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<p class="caption"><span class="caption-text">ํ์ดํ ์น(PyTorch) ๋ ์ํผ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../../recipes/recipes_index.html">๋ชจ๋ ๋ ์ํผ ๋ณด๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../prototype/prototype_index.html">๋ชจ๋ ํ๋กํ ํ์
๋ ์ํผ ๋ณด๊ธฐ</a></li>
</ul>
<p class="caption"><span class="caption-text">ํ์ดํ ์น(PyTorch) ์์ํ๊ธฐ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../basics/intro.html">ํ์ดํ ์น(PyTorch) ๊ธฐ๋ณธ ์ตํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/quickstart_tutorial.html">๋น ๋ฅธ ์์(Quickstart)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/tensorqs_tutorial.html">ํ
์(Tensor)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/data_tutorial.html">Dataset๊ณผ DataLoader</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/transforms_tutorial.html">๋ณํ(Transform)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/buildmodel_tutorial.html">์ ๊ฒฝ๋ง ๋ชจ๋ธ ๊ตฌ์ฑํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/autogradqs_tutorial.html"><code class="docutils literal notranslate"><span class="pre">torch.autograd</span></code>๋ฅผ ์ฌ์ฉํ ์๋ ๋ฏธ๋ถ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/optimization_tutorial.html">๋ชจ๋ธ ๋งค๊ฐ๋ณ์ ์ต์ ํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../basics/saveloadrun_tutorial.html">๋ชจ๋ธ ์ ์ฅํ๊ณ ๋ถ๋ฌ์ค๊ธฐ</a></li>
</ul>
<p class="caption"><span class="caption-text">Introduction to PyTorch on YouTube</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../introyt.html">Introduction to PyTorch - YouTube Series</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/introyt1_tutorial.html">Introduction to PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/tensors_deeper_tutorial.html">Introduction to PyTorch Tensors</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/autogradyt_tutorial.html">The Fundamentals of Autograd</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/modelsyt_tutorial.html">Building Models with PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/tensorboardyt_tutorial.html">PyTorch TensorBoard Support</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/trainingyt.html">Training with PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../introyt/captumyt.html">Model Understanding with Captum</a></li>
</ul>
<p class="caption"><span class="caption-text">ํ์ดํ ์น(PyTorch) ๋ฐฐ์ฐ๊ธฐ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../deep_learning_60min_blitz.html">PyTorch๋ก ๋ฅ๋ฌ๋ํ๊ธฐ: 60๋ถ๋ง์ ๋์ฅ๋ด๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../pytorch_with_examples.html">์์ ๋ก ๋ฐฐ์ฐ๋ ํ์ดํ ์น(PyTorch)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../nn_tutorial.html"><cite>torch.nn</cite> ์ด <em>์ค์ ๋ก</em> ๋ฌด์์ธ๊ฐ์?</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/tensorboard_tutorial.html">TensorBoard๋ก ๋ชจ๋ธ, ๋ฐ์ดํฐ, ํ์ต ์๊ฐํํ๊ธฐ</a></li>
</ul>
<p class="caption"><span class="caption-text">์ด๋ฏธ์ง/๋น๋์ค</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../../intermediate/torchvision_tutorial.html">TorchVision ๊ฐ์ฒด ๊ฒ์ถ ๋ฏธ์ธ์กฐ์ (Finetuning) ํํ ๋ฆฌ์ผ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../transfer_learning_tutorial.html">์ปดํจํฐ ๋น์ (Vision)์ ์ํ ์ ์ดํ์ต(Transfer Learning)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../fgsm_tutorial.html">์ ๋์ ์์ ์์ฑ(Adversarial Example Generation)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../dcgan_faces_tutorial.html">DCGAN ํํ ๋ฆฌ์ผ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../vt_tutorial.html">๋ฐฐํฌ๋ฅผ ์ํ ๋น์ ํธ๋์คํฌ๋จธ(Vision Transformer) ๋ชจ๋ธ ์ต์ ํํ๊ธฐ</a></li>
</ul>
<p class="caption"><span class="caption-text">์ค๋์ค</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../audio_io_tutorial.html">Audio I/O</a></li>
<li class="toctree-l1"><a class="reference internal" href="../audio_resampling_tutorial.html">Audio Resampling</a></li>
<li class="toctree-l1"><a class="reference internal" href="../audio_data_augmentation_tutorial.html">Audio Data Augmentation</a></li>
<li class="toctree-l1"><a class="reference internal" href="../audio_feature_extractions_tutorial.html">Audio Feature Extractions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../audio_feature_augmentation_tutorial.html">Audio Feature Augmentation</a></li>
<li class="toctree-l1"><a class="reference internal" href="../audio_datasets_tutorial.html">Audio Datasets</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/speech_recognition_pipeline_tutorial.html">Speech Recognition with Wav2Vec2</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/speech_command_classification_with_torchaudio_tutorial.html">Speech Command Classification with torchaudio</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/text_to_speech_with_torchaudio.html">Text-to-speech with torchaudio</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/forced_alignment_with_torchaudio_tutorial.html">Forced Alignment with Wav2Vec2</a></li>
</ul>
<p class="caption"><span class="caption-text">ํ
์คํธ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../transformer_tutorial.html">nn.Transformer ์ TorchText ๋ก ์ํ์ค-ํฌ-์ํ์ค(Sequence-to-Sequence) ๋ชจ๋ธ๋งํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/char_rnn_classification_tutorial.html">๊ธฐ์ด๋ถํฐ ์์ํ๋ NLP: ๋ฌธ์-๋จ์ RNN์ผ๋ก ์ด๋ฆ ๋ถ๋ฅํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../intermediate/char_rnn_generation_tutorial.html">๊ธฐ์ด๋ถํฐ ์์ํ๋ NLP: ๋ฌธ์-๋จ์ RNN์ผ๋ก ์ด๋ฆ ์์ฑํ๊ธฐ</a></li>
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<div class="sphx-glr-example-title section" id="introduction-to-pytorch">
<span id="sphx-glr-beginner-nlp-pytorch-tutorial-py"></span><h1>Introduction to PyTorch<a class="headerlink" href="#introduction-to-pytorch" title="Permalink to this headline">ยถ</a></h1>
<div class="section" id="introduction-to-torch-s-tensor-library">
<h2>Introduction to Torchโs tensor library<a class="headerlink" href="#introduction-to-torch-s-tensor-library" title="Permalink to this headline">ยถ</a></h2>
<p>All of deep learning is computations on tensors, which are
generalizations of a matrix that can be indexed in more than 2
dimensions. We will see exactly what this means in-depth later. First,
letโs look what we can do with tensors.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Author: Robert Guthrie</span>
<span class="kn">import</span> <span class="nn">torch</span>
<span class="n">torch</span><span class="o">.</span><span class="n">manual_seed</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="creating-tensors">
<h3>Creating Tensors<a class="headerlink" href="#creating-tensors" title="Permalink to this headline">ยถ</a></h3>
<p>Tensors can be created from Python lists with the torch.tensor()
function.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># torch.tensor(data) creates a torch.Tensor object with the given data.</span>
<span class="n">V_data</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">]</span>
<span class="n">V</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="n">V_data</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">V</span><span class="p">)</span>
<span class="c1"># Creates a matrix</span>
<span class="n">M_data</span> <span class="o">=</span> <span class="p">[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">],</span> <span class="p">[</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mi">6</span><span class="p">]]</span>
<span class="n">M</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="n">M_data</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">M</span><span class="p">)</span>
<span class="c1"># Create a 3D tensor of size 2x2x2.</span>
<span class="n">T_data</span> <span class="o">=</span> <span class="p">[[[</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">],</span> <span class="p">[</span><span class="mf">3.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">]],</span>
<span class="p">[[</span><span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">],</span> <span class="p">[</span><span class="mf">7.</span><span class="p">,</span> <span class="mf">8.</span><span class="p">]]]</span>
<span class="n">T</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">(</span><span class="n">T_data</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">T</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([1., 2., 3.])
tensor([[1., 2., 3.],
[4., 5., 6.]])
tensor([[[1., 2.],
[3., 4.]],
[[5., 6.],
[7., 8.]]])
</pre></div>
</div>
<p>What is a 3D tensor anyway? Think about it like this. If you have a
vector, indexing into the vector gives you a scalar. If you have a
matrix, indexing into the matrix gives you a vector. If you have a 3D
tensor, then indexing into the tensor gives you a matrix!</p>
<p>A note on terminology:
when I say โtensorโ in this tutorial, it refers
to any torch.Tensor object. Matrices and vectors are special cases of
torch.Tensors, where their dimension is 2 and 1 respectively. When I am
talking about 3D tensors, I will explicitly use the term โ3D tensorโ.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Index into V and get a scalar (0 dimensional tensor)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">V</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="c1"># Get a Python number from it</span>
<span class="nb">print</span><span class="p">(</span><span class="n">V</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">item</span><span class="p">())</span>
<span class="c1"># Index into M and get a vector</span>
<span class="nb">print</span><span class="p">(</span><span class="n">M</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="c1"># Index into T and get a matrix</span>
<span class="nb">print</span><span class="p">(</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor(1.)
1.0
tensor([1., 2., 3.])
tensor([[1., 2.],
[3., 4.]])
</pre></div>
</div>
<p>You can also create tensors of other data types. To create a tensor of integer types, try
torch.tensor([[1, 2], [3, 4]]) (where all elements in the list are integers).
You can also specify a data type by passing in <code class="docutils literal notranslate"><span class="pre">dtype=torch.data_type</span></code>.
Check the documentation for more data types, but
Float and Long will be the most common.</p>
<p>You can create a tensor with random data and the supplied dimensionality
with torch.randn()</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([[[-1.5256, -0.7502, -0.6540, -1.6095, -0.1002],
[-0.6092, -0.9798, -1.6091, -0.7121, 0.3037],
[-0.7773, -0.2515, -0.2223, 1.6871, 0.2284],
[ 0.4676, -0.6970, -1.1608, 0.6995, 0.1991]],
[[ 0.8657, 0.2444, -0.6629, 0.8073, 1.1017],
[-0.1759, -2.2456, -1.4465, 0.0612, -0.6177],
[-0.7981, -0.1316, 1.8793, -0.0721, 0.1578],
[-0.7735, 0.1991, 0.0457, 0.1530, -0.4757]],
[[-0.1110, 0.2927, -0.1578, -0.0288, 0.4533],
[ 1.1422, 0.2486, -1.7754, -0.0255, -1.0233],
[-0.5962, -1.0055, 0.4285, 1.4761, -1.7869],
[ 1.6103, -0.7040, -0.1853, -0.9962, -0.8313]]])
</pre></div>
</div>
</div>
<div class="section" id="operations-with-tensors">
<h3>Operations with Tensors<a class="headerlink" href="#operations-with-tensors" title="Permalink to this headline">ยถ</a></h3>
<p>You can operate on tensors in the ways you would expect.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mf">3.</span><span class="p">])</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">])</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([5., 7., 9.])
</pre></div>
</div>
<p>See <a class="reference external" href="https://pytorch.org/docs/torch.html">the documentation</a> for a
complete list of the massive number of operations available to you. They
expand beyond just mathematical operations.</p>
<p>One helpful operation that we will make use of later is concatenation.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># By default, it concatenates along the first axis (concatenates rows)</span>
<span class="n">x_1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">y_1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="n">z_1</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">([</span><span class="n">x_1</span><span class="p">,</span> <span class="n">y_1</span><span class="p">])</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z_1</span><span class="p">)</span>
<span class="c1"># Concatenate columns:</span>
<span class="n">x_2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="n">y_2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="c1"># second arg specifies which axis to concat along</span>
<span class="n">z_2</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">cat</span><span class="p">([</span><span class="n">x_2</span><span class="p">,</span> <span class="n">y_2</span><span class="p">],</span> <span class="mi">1</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z_2</span><span class="p">)</span>
<span class="c1"># If your tensors are not compatible, torch will complain. Uncomment to see the error</span>
<span class="c1"># torch.cat([x_1, x_2])</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([[-0.8029, 0.2366, 0.2857, 0.6898, -0.6331],
[ 0.8795, -0.6842, 0.4533, 0.2912, -0.8317],
[-0.5525, 0.6355, -0.3968, -0.6571, -1.6428],
[ 0.9803, -0.0421, -0.8206, 0.3133, -1.1352],
[ 0.3773, -0.2824, -2.5667, -1.4303, 0.5009]])
tensor([[ 0.5438, -0.4057, 1.1341, -0.1473, 0.6272, 1.0935, 0.0939, 1.2381],
[-1.1115, 0.3501, -0.7703, -1.3459, 0.5119, -0.6933, -0.1668, -0.9999]])
</pre></div>
</div>
</div>
<div class="section" id="reshaping-tensors">
<h3>Reshaping Tensors<a class="headerlink" href="#reshaping-tensors" title="Permalink to this headline">ยถ</a></h3>
<p>Use the .view() method to reshape a tensor. This method receives heavy
use, because many neural network components expect their inputs to have
a certain shape. Often you will need to reshape before passing your data
to the component.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">12</span><span class="p">))</span> <span class="c1"># Reshape to 2 rows, 12 columns</span>
<span class="c1"># Same as above. If one of the dimensions is -1, its size can be inferred</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">view</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">))</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([[[ 0.4175, -0.2127, -0.8400, -0.4200],
[-0.6240, -0.9773, 0.8748, 0.9873],
[-0.0594, -2.4919, 0.2423, 0.2883]],
[[-0.1095, 0.3126, 1.5038, 0.5038],
[ 0.6223, -0.4481, -0.2856, 0.3880],
[-1.1435, -0.6512, -0.1032, 0.6937]]])
tensor([[ 0.4175, -0.2127, -0.8400, -0.4200, -0.6240, -0.9773, 0.8748, 0.9873,
-0.0594, -2.4919, 0.2423, 0.2883],
[-0.1095, 0.3126, 1.5038, 0.5038, 0.6223, -0.4481, -0.2856, 0.3880,
-1.1435, -0.6512, -0.1032, 0.6937]])
tensor([[ 0.4175, -0.2127, -0.8400, -0.4200, -0.6240, -0.9773, 0.8748, 0.9873,
-0.0594, -2.4919, 0.2423, 0.2883],
[-0.1095, 0.3126, 1.5038, 0.5038, 0.6223, -0.4481, -0.2856, 0.3880,
-1.1435, -0.6512, -0.1032, 0.6937]])
</pre></div>
</div>
</div>
</div>
<div class="section" id="computation-graphs-and-automatic-differentiation">
<h2>Computation Graphs and Automatic Differentiation<a class="headerlink" href="#computation-graphs-and-automatic-differentiation" title="Permalink to this headline">ยถ</a></h2>
<p>The concept of a computation graph is essential to efficient deep
learning programming, because it allows you to not have to write the
back propagation gradients yourself. A computation graph is simply a
specification of how your data is combined to give you the output. Since
the graph totally specifies what parameters were involved with which
operations, it contains enough information to compute derivatives. This
probably sounds vague, so letโs see what is going on using the
fundamental flag <code class="docutils literal notranslate"><span class="pre">requires_grad</span></code>.</p>
<p>First, think from a programmers perspective. What is stored in the
torch.Tensor objects we were creating above? Obviously the data and the
shape, and maybe a few other things. But when we added two tensors
together, we got an output tensor. All this output tensor knows is its
data and shape. It has no idea that it was the sum of two other tensors
(it could have been read in from a file, it could be the result of some
other operation, etc.)</p>
<p>If <code class="docutils literal notranslate"><span class="pre">requires_grad=True</span></code>, the Tensor object keeps track of how it was
created. Letโs see it in action.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Tensor factory methods have a ``requires_grad`` flag</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">2.</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># With requires_grad=True, you can still do all the operations you previously</span>
<span class="c1"># could</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">tensor</span><span class="p">([</span><span class="mf">4.</span><span class="p">,</span> <span class="mf">5.</span><span class="p">,</span> <span class="mi">6</span><span class="p">],</span> <span class="n">requires_grad</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
<span class="c1"># BUT z knows something extra.</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([5., 7., 9.], grad_fn=<AddBackward0>)
<AddBackward0 object at 0x7f2891924250>
</pre></div>
</div>
<p>So Tensors know what created them. z knows that it wasnโt read in from
a file, it wasnโt the result of a multiplication or exponential or
whatever. And if you keep following z.grad_fn, you will find yourself at
x and y.</p>
<p>But how does that help us compute a gradient?</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># Let's sum up all the entries in z</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">s</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor(21., grad_fn=<SumBackward0>)
<SumBackward0 object at 0x7f2891924c70>
</pre></div>
</div>
<p>So now, what is the derivative of this sum with respect to the first
component of x? In math, we want</p>
<div class="math">
\[\frac{\partial s}{\partial x_0}\]</div>
<p>Well, s knows that it was created as a sum of the tensor z. z knows
that it was the sum x + y. So</p>
<div class="math">
\[s = \overbrace{x_0 + y_0}^\text{$z_0$} + \overbrace{x_1 + y_1}^\text{$z_1$} + \overbrace{x_2 + y_2}^\text{$z_2$}
\]</div>
<p>And so s contains enough information to determine that the derivative
we want is 1!</p>
<p>Of course this glosses over the challenge of how to actually compute
that derivative. The point here is that s is carrying along enough
information that it is possible to compute it. In reality, the
developers of Pytorch program the sum() and + operations to know how to
compute their gradients, and run the back propagation algorithm. An
in-depth discussion of that algorithm is beyond the scope of this
tutorial.</p>
<p>Letโs have Pytorch compute the gradient, and see that we were right:
(note if you run this block multiple times, the gradient will increment.
That is because Pytorch <em>accumulates</em> the gradient into the .grad
property, since for many models this is very convenient.)</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># calling .backward() on any variable will run backprop, starting from it.</span>
<span class="n">s</span><span class="o">.</span><span class="n">backward</span><span class="p">()</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">grad</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([1., 1., 1.])
</pre></div>
</div>
<p>Understanding what is going on in the block below is crucial for being a
successful programmer in deep learning.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="c1"># By default, user created Tensors have ``requires_grad=False``</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">,</span> <span class="n">y</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>
<span class="c1"># So you can't backprop through z</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
<span class="c1"># ``.requires_grad_( ... )`` changes an existing Tensor's ``requires_grad``</span>
<span class="c1"># flag in-place. The input flag defaults to ``True`` if not given.</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">()</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">y</span><span class="o">.</span><span class="n">requires_grad_</span><span class="p">()</span>
<span class="c1"># z contains enough information to compute gradients, as we saw above</span>
<span class="n">z</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
<span class="c1"># If any input to an operation has ``requires_grad=True``, so will the output</span>
<span class="nb">print</span><span class="p">(</span><span class="n">z</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="c1"># Now z has the computation history that relates itself to x and y</span>
<span class="c1"># Can we just take its values, and **detach** it from its history?</span>
<span class="n">new_z</span> <span class="o">=</span> <span class="n">z</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span>
<span class="c1"># ... does new_z have information to backprop to x and y?</span>
<span class="c1"># NO!</span>
<span class="nb">print</span><span class="p">(</span><span class="n">new_z</span><span class="o">.</span><span class="n">grad_fn</span><span class="p">)</span>
<span class="c1"># And how could it? ``z.detach()`` returns a tensor that shares the same storage</span>
<span class="c1"># as ``z``, but with the computation history forgotten. It doesn't know anything</span>
<span class="c1"># about how it was computed.</span>
<span class="c1"># In essence, we have broken the Tensor away from its past history</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>False False
None
<AddBackward0 object at 0x7f2891db0b20>
True
None
</pre></div>
</div>
<p>You can also stop autograd from tracking history on Tensors
with <code class="docutils literal notranslate"><span class="pre">.requires_grad=True</span></code> by wrapping the code block in
<code class="docutils literal notranslate"><span class="pre">with</span> <span class="pre">torch.no_grad():</span></code></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="nb">print</span><span class="p">((</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
<span class="k">with</span> <span class="n">torch</span><span class="o">.</span><span class="n">no_grad</span><span class="p">():</span>
<span class="nb">print</span><span class="p">((</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">requires_grad</span><span class="p">)</span>
</pre></div>
</div>
<p class="sphx-glr-script-out">Out:</p>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>True
True
False
</pre></div>
</div>
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<div class="pytorch-side-scroll" id="pytorch-side-scroll-right">
<ul>
<li><a class="reference internal" href="#">Introduction to PyTorch</a><ul>
<li><a class="reference internal" href="#introduction-to-torch-s-tensor-library">Introduction to Torchโs tensor library</a><ul>
<li><a class="reference internal" href="#creating-tensors">Creating Tensors</a></li>
<li><a class="reference internal" href="#operations-with-tensors">Operations with Tensors</a></li>
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