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Add 1-intro materials

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Patryk Żywica 2020-12-02 13:10:58 +01:00
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# System setup\n",
"\n",
"Requirements:\n",
"* Ubuntu 20.04\n",
"* Python 3.6+\n",
"* docker-ce 19.03+\n",
"* nvidia-container-toolkit 1.3+\n",
"* docker-compose 1.28+ (install docker-compose version that support GPU (https://github.com/docker/compose/pull/7929))\n",
"```\n",
"sudo pip3 install wheel\n",
"sudo pip3 install --upgrade git+https://github.com/docker/compose.git@854c003359bd07d0d3ca137d7a08509cfeab0436#egg=docker-compose\n",
"```\n",
"\n",
"# Tests\n",
"\n",
"Simple stress test example is avaiable at (it also includes install script):\n",
"https://git.wmi.amu.edu.pl/bikol/docker-gpu-tests"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"What is PyTorch?\n",
"================\n",
"\n",
"It’s a Python-based scientific computing package targeted at two sets of\n",
"audiences:\n",
"\n",
"- A replacement for NumPy to use the power of GPUs\n",
"- a deep learning research platform that provides maximum flexibility\n",
" and speed\n",
"\n",
"Getting Started\n",
"---------------\n",
"\n",
"Tensors\n",
"^^^^^^^\n",
"\n",
"Tensors are similar to NumPy’s ndarrays, with the addition being that\n",
"Tensors can also be used on a GPU to accelerate computing.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"import torch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-info\"><h4>Note</h4><p>An uninitialized matrix is declared,\n",
" but does not contain definite known\n",
" values before it is used. When an\n",
" uninitialized matrix is created,\n",
" whatever values were in the allocated\n",
" memory at the time will appear as the initial values.</p></div>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Construct a 5x3 matrix, uninitialized:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[-1.7501e-10, 4.5822e-41, -1.7501e-10],\n",
" [ 4.5822e-41, -9.8701e-38, 4.5822e-41],\n",
" [-9.8892e-38, 4.5822e-41, -9.8700e-38],\n",
" [ 4.5822e-41, -9.8702e-38, 4.5822e-41],\n",
" [-9.8701e-38, 4.5822e-41, -9.8703e-38]])\n"
]
}
],
"source": [
"x = torch.empty(5, 3)\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Construct a randomly initialized matrix:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[0.8525, 0.7922, 0.2553],\n",
" [0.2792, 0.6800, 0.7858],\n",
" [0.4438, 0.6987, 0.0985],\n",
" [0.7342, 0.1807, 0.5665],\n",
" [0.0847, 0.8206, 0.6820]])\n"
]
}
],
"source": [
"x = torch.rand(5, 3)\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Construct a matrix filled zeros and of dtype long:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[0, 0, 0],\n",
" [0, 0, 0],\n",
" [0, 0, 0],\n",
" [0, 0, 0],\n",
" [0, 0, 0]])\n"
]
}
],
"source": [
"x = torch.zeros(5, 3, dtype=torch.long)\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Construct a tensor directly from data:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([5.5000, 3.0000])\n"
]
}
],
"source": [
"x = torch.tensor([5.5, 3])\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"or create a tensor based on an existing tensor. These methods\n",
"will reuse properties of the input tensor, e.g. dtype, unless\n",
"new values are provided by user\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[1., 1., 1.],\n",
" [1., 1., 1.],\n",
" [1., 1., 1.],\n",
" [1., 1., 1.],\n",
" [1., 1., 1.]], dtype=torch.float64)\n",
"tensor([[ 1.0131, 1.4739, -0.2482],\n",
" [-1.8965, -1.6178, 0.4807],\n",
" [ 0.1839, 0.3258, -0.6664],\n",
" [-0.9516, -1.7041, 1.1624],\n",
" [-0.4448, -1.1328, -0.5092]])\n"
]
}
],
"source": [
"x = x.new_ones(5, 3, dtype=torch.double) # new_* methods take in sizes\n",
"print(x)\n",
"\n",
"x = torch.randn_like(x, dtype=torch.float) # override dtype!\n",
"print(x) # result has the same size"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get its size:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"torch.Size([5, 3])\n"
]
}
],
"source": [
"print(x.size())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-info\"><h4>Note</h4><p>``torch.Size`` is in fact a tuple, so it supports all tuple operations.</p></div>\n",
"\n",
"Operations\n",
"^^^^^^^^^^\n",
"There are multiple syntaxes for operations. In the following\n",
"example, we will take a look at the addition operation.\n",
"\n",
"Addition: syntax 1\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[ 1.6789, 1.8680, -0.0202],\n",
" [-1.2243, -1.5905, 0.8047],\n",
" [ 0.5959, 0.7308, -0.1883],\n",
" [-0.6292, -0.7051, 1.8369],\n",
" [-0.0381, -0.2377, -0.1590]])\n"
]
}
],
"source": [
"y = torch.rand(5, 3)\n",
"print(x + y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Addition: syntax 2\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[ 1.6789, 1.8680, -0.0202],\n",
" [-1.2243, -1.5905, 0.8047],\n",
" [ 0.5959, 0.7308, -0.1883],\n",
" [-0.6292, -0.7051, 1.8369],\n",
" [-0.0381, -0.2377, -0.1590]])\n"
]
}
],
"source": [
"print(torch.add(x, y))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Addition: providing an output tensor as argument\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[ 1.6789, 1.8680, -0.0202],\n",
" [-1.2243, -1.5905, 0.8047],\n",
" [ 0.5959, 0.7308, -0.1883],\n",
" [-0.6292, -0.7051, 1.8369],\n",
" [-0.0381, -0.2377, -0.1590]])\n"
]
}
],
"source": [
"result = torch.empty(5, 3)\n",
"torch.add(x, y, out=result)\n",
"print(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Addition: in-place\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[ 1.6789, 1.8680, -0.0202],\n",
" [-1.2243, -1.5905, 0.8047],\n",
" [ 0.5959, 0.7308, -0.1883],\n",
" [-0.6292, -0.7051, 1.8369],\n",
" [-0.0381, -0.2377, -0.1590]])\n"
]
}
],
"source": [
"# adds x to y\n",
"y.add_(x)\n",
"print(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<div class=\"alert alert-info\"><h4>Note</h4><p>Any operation that mutates a tensor in-place is post-fixed with an ``_``.\n",
" For example: ``x.copy_(y)``, ``x.t_()``, will change ``x``.</p></div>\n",
"\n",
"You can use standard NumPy-like indexing with all bells and whistles!\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([ 1.4739, -1.6178, 0.3258, -1.7041, -1.1328])\n"
]
}
],
"source": [
"print(x[:, 1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Resizing: If you want to resize/reshape tensor, you can use ``torch.view``:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"torch.Size([4, 4]) torch.Size([16]) torch.Size([2, 8])\n"
]
}
],
"source": [
"x = torch.randn(4, 4)\n",
"y = x.view(16)\n",
"z = x.view(-1, 8) # the size -1 is inferred from other dimensions\n",
"print(x.size(), y.size(), z.size())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you have a one element tensor, use ``.item()`` to get the value as a\n",
"Python number\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([-0.8622])\n",
"-0.8622472882270813\n"
]
}
],
"source": [
"x = torch.randn(1)\n",
"print(x)\n",
"print(x.item())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Read later:**\n",
"\n",
"\n",
" 100+ Tensor operations, including transposing, indexing, slicing,\n",
" mathematical operations, linear algebra, random numbers, etc.,\n",
" are described\n",
" `here <https://pytorch.org/docs/torch>`_.\n",
"\n",
"NumPy Bridge\n",
"------------\n",
"\n",
"Converting a Torch Tensor to a NumPy array and vice versa is a breeze.\n",
"\n",
"The Torch Tensor and NumPy array will share their underlying memory\n",
"locations (if the Torch Tensor is on CPU), and changing one will change\n",
"the other.\n",
"\n",
"Converting a Torch Tensor to a NumPy Array\n",
"^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([1., 1., 1., 1., 1.])\n"
]
}
],
"source": [
"a = torch.ones(5)\n",
"print(a)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1. 1. 1. 1. 1.]\n"
]
}
],
"source": [
"b = a.numpy()\n",
"print(b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See how the numpy array changed in value.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([2., 2., 2., 2., 2.])\n",
"[2. 2. 2. 2. 2.]\n"
]
}
],
"source": [
"a.add_(1)\n",
"print(a)\n",
"print(b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Converting NumPy Array to Torch Tensor\n",
"See how changing the np array changed the Torch Tensor automatically\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2. 2. 2. 2. 2.]\n",
"tensor([2., 2., 2., 2., 2.], dtype=torch.float64)\n"
]
}
],
"source": [
"import numpy as np\n",
"a = np.ones(5)\n",
"b = torch.from_numpy(a)\n",
"np.add(a, 1, out=a)\n",
"print(a)\n",
"print(b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All the Tensors on the CPU except a CharTensor support converting to\n",
"NumPy and back.\n",
"\n",
"CUDA Tensors\n",
"------------\n",
"\n",
"Tensors can be moved onto any device using the ``.to`` method.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.7.0\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/torch/cuda/__init__.py:81: UserWarning: \n",
" Found GPU0 GeForce GTX 760 which is of cuda capability 3.0.\n",
" PyTorch no longer supports this GPU because it is too old.\n",
" The minimum cuda capability that we support is 3.5.\n",
" \n",
" warnings.warn(old_gpu_warn % (d, name, major, capability[1]))\n"
]
},
{
"ename": "RuntimeError",
"evalue": "CUDA error: no kernel image is available for execution on the device",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-20-9fca8bb14c5b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcuda\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_available\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mdevice\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdevice\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"cuda\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# a CUDA device object\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones_like\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdevice\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdevice\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# directly create a tensor on GPU\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdevice\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# or just use strings ``.to(\"cuda\")``\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mRuntimeError\u001b[0m: CUDA error: no kernel image is available for execution on the device"
]
}
],
"source": [
"# let us run this cell only if CUDA is available\n",
"# We will use ``torch.device`` objects to move tensors in and out of GPU\n",
"print(torch.__version__)\n",
"if torch.cuda.is_available():\n",
" device = torch.device(\"cuda\") # a CUDA device object\n",
" y = torch.ones_like(x, device=device) # directly create a tensor on GPU\n",
" x = x.to(device) # or just use strings ``.to(\"cuda\")``\n",
" z = x + y\n",
" print(z)\n",
" print(z.to(\"cpu\", torch.double)) # ``.to`` can also change dtype together!\n",
" "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 1
}

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Autograd: Automatic Differentiation\n",
"===================================\n",
"\n",
"Central to all neural networks in PyTorch is the ``autograd`` package.\n",
"Let’s first briefly visit this, and we will then go to training our\n",
"first neural network.\n",
"\n",
"\n",
"The ``autograd`` package provides automatic differentiation for all operations\n",
"on Tensors. It is a define-by-run framework, which means that your backprop is\n",
"defined by how your code is run, and that every single iteration can be\n",
"different.\n",
"\n",
"Let us see this in more simple terms with some examples.\n",
"\n",
"Tensor\n",
"--------\n",
"\n",
"``torch.Tensor`` is the central class of the package. If you set its attribute\n",
"``.requires_grad`` as ``True``, it starts to track all operations on it. When\n",
"you finish your computation you can call ``.backward()`` and have all the\n",
"gradients computed automatically. The gradient for this tensor will be\n",
"accumulated into ``.grad`` attribute.\n",
"\n",
"To stop a tensor from tracking history, you can call ``.detach()`` to detach\n",
"it from the computation history, and to prevent future computation from being\n",
"tracked.\n",
"\n",
"To prevent tracking history (and using memory), you can also wrap the code block\n",
"in ``with torch.no_grad():``. This can be particularly helpful when evaluating a\n",
"model because the model may have trainable parameters with\n",
"``requires_grad=True``, but for which we don't need the gradients.\n",
"\n",
"There’s one more class which is very important for autograd\n",
"implementation - a ``Function``.\n",
"\n",
"``Tensor`` and ``Function`` are interconnected and build up an acyclic\n",
"graph, that encodes a complete history of computation. Each tensor has\n",
"a ``.grad_fn`` attribute that references a ``Function`` that has created\n",
"the ``Tensor`` (except for Tensors created by the user - their\n",
"``grad_fn is None``).\n",
"\n",
"If you want to compute the derivatives, you can call ``.backward()`` on\n",
"a ``Tensor``. If ``Tensor`` is a scalar (i.e. it holds a one element\n",
"data), you don’t need to specify any arguments to ``backward()``,\n",
"however if it has more elements, you need to specify a ``gradient``\n",
"argument that is a tensor of matching shape.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import torch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create a tensor and set ``requires_grad=True`` to track computation with it\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[1., 1.],\n",
" [1., 1.]], requires_grad=True)\n"
]
}
],
"source": [
"x = torch.ones(2, 2, requires_grad=True)\n",
"print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do a tensor operation:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[3., 3.],\n",
" [3., 3.]], grad_fn=<AddBackward0>)\n"
]
}
],
"source": [
"y = x + 2\n",
"print(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"``y`` was created as a result of an operation, so it has a ``grad_fn``.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<AddBackward0 object at 0x7f0d183e5160>\n"
]
}
],
"source": [
"print(y.grad_fn)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Do more operations on ``y``\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[27., 27.],\n",
" [27., 27.]], grad_fn=<MulBackward0>) tensor(27., grad_fn=<MeanBackward0>)\n"
]
}
],
"source": [
"z = y * y * 3\n",
"out = z.mean()\n",
"\n",
"print(z, out)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"``.requires_grad_( ... )`` changes an existing Tensor's ``requires_grad``\n",
"flag in-place. The input flag defaults to ``False`` if not given.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"False\n",
"True\n",
"<SumBackward0 object at 0x7f0cc743b438>\n"
]
}
],
"source": [
"a = torch.randn(2, 2)\n",
"a = ((a * 3) / (a - 1))\n",
"print(a.requires_grad)\n",
"a.requires_grad_(True)\n",
"print(a.requires_grad)\n",
"b = (a * a).sum()\n",
"print(b.grad_fn)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gradients\n",
"---------\n",
"Let's backprop now.\n",
"Because ``out`` contains a single scalar, ``out.backward()`` is\n",
"equivalent to ``out.backward(torch.tensor(1.))``.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"out.backward()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Print gradients d(out)/dx\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([[4.5000, 4.5000],\n",
" [4.5000, 4.5000]])\n"
]
}
],
"source": [
"print(x.grad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You should have got a matrix of ``4.5``. Let’s call the ``out``\n",
"*Tensor* “$o$”.\n",
"We have that $o = \\frac{1}{4}\\sum_i z_i$,\n",
"$z_i = 3(x_i+2)^2$ and $z_i\\bigr\\rvert_{x_i=1} = 27$.\n",
"Therefore,\n",
"$\\frac{\\partial o}{\\partial x_i} = \\frac{3}{2}(x_i+2)$, hence\n",
"$\\frac{\\partial o}{\\partial x_i}\\bigr\\rvert_{x_i=1} = \\frac{9}{2} = 4.5$.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Mathematically, if you have a vector valued function $\\vec{y}=f(\\vec{x})$,\n",
"then the gradient of $\\vec{y}$ with respect to $\\vec{x}$\n",
"is a Jacobian matrix:\n",
"\n",
"\\begin{align}J=\\left(\\begin{array}{ccc}\n",
" \\frac{\\partial y_{1}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{1}}{\\partial x_{n}}\\\\\n",
" \\vdots & \\ddots & \\vdots\\\\\n",
" \\frac{\\partial y_{m}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{n}}\n",
" \\end{array}\\right)\\end{align}\n",
"\n",
"Generally speaking, ``torch.autograd`` is an engine for computing\n",
"vector-Jacobian product. That is, given any vector\n",
"$v=\\left(\\begin{array}{cccc} v_{1} & v_{2} & \\cdots & v_{m}\\end{array}\\right)^{T}$,\n",
"compute the product $v^{T}\\cdot J$. If $v$ happens to be\n",
"the gradient of a scalar function $l=g\\left(\\vec{y}\\right)$,\n",
"that is,\n",
"$v=\\left(\\begin{array}{ccc}\\frac{\\partial l}{\\partial y_{1}} & \\cdots & \\frac{\\partial l}{\\partial y_{m}}\\end{array}\\right)^{T}$,\n",
"then by the chain rule, the vector-Jacobian product would be the\n",
"gradient of $l$ with respect to $\\vec{x}$:\n",
"\n",
"\\begin{align}J^{T}\\cdot v=\\left(\\begin{array}{ccc}\n",
" \\frac{\\partial y_{1}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{1}}\\\\\n",
" \\vdots & \\ddots & \\vdots\\\\\n",
" \\frac{\\partial y_{1}}{\\partial x_{n}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{n}}\n",
" \\end{array}\\right)\\left(\\begin{array}{c}\n",
" \\frac{\\partial l}{\\partial y_{1}}\\\\\n",
" \\vdots\\\\\n",
" \\frac{\\partial l}{\\partial y_{m}}\n",
" \\end{array}\\right)=\\left(\\begin{array}{c}\n",
" \\frac{\\partial l}{\\partial x_{1}}\\\\\n",
" \\vdots\\\\\n",
" \\frac{\\partial l}{\\partial x_{n}}\n",
" \\end{array}\\right)\\end{align}\n",
"\n",
"(Note that $v^{T}\\cdot J$ gives a row vector which can be\n",
"treated as a column vector by taking $J^{T}\\cdot v$.)\n",
"\n",
"This characteristic of vector-Jacobian product makes it very\n",
"convenient to feed external gradients into a model that has\n",
"non-scalar output.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's take a look at an example of vector-Jacobian product:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([1688.6201, -110.9400, 181.5985], grad_fn=<MulBackward0>)\n"
]
}
],
"source": [
"x = torch.randn(3, requires_grad=True)\n",
"\n",
"y = x * 2\n",
"while y.data.norm() < 1000:\n",
" y = y * 2\n",
"\n",
"print(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now in this case ``y`` is no longer a scalar. ``torch.autograd``\n",
"could not compute the full Jacobian directly, but if we just\n",
"want the vector-Jacobian product, simply pass the vector to\n",
"``backward`` as argument:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"tensor([1.0240e+02, 1.0240e+03, 1.0240e-01])\n"
]
}
],
"source": [
"v = torch.tensor([0.1, 1.0, 0.0001], dtype=torch.float)\n",
"y.backward(v)\n",
"\n",
"print(x.grad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can also stop autograd from tracking history on Tensors\n",
"with ``.requires_grad=True`` either by wrapping the code block in\n",
"``with torch.no_grad():``\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True\n",
"True\n",
"False\n"
]
}
],
"source": [
"print(x.requires_grad)\n",
"print((x ** 2).requires_grad)\n",
"\n",
"with torch.no_grad():\n",
"\tprint((x ** 2).requires_grad)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or by using ``.detach()`` to get a new Tensor with the same\n",
"content but that does not require gradients:\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True\n",
"False\n",
"tensor(True)\n"
]
}
],
"source": [
"print(x.requires_grad)\n",
"y = x.detach()\n",
"print(y.requires_grad)\n",
"print(x.eq(y).all())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Read Later:**\n",
"\n",
"Document about ``autograd.Function`` is at\n",
"https://pytorch.org/docs/stable/autograd.html#function\n",
"\n"
]
}
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