11357108aefcaa",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: 0.5961902141571045\n",
      "100: 0.5957861542701721\n",
      "200: 0.5953940749168396\n",
      "300: 0.5950131416320801\n",
      "400: 0.5946427583694458\n",
      "500: 0.5942821502685547\n",
      "600: 0.5939308404922485\n",
      "700: 0.5935882925987244\n",
      "800: 0.5932542681694031\n",
      "900: 0.5929282307624817\n",
      "1000: 0.592609703540802\n",
      "1100: 0.5922985076904297\n",
      "1200: 0.5919941067695618\n",
      "1300: 0.5916964411735535\n",
      "1400: 0.5914053916931152\n",
      "1500: 0.591120183467865\n",
      "1600: 0.5908411741256714\n",
      "1700: 0.5905678272247314\n",
      "1800: 0.5903000235557556\n",
      "1900: 0.5900377631187439\n",
      "2000: 0.5897807478904724\n",
      "2100: 0.5895287990570068\n",
      "2200: 0.5892817974090576\n",
      "2300: 0.5890397429466248\n",
      "2400: 0.5888022780418396\n",
      "2500: 0.5885694622993469\n",
      "2600: 0.5883411169052124\n",
      "2700: 0.588117241859436\n",
      "2800: 0.5878977179527283\n",
      "2900: 0.5876822471618652\n",
      "3000: 0.587471067905426\n",
      "3100: 0.5872639417648315\n",
      "3200: 0.587060809135437\n",
      "3300: 0.5868615508079529\n",
      "3400: 0.5866661071777344\n",
      "3500: 0.5864744782447815\n",
      "3600: 0.5862865447998047\n",
      "3700: 0.586102306842804\n",
      "3800: 0.5859214663505554\n",
      "3900: 0.5857442617416382\n",
      "4000: 0.5855706334114075\n",
      "4100: 0.5854002237319946\n",
      "4200: 0.5852330327033997\n",
      "4300: 0.5850693583488464\n",
      "4400: 0.5849087834358215\n",
      "4500: 0.5847513675689697\n",
      "4600: 0.5845970511436462\n",
      "4700: 0.5844457149505615\n",
      "4800: 0.5842972993850708\n",
      "4900: 0.5841518640518188\n"
     ]
    }
   ],
   "execution_count": 192
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:56:44.077754Z",
     "start_time": "2024-05-18T06:56:44.057216Z"
    }
   },
   "cell_type": "code",
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_ = model(X.to(device))\n",
    "acc = torch.sum(Y == y_.argmax(dim=1).cpu()) / len(Y)\n",
    "print(acc.item())"
   ],
   "id": "be3bc0471fa412bf",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9733333587646484\n"
     ]
    }
   ],
   "execution_count": 195
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:58:56.458213Z",
     "start_time": "2024-05-18T06:58:56.438590Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.datasets import load_iris\n",
    "import numpy as np\n",
    "df = load_iris(as_frame=True)"
   ],
   "id": "22e03210e086c272",
   "outputs": [],
   "execution_count": 200
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T06:59:52.936402Z",
     "start_time": "2024-05-18T06:59:52.922373Z"
    }
   },
   "cell_type": "code",
   "source": [
    "itrain = np.r_[0:25, 50:75, 100:125]\n",
    "itest = np.r_[25:50, 75:100, 125:150]\n",
    "xtrain = df['data'].iloc[itrain].values\n",
    "xtest = df['data'].iloc[itest].values\n",
    "ytrain = df['target'].iloc[itrain].values\n",
    "ytest = df['target'].iloc[itest].values"
   ],
   "id": "5daa8f02316fd4db",
   "outputs": [],
   "execution_count": 201
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:04:09.517298Z",
     "start_time": "2024-05-18T07:04:09.500230Z"
    }
   },
   "cell_type": "code",
   "source": "xtrain.shape",
   "id": "29636fd574cb64a1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(75, 4)"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 203
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:14:33.129423Z",
     "start_time": "2024-05-18T07:14:33.117879Z"
    }
   },
   "cell_type": "code",
   "source": "len(np.unique(ytrain))",
   "id": "fccbd2c04fb315cd",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 204
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:44:14.822704Z",
     "start_time": "2024-05-18T07:44:14.809695Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# [4] 128 [3]\n",
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(4, 128)\n",
    "        self.fc2 = nn.Linear(128, 3)\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.fc1(x))\n",
    "        return torch.softmax(self.fc2(x), dim=1)"
   ],
   "id": "a5adbcaeb19cb667",
   "outputs": [],
   "execution_count": 285
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:35:59.180658Z",
     "start_time": "2024-05-18T07:35:59.175372Z"
    }
   },
   "cell_type": "code",
   "source": "xtrain_ = torch.tensor(xtrain, dtype=torch.float32)",
   "id": "80fb5ed5e7016d14",
   "outputs": [],
   "execution_count": 250
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:35:59.508073Z",
     "start_time": "2024-05-18T07:35:59.501553Z"
    }
   },
   "cell_type": "code",
   "source": "xtest_ = torch.tensor(xtest, dtype=torch.float32)",
   "id": "e6bbfa4619e44e38",
   "outputs": [],
   "execution_count": 251
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:35:59.805194Z",
     "start_time": "2024-05-18T07:35:59.793609Z"
    }
   },
   "cell_type": "code",
   "source": "ytrain_ = torch.tensor(ytrain, dtype=torch.long)",
   "id": "bf6cb7b1d5824bf",
   "outputs": [],
   "execution_count": 252
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:36:00.131263Z",
     "start_time": "2024-05-18T07:36:00.117115Z"
    }
   },
   "cell_type": "code",
   "source": "ytest_ = torch.tensor(ytest, dtype=torch.long)",
   "id": "549f38a314b1e7eb",
   "outputs": [],
   "execution_count": 253
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:44:17.835857Z",
     "start_time": "2024-05-18T07:44:17.819809Z"
    }
   },
   "cell_type": "code",
   "source": "model = Classifier()",
   "id": "b5237e5559bdc5f9",
   "outputs": [],
   "execution_count": 286
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:45:50.949063Z",
     "start_time": "2024-05-18T07:45:39.152320Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "\n",
    "model = model.to(device)\n",
    "\n",
    "criterion = nn.CrossEntropyLoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "\n",
    "model.train()\n",
    "for epoch in range(5000):\n",
    "    y_ = model(xtrain_.to(device))\n",
    "    loss = criterion(y_, ytrain_.to(device))\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 100 == 0:\n",
    "        print(f'{epoch}: {loss.item()}')"
   ],
   "id": "3cf5c9abdc983aa6",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: 0.5514465570449829\n",
      "100: 0.5514461994171143\n",
      "200: 0.5514460802078247\n",
      "300: 0.5514460802078247\n",
      "400: 0.5514460802078247\n",
      "500: 0.5514460802078247\n",
      "600: 0.5514460206031799\n",
      "700: 0.5514460206031799\n",
      "800: 0.5514459609985352\n",
      "900: 0.5514459609985352\n",
      "1000: 0.5514459609985352\n",
      "1100: 0.5514459609985352\n",
      "1200: 0.5514459609985352\n",
      "1300: 0.5514459013938904\n",
      "1400: 0.5514459013938904\n",
      "1500: 0.5514459013938904\n",
      "1600: 0.5514459013938904\n",
      "1700: 0.5514459013938904\n",
      "1800: 0.5514459013938904\n",
      "1900: 0.5514459013938904\n",
      "2000: 0.5514459013938904\n",
      "2100: 0.5514459013938904\n",
      "2200: 0.5514459013938904\n",
      "2300: 0.5514459013938904\n",
      "2400: 0.5514459013938904\n",
      "2500: 0.5514458417892456\n",
      "2600: 0.5514458417892456\n",
      "2700: 0.5514457821846008\n",
      "2800: 0.5514457821846008\n",
      "2900: 0.5514457821846008\n",
      "3000: 0.551445722579956\n",
      "3100: 0.5514456629753113\n",
      "3200: 0.5514456629753113\n",
      "3300: 0.5514456629753113\n",
      "3400: 0.5514456629753113\n",
      "3500: 0.5514456629753113\n",
      "3600: 0.5514456629753113\n",
      "3700: 0.5514456629753113\n",
      "3800: 0.5514456033706665\n",
      "3900: 0.5514455437660217\n",
      "4000: 0.5514455437660217\n",
      "4100: 0.5514455437660217\n",
      "4200: 0.5514455437660217\n",
      "4300: 0.5514455437660217\n",
      "4400: 0.5514455437660217\n",
      "4500: 0.551445484161377\n",
      "4600: 0.551445484161377\n",
      "4700: 0.551445484161377\n",
      "4800: 0.551445484161377\n",
      "4900: 0.551445484161377\n"
     ]
    }
   ],
   "execution_count": 291
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:45:52.440165Z",
     "start_time": "2024-05-18T07:45:52.430631Z"
    }
   },
   "cell_type": "code",
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_ = model(xtest_.to(device))\n",
    "acc = torch.sum(ytest_ == y_.argmax(dim=1).cpu()) / len(y_)\n",
    "print(acc.item())"
   ],
   "id": "6af959e9e00f8fb5",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9200000166893005\n"
     ]
    }
   ],
   "execution_count": 292
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:48:28.903825Z",
     "start_time": "2024-05-18T07:48:28.880201Z"
    }
   },
   "cell_type": "code",
   "source": "torch.save(model.state_dict(), 'model.pth')",
   "id": "6576525e3c7feda7",
   "outputs": [],
   "execution_count": 294
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:47:34.920942Z",
     "start_time": "2024-05-18T07:47:34.849734Z"
    }
   },
   "cell_type": "code",
   "source": "model.state_dict()",
   "id": "53f820a3e43767e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OrderedDict([('fc1.weight',\n",
       "              tensor([[ 1.5635e-02,  9.3973e-01, -5.1401e-02, -1.8669e+00],\n",
       "                      [-1.2709e-01,  9.8758e-01,  2.5959e-02, -1.5577e+00],\n",
       "                      [ 1.9789e-02,  8.1291e-01, -1.0007e-01, -1.4440e+00],\n",
       "                      [ 1.6696e-01, -4.8432e-01,  5.1615e-01,  1.0068e+00],\n",
       "                      [-1.9540e-01, -3.9771e-02,  7.7054e-01,  1.3444e+00],\n",
       "                      [ 1.8247e-01, -3.0524e-02,  3.4909e-01, -3.6004e-01],\n",
       "                      [ 6.0604e-02, -3.5066e-01,  7.4853e-01,  1.8979e-01],\n",
       "                      [-1.4475e-01, -2.3354e-01,  5.5877e-01,  8.0914e-01],\n",
       "                      [-9.1416e-02, -4.5914e-01,  1.7087e-01,  1.0934e-01],\n",
       "                      [-1.8097e-01,  1.9661e-01, -2.1704e-01,  1.1011e-01],\n",
       "                      [-2.2164e-01, -1.6700e-01,  3.1598e-01,  1.4507e+00],\n",
       "                      [-3.7634e-01,  4.4914e-01, -2.1666e-01,  8.8050e-03],\n",
       "                      [-3.2349e-01, -5.4216e-02,  6.4399e-01,  1.2370e+00],\n",
       "                      [ 2.7518e-01,  6.5468e-01, -5.7265e-01, -8.1373e-01],\n",
       "                      [-1.2852e-02, -3.1577e-01,  6.3070e-01,  8.3755e-01],\n",
       "                      [ 2.2732e-02, -4.7506e-01, -1.6581e-01,  3.1004e-01],\n",
       "                      [-2.0740e-01,  1.2056e-01, -4.6104e-01, -2.0024e-01],\n",
       "                      [-1.5718e-01, -4.6705e-01,  8.0366e-02, -4.8402e-01],\n",
       "                      [ 4.7817e-01,  2.6106e-01, -6.3613e-01, -6.7069e-01],\n",
       "                      [-1.4061e-01,  2.3301e-01, -3.0289e-01, -3.3369e-01],\n",
       "                      [ 5.1246e-01,  6.5079e-01, -6.6865e-01, -1.1961e+00],\n",
       "                      [ 4.7917e-01,  5.3917e-01, -4.6583e-01, -1.0888e+00],\n",
       "                      [-2.3972e-01, -3.3651e-01,  4.9626e-02, -3.4927e-01],\n",
       "                      [-1.0329e-01, -2.7568e-02,  5.8099e-01,  1.5051e+00],\n",
       "                      [-2.5453e-01, -7.0362e-02,  6.0673e-01,  1.3497e+00],\n",
       "                      [ 2.2301e-01,  7.5421e-01, -1.0090e+00, -9.4318e-01],\n",
       "                      [ 4.0083e-01,  7.1346e-01, -5.1256e-01, -1.1798e+00],\n",
       "                      [ 1.3879e-02, -3.0039e-01, -9.9318e-02, -4.1627e-01],\n",
       "                      [ 3.4055e-01,  2.1652e-01, -3.6368e-01, -3.8358e-01],\n",
       "                      [ 5.5364e-01,  1.3594e+00, -1.1707e+00, -1.9775e+00],\n",
       "                      [-4.9627e-01, -2.7934e-01,  4.5762e-01,  6.3024e-02],\n",
       "                      [ 1.8918e-01,  7.7213e-01, -5.0468e-01, -1.0138e+00],\n",
       "                      [-2.3891e-01, -2.4474e-01, -2.9156e-01,  2.5274e-01],\n",
       "                      [ 1.7647e-01, -2.3382e-01,  4.4616e-01,  6.0633e-01],\n",
       "                      [-1.4428e-01, -2.2139e-01,  3.2080e-01, -4.6078e-01],\n",
       "                      [-1.9732e-01,  2.8354e-01,  1.1303e-01,  5.5019e-01],\n",
       "                      [ 2.3734e-02, -3.2878e-01,  5.0795e-01,  1.0296e+00],\n",
       "                      [ 1.0332e-01, -4.9351e-01,  4.6370e-01,  1.6023e+00],\n",
       "                      [-1.6967e-01, -1.0713e-01,  2.8501e-01,  7.1669e-01],\n",
       "                      [-2.2516e-01, -3.1059e-02,  2.4202e-01, -4.3950e-01],\n",
       "                      [-4.1838e-01,  1.4214e-01,  3.2086e-01,  7.2329e-02],\n",
       "                      [ 3.7151e-01,  5.9127e-01, -3.2556e-01, -1.5343e+00],\n",
       "                      [-4.2301e-01,  3.4859e-01, -3.5566e-01,  1.9338e-01],\n",
       "                      [ 3.6446e-01, -8.7809e-01,  6.9543e-01,  7.5874e-01],\n",
       "                      [-6.3685e-02,  2.0671e-01, -4.6828e-01, -1.5244e-01],\n",
       "                      [-5.2308e-02, -1.3450e-01,  6.8763e-01,  1.4015e+00],\n",
       "                      [ 3.2188e-01,  7.2183e-01, -2.8336e-01, -1.1273e+00],\n",
       "                      [ 3.9349e-02, -8.0616e-02,  2.3907e-01, -2.4381e-01],\n",
       "                      [ 3.3574e-01, -7.1392e-01,  6.4942e-01,  1.2353e+00],\n",
       "                      [-2.7059e-01, -3.7500e-01, -2.4267e-01, -1.3109e-01],\n",
       "                      [ 4.9376e-01,  1.1474e+00, -1.1598e+00, -1.1033e+00],\n",
       "                      [ 2.6169e-01, -4.3323e-01,  4.9637e-01, -9.6027e-01],\n",
       "                      [ 3.2827e-01,  5.2526e-01,  6.7615e-02, -5.0596e-01],\n",
       "                      [ 2.8902e-01, -9.4654e-01,  1.7117e-01,  2.1394e+00],\n",
       "                      [-9.1946e-02, -3.6048e-01,  5.6331e-01, -4.0250e-01],\n",
       "                      [-3.1026e-01,  1.7436e-01,  8.6768e-02,  3.9490e-01],\n",
       "                      [-4.2136e-01,  1.5282e-01,  2.0430e-01, -3.9043e-01],\n",
       "                      [-2.5851e-01,  3.9067e-02, -3.6247e-01, -3.8420e-01],\n",
       "                      [-4.1640e-01, -4.6914e-01, -3.2050e-01, -1.5534e-02],\n",
       "                      [ 4.2268e-01,  9.3373e-01, -7.3386e-01, -1.0925e+00],\n",
       "                      [-4.3906e-01,  3.8001e-01, -2.9450e-01, -7.0427e-02],\n",
       "                      [ 6.1214e-01,  1.0326e-01, -5.4632e-01, -9.6594e-01],\n",
       "                      [-1.2925e-01, -4.0089e-02, -2.9624e-02, -1.3774e-01],\n",
       "                      [ 5.5279e-01,  3.2085e-01, -1.3847e-01, -1.1745e+00],\n",
       "                      [-3.0367e-01,  2.8390e-01, -1.5116e-01,  4.4228e-02],\n",
       "                      [ 2.4712e-01,  5.7999e-01, -2.7680e-01, -1.4210e+00],\n",
       "                      [-3.7094e-01,  2.8167e-01,  1.7368e-02, -5.0240e-01],\n",
       "                      [ 1.3814e-01, -2.7257e-01,  3.5221e-01,  3.2837e-01],\n",
       "                      [-2.8057e-01, -1.9666e-01, -2.9645e-01, -4.3560e-01],\n",
       "                      [-3.4563e-01, -1.0132e-01,  7.1141e-01,  9.8008e-01],\n",
       "                      [-2.8664e-01,  3.2550e-01, -3.7924e-01,  1.1333e-01],\n",
       "                      [ 4.4041e-01,  2.4872e-01, -1.7230e-01,  8.7307e-01],\n",
       "                      [ 4.3006e-01, -2.1814e-01,  3.1719e-01, -9.1727e-01],\n",
       "                      [-1.7382e-01, -3.9181e-01,  6.7288e-01,  5.0258e-01],\n",
       "                      [ 4.8961e-01,  4.7816e-01, -5.4645e-01, -1.3155e+00],\n",
       "                      [-2.6418e-04,  6.4138e-03,  6.3156e-01,  2.5722e-01],\n",
       "                      [ 5.9106e-01,  8.0099e-01, -4.3739e-01, -1.0421e+00],\n",
       "                      [-4.5260e-01, -2.9013e-01, -1.5100e-01, -4.2278e-01],\n",
       "                      [-4.7355e-01, -4.6531e-01, -3.6451e-01,  1.2880e-01],\n",
       "                      [ 4.6203e-01,  7.7615e-01, -6.6397e-01, -8.9393e-01],\n",
       "                      [ 2.1614e-01, -3.7760e-02,  7.3585e-01,  4.5367e-01],\n",
       "                      [ 3.9781e-01,  5.0609e-01, -3.1023e-01, -4.7221e-01],\n",
       "                      [ 3.1085e-01,  5.5569e-01, -2.1819e-01, -1.6240e+00],\n",
       "                      [-7.0582e-02,  1.3370e-02, -7.4982e-02, -4.8755e-01],\n",
       "                      [-3.3614e-01,  2.1680e-01,  1.9500e-01, -4.2316e-01],\n",
       "                      [-2.2735e-01, -1.7449e-01,  4.2986e-02,  2.1932e-01],\n",
       "                      [ 4.5340e-01,  7.1446e-01, -3.0895e-01, -9.4495e-01],\n",
       "                      [-3.3315e-01,  1.4986e-01, -2.7211e-01,  3.0562e-01],\n",
       "                      [ 3.0820e-01,  1.7609e-01,  4.4934e-01,  2.4286e-01],\n",
       "                      [-1.6286e-01,  2.4770e-01, -1.5926e-01,  3.9578e-01],\n",
       "                      [-3.4196e-01, -1.6582e-01,  2.1694e-01,  1.6892e+00],\n",
       "                      [-2.0759e-01, -4.9936e-01,  4.2676e-01, -4.3759e-01],\n",
       "                      [ 2.5679e-01,  2.2191e-01, -2.6913e-02, -7.8022e-01],\n",
       "                      [ 6.2272e-01,  6.3813e-01, -7.6298e-01, -1.1147e+00],\n",
       "                      [ 2.4978e-01,  5.2084e-01, -4.8507e-01, -7.9260e-01],\n",
       "                      [-2.1323e-01, -2.4021e-01, -2.2843e-02,  4.8535e-01],\n",
       "                      [ 2.6448e-01,  7.7144e-01, -3.7776e-01, -1.2557e+00],\n",
       "                      [-4.0639e-01,  2.9495e-01, -3.3840e-01, -4.2591e-02],\n",
       "                      [ 2.3238e-01, -5.7857e-01,  7.0782e-01,  1.5138e+00],\n",
       "                      [ 5.5984e-01,  3.1222e-01, -6.0285e-01, -1.1132e+00],\n",
       "                      [ 1.4779e-01,  9.5947e-01, -1.5988e-01, -1.4539e+00],\n",
       "                      [-2.8188e-01,  1.6066e-01,  4.7657e-01,  3.6842e-01],\n",
       "                      [ 5.8857e-01, -2.3520e-01, -4.1805e-01, -3.7852e-01],\n",
       "                      [ 2.0158e-01,  7.4520e-01, -2.3482e-01, -1.7970e+00],\n",
       "                      [-1.9111e-01, -2.5223e-01,  1.1115e-01,  3.9063e-01],\n",
       "                      [-3.0718e-01, -2.6455e-01,  4.2234e-01, -1.0484e-01],\n",
       "                      [ 3.1746e-01,  8.5366e-01, -6.2714e-01, -9.8328e-01],\n",
       "                      [ 2.1593e-02, -5.3882e-01,  8.2195e-01,  1.5329e+00],\n",
       "                      [-1.1420e-01, -3.0945e-01,  6.9940e-02,  3.4410e-01],\n",
       "                      [-1.3821e-01,  1.0763e-01, -4.8039e-01,  1.2263e-02],\n",
       "                      [-4.5893e-01,  4.2593e-01, -2.9088e-01, -4.6635e-01],\n",
       "                      [-4.0805e-01,  3.4835e-01, -2.6509e-01, -4.4102e-01],\n",
       "                      [-2.7222e-02, -4.3362e-03, -4.1825e-01,  1.7749e-01],\n",
       "                      [ 3.7312e-01, -8.8228e-02,  2.1585e-01, -1.3777e-01],\n",
       "                      [-4.3975e-01, -4.4612e-03, -4.3493e-01,  2.5513e-01],\n",
       "                      [-5.8048e-02,  2.1149e-01, -9.0457e-02,  8.1978e-01],\n",
       "                      [ 4.4151e-01,  5.0468e-01, -6.7425e-01, -9.6446e-01],\n",
       "                      [-3.4855e-01, -3.8760e-01,  3.1449e-02,  4.5402e-01],\n",
       "                      [ 3.7591e-01, -7.4996e-01,  3.0208e-01,  1.0702e+00],\n",
       "                      [ 2.5532e-01,  1.6309e-01,  2.9311e-01,  3.7622e-01],\n",
       "                      [ 2.8829e-01, -5.4732e-01,  2.6123e-01,  9.0736e-01],\n",
       "                      [-3.5425e-01,  4.9272e-01, -4.0246e-01,  1.0535e-01],\n",
       "                      [ 2.6927e-01,  9.1038e-01, -5.0817e-01, -9.2645e-01],\n",
       "                      [-1.9885e-02, -2.0347e-01, -4.4286e-02, -6.3761e-02],\n",
       "                      [-3.4909e-01,  3.4742e-01, -1.8929e-01, -6.7905e-02],\n",
       "                      [ 1.8714e-01, -3.7786e-01, -2.8497e-01,  9.1052e-02],\n",
       "                      [ 5.5153e-01,  3.1183e-01, -6.8600e-01, -5.0606e-01],\n",
       "                      [-2.9077e-01, -1.6604e-01,  1.9932e-01, -2.3580e-01]], device='cuda:0')),\n",
       "             ('fc1.bias',\n",
       "              tensor([ 0.9801,  1.6043,  1.1496, -0.8402, -0.8038,  0.5725, -0.7899, -0.1263,\n",
       "                       0.2076,  0.1938, -1.2970, -0.4794, -0.9528,  0.9924, -0.4462, -0.0399,\n",
       "                       0.1855, -0.2007,  1.3344, -0.0373,  0.7596,  0.4641, -0.4366, -1.1310,\n",
       "                      -0.3702,  0.0574,  1.0943, -0.3628,  0.1173,  0.7313,  0.3113,  1.2103,\n",
       "                      -0.2414, -0.7507,  0.0592, -0.2397, -0.7549, -1.1050, -0.9508, -0.3840,\n",
       "                      -0.2897,  0.9651, -0.0888, -0.5723, -0.1850, -0.4782,  0.5234,  0.7890,\n",
       "                      -1.0443, -0.4798,  0.1697,  0.2250,  0.6493, -1.5490,  0.1398, -0.4719,\n",
       "                      -0.4684,  0.1852,  0.3604,  0.8656, -0.1440,  1.0514,  0.1875,  1.0536,\n",
       "                       0.2387,  1.2366,  0.3773, -0.1508, -0.1887, -0.8937, -0.4716, -0.5756,\n",
       "                       0.6128, -0.2220,  1.1550, -0.7893,  0.5712, -0.1759, -0.1913,  0.8031,\n",
       "                      -0.8984,  0.5643,  1.4319, -0.2206,  0.1318,  0.1459,  1.3558, -0.1409,\n",
       "                      -0.9146, -0.2648, -0.9200, -0.2007,  0.8130,  1.3238,  1.3208, -0.4790,\n",
       "                       0.4883,  0.3970, -1.0500,  1.1659,  1.1482, -0.5733,  0.1737,  1.5925,\n",
       "                       0.1930,  0.0563,  1.2370, -0.4189, -0.0719, -0.3504, -0.3674,  0.3507,\n",
       "                      -0.0225,  0.8811,  0.2212, -0.6592,  1.3149, -0.2734, -0.1922, -0.5847,\n",
       "                      -0.9577, -0.0616,  0.4846,  0.2039,  0.2641,  0.2486,  0.4643,  0.3073],\n",
       "                     device='cuda:0')),\n",
       "             ('fc2.weight',\n",
       "              tensor([[ 1.1217e+00,  1.0217e+00,  5.7233e-01, -6.6229e-01, -6.4390e-01,\n",
       "                       -3.0561e-01, -7.2032e-01, -7.7411e-01,  1.9949e-02,  2.8222e-02,\n",
       "                       -2.5669e-01, -3.8161e-02, -4.6616e-01,  9.5068e-01, -7.0810e-01,\n",
       "                        2.0769e-02, -5.1183e-02,  1.3753e-02,  7.1872e-01,  1.3699e-04,\n",
       "                        7.5809e-01,  7.5305e-01,  2.6603e-02, -7.0445e-01, -7.3579e-01,\n",
       "                        7.8356e-01,  6.0260e-01, -8.4629e-02,  4.7403e-01,  9.3941e-01,\n",
       "                       -4.0650e-02,  8.6254e-01,  6.9022e-02, -4.5514e-01, -2.6485e-02,\n",
       "                       -6.6869e-02, -5.1971e-01, -6.0402e-01, -7.1220e-02, -3.6609e-02,\n",
       "                       -2.6415e-02,  6.2215e-01, -2.9146e-02, -7.1142e-01,  1.9313e-02,\n",
       "                       -5.1427e-01,  5.5557e-01, -2.7715e-01, -6.8051e-01,  4.2565e-02,\n",
       "                        9.7241e-01, -4.2640e-01,  2.4655e-01, -5.6305e-01, -5.2056e-01,\n",
       "                       -1.8419e-02,  6.7638e-02,  2.8679e-02,  8.7629e-02,  6.6017e-01,\n",
       "                       -2.8335e-02,  5.7565e-01, -2.7109e-02,  4.0945e-01,  6.3940e-02,\n",
       "                        5.9306e-01,  3.7575e-02, -3.7723e-01,  4.4530e-02, -5.6495e-01,\n",
       "                       -3.3402e-02,  1.3533e-01, -9.0036e-02, -8.0647e-01,  6.8906e-01,\n",
       "                       -4.9030e-01,  5.8523e-01,  7.3758e-02, -6.6874e-02,  6.2791e-01,\n",
       "                       -4.6229e-01,  4.8610e-01,  6.6549e-01,  2.5107e-02,  2.6021e-02,\n",
       "                       -2.6950e-02,  4.8593e-01, -7.6255e-02, -1.8610e-01,  7.1509e-02,\n",
       "                       -4.4911e-02, -5.0240e-02,  2.9822e-01,  7.4075e-01,  6.2299e-01,\n",
       "                        3.9430e-02,  8.4307e-01, -3.0723e-02, -5.4078e-01,  7.4875e-01,\n",
       "                        6.1218e-01, -3.6432e-01,  5.6725e-01,  6.3475e-01,  6.0696e-02,\n",
       "                       -3.5336e-02,  6.3135e-01, -7.6950e-01, -3.0872e-02, -7.6777e-02,\n",
       "                       -2.1641e-02, -7.3755e-02, -2.4719e-02, -1.8824e-01,  2.9115e-02,\n",
       "                       -5.1776e-02,  6.8766e-01,  7.9263e-02, -5.0054e-01, -1.4071e-01,\n",
       "                       -5.0238e-01,  4.2491e-02,  6.9288e-01, -3.1915e-02,  1.9977e-02,\n",
       "                       -4.5760e-02,  8.5022e-01, -2.5551e-02],\n",
       "                      [ 3.3014e+00,  1.3170e+00,  1.3297e+00, -2.8778e-01, -2.1164e-01,\n",
       "                        1.5991e-01, -2.4332e-02, -2.4691e-01,  5.7387e-02,  1.1515e-02,\n",
       "                       -8.6830e-01, -2.7888e-02, -3.9369e-01,  1.5085e+00, -1.0848e-01,\n",
       "                       -1.4793e-02, -2.0605e-02,  1.9952e-03,  7.7161e-01,  4.2370e-02,\n",
       "                        1.0866e+00,  7.3144e-01, -2.2039e-03, -3.1960e-01, -2.9029e-01,\n",
       "                       -1.8950e+00,  8.2013e-01, -5.3952e-02,  2.2491e-01, -5.2498e+00,\n",
       "                        2.0602e-02,  1.8260e+00, -3.7008e-02, -1.1916e-01,  4.6117e-02,\n",
       "                       -1.3020e-01, -2.3506e-01, -3.9430e-01, -1.4331e+00, -5.0451e-02,\n",
       "                        1.0422e-02,  9.5431e-01,  6.6561e-02, -1.3963e-01, -5.6151e-02,\n",
       "                       -1.2996e-01,  5.6597e-01,  1.5605e-01, -2.1538e-01, -2.1775e-02,\n",
       "                       -4.4302e+00,  3.1103e-01,  8.2139e-02, -7.9492e-01,  1.4729e-01,\n",
       "                        3.3041e-02, -5.8879e-02,  1.5883e-02, -8.5221e-02,  8.8517e-01,\n",
       "                        1.8034e-02,  8.7469e-01, -6.9706e-02,  3.5687e-01,  2.7759e-02,\n",
       "                        1.3015e+00, -4.2751e-02, -7.5188e-03,  7.8677e-02, -4.6187e-01,\n",
       "                        4.1053e-02, -1.9351e-01,  3.0782e-01, -3.8510e-01,  1.0919e+00,\n",
       "                       -5.9812e-02,  3.4985e-01,  1.4186e-02,  7.0412e-02,  6.0768e-01,\n",
       "                       -1.1730e-01,  1.2148e-01,  8.4575e-01,  1.9021e-02, -6.9143e-02,\n",
       "                       -1.6759e-02,  2.9137e-01, -6.0568e-02, -8.2613e-02,  1.4452e-02,\n",
       "                       -1.7314e+00,  2.3730e-02,  2.9999e-01,  6.6126e-01,  1.0770e+00,\n",
       "                        3.9036e-02,  1.7579e+00,  6.2774e-02, -1.6176e-01,  1.1866e+00,\n",
       "                        6.0921e-01, -1.4110e-01,  4.0073e-01,  1.5194e+00,  5.4988e-02,\n",
       "                        1.5015e-02,  7.0499e-01, -2.7371e-01, -3.1217e-02, -4.9234e-03,\n",
       "                       -7.0079e-02, -4.3969e-02, -7.6395e-02,  1.6889e-01,  8.9895e-03,\n",
       "                       -5.4593e-01,  1.0106e+00, -4.8456e-02, -1.3874e-01, -7.5270e-02,\n",
       "                       -3.0929e-01,  1.9304e-03,  7.8459e-01, -1.0417e-02,  6.0461e-02,\n",
       "                       -7.7825e-02,  5.8769e-01,  2.9169e-02],\n",
       "                      [-3.7085e+00, -1.7503e+00, -1.6860e+00,  4.5037e-01,  4.8870e-01,\n",
       "                       -7.9748e-02,  3.0442e-01,  5.2253e-01, -5.2458e-02, -2.8964e-02,\n",
       "                        1.0334e+00,  8.2655e-02,  6.0979e-01, -2.1150e+00,  4.4078e-01,\n",
       "                       -7.8675e-02,  4.2099e-02,  3.3091e-02, -1.0781e+00, -7.1267e-02,\n",
       "                       -1.7655e+00, -1.0735e+00,  4.9978e-02,  5.2302e-01,  6.0159e-01,\n",
       "                       -1.8093e-01, -9.4501e-01, -6.4967e-02, -3.6415e-01, -2.0012e-01,\n",
       "                        3.9446e-02, -2.2761e+00,  3.6031e-02,  2.6552e-01, -5.7467e-02,\n",
       "                        2.1421e-01,  4.3725e-01,  5.0731e-01,  1.3903e+00, -6.3424e-02,\n",
       "                       -2.2906e-02, -1.2610e+00,  7.2307e-02,  2.9755e-01, -1.2123e-02,\n",
       "                        3.2640e-01, -9.0830e-01, -7.2179e-02,  4.8737e-01, -1.5935e-02,\n",
       "                       -1.8698e-01, -1.0776e-01, -2.0675e-01,  9.0527e-01,  1.2042e-01,\n",
       "                       -1.8735e-02,  9.2044e-03,  5.7278e-02,  5.1584e-02, -1.2664e+00,\n",
       "                       -1.2054e-02, -1.1069e+00,  1.5259e-02, -4.7966e-01, -3.2762e-02,\n",
       "                       -1.6917e+00, -1.3548e-01,  1.3999e-01,  4.7283e-02,  6.9275e-01,\n",
       "                       -2.3388e-02,  1.1664e-01, -1.5145e-01,  5.3229e-01, -1.3609e+00,\n",
       "                        2.3694e-01, -6.3682e-01,  2.0457e-03,  6.1871e-02, -8.8052e-01,\n",
       "                        2.2354e-01, -3.2813e-01, -1.1404e+00,  8.4708e-02,  1.9009e-02,\n",
       "                       -5.3083e-02, -5.2405e-01, -1.0363e-02,  1.4087e-01, -6.7116e-02,\n",
       "                        1.7992e+00, -2.2880e-02, -3.5451e-01, -9.4958e-01, -1.3157e+00,\n",
       "                        3.7273e-02, -2.5060e+00, -1.1984e-02,  4.1027e-01, -1.3547e+00,\n",
       "                       -1.0290e+00,  1.8062e-01, -4.5919e-01, -1.7698e+00,  7.2878e-02,\n",
       "                        7.8175e-03, -9.8400e-01,  3.8345e-01,  5.1182e-02, -8.9760e-03,\n",
       "                        6.8139e-02,  6.2222e-02, -1.1562e-01, -6.1687e-02,  1.1640e-02,\n",
       "                        4.6274e-01, -1.3016e+00,  3.7658e-02,  3.4772e-01,  1.0277e-01,\n",
       "                        4.9648e-01, -6.0484e-02, -1.2181e+00, -7.0737e-02, -6.0736e-02,\n",
       "                       -1.9122e-03, -1.0259e+00,  8.7499e-02]], device='cuda:0')),\n",
       "             ('fc2.bias',\n",
       "              tensor([ 0.1916,  0.4774, -0.5946], device='cuda:0'))])"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 293
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:53:07.694077Z",
     "start_time": "2024-05-18T07:53:07.679974Z"
    }
   },
   "cell_type": "code",
   "source": "df['data'].columns",
   "id": "71671c20b97dbcd7",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)',\n",
       "       'petal width (cm)'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 296,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 296
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T07:53:53.638443Z",
     "start_time": "2024-05-18T07:53:53.621904Z"
    }
   },
   "cell_type": "code",
   "source": "df['data'].max()",
   "id": "a1aa087817e8c39b",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sepal length (cm)    7.9\n",
       "sepal width (cm)     4.4\n",
       "petal length (cm)    6.9\n",
       "petal width (cm)     2.5\n",
       "dtype: float64"
      ]
     },
     "execution_count": 297,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 297
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:27:48.001766Z",
     "start_time": "2024-05-18T08:27:47.830989Z"
    }
   },
   "cell_type": "code",
   "source": "import seaborn as sns",
   "id": "75e00ccecb343b3",
   "outputs": [],
   "execution_count": 298
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:28:09.785300Z",
     "start_time": "2024-05-18T08:28:09.727821Z"
    }
   },
   "cell_type": "code",
   "source": [
    "df = sns.load_dataset('titanic')\n",
    "df"
   ],
   "id": "f9b5bdda94e74647",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     survived  pclass     sex   age  sibsp  parch     fare embarked   class   \n",
       "0           0       3    male  22.0      1      0   7.2500        S   Third  \\\n",
       "1           1       1  female  38.0      1      0  71.2833        C   First   \n",
       "2           1       3  female  26.0      0      0   7.9250        S   Third   \n",
       "3           1       1  female  35.0      1      0  53.1000        S   First   \n",
       "4           0       3    male  35.0      0      0   8.0500        S   Third   \n",
       "..        ...     ...     ...   ...    ...    ...      ...      ...     ...   \n",
       "886         0       2    male  27.0      0      0  13.0000        S  Second   \n",
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       "889         1       1    male  26.0      0      0  30.0000        C   First   \n",
       "890         0       3    male  32.0      0      0   7.7500        Q   Third   \n",
       "\n",
       "       who  adult_male deck  embark_town alive  alone  \n",
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       "..     ...         ...  ...          ...   ...    ...  \n",
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       "887  woman       False    B  Southampton   yes   True  \n",
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       "889    man        True    C    Cherbourg   yes   True  \n",
       "890    man        True  NaN   Queenstown    no   True  \n",
       "\n",
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     },
     "execution_count": 299,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 299
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:29:51.399764Z",
     "start_time": "2024-05-18T08:29:51.374733Z"
    }
   },
   "cell_type": "code",
   "source": "df.nunique()",
   "id": "194ad14229a4b449",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "survived         2\n",
       "pclass           3\n",
       "sex              2\n",
       "age             88\n",
       "sibsp            7\n",
       "parch            7\n",
       "fare           248\n",
       "embarked         3\n",
       "class            3\n",
       "who              3\n",
       "adult_male       2\n",
       "deck             7\n",
       "embark_town      3\n",
       "alive            2\n",
       "alone            2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 300,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 300
  },
  {
   "metadata": {
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     "end_time": "2024-05-18T08:42:44.996418Z",
     "start_time": "2024-05-18T08:42:44.989882Z"
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   },
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   "source": "df = df.drop(columns=['class', 'adult_male', 'deck', 'embark_town', 'alive', 'alone'])",
   "id": "1d0dcabfb35e1124",
   "outputs": [],
   "execution_count": 306
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:32:22.769788Z",
     "start_time": "2024-05-18T08:32:22.756236Z"
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   },
   "cell_type": "code",
   "source": "import pandas as pd",
   "id": "ddfee35826b69f65",
   "outputs": [],
   "execution_count": 302
  },
  {
   "metadata": {
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     "end_time": "2024-05-18T08:42:55.826332Z",
     "start_time": "2024-05-18T08:42:55.786362Z"
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   },
   "cell_type": "code",
   "source": "df = pd.get_dummies(df, dtype=float)",
   "id": "a24dae845277eabb",
   "outputs": [],
   "execution_count": 307
  },
  {
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     "start_time": "2024-05-18T08:42:59.455184Z"
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   },
   "cell_type": "code",
   "source": "df",
   "id": "94c3e862ae9df12e",
   "outputs": [
    {
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       "     survived  pclass   age  sibsp  parch     fare  sex_female  sex_male   \n",
       "0           0       3  22.0      1      0   7.2500         0.0       1.0  \\\n",
       "1           1       1  38.0      1      0  71.2833         1.0       0.0   \n",
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       "..        ...     ...   ...    ...    ...      ...         ...       ...   \n",
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       "889         1       1  26.0      0      0  30.0000         0.0       1.0   \n",
       "890         0       3  32.0      0      0   7.7500         0.0       1.0   \n",
       "\n",
       "     embarked_C  embarked_Q  embarked_S  who_child  who_man  who_woman  \n",
       "0           0.0         0.0         1.0        0.0      1.0        0.0  \n",
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       "..          ...         ...         ...        ...      ...        ...  \n",
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       "[891 rows x 14 columns]"
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     "execution_count": 308,
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   "execution_count": 308
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   "outputs": [],
   "execution_count": 312
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  {
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       "     survived  pclass   age  sibsp  parch     fare  sex_male  embarked_C   \n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>886</th>\n",
       "      <td>2</td>\n",
       "      <td>27.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>13.0000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>887</th>\n",
       "      <td>1</td>\n",
       "      <td>19.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>889</th>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30.0000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>890</th>\n",
       "      <td>3</td>\n",
       "      <td>32.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>714 rows × 12 columns</p>\n",
       "</div>"
      ]
     },
     "execution_count": 320,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 320
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:47:00.404344Z",
     "start_time": "2024-05-18T08:47:00.382045Z"
    }
   },
   "cell_type": "code",
   "source": "Y",
   "id": "30160e4e4f2c9bfe",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0\n",
       "1      1\n",
       "2      1\n",
       "3      1\n",
       "4      0\n",
       "      ..\n",
       "885    0\n",
       "886    0\n",
       "887    1\n",
       "889    1\n",
       "890    0\n",
       "Name: survived, Length: 714, dtype: int64"
      ]
     },
     "execution_count": 321,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 321
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:47:52.349522Z",
     "start_time": "2024-05-18T08:47:52.215940Z"
    }
   },
   "cell_type": "code",
   "source": "from sklearn.model_selection import train_test_split",
   "id": "d048cbe71f0d1c9",
   "outputs": [],
   "execution_count": 322
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:55:06.394601Z",
     "start_time": "2024-05-18T08:55:06.380978Z"
    }
   },
   "cell_type": "code",
   "source": "xtrain, xtest, ytrain, ytest = train_test_split(X, Y, test_size=0.2)",
   "id": "9e5e0ef1246af377",
   "outputs": [],
   "execution_count": 336
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:55:23.440853Z",
     "start_time": "2024-05-18T08:55:23.432719Z"
    }
   },
   "cell_type": "code",
   "source": [
    "xtrain = torch.tensor(xtrain.values, dtype=torch.float32)\n",
    "xtest = torch.tensor(xtest.values, dtype=torch.float32)\n",
    "ytrain = torch.tensor(ytrain.values, dtype=torch.float32)\n",
    "ytest = torch.tensor(ytest.values, dtype=torch.float32)\n",
    "ytrain = ytrain.reshape(-1, 1)\n",
    "ytest = ytest.reshape(-1, 1)"
   ],
   "id": "397da49570e62331",
   "outputs": [],
   "execution_count": 337
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:50:28.110868Z",
     "start_time": "2024-05-18T08:50:28.093702Z"
    }
   },
   "cell_type": "code",
   "source": "xtrain.shape",
   "id": "af4d585a171897dc",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([571, 12])"
      ]
     },
     "execution_count": 327,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 327
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:50:42.963420Z",
     "start_time": "2024-05-18T08:50:42.945779Z"
    }
   },
   "cell_type": "code",
   "source": "ytrain.unique()",
   "id": "4584eed0c14c126",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0, 1])"
      ]
     },
     "execution_count": 328,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 328
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:52:30.425175Z",
     "start_time": "2024-05-18T08:52:30.411664Z"
    }
   },
   "cell_type": "code",
   "source": [
    "class Classifier(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.fc1 = nn.Linear(12, 128)\n",
    "        self.fc2 = nn.Linear(128, 1)\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.fc1(x))\n",
    "        return torch.sigmoid(self.fc2(x))"
   ],
   "id": "90889c8a883cd411",
   "outputs": [],
   "execution_count": 329
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:52:53.830379Z",
     "start_time": "2024-05-18T08:52:53.816235Z"
    }
   },
   "cell_type": "code",
   "source": "model = Classifier()",
   "id": "c52b0ddafcc3c8d5",
   "outputs": [],
   "execution_count": 330
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:54:30.677846Z",
     "start_time": "2024-05-18T08:54:30.664323Z"
    }
   },
   "cell_type": "code",
   "source": "",
   "id": "7b3e5be69e5e4f1a",
   "outputs": [],
   "execution_count": 333
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:54:35.716806Z",
     "start_time": "2024-05-18T08:54:35.696800Z"
    }
   },
   "cell_type": "code",
   "source": "ytrain.shape",
   "id": "fb6ae05b3cd1d2b3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([571, 1])"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 334
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:55:39.677213Z",
     "start_time": "2024-05-18T08:55:28.435834Z"
    }
   },
   "cell_type": "code",
   "source": [
    "device = 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "\n",
    "model = model.to(device)\n",
    "\n",
    "criterion = nn.BCELoss()\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "\n",
    "model.train()\n",
    "for epoch in range(5000):\n",
    "    y_ = model(xtrain.to(device))\n",
    "    loss = criterion(y_, ytrain.to(device))\n",
    "    \n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    if epoch % 100 == 0:\n",
    "        print(f'{epoch}: {loss.item()}')"
   ],
   "id": "ac6a8397c74fb70b",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0: 1.9674535989761353\n",
      "100: 0.40957778692245483\n",
      "200: 0.38515743613243103\n",
      "300: 0.3578585088253021\n",
      "400: 0.3382408916950226\n",
      "500: 0.32195284962654114\n",
      "600: 0.30724281072616577\n",
      "700: 0.2943097949028015\n",
      "800: 0.29280877113342285\n",
      "900: 0.27805888652801514\n",
      "1000: 0.2985757887363434\n",
      "1100: 0.2588392496109009\n",
      "1200: 0.25733980536460876\n",
      "1300: 0.25166189670562744\n",
      "1400: 0.24589169025421143\n",
      "1500: 0.234882652759552\n",
      "1600: 0.2277156412601471\n",
      "1700: 0.22147388756275177\n",
      "1800: 0.22005273401737213\n",
      "1900: 0.21301722526550293\n",
      "2000: 0.21664689481258392\n",
      "2100: 0.20287403464317322\n",
      "2200: 0.6750779747962952\n",
      "2300: 0.20300741493701935\n",
      "2400: 0.19981348514556885\n",
      "2500: 0.19683337211608887\n",
      "2600: 0.19390550255775452\n",
      "2700: 0.1919807493686676\n",
      "2800: 0.18757756054401398\n",
      "2900: 0.1858178824186325\n",
      "3000: 0.18612076342105865\n",
      "3100: 0.17776937782764435\n",
      "3200: 0.18426689505577087\n",
      "3300: 0.17941492795944214\n",
      "3400: 0.1763719767332077\n",
      "3500: 0.17378152906894684\n",
      "3600: 0.17525672912597656\n",
      "3700: 0.17131665349006653\n",
      "3800: 0.16749726235866547\n",
      "3900: 0.16467022895812988\n",
      "4000: 0.16091184318065643\n",
      "4100: 0.16317403316497803\n",
      "4200: 0.16292797029018402\n",
      "4300: 0.15790091454982758\n",
      "4400: 0.15169432759284973\n",
      "4500: 0.1636294722557068\n",
      "4600: 0.15679720044136047\n",
      "4700: 0.15231305360794067\n",
      "4800: 0.1504482924938202\n",
      "4900: 0.14877305924892426\n"
     ]
    }
   ],
   "execution_count": 338
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-05-18T08:57:11.296741Z",
     "start_time": "2024-05-18T08:57:11.277681Z"
    }
   },
   "cell_type": "code",
   "source": [
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_ = model(xtest.to(device))\n",
    "acc = torch.sum(ytest == y_.round().cpu()) / len(y_)\n",
    "print(acc.item())"
   ],
   "id": "a3af4cbaecf0c8ea",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7832167744636536\n"
     ]
    }
   ],
   "execution_count": 342
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "f40c4ac125412daf"
  }
 ],
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