PyTorch_101.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "705a29f9",
   "metadata": {},
   "source": [
    "# PyTorch Introduction 101\n",
    "### reference : 1.  https://pytorch.org/tutorials/beginner/basics/quickstart_tutorial.html,  \n",
    "###                    2.  https://github.com/phlippe/uvadlc_notebooks/tree/master "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b685bcbf",
   "metadata": {},
   "source": [
    "## Basic introduction to PyTorch tensors & comparison with Numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0b00d4c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/27/j7vqc09s6999lx6q2v5txbrm0000gn/T/ipykernel_26248/2930680000.py:12: DeprecationWarning: `set_matplotlib_formats` is deprecated since IPython 7.23, directly use `matplotlib_inline.backend_inline.set_matplotlib_formats()`\n",
      "  set_matplotlib_formats('svg', 'pdf') # For export\n"
     ]
    }
   ],
   "source": [
    "## Standard libraries\n",
    "import os\n",
    "import math\n",
    "import numpy as np \n",
    "import time\n",
    "\n",
    "## Imports for plotting\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline \n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('svg', 'pdf') # For export\n",
    "#matplotlib_inline.backend_inline.set_matplotlib_formats()\n",
    "from matplotlib.colors import to_rgba\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "## Progress bar\n",
    "from tqdm.notebook import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "82c6f82f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using torch 2.0.1\n"
     ]
    }
   ],
   "source": [
    "## porting pytorch\n",
    "import torch\n",
    "print(\"Using torch\", torch.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e0405793",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mps\n"
     ]
    }
   ],
   "source": [
    "## finding and setting the right computational device \n",
    "device = (\n",
    "    \"cuda\"\n",
    "    if torch.cuda.is_available()\n",
    "    else \"mps\"\n",
    "    if torch.backends.mps.is_available()\n",
    "    else \"cpu\"\n",
    ")\n",
    "print(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "384426c4",
   "metadata": {},
   "source": [
    "#### Set the seed for reproducibility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "261b63dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setting the seed\n",
    "torch.manual_seed(42) \n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69e1884b",
   "metadata": {},
   "source": [
    "### Tensors\n",
    "\n",
    "Tensors are the PyTorch equivalent to Numpy arrays, with the addition to also have support for GPU acceleration (more on that later).\n",
    "The name \"tensor\" is a generalization of concepts you already know. For instance, a vector is a 1-D tensor, and a matrix a 2-D tensor. When working with neural networks, we will use tensors of various shapes and number of dimensions.\n",
    "\n",
    "Most common functions you know from numpy can be used on tensors as well. Actually, since numpy arrays are so similar to tensors, we can convert most tensors to numpy arrays (and back) but we don't need it too often.\n",
    "\n",
    "#### Initialization\n",
    "\n",
    "Let's first start by looking at different ways of creating a tensor. There are many possible options, the simplest one is to call `torch.Tensor` passing the desired shape as input argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4dfb861c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1, 2],\n",
       "        [3, 4]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = [[1, 2],[3, 4]]\n",
    "x_data = torch.tensor(data)\n",
    "x_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e46122ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np_array = np.array(data)\n",
    "np_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7ba4c757",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PyTorch tensor: tensor([[1, 2],\n",
      "        [3, 4]])\n",
      "<class 'torch.Tensor'>\n"
     ]
    }
   ],
   "source": [
    "x_data_np = torch.from_numpy(np_array)\n",
    "print('PyTorch tensor:', x_data_np); print(type(x_data_np))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b7384161",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print( type(np.array(x_data)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2f1a353d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numpy ndarray :  [[1 2]\n",
      " [3 4]]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print( 'Numpy ndarray : ', x_data.numpy() ); print(type(x_data.numpy() ))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d496571",
   "metadata": {},
   "source": [
    "The function `torch.Tensor` allocates memory for the desired tensor, but reuses any values that have already been in the memory. To directly assign values to the tensor during initialization, there are many alternatives including:\n",
    "\n",
    "* `torch.zeros`: Creates a tensor filled with zeros\n",
    "* `torch.ones`: Creates a tensor filled with ones\n",
    "* `torch.rand`: Creates a tensor with random values uniformly sampled between 0 and 1\n",
    "* `torch.randn`: Creates a tensor with random values sampled from a normal distribution with mean 0 and variance 1\n",
    "* `torch.arange`: Creates a tensor containing the values $N,N+1,N+2,...,M$\n",
    "* `torch.Tensor` (input list): Creates a tensor from the list elements you provide"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e39a6c1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 0.3367,  0.1288,  0.2345],\n",
       "        [ 0.2303, -1.1229, -0.1863]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#torch.randn??\n",
    "torch.randn(2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6128a134",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.49671415, -0.1382643 ,  0.64768854],\n",
       "       [ 1.52302986, -0.23415337, -0.23413696]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(size=(2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "baa72a10",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random Tensor: \n",
      " tensor([[0.8694, 0.5677, 0.7411],\n",
      "        [0.4294, 0.8854, 0.5739]]) \n",
      "\n",
      "Ones Tensor: \n",
      " tensor([[1., 1., 1.],\n",
      "        [1., 1., 1.]]) \n",
      "\n",
      "Zeros Tensor: \n",
      " tensor([[0., 0., 0.],\n",
      "        [0., 0., 0.]])\n"
     ]
    }
   ],
   "source": [
    "shape = (2,3,)\n",
    "rand_tensor = torch.rand(shape)\n",
    "ones_tensor = torch.ones(shape)\n",
    "zeros_tensor = torch.zeros(shape)\n",
    "\n",
    "print(f\"Random Tensor: \\n {rand_tensor} \\n\")\n",
    "print(f\"Ones Tensor: \\n {ones_tensor} \\n\")\n",
    "print(f\"Zeros Tensor: \\n {zeros_tensor}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c989b435",
   "metadata": {},
   "source": [
    "#### Operations\n",
    "\n",
    "Most operations that exist in numpy, also exist in PyTorch. A full list of operations can be found in the [PyTorch documentation](https://pytorch.org/docs/stable/tensors.html#), but we will review the most important ones here.\n",
    "\n",
    "The simplest operation is to add two tensors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d738e6bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 tensor([[0.2666, 0.6274, 0.2696],\n",
      "        [0.4414, 0.2969, 0.8317]])\n",
      "X2 tensor([[0.1053, 0.2695, 0.3588],\n",
      "        [0.1994, 0.5472, 0.0062]])\n",
      "Y tensor([[0.3719, 0.8969, 0.6284],\n",
      "        [0.6407, 0.8441, 0.8378]])\n"
     ]
    }
   ],
   "source": [
    "x1 = torch.rand(2, 3)\n",
    "x2 = torch.rand(2, 3)\n",
    "y = x1 + x2\n",
    "\n",
    "print(\"X1\", x1)\n",
    "print(\"X2\", x2)\n",
    "print(\"Y\", y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fab80dc2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "device(type='cpu')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d84aec2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "device(type='mps', index=0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1 = y.to(device)\n",
    "y1.device"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ec768a41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "default device :  cpu\n",
      "set device :  mps:0\n"
     ]
    }
   ],
   "source": [
    "data = [[1, 2],[3, 4]]\n",
    "x_data = torch.tensor(data)\n",
    "print('default device : ', x_data.device)\n",
    "x_data = torch.tensor(data, device=device)\n",
    "print('set device : ', x_data.device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc3543c8",
   "metadata": {},
   "source": [
    "Calling `x1 + x2` creates a new tensor containing the sum of the two inputs. However, we can also use in-place operations that are applied directly on the memory of a tensor. We therefore change the values of `x2` without the chance to re-accessing the values of `x2` before the operation. An example is shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f3fd5fc9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 (before) tensor([[0.9516, 0.0753, 0.8860],\n",
      "        [0.5832, 0.3376, 0.8090]])\n",
      "X2 (before) tensor([[0.5779, 0.9040, 0.5547],\n",
      "        [0.3423, 0.6343, 0.3644]])\n",
      "X1 (after) tensor([[0.9516, 0.0753, 0.8860],\n",
      "        [0.5832, 0.3376, 0.8090]])\n",
      "X2 (after) tensor([[1.5295, 0.9792, 1.4407],\n",
      "        [0.9255, 0.9720, 1.1734]])\n"
     ]
    }
   ],
   "source": [
    "x1 = torch.rand(2, 3)\n",
    "x2 = torch.rand(2, 3)\n",
    "print(\"X1 (before)\", x1)\n",
    "print(\"X2 (before)\", x2)\n",
    "\n",
    "x2.add_(x1)\n",
    "print(\"X1 (after)\", x1)\n",
    "print(\"X2 (after)\", x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5a4e3b1",
   "metadata": {},
   "source": [
    "In-place operations are usually marked with a underscore postfix (e.g. \"add_\" instead of \"add\").\n",
    "\n",
    "Another common operation aims at changing the shape of a tensor. A tensor of size (2,3) can be re-organized to any other shape with the same number of elements (e.g. a tensor of size (6), or (3,2), ...). In PyTorch, this operation is called `view`:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5584c832",
   "metadata": {},
   "source": [
    "The 'view' function and its usages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b8c37a59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 1.5736, -0.8455,  1.3123,  0.6872],\n",
       "        [-1.0892, -0.3553, -0.9138, -0.6581],\n",
       "        [ 0.0499,  2.2667,  1.1790, -0.4345],\n",
       "        [-1.3864, -1.2862, -1.4032,  0.0360]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.randn(4, 4)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "88df5c9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([4, 4]), torch.Size([4, 4]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.size(), x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2cd70361",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = x.view(16)\n",
    "y.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8ec499ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 8])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = x.view(-1, 8)  # the size -1 is inferred from other dimensions\n",
    "z.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cd7a9d77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 2, 3, 4])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = torch.randn(1, 2, 3, 4)\n",
    "a.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f49a9897",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 3, 2, 4])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a.transpose(1, 2)  # Swaps 2nd and 3rd dimension\n",
    "b.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "338f78d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 3, 2, 4])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a.view(1, 3, 2, 4)  # Does not change tensor layout in memory\n",
    "c.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a3fd718a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.Size([1, 3, 2, 4])\n",
    "torch.equal(b, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d08ea1",
   "metadata": {},
   "source": [
    "Transpose & permutation of matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2c0a1454",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X tensor([0, 1, 2, 3, 4, 5])\n"
     ]
    }
   ],
   "source": [
    "x = torch.arange(6)\n",
    "print(\"X\", x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a0838b60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X tensor([[0, 1, 2],\n",
      "        [3, 4, 5]])\n"
     ]
    }
   ],
   "source": [
    "x = x.view(2, 3)\n",
    "print(\"X\", x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8bb46b52",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X tensor([[0, 3],\n",
      "        [1, 4],\n",
      "        [2, 5]])\n"
     ]
    }
   ],
   "source": [
    "x = x.permute(1, 0) # Swapping dimension 0 and 1\n",
    "print(\"X\", x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "395b9faa",
   "metadata": {},
   "outputs": [],
   "source": [
    "#x.transpose??"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0e66cc5",
   "metadata": {},
   "source": [
    "Other commonly used operations include matrix multiplications, which are essential for neural networks. Quite often, we have an input vector $\\mathbf{x}$, which is transformed using a learned weight matrix $\\mathbf{W}$. There are multiple ways and functions to perform matrix multiplication, some of which we list below:\n",
    "\n",
    "* `torch.matmul`: Performs the matrix product over two tensors, where the specific behavior depends on the dimensions. If both inputs are matrices (2-dimensional tensors), it performs the standard matrix product. For higher dimensional inputs, the function supports broadcasting (for details see the [documentation](https://pytorch.org/docs/stable/generated/torch.matmul.html?highlight=matmul#torch.matmul)). Can also be written as `a @ b`, similar to numpy. \n",
    "* `torch.mm`: Performs the matrix product over two matrices, but doesn't support broadcasting (see [documentation](https://pytorch.org/docs/stable/generated/torch.mm.html?highlight=torch%20mm#torch.mm))\n",
    "* `torch.bmm`: Performs the matrix product with a support batch dimension. If the first tensor $T$ is of shape ($b\\times n\\times m$), and the second tensor $R$ ($b\\times m\\times p$), the output $O$ is of shape ($b\\times n\\times p$), and has been calculated by performing $b$ matrix multiplications of the submatrices of $T$ and $R$: $O_i = T_i @ R_i$\n",
    "* `torch.einsum`: Performs matrix multiplications and more (i.e. sums of products) using the Einstein summation convention. Explanation of the Einstein sum can be found in assignment 1.\n",
    "\n",
    "Usually, we use `torch.matmul` or `torch.bmm`. We can try a matrix multiplication with `torch.matmul` below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "6705fd44",
   "metadata": {},
   "outputs": [],
   "source": [
    "#torch.matmul??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "aa668e2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X tensor([[0, 1, 2],\n",
      "        [3, 4, 5]])\n",
      "X shape :  torch.Size([2, 3])\n"
     ]
    }
   ],
   "source": [
    "x = torch.arange(6)\n",
    "x = x.view(2, 3)\n",
    "print(\"X\", x)\n",
    "print(\"X shape : \", x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "c0fab39f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W tensor([[0, 1, 2],\n",
      "        [3, 4, 5],\n",
      "        [6, 7, 8]])\n",
      "W shape :  torch.Size([3, 3])\n"
     ]
    }
   ],
   "source": [
    "W = torch.arange(9).view(3, 3) # We can also stack multiple operations in a single line\n",
    "print(\"W\", W)\n",
    "print(\"W shape : \", W.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "cee8ec24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[15, 18, 21],\n",
       "        [42, 54, 66]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x @ W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bb853dce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[15, 18, 21],\n",
       "        [42, 54, 66]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.matmul(x, W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "359f543d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#torch.bmm??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "453f689a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out matrix shape :  torch.Size([10, 3, 5])\n"
     ]
    }
   ],
   "source": [
    "mat1 = torch.randn(10, 3, 4)\n",
    "mat2 = torch.randn(10, 4, 5)\n",
    "mat3 = torch.bmm(mat1, mat2)\n",
    "print(\"Out matrix shape : \", mat3.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "fa39869d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Out matrix shape :  torch.Size([10, 3, 5])\n"
     ]
    }
   ],
   "source": [
    "mat1 = torch.randn(10, 3, 4)\n",
    "mat2 = torch.randn(10, 4, 5)\n",
    "mat3 = torch.einsum('bij, bjk -> bik', mat1, mat2)\n",
    "print(\"Out matrix shape : \", mat3.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73e86437",
   "metadata": {},
   "source": [
    "### Dynamic Computation Graph and Backpropagation\n",
    "\n",
    "One of the main reasons for using PyTorch in Deep Learning projects is that we can automatically get **gradients/derivatives** of functions that we define. We will mainly use PyTorch for implementing neural networks, and they are just fancy functions. If we use weight matrices in our function that we want to learn, then those are called the **parameters** or simply the **weights**.\n",
    "\n",
    "If our neural network would output a single scalar value, we would talk about taking the **derivative**, but you will see that quite often we will have **multiple** output variables (\"values\"); in that case we talk about **gradients**. It's a more general term.\n",
    "\n",
    "Given an input $\\mathbf{x}$, we define our function by **manipulating** that input, usually by matrix-multiplications with weight matrices and additions with so-called bias vectors. As we manipulate our input, we are automatically creating a **computational graph**. This graph shows how to arrive at our output from our input. \n",
    "PyTorch is a **define-by-run** framework; this means that we can just do our manipulations, and PyTorch will keep track of that graph for us. Thus, we create a dynamic computation graph along the way.\n",
    "\n",
    "So, to recap: the only thing we have to do is to compute the **output**, and then we can ask PyTorch to automatically get the **gradients**. \n",
    "\n",
    "> **Note:  Why do we want gradients?** Consider that we have defined a function, a neural net, that is supposed to compute a certain output $y$ for an input vector $\\mathbf{x}$. We then define an **error measure** that tells us how wrong our network is; how bad it is in predicting output $y$ from input $\\mathbf{x}$. Based on this error measure, we can use the gradients to **update** the weights $\\mathbf{W}$ that were responsible for the output, so that the next time we present input $\\mathbf{x}$ to our network, the output will be closer to what we want.\n",
    "\n",
    "The first thing we have to do is to specify which tensors require gradients. By default, when we create a tensor, it does not require gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1ecb785d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "x = torch.ones((3,))\n",
    "print(x.requires_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18e31817",
   "metadata": {},
   "source": [
    "We can change this for an existing tensor using the function `requires_grad_()` (underscore indicating that this is a in-place operation). Alternatively, when creating a tensor, you can pass the argument `requires_grad=True` to most initializers we have seen above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "5a4e92cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "x.requires_grad_(True)\n",
    "print(x.requires_grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d416e902",
   "metadata": {},
   "source": [
    "In order to get familiar with the concept of a computation graph, we will create one for the following function:\n",
    "\n",
    "$$y = \\frac{1}{|x|}\\sum_i \\left[(x_i + 2)^2 + 3\\right]$$\n",
    "\n",
    "You could imagine that $x$ are our parameters, and we want to optimize (either maximize or minimize) the output $y$. For this, we want to obtain the gradients $\\partial y / \\partial \\mathbf{x}$. For our example, we'll use $\\mathbf{x}=[0,1,2]$ as our input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "f6885425",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X tensor([0., 1., 2.], requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "x = torch.arange(3, dtype=torch.float32, requires_grad=True) # Only float tensors can have gradients\n",
    "print(\"X\", x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16bbf9c1",
   "metadata": {},
   "source": [
    "Now let's build the computation graph step by step. You can combine multiple operations in a single line, but we will separate them here to get a better understanding of how each operation is added to the computation graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "cd726496",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y tensor(12.6667, grad_fn=<MeanBackward0>)\n"
     ]
    }
   ],
   "source": [
    "a = x + 2\n",
    "b = a ** 2\n",
    "c = b + 3\n",
    "y = c.mean()\n",
    "print(\"Y\", y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16ef5157",
   "metadata": {},
   "source": [
    "Using the statements above, we have created a computation graph that looks similar to the figure below:\n",
    "\n",
    "<center style=\"width: 100%\"><img src=\"./pytorch_computation_graph.pdf\" width=\"600px\"></center>\n",
    "\n",
    "We calculate $a$ based on the inputs $x$ and the constant $2$, $b$ is $a$ squared, and so on. The visualization is an abstraction of the dependencies between inputs and outputs of the operations we have applied.\n",
    "Each node of the computation graph has automatically defined a function for calculating the gradients with respect to its inputs, `grad_fn`. You can see this when we printed the output tensor $y$. This is why the computation graph is usually visualized in the reverse direction (arrows point from the result to the inputs). We can perform backpropagation on the computation graph by calling the function `backward()` on the last output, which effectively calculates the gradients for each tensor that has the property `requires_grad=True`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "57ba3110",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(x.grad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "1b174f97",
   "metadata": {},
   "outputs": [],
   "source": [
    "y.backward() # the function to call to store the gradie"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "629a6737",
   "metadata": {},
   "source": [
    "`x.grad` will now contain the gradient $\\partial y/ \\partial \\mathcal{x}$, and this gradient indicates how a change in $\\mathbf{x}$ will affect output $y$ given the current input $\\mathbf{x}=[0,1,2]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "6d3a61e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1.3333, 2.0000, 2.6667])\n"
     ]
    }
   ],
   "source": [
    "print(x.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37afec35",
   "metadata": {},
   "source": [
    "We can also verify these gradients by hand. We will calculate the gradients using the chain rule, in the same way as PyTorch did it:\n",
    "\n",
    "$$\\frac{\\partial y}{\\partial x_i} = \\frac{\\partial y}{\\partial c_i}\\frac{\\partial c_i}{\\partial b_i}\\frac{\\partial b_i}{\\partial a_i}\\frac{\\partial a_i}{\\partial x_i}$$\n",
    "\n",
    "Note that we have simplified this equation to index notation, and by using the fact that all operation besides the mean do not combine the elements in the tensor. The partial derivatives are:\n",
    "\n",
    "$$\n",
    "\\frac{\\partial a_i}{\\partial x_i} = 1,\\hspace{1cm}\n",
    "\\frac{\\partial b_i}{\\partial a_i} = 2\\cdot a_i\\hspace{1cm}\n",
    "\\frac{\\partial c_i}{\\partial b_i} = 1\\hspace{1cm}\n",
    "\\frac{\\partial y}{\\partial c_i} = \\frac{1}{3}\n",
    "$$\n",
    "\n",
    "Hence, with the input being $\\mathbf{x}=[0,1,2]$, our gradients are $\\partial y/\\partial \\mathbf{x}=[4/3,2,8/3]$. The previous code cell should have printed the same result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6120be96",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "8d9a6c34",
   "metadata": {},
   "source": [
    "### Doing a backpropagation in the numpy way with torch tensors\n",
    "\n",
    "$$ y_{pred} = W_2 ( \\sigma( W_1 . x ) )$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "0c2e86ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49 15003.4951171875\n",
      "99 814.7637329101562\n",
      "149 76.71509552001953\n",
      "199 8.781590461730957\n",
      "249 1.1065536737442017\n",
      "299 0.1472855806350708\n",
      "349 0.020445531234145164\n",
      "399 0.003165598027408123\n",
      "449 0.000675841118209064\n",
      "499 0.00021863274741917849\n"
     ]
    }
   ],
   "source": [
    "\n",
    "dtype = torch.float\n",
    "#device = cuddevice\n",
    "# device = torch.device(\"cuda:0\") # Uncomment this to run on GPU\n",
    "\n",
    "# N is batch size; D_in is input dimension;\n",
    "# H is hidden dimension; D_out is output dimension.\n",
    "N, D_in, H, D_out = 64, 1000, 100, 10\n",
    "\n",
    "# Create random input and output data\n",
    "x = torch.randn(N, D_in, device=device, dtype=dtype)\n",
    "y = torch.randn(N, D_out, device=device, dtype=dtype)\n",
    "\n",
    "# Randomly initialize weights\n",
    "w1 = torch.randn(D_in, H, device=device, dtype=dtype)\n",
    "w2 = torch.randn(H, D_out, device=device, dtype=dtype)\n",
    "\n",
    "learning_rate = 1e-6\n",
    "for t in range(500):\n",
    "    # Forward pass: compute predicted y\n",
    "    h = x.mm(w1)\n",
    "    h_relu = h.clamp(min=0) # -- the clamp filters out < 0 values\n",
    "    y_pred = h_relu.mm(w2)\n",
    "\n",
    "    # Compute and print loss\n",
    "    loss = (y_pred - y).pow(2).sum().item()\n",
    "    if t % 50 == 49:\n",
    "        print(t, loss)\n",
    "\n",
    "    # Backprop to compute gradients of w1 and w2 with respect to loss\n",
    "    grad_y_pred = 2.0 * (y_pred - y)\n",
    "    grad_w2 = h_relu.t().mm(grad_y_pred)\n",
    "    grad_h_relu = grad_y_pred.mm(w2.t())\n",
    "    grad_h = grad_h_relu.clone()\n",
    "    grad_h[h < 0] = 0\n",
    "    grad_w1 = x.t().mm(grad_h) # -- we had x.T for numpy arrays\n",
    "\n",
    "    # Update weights using gradient descent\n",
    "    w1 -= learning_rate * grad_w1\n",
    "    w2 -= learning_rate * grad_w2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1636d100",
   "metadata": {},
   "source": [
    "### The PyTorch nn Modeule, contains the basic NN layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "eb0b5b6f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49 38.46702575683594\n",
      "99 2.6432113647460938\n",
      "149 0.3023982644081116\n",
      "199 0.04455281049013138\n",
      "249 0.007486585061997175\n",
      "299 0.0013749762438237667\n",
      "349 0.0002715742157306522\n",
      "399 5.800240614917129e-05\n",
      "449 1.352568779111607e-05\n",
      "499 3.459010940787266e-06\n"
     ]
    }
   ],
   "source": [
    "# N is batch size; D_in is input dimension;\n",
    "# H is hidden dimension; D_out is output dimension.\n",
    "N, D_in, H, D_out = 64, 1000, 100, 10\n",
    "\n",
    "# Create random Tensors to hold inputs and outputs\n",
    "x = torch.randn(N, D_in, device=device)\n",
    "y = torch.randn(N, D_out, device=device)\n",
    "\n",
    "# Use the nn package to define our model as a sequence of layers. nn.Sequential\n",
    "# is a Module which contains other Modules, and applies them in sequence to\n",
    "# produce its output. Each Linear Module computes output from input using a\n",
    "# linear function, and holds internal Tensors for its weight and bias.\n",
    "model = torch.nn.Sequential(\n",
    "    torch.nn.Linear(D_in, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, D_out),\n",
    ")\n",
    "\n",
    "model.to(device)\n",
    "\n",
    "# The nn package also contains definitions of popular loss functions; in this\n",
    "# case we will use Mean Squared Error (MSE) as our loss function.\n",
    "loss_fn = torch.nn.MSELoss(reduction='sum')\n",
    "\n",
    "learning_rate = 1e-4\n",
    "for t in range(500):\n",
    "    # Forward pass: compute predicted y by passing x to the model. Module objects\n",
    "    # override the __call__ operator so you can call them like functions. When\n",
    "    # doing so you pass a Tensor of input data to the Module and it produces\n",
    "    # a Tensor of output data.\n",
    "    y_pred = model(x)\n",
    "\n",
    "    # Compute and print loss. We pass Tensors containing the predicted and true\n",
    "    # values of y, and the loss function returns a Tensor containing the\n",
    "    # loss.\n",
    "    loss = loss_fn(y_pred, y)\n",
    "    if t % 50 == 49:\n",
    "        print(t, loss.item())\n",
    "\n",
    "    # Zero the gradients before running the backward pass.\n",
    "    model.zero_grad()\n",
    "\n",
    "    # Backward pass: compute gradient of the loss with respect to all the learnable\n",
    "    # parameters of the model. Internally, the parameters of each Module are stored\n",
    "    # in Tensors with requires_grad=True, so this call will compute gradients for\n",
    "    # all learnable parameters in the model.\n",
    "    loss.backward()\n",
    "\n",
    "    # Update the weights using gradient descent. Each parameter is a Tensor, so\n",
    "    # we can access its gradients like we did before.\n",
    "    with torch.no_grad():\n",
    "        for param in model.parameters():\n",
    "            param -= learning_rate * param.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b322d42f",
   "metadata": {},
   "source": [
    "### Updating the weights through PyTorch optim "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0bf3004b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49 194.01768493652344\n",
      "99 42.58795928955078\n",
      "149 5.385366439819336\n",
      "199 0.40881234407424927\n",
      "249 0.022810500115156174\n",
      "299 0.0013532309094443917\n",
      "349 0.00012053031241521239\n",
      "399 1.3493299775291234e-05\n",
      "449 1.4780346191400895e-06\n",
      "499 1.4088730893035972e-07\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# N is batch size; D_in is input dimension;\n",
    "# H is hidden dimension; D_out is output dimension.\n",
    "N, D_in, H, D_out = 64, 1000, 100, 10\n",
    "\n",
    "# Create random Tensors to hold inputs and outputs\n",
    "x = torch.randn(N, D_in, device=device)\n",
    "y = torch.randn(N, D_out, device=device)\n",
    "\n",
    "# Use the nn package to define our model and loss function.\n",
    "model = torch.nn.Sequential(\n",
    "    torch.nn.Linear(D_in, H),\n",
    "    torch.nn.ReLU(),\n",
    "    torch.nn.Linear(H, D_out),\n",
    ")\n",
    "loss_fn = torch.nn.MSELoss(reduction='sum')\n",
    "\n",
    "model.to(device)\n",
    "\n",
    "# Use the optim package to define an Optimizer that will update the weights of\n",
    "# the model for us. Here we will use Adam; the optim package contains many other\n",
    "# optimization algoriths. The first argument to the Adam constructor tells the\n",
    "# optimizer which Tensors it should update.\n",
    "learning_rate = 1e-4\n",
    "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)\n",
    "for t in range(500):\n",
    "    # Forward pass: compute predicted y by passing x to the model.\n",
    "    y_pred = model(x)\n",
    "\n",
    "    # Compute and print loss.\n",
    "    loss = loss_fn(y_pred, y)\n",
    "    if t % 50 == 49:\n",
    "        print(t, loss.item())\n",
    "\n",
    "    # Before the backward pass, use the optimizer object to zero all of the\n",
    "    # gradients for the variables it will update (which are the learnable\n",
    "    # weights of the model). This is because by default, gradients are\n",
    "    # accumulated in buffers( i.e, not overwritten) whenever .backward()\n",
    "    # is called. Checkout docs of torch.autograd.backward for more details.\n",
    "    optimizer.zero_grad()\n",
    "\n",
    "    # Backward pass: compute gradient of the loss with respect to model\n",
    "    # parameters\n",
    "    loss.backward()\n",
    "\n",
    "    # Calling the step function on an Optimizer makes an update to its\n",
    "    # parameters\n",
    "    optimizer.step()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d396afa3",
   "metadata": {},
   "source": [
    "### The model\n",
    "\n",
    "The package `torch.nn` defines a series of useful classes like linear networks layers, activation functions, loss functions etc. A full list can be found [here](https://pytorch.org/docs/stable/nn.html). In case you need a certain network layer, check the documentation of the package first before writing the layer yourself as the package likely contains the code for it already. We import it below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9d30e3f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b91dee13",
   "metadata": {},
   "source": [
    "Additionally to `torch.nn`, there is also `torch.nn.functional`. It contains functions that are used in network layers. This is in contrast to `torch.nn` which defines them as `nn.Modules` (more on it below), and `torch.nn` actually uses a lot of functionalities from `torch.nn.functional`. Hence, the functional package is useful in many situations, and so we import it as well here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "35d67a50",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec517ece",
   "metadata": {},
   "source": [
    "#### nn.Module\n",
    "\n",
    "In PyTorch, a neural network is built up out of modules. Modules can contain other modules, and a neural network is considered to be a module itself as well. The basic template of a module is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "b9a6d78a",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyModule(nn.Module):\n",
    "    \n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        # Some init for my module\n",
    "        \n",
    "    def forward(self, x):\n",
    "        # Function for performing the calculation of the module.\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1af67826",
   "metadata": {},
   "source": [
    "The forward function is where the computation of the module is taken place, and is executed when you call the module (`nn = MyModule(); nn(x)`). In the init function, we usually create the parameters of the module, using `nn.Parameter`, or defining other modules that are used in the forward function. The backward calculation is done automatically, but could be overwritten as well if wanted.\n",
    "\n",
    "#### Simple classifier\n",
    "We can now make use of the pre-defined modules in the `torch.nn` package, and define our own small neural network. We will use a minimal network with a input layer, one hidden layer with tanh as activation function, and a output layer. In other words, our networks should look something like this:\n",
    "\n",
    "<center width=\"100%\"><img src=\"small_neural_network.svg\" width=\"500px\"></center>\n",
    "\n",
    "The input neurons are shown in blue, which represent the coordinates $x_1$ and $x_2$ of a data point. The hidden neurons including a tanh activation are shown in white, and the output neuron in red.\n",
    "In PyTorch, we can define this as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "34e35692",
   "metadata": {},
   "outputs": [],
   "source": [
    "class SimpleClassifier(nn.Module):\n",
    "\n",
    "    def __init__(self, num_inputs, num_hidden, num_outputs):\n",
    "        super().__init__()\n",
    "        # Initialize the modules we need to build the network\n",
    "        self.linear1 = nn.Linear(num_inputs, num_hidden)\n",
    "        self.act_fn = nn.Tanh()\n",
    "        self.linear2 = nn.Linear(num_hidden, num_outputs)\n",
    "\n",
    "    def forward(self, x):\n",
    "        # Perform the calculation of the model to determine the prediction\n",
    "        x = self.linear1(x)\n",
    "        x = self.act_fn(x)\n",
    "        x = self.linear2(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a107d1",
   "metadata": {},
   "source": [
    "For the examples in this notebook, we will use a tiny neural network with two input neurons and four hidden neurons. As we perform binary classification, we will use a single output neuron. Note that we do not apply a sigmoid on the output yet. This is because other functions, especially the loss, are more efficient and precise to calculate on the original outputs instead of the sigmoid output. We will discuss the detailed reason later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09fe00c9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1fba6f8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SimpleClassifier(\n",
      "  (linear1): Linear(in_features=2, out_features=4, bias=True)\n",
      "  (act_fn): Tanh()\n",
      "  (linear2): Linear(in_features=4, out_features=1, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = SimpleClassifier(num_inputs=2, num_hidden=4, num_outputs=1)\n",
    "# Printing a module shows all its submodules\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "736aaa2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<bound method Module.children of SimpleClassifier(\n",
      "  (linear1): Linear(in_features=2, out_features=4, bias=True)\n",
      "  (act_fn): Tanh()\n",
      "  (linear2): Linear(in_features=4, out_features=1, bias=True)\n",
      ")>\n"
     ]
    }
   ],
   "source": [
    "print(model.children)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fe4bfc9",
   "metadata": {},
   "source": [
    "Printing the model lists all submodules it contains. The parameters of a module can be obtained by using its `parameters()` functions, or `named_parameters()` to get a name to each parameter object. For our small neural network, we have the following parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "40acf99b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter linear1.weight, shape torch.Size([4, 2])\n",
      "Parameter linear1.bias, shape torch.Size([4])\n",
      "Parameter linear2.weight, shape torch.Size([1, 4])\n",
      "Parameter linear2.bias, shape torch.Size([1])\n"
     ]
    }
   ],
   "source": [
    "for name, param in model.named_parameters():\n",
    "    print(f\"Parameter {name}, shape {param.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db6d1e2e",
   "metadata": {},
   "source": [
    "Each linear layer has a weight matrix of the shape `[output, input]`, and a bias of the shape `[output]`. The tanh activation function does not have any parameters. Note that parameters are only registered for `nn.Module` objects that are direct object attributes, i.e. `self.a = ...`. If you define a list of modules, the parameters of those are not registered for the outer module and can cause some issues when you try to optimize your module. There are alternatives, like `nn.ModuleList`, `nn.ModuleDict` and `nn.Sequential`, that allow you to have different data structures of modules. We will use them in a few later tutorials and explain them there. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a85ae62b",
   "metadata": {},
   "source": [
    "### The data\n",
    "\n",
    "PyTorch also provides a few functionalities to load the training and test data efficiently, summarized in the package `torch.utils.data`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "89fe9956",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a0ccbc3",
   "metadata": {},
   "source": [
    "The data package defines two classes which are the standard interface for handling data in PyTorch: `data.Dataset`, and `data.DataLoader`. The dataset class provides an uniform interface to access the training/test data, while the data loader makes sure to efficiently load and stack the data points from the dataset into batches during training."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cb5d0e7",
   "metadata": {},
   "source": [
    "#### The dataset class\n",
    "\n",
    "The dataset class summarizes the basic functionality of a dataset in a natural way. To define a dataset in PyTorch, we simply specify two functions: `__getitem__`, and `__len__`. The get-item function has to return the $i$-th data point in the dataset, while the len function returns the size of the dataset. For the XOR dataset, we can define the dataset class as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "1db80c2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class XORDataset(data.Dataset):\n",
    "\n",
    "    def __init__(self, size, std=0.1):\n",
    "        \"\"\"\n",
    "        Inputs:\n",
    "            size - Number of data points we want to generate\n",
    "            std - Standard deviation of the noise (see generate_continuous_xor function)\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "        self.size = size\n",
    "        self.std = std\n",
    "        self.generate_continuous_xor()\n",
    "\n",
    "    def generate_continuous_xor(self):\n",
    "        # Each data point in the XOR dataset has two variables, x and y, that can be either 0 or 1\n",
    "        # The label is their XOR combination, i.e. 1 if only x or only y is 1 while the other is 0.\n",
    "        # If x=y, the label is 0.\n",
    "        data = torch.randint(low=0, high=2, size=(self.size, 2), dtype=torch.float32)\n",
    "        label = (data.sum(dim=1) == 1).to(torch.long)\n",
    "        # To make it slightly more challenging, we add a bit of gaussian noise to the data points.\n",
    "        data += self.std * torch.randn(data.shape)\n",
    "\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "\n",
    "    def __len__(self):\n",
    "        # Number of data point we have. Alternatively self.data.shape[0], or self.label.shape[0]\n",
    "        return self.size\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        # Return the idx-th data point of the dataset\n",
    "        # If we have multiple things to return (data point and label), we can return them as tuple\n",
    "        data_point = self.data[idx]\n",
    "        data_label = self.label[idx]\n",
    "        return data_point, data_label"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a4a546e",
   "metadata": {},
   "source": [
    "Let's try to create such a dataset and inspect it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "5d97edf1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of dataset: 200\n",
      "Data point 0: (tensor([-0.0310,  0.9223]), tensor(1))\n"
     ]
    }
   ],
   "source": [
    "dataset = XORDataset(size=200)\n",
    "print(\"Size of dataset:\", len(dataset))\n",
    "print(\"Data point 0:\", dataset[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c672d1e",
   "metadata": {},
   "source": [
    "To better relate to the dataset, we visualize the samples below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "aaefd9a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_samples(data, label, marker='o'):\n",
    "    if isinstance(data, torch.Tensor):\n",
    "        data = data.cpu().numpy()\n",
    "    if isinstance(label, torch.Tensor):\n",
    "        label = label.cpu().numpy()\n",
    "    data_0 = data[label == 0]\n",
    "    data_1 = data[label == 1]\n",
    "    \n",
    "    plt.figure(figsize=(4,4))\n",
    "    plt.scatter(data_0[:,0], data_0[:,1], edgecolor=\"#333\", marker=marker, label=\"Class 0\")\n",
    "    plt.scatter(data_1[:,0], data_1[:,1], edgecolor=\"#333\", marker=marker, label=\"Class 1\")\n",
    "    plt.title(\"Dataset samples\")\n",
    "    plt.ylabel(r\"$x_2$\")\n",
    "    plt.xlabel(r\"$x_1$\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "b004fe49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data shape :  torch.Size([200, 2]) Label shape :  torch.Size([200])\n"
     ]
    }
   ],
   "source": [
    "print('Data shape : ', dataset.data.shape, 'Label shape : ', dataset.label.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "bb64913e",
   "metadata": {},
   "outputs": [
    {
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   ],
   "source": [
    "visualize_samples(dataset.data, dataset.label)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbda6e9a",
   "metadata": {},
   "source": [
    "#### The data loader class\n",
    "\n",
    "The class `torch.utils.data.DataLoader` represents a Python iterable over a dataset with support for automatic batching, multi-process data loading and many more features. The data loader communicates with the dataset using the function `__getitem__`, and stacks its outputs as tensors over the first dimension to form a batch.\n",
    "In contrast to the dataset class, we usually don't have to define our own data loader class, but can just create an object of it with the dataset as input. Additionally, we can configure our data loader with the following input arguments (only a selection, see full list [here](https://pytorch.org/docs/stable/data.html#torch.utils.data.DataLoader)):\n",
    "\n",
    "* `batch_size`: Number of samples to stack per batch\n",
    "* `shuffle`: If True, the data is returned in a random order. This is important during training for introducing stochasticity. \n",
    "* `num_workers`: Number of subprocesses to use for data loading. The default, 0, means that the data will be loaded in the main process which can slow down training for datasets where loading a data point takes a considerable amount of time (e.g. large images). More workers are recommended for those, but can cause issues on Windows computers. For tiny datasets as ours, 0 workers are usually faster.\n",
    "* `pin_memory`: If True, the data loader will copy Tensors into CUDA pinned memory before returning them. This can save some time for large data points on GPUs. Usually a good practice to use for a training set, but not necessarily for validation and test to save memory on the GPU.\n",
    "* `drop_last`: If True, the last batch is dropped in case it is smaller than the specified batch size. This occurs when the dataset size is not a multiple of the batch size. Only potentially helpful during training to keep a consistent batch size.\n",
    "\n",
    "Let's create a simple data loader below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "b83dc622",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_loader = data.DataLoader(dataset, batch_size=8, shuffle=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "e2bbc663",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data inputs torch.Size([8, 2]) \n",
      " tensor([[ 0.9460,  0.9904],\n",
      "        [ 0.0189,  0.9758],\n",
      "        [ 0.0695,  0.1925],\n",
      "        [ 0.1620,  0.8923],\n",
      "        [ 0.9935, -0.0929],\n",
      "        [-0.0390,  1.1351],\n",
      "        [ 0.8599,  0.0081],\n",
      "        [ 1.0776,  0.0328]])\n",
      "Data labels torch.Size([8]) \n",
      " tensor([0, 1, 0, 1, 1, 1, 1, 1])\n"
     ]
    }
   ],
   "source": [
    "# next(iter(...)) catches the first batch of the data loader\n",
    "# If shuffle is True, this will return a different batch every time we run this cell\n",
    "# For iterating over the whole dataset, we can simple use \"for batch in data_loader: ...\"\n",
    "data_inputs, data_labels = next(iter(data_loader))\n",
    "\n",
    "# The shape of the outputs are [batch_size, d_1,...,d_N] where d_1,...,d_N are the \n",
    "# dimensions of the data point returned from the dataset class\n",
    "print(\"Data inputs\", data_inputs.shape, \"\\n\", data_inputs)\n",
    "print(\"Data labels\", data_labels.shape, \"\\n\", data_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bec22d6",
   "metadata": {},
   "source": [
    "### Optimization\n",
    "\n",
    "After defining the model and the dataset, it is time to prepare the optimization of the model. During training, we will perform the following steps:\n",
    "\n",
    "1. Get a batch from the data loader\n",
    "2. Obtain the predictions from the model for the batch\n",
    "3. Calculate the loss based on the difference between predictions and labels\n",
    "4. Backpropagation: calculate the gradients for every parameter with respect to the loss\n",
    "5. Update the parameters of the model in the direction of the gradients\n",
    "\n",
    "We have seen how we can do step 1, 2 and 4 in PyTorch. Now, we will look at step 3 and 5."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c19bb56a",
   "metadata": {},
   "source": [
    "### Loss modules\n",
    "\n",
    "We can calculate the loss for a batch by simply performing a few tensor operations as those are automatically added to the computation graph. For instance, for binary classification, we can use Binary Cross Entropy (BCE) which is defined as follows:\n",
    "\n",
    "$$\\mathcal{L}_{BCE} = -\\sum_i \\left[ y_i \\log x_i + (1 - y_i) \\log (1 - x_i) \\right]$$\n",
    "\n",
    "where $y$ are our labels, and $x$ our predictions, both in the range of $[0,1]$. However, PyTorch already provides a list of predefined loss functions which we can use (see [here](https://pytorch.org/docs/stable/nn.html#loss-functions) for a full list). For instance, for BCE, PyTorch has two modules: `nn.BCELoss()`, `nn.BCEWithLogitsLoss()`. While `nn.BCELoss` expects the inputs $x$ to be in the range $[0,1]$, i.e. the output of a sigmoid, `nn.BCEWithLogitsLoss` combines a sigmoid layer and the BCE loss in a single class. This version is numerically more stable than using a plain Sigmoid followed by a BCE loss because of the logarithms applied in the loss function. Hence, it is adviced to use loss functions applied on \"logits\" where possible (remember to not apply a sigmoid on the output of the model in this case!). For our model defined above, we therefore use the module `nn.BCEWithLogitsLoss`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "87b2b71f",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_module = nn.BCEWithLogitsLoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13acf53d",
   "metadata": {},
   "source": [
    "#### Stochastic Gradient Descent\n",
    "\n",
    "For updating the parameters, PyTorch provides the package `torch.optim` that has most popular optimizers implemented. We will discuss the specific optimizers and their differences later in the course, but will for now use the simplest of them: `torch.optim.SGD`. Stochastic Gradient Descent updates parameters by multiplying the gradients with a small constant, called learning rate, and subtracting those from the parameters (hence minimizing the loss). Therefore, we slowly move towards the direction of minimizing the loss. A good default value of the learning rate for a small network as ours is 0.1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "fd98b67c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input to the optimizer are the parameters of the model: model.parameters()\n",
    "optimizer = torch.optim.SGD(model.parameters(), lr=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d60d4d5",
   "metadata": {},
   "source": [
    "The optimizer provides two useful functions: `optimizer.step()`, and `optimizer.zero_grad()`. The step function updates the parameters based on the gradients as explained above. The function `optimizer.zero_grad()` sets the gradients of all parameters to zero. While this function seems less relevant at first, it is a crucial pre-step before performing backpropagation. If we call the `backward` function on the loss while the parameter gradients are non-zero from the previous batch, the new gradients would actually be added to the previous ones instead of overwriting them. This is done because a parameter might occur multiple times in a computation graph, and we need to sum the gradients in this case instead of replacing them. Hence, remember to call `optimizer.zero_grad()` before calculating the gradients of a batch."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45a4749c",
   "metadata": {},
   "source": [
    "### Training\n",
    "\n",
    "Finally, we are ready to train our model. As a first step, we create a slightly larger dataset and specify a data loader with a larger batch size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "80d284e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dataset = XORDataset(size=2500)\n",
    "train_data_loader = data.DataLoader(train_dataset, batch_size=128, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22fce4c1",
   "metadata": {},
   "source": [
    "Now, we can write a small training function. Remember our five steps: load a batch, obtain the predictions, calculate the loss, backpropagate, and update. Additionally, we have to push all data and model parameters to the device of our choice (GPU if available). For the tiny neural network we have, communicating the data to the GPU actually takes much more time than we could save from running the operation on GPU. For large networks, the communication time is significantly smaller than the actual runtime making a GPU crucial in these cases. Still, to practice, we will push the data to GPU here. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "31335e82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SimpleClassifier(\n",
       "  (linear1): Linear(in_features=2, out_features=4, bias=True)\n",
       "  (act_fn): Tanh()\n",
       "  (linear2): Linear(in_features=4, out_features=1, bias=True)\n",
       ")"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Push model to device. Has to be only done once\n",
    "model.to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a10f46b4",
   "metadata": {},
   "source": [
    "In addition, we set our model to training mode. This is done by calling `model.train()`. There exist certain modules that need to perform a different forward step during training than during testing (e.g. BatchNorm and Dropout), and we can switch between them using `model.train()` and `model.eval()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "e41f78d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_model(model, optimizer, data_loader, loss_module, num_epochs=100):\n",
    "    # Set model to train mode\n",
    "    model.train() \n",
    "    \n",
    "    # Training loop\n",
    "    for epoch in tqdm(range(num_epochs)):\n",
    "        for data_inputs, data_labels in data_loader:\n",
    "            \n",
    "            ## Step 1: Move input data to device (only strictly necessary if we use GPU)\n",
    "            data_inputs = data_inputs.to(device)\n",
    "            data_labels = data_labels.to(device)\n",
    "            \n",
    "            ## Step 2: Run the model on the input data\n",
    "            preds = model(data_inputs)\n",
    "            preds = preds.squeeze(dim=1) # Output is [Batch size, 1], but we want [Batch size]\n",
    "            \n",
    "            ## Step 3: Calculate the loss\n",
    "            loss = loss_module(preds, data_labels.float())\n",
    "            \n",
    "            ## Step 4: Perform backpropagation\n",
    "            # Before calculating the gradients, we need to ensure that they are all zero. \n",
    "            # The gradients would not be overwritten, but actually added to the existing ones.\n",
    "            optimizer.zero_grad() \n",
    "            # Perform backpropagation\n",
    "            loss.backward()\n",
    "            \n",
    "            ## Step 5: Update the parameters\n",
    "            optimizer.step()\n",
    "            \n",
    "        print('epoch : ', epoch, ', Loss : ', loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "df293a6b",
   "metadata": {},
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     "name": "stdout",
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     "text": [
      "epoch :  0 , Loss :  tensor(0.0083, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  1 , Loss :  tensor(0.0086, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  2 , Loss :  tensor(0.0101, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  3 , Loss :  tensor(0.0084, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  4 , Loss :  tensor(0.0086, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  5 , Loss :  tensor(0.0074, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  6 , Loss :  tensor(0.0077, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  7 , Loss :  tensor(0.0071, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  8 , Loss :  tensor(0.0085, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  9 , Loss :  tensor(0.0085, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  10 , Loss :  tensor(0.0096, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  11 , Loss :  tensor(0.0071, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  12 , Loss :  tensor(0.0105, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  13 , Loss :  tensor(0.0076, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  14 , Loss :  tensor(0.0094, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  15 , Loss :  tensor(0.0067, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  16 , Loss :  tensor(0.0095, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  17 , Loss :  tensor(0.0076, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  18 , Loss :  tensor(0.0084, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  19 , Loss :  tensor(0.0121, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  20 , Loss :  tensor(0.0088, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  21 , Loss :  tensor(0.0076, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  22 , Loss :  tensor(0.0069, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  23 , Loss :  tensor(0.0082, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  24 , Loss :  tensor(0.0081, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  25 , Loss :  tensor(0.0087, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  26 , Loss :  tensor(0.0088, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  27 , Loss :  tensor(0.0074, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  28 , Loss :  tensor(0.0072, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  29 , Loss :  tensor(0.0077, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  30 , Loss :  tensor(0.0089, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  31 , Loss :  tensor(0.0071, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  32 , Loss :  tensor(0.0074, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  33 , Loss :  tensor(0.0075, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  34 , Loss :  tensor(0.0078, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  35 , Loss :  tensor(0.0084, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  36 , Loss :  tensor(0.0075, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  37 , Loss :  tensor(0.0081, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  38 , Loss :  tensor(0.0072, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  39 , Loss :  tensor(0.0090, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  40 , Loss :  tensor(0.0069, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  41 , Loss :  tensor(0.0064, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  42 , Loss :  tensor(0.0072, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  43 , Loss :  tensor(0.0068, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  44 , Loss :  tensor(0.0071, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  45 , Loss :  tensor(0.0072, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  46 , Loss :  tensor(0.0062, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  47 , Loss :  tensor(0.0075, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  48 , Loss :  tensor(0.0066, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  49 , Loss :  tensor(0.0065, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  50 , Loss :  tensor(0.0061, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  51 , Loss :  tensor(0.0061, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  52 , Loss :  tensor(0.0068, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  53 , Loss :  tensor(0.0062, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  54 , Loss :  tensor(0.0082, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  55 , Loss :  tensor(0.0059, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  56 , Loss :  tensor(0.0065, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  57 , Loss :  tensor(0.0070, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  58 , Loss :  tensor(0.0063, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  59 , Loss :  tensor(0.0055, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  60 , Loss :  tensor(0.0064, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  61 , Loss :  tensor(0.0062, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  62 , Loss :  tensor(0.0061, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  63 , Loss :  tensor(0.0061, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  64 , Loss :  tensor(0.0063, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  65 , Loss :  tensor(0.0056, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  66 , Loss :  tensor(0.0060, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  67 , Loss :  tensor(0.0056, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  68 , Loss :  tensor(0.0068, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  69 , Loss :  tensor(0.0066, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  70 , Loss :  tensor(0.0060, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  71 , Loss :  tensor(0.0063, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  72 , Loss :  tensor(0.0093, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  73 , Loss :  tensor(0.0059, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  74 , Loss :  tensor(0.0069, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  75 , Loss :  tensor(0.0053, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  76 , Loss :  tensor(0.0053, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  77 , Loss :  tensor(0.0064, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  78 , Loss :  tensor(0.0053, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  79 , Loss :  tensor(0.0059, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  80 , Loss :  tensor(0.0061, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  81 , Loss :  tensor(0.0055, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  82 , Loss :  tensor(0.0053, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  83 , Loss :  tensor(0.0090, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch :  84 , Loss :  tensor(0.0043, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  85 , Loss :  tensor(0.0050, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  86 , Loss :  tensor(0.0051, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  87 , Loss :  tensor(0.0067, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  88 , Loss :  tensor(0.0051, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  89 , Loss :  tensor(0.0066, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  90 , Loss :  tensor(0.0058, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  91 , Loss :  tensor(0.0052, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  92 , Loss :  tensor(0.0064, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  93 , Loss :  tensor(0.0065, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  94 , Loss :  tensor(0.0058, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  95 , Loss :  tensor(0.0057, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  96 , Loss :  tensor(0.0050, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  97 , Loss :  tensor(0.0058, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  98 , Loss :  tensor(0.0099, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n",
      "epoch :  99 , Loss :  tensor(0.0050, device='mps:0', grad_fn=<BinaryCrossEntropyWithLogitsBackward0>)\n"
     ]
    }
   ],
   "source": [
    "train_model(model, optimizer, train_data_loader, loss_module)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccdf7e92",
   "metadata": {},
   "source": [
    "#### Saving a model\n",
    "\n",
    "After finish training a model, we save the model to disk so that we can load the same weights at a later time. For this, we extract the so-called `state_dict` from the model which contains all learnable parameters. For our simple model, the state dict contains the following entries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4193421d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OrderedDict([('linear1.weight', tensor([[ 2.2923, -3.6011],\n",
      "        [ 4.0393, -2.9665],\n",
      "        [ 0.8683, -1.4337],\n",
      "        [-2.7049, -2.6998]], device='mps:0')), ('linear1.bias', tensor([-0.6087,  1.0527, -0.3302,  0.6301], device='mps:0')), ('linear2.weight', tensor([[ 5.1387, -5.6920,  1.0020, -4.3383]], device='mps:0')), ('linear2.bias', tensor([1.7424], device='mps:0'))])\n"
     ]
    }
   ],
   "source": [
    "state_dict = model.state_dict()\n",
    "print(state_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c766ce34",
   "metadata": {},
   "source": [
    "To save the state dictionary, we can use `torch.save`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "06c2c8e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# torch.save(object, filename). For the filename, any extension can be used\n",
    "torch.save(state_dict, \"our_model.pt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6602e932",
   "metadata": {},
   "source": [
    "To load a model from a state dict, we use the function `torch.load` to load the state dict from the disk, and the module function `load_state_dict` to overwrite our parameters with the new values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "6d9ab226",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original model\n",
      " OrderedDict([('linear1.weight', tensor([[ 2.2923, -3.6011],\n",
      "        [ 4.0393, -2.9665],\n",
      "        [ 0.8683, -1.4337],\n",
      "        [-2.7049, -2.6998]], device='mps:0')), ('linear1.bias', tensor([-0.6087,  1.0527, -0.3302,  0.6301], device='mps:0')), ('linear2.weight', tensor([[ 5.1387, -5.6920,  1.0020, -4.3383]], device='mps:0')), ('linear2.bias', tensor([1.7424], device='mps:0'))])\n",
      "\n",
      "Loaded model\n",
      " OrderedDict([('linear1.weight', tensor([[ 2.2923, -3.6011],\n",
      "        [ 4.0393, -2.9665],\n",
      "        [ 0.8683, -1.4337],\n",
      "        [-2.7049, -2.6998]])), ('linear1.bias', tensor([-0.6087,  1.0527, -0.3302,  0.6301])), ('linear2.weight', tensor([[ 5.1387, -5.6920,  1.0020, -4.3383]])), ('linear2.bias', tensor([1.7424]))])\n"
     ]
    }
   ],
   "source": [
    "# Load state dict from the disk (make sure it is the same name as above)\n",
    "state_dict = torch.load(\"our_model.pt\")\n",
    "\n",
    "# Create a new model and load the state\n",
    "new_model = SimpleClassifier(num_inputs=2, num_hidden=4, num_outputs=1)\n",
    "new_model.load_state_dict(state_dict)\n",
    "\n",
    "# Verify that the parameters are the same\n",
    "print(\"Original model\\n\", model.state_dict())\n",
    "print(\"\\nLoaded model\\n\", new_model.state_dict())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69c3314b",
   "metadata": {},
   "source": [
    "### Evaluation\n",
    "\n",
    "Once we have trained a model, it is time to evaluate it on a held-out test set. As our dataset consist of randomly generated data points, we need to first create a test set with a corresponding data loader."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "70c50752",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dataset = XORDataset(size=500)\n",
    "# drop_last -> Don't drop the last batch although it is smaller than 128\n",
    "test_data_loader = data.DataLoader(test_dataset, batch_size=128, shuffle=False, drop_last=False) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccfe1ed2",
   "metadata": {},
   "source": [
    "As metric, we will use accuracy which is calculated as follows:\n",
    "\n",
    "$$acc = \\frac{\\#\\text{correct predictions}}{\\#\\text{all predictions}} = \\frac{TP+TN}{TP+TN+FP+FN}$$\n",
    "\n",
    "where TP are the true positives, TN true negatives, FP false positives, and FN the fale negatives. \n",
    "\n",
    "When evaluating the model, we don't need to keep track of the computation graph as we don't intend to calculate the gradients. This reduces the required memory and speed up the model. In PyTorch, we can deactivate the computation graph using `with torch.no_grad(): ...`. Remember to additionally set the model to eval mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "1a67d68c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def eval_model(model, data_loader):\n",
    "    model.eval() # Set model to eval mode\n",
    "    true_preds, num_preds = 0., 0.\n",
    "    \n",
    "    with torch.no_grad(): # Deactivate gradients for the following code\n",
    "        for data_inputs, data_labels in data_loader:\n",
    "            \n",
    "            # Determine prediction of model on dev set\n",
    "            data_inputs, data_labels = data_inputs.to(device), data_labels.to(device)\n",
    "            preds = model(data_inputs)\n",
    "            preds = preds.squeeze(dim=1)\n",
    "            preds = torch.sigmoid(preds) # Sigmoid to map predictions between 0 and 1\n",
    "            pred_labels = (preds >= 0.5).long() # Binarize predictions to 0 and 1\n",
    "            \n",
    "            # Keep records of predictions for the accuracy metric (true_preds=TP+TN, num_preds=TP+TN+FP+FN)\n",
    "            true_preds += (pred_labels == data_labels).sum()\n",
    "            num_preds += data_labels.shape[0]\n",
    "            \n",
    "    acc = true_preds / num_preds\n",
    "    print(f\"Accuracy of the model: {100.0*acc:4.2f}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "67c01542",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the model: 100.00%\n"
     ]
    }
   ],
   "source": [
    "eval_model(model, test_data_loader)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "1a029f01",
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "visualize_samples(test_dataset.data, pred_labels, marker)\n",
    "plt.show()"
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  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "3d066321",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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    "visualize_samples(test_dataset.data, test_dataset.label, marker='s')\n",
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   "source": [
    "#### Visualizing classification boundaries\n",
    "\n",
    "To visualize what our model has learned, we can perform a prediction for every data point in a range of $[-0.5, 1.5]$, and visualize the predicted class as in the sample figure at the beginning of this section. This shows where the model has created decision boundaries, and which points would be classified as $0$, and which as $1$. We therefore get a background image out of blue (class 0) and orange (class 1). The spots where the model is uncertain we will see a blurry overlap. The specific code is less relevant compared to the output figure which should hopefully show us a clear separation of classes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ed7ccb59",
   "metadata": {},
   "outputs": [
    {
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       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pc676546cf1\">\n",
       "   <rect x=\"59.506094\" y=\"21.789375\" width=\"221.76\" height=\"221.76\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@torch.no_grad() # Decorator, same effect as \"with torch.no_grad(): ...\" over the whole function.\n",
    "def visualize_classification(model, data, label):\n",
    "    if isinstance(data, torch.Tensor):\n",
    "        data = data.cpu().numpy()\n",
    "    if isinstance(label, torch.Tensor):\n",
    "        label = label.cpu().numpy()\n",
    "    data_0 = data[label == 0]\n",
    "    data_1 = data[label == 1]\n",
    "    \n",
    "    fig = plt.figure(figsize=(4,4), dpi=500)\n",
    "    plt.scatter(data_0[:,0], data_0[:,1], edgecolor=\"#333\", label=\"Class 0\")\n",
    "    plt.scatter(data_1[:,0], data_1[:,1], edgecolor=\"#333\", label=\"Class 1\")\n",
    "    plt.title(\"Dataset samples\")\n",
    "    plt.ylabel(r\"$x_2$\")\n",
    "    plt.xlabel(r\"$x_1$\")\n",
    "    plt.legend()\n",
    "    \n",
    "    # Let's make use of a lot of operations we have learned above\n",
    "    model.to(device)\n",
    "    c0 = torch.Tensor(to_rgba(\"C0\")).to(device)\n",
    "    c1 = torch.Tensor(to_rgba(\"C1\")).to(device)\n",
    "    x1 = torch.arange(-0.5, 1.5, step=0.01, device=device)\n",
    "    x2 = torch.arange(-0.5, 1.5, step=0.01, device=device)\n",
    "    xx1, xx2 = torch.meshgrid(x1, x2, indexing='ij')  # Meshgrid function as in numpy\n",
    "    model_inputs = torch.stack([xx1, xx2], dim=-1)\n",
    "    preds = model(model_inputs)\n",
    "    preds = torch.sigmoid(preds)\n",
    "    output_image = (1 - preds) * c0[None,None] + preds * c1[None,None]  # Specifying \"None\" in a dimension creates a new one\n",
    "    output_image = output_image.cpu().numpy()  # Convert to numpy array. This only works for tensors on CPU, hence first push to CPU\n",
    "    plt.imshow(output_image, origin='lower', extent=(-0.5, 1.5, -0.5, 1.5))\n",
    "    plt.grid(False)\n",
    "    return fig\n",
    "\n",
    "_ = visualize_classification(model, test_dataset.data, test_dataset.label)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "580ff05b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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