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<li class="toctree-l1"><a class="reference internal" href="../prototype/prototype_index.html">๋ชจ๋ ํ๋กํ ํ์
๋ ์ํผ ๋ณด๊ธฐ</a></li>
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<p class="caption" role="heading"><span class="caption-text">ํ์ดํ ์น(PyTorch) ์์ํ๊ธฐ</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/intro.html">ํ์ดํ ์น(PyTorch) ๊ธฐ๋ณธ ์ตํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/quickstart_tutorial.html">๋น ๋ฅธ ์์(Quickstart)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/tensorqs_tutorial.html">ํ
์(Tensor)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/data_tutorial.html">Dataset๊ณผ DataLoader</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/buildmodel_tutorial.html">์ ๊ฒฝ๋ง ๋ชจ๋ธ ๊ตฌ์ฑํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/autogradqs_tutorial.html"><code class="docutils literal notranslate"><span class="pre">torch.autograd</span></code>๋ฅผ ์ฌ์ฉํ ์๋ ๋ฏธ๋ถ</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/introyt1_tutorial.html">Introduction to PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/tensors_deeper_tutorial.html">Introduction to PyTorch Tensors</a></li>
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<p class="caption" role="heading"><span class="caption-text">ํ์ดํ ์น(PyTorch) ๋ฐฐ์ฐ๊ธฐ</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/deep_learning_60min_blitz.html">PyTorch๋ก ๋ฅ๋ฌ๋ํ๊ธฐ: 60๋ถ๋ง์ ๋์ฅ๋ด๊ธฐ</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/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>
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<p class="caption" role="heading"><span class="caption-text">์ด๋ฏธ์ง/๋น๋์ค</span></p>
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<p class="caption" role="heading"><span class="caption-text">์ค๋์ค</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_resampling_tutorial.html">Audio Resampling</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_feature_extractions_tutorial.html">Audio Feature Extractions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_feature_augmentation_tutorial.html">Audio Feature Augmentation</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/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>
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<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" role="heading"><span class="caption-text">ํ
์คํธ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/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>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/seq2seq_translation_tutorial.html">๊ธฐ์ด๋ถํฐ ์์ํ๋ NLP: Sequence to Sequence ๋คํธ์ํฌ์ Attention์ ์ด์ฉํ ๋ฒ์ญ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/text_sentiment_ngrams_tutorial.html">torchtext ๋ผ์ด๋ธ๋ฌ๋ฆฌ๋ก ํ
์คํธ ๋ถ๋ฅํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/translation_transformer.html">nn.Transformer์ torchtext๋ก ์ธ์ด ๋ฒ์ญํ๊ธฐ</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">๊ฐํํ์ต</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/reinforcement_q_learning.html">๊ฐํ ํ์ต (DQN) ํํ ๋ฆฌ์ผ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/mario_rl_tutorial.html">๋ง๋ฆฌ์ค ๊ฒ์ RL ์์ด์ ํธ๋ก ํ์ตํ๊ธฐ</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">PyTorch ๋ชจ๋ธ์ ํ๋ก๋์
ํ๊ฒฝ์ ๋ฐฐํฌํ๊ธฐ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/flask_rest_api_tutorial.html">Flask๋ฅผ ์ฌ์ฉํ์ฌ Python์์ PyTorch๋ฅผ REST API๋ก ๋ฐฐํฌํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/Intro_to_TorchScript_tutorial.html">TorchScript ์๊ฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpp_export.html">C++์์ TorchScript ๋ชจ๋ธ ๋ก๋ฉํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="super_resolution_with_onnxruntime.html">(์ ํ) PyTorch ๋ชจ๋ธ์ ONNX์ผ๋ก ๋ณํํ๊ณ ONNX ๋ฐํ์์์ ์คํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/realtime_rpi.html">Real Time Inference on Raspberry Pi 4 (30 fps!)</a></li>
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<p class="caption" role="heading"><span class="caption-text">Code Transforms with FX</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/fx_conv_bn_fuser.html">(๋ฒ ํ) FX์์ ํฉ์ฑ๊ณฑ/๋ฐฐ์น ์ ๊ทํ(Convolution/Batch Norm) ๊ฒฐํฉ๊ธฐ(Fuser) ๋ง๋ค๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/fx_profiling_tutorial.html">(beta) Building a Simple CPU Performance Profiler with FX</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">ํ๋ก ํธ์๋ API</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/memory_format_tutorial.html">(๋ฒ ํ) PyTorch๋ฅผ ์ฌ์ฉํ Channels Last ๋ฉ๋ชจ๋ฆฌ ํ์</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/forward_ad_usage.html">Forward-mode Automatic Differentiation (Beta)</a></li>
<li class="toctree-l1"><a class="reference internal" href="cpp_frontend.html">PyTorch C++ ํ๋ก ํธ์๋ ์ฌ์ฉํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch-script-parallelism.html">TorchScript์ ๋์ ๋ณ๋ ฌ ์ฒ๋ฆฌ(Dynamic Parallelism)</a></li>
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<p class="caption" role="heading"><span class="caption-text">PyTorch ํ์ฅํ๊ธฐ</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../intermediate/custom_function_double_backward_tutorial.html">Double Backward with Custom Functions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/custom_function_conv_bn_tutorial.html">Fusing Convolution and Batch Norm using Custom Function</a></li>
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C++ ํด๋์ค๋ก TorchScript ํ์ฅํ๊ธฐ</a></li>
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<p class="caption" role="heading"><span class="caption-text">๋ชจ๋ธ ์ต์ ํ</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/profiler.html">PyTorch ๋ชจ๋ ํ๋กํ์ผ๋ง ํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/tensorboard_profiler_tutorial.html">PyTorch Profiler With TensorBoard</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/hyperparameter_tuning_tutorial.html">Hyperparameter tuning with Ray Tune</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/vt_tutorial.html">๋ฐฐํฌ๋ฅผ ์ํ ๋น์ ํธ๋์คํฌ๋จธ(Vision Transformer) ๋ชจ๋ธ ์ต์ ํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/parametrizations.html">Parametrizations Tutorial</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/pruning_tutorial.html">๊ฐ์ง์น๊ธฐ ๊ธฐ๋ฒ(Pruning) ํํ ๋ฆฌ์ผ</a></li>
<li class="toctree-l1"><a class="reference internal" href="dynamic_quantization_tutorial.html">(๋ฒ ํ) LSTM ๊ธฐ๋ฐ ๋จ์ด ๋จ์ ์ธ์ด ๋ชจ๋ธ์ ๋์ ์์ํ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/dynamic_quantization_bert_tutorial.html">(๋ฒ ํ) BERT ๋ชจ๋ธ ๋์ ์์ํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/quantized_transfer_learning_tutorial.html">(๋ฒ ํ) ์ปดํจํฐ ๋น์ ํํ ๋ฆฌ์ผ์ ์ํ ์์ํ๋ ์ ์ดํ์ต(Quantized Transfer Learning)</a></li>
<li class="toctree-l1"><a class="reference internal" href="static_quantization_tutorial.html">(๋ฒ ํ) PyTorch์์ Eager Mode๋ฅผ ์ด์ฉํ ์ ์ ์์ํ</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">๋ณ๋ ฌ ๋ฐ ๋ถ์ฐ ํ์ต</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/dist_overview.html">PyTorch Distributed Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/model_parallel_tutorial.html">๋จ์ผ ๋จธ์ ์ ์ฌ์ฉํ ๋ชจ๋ธ ๋ณ๋ ฌํ ๋ชจ๋ฒ ์ฌ๋ก</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../intermediate/dist_tuto.html">PyTorch๋ก ๋ถ์ฐ ์ดํ๋ฆฌ์ผ์ด์
๊ฐ๋ฐํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/FSDP_tutorial.html">Getting Started with Fully Sharded Data Parallel(FSDP)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/process_group_cpp_extension_tutorial.html">Customize Process Group Backends Using Cpp Extensions</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../intermediate/rpc_param_server_tutorial.html">Implementing a Parameter Server Using Distributed RPC Framework</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/dist_pipeline_parallel_tutorial.html">Distributed Pipeline Parallelism Using RPC</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/rpc_async_execution.html">Implementing Batch RPC Processing Using Asynchronous Executions</a></li>
<li class="toctree-l1"><a class="reference internal" href="rpc_ddp_tutorial.html">๋ถ์ฐ ๋ฐ์ดํฐ ๋ณ๋ ฌ(DDP)๊ณผ ๋ถ์ฐ RPC ํ๋ ์์ํฌ ๊ฒฐํฉ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/pipeline_tutorial.html">ํ์ดํ๋ผ์ธ ๋ณ๋ ฌํ๋ก ํธ๋์คํฌ๋จธ ๋ชจ๋ธ ํ์ต์ํค๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="ddp_pipeline.html">๋ถ์ฐ ๋ฐ์ดํฐ ๋ณ๋ ฌ ์ฒ๋ฆฌ์ ๋ณ๋ ฌ ์ฒ๋ฆฌ ํ์ดํ๋ผ์ธ์ ์ฌ์ฉํ ํธ๋์คํฌ๋จธ ๋ชจ๋ธ ํ์ต</a></li>
<li class="toctree-l1"><a class="reference internal" href="generic_join.html">Distributed Training with Uneven Inputs Using the Join Context Manager</a></li>
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<div class="sphx-glr-example-title section" id="numpy-scipy-extensions">
<span id="sphx-glr-advanced-numpy-extensions-tutorial-py"></span><h1>numpy ์ scipy ๋ฅผ ์ด์ฉํ ํ์ฅ(Extensions) ๋ง๋ค๊ธฐ<a class="headerlink" href="#numpy-scipy-extensions" title="Permalink to this headline">ยถ</a></h1>
<p><strong>Author</strong>: <a class="reference external" href="https://github.com/apaszke">Adam Paszke</a></p>
<p><strong>Updated by</strong>: <a class="reference external" href="https://github.com/adam-dziedzic">Adam Dziedzic</a></p>
<p><strong>๋ฒ์ญ</strong>: <a class="reference external" href="https://github.com/ajin-jng">Ajin Jeong</a></p>
<p>์ด๋ฒ ํํ ๋ฆฌ์ผ์์๋ ๋ ๊ฐ์ง ์์
์ ์ํํ ๊ฒ์
๋๋ค:</p>
<ol class="arabic simple">
<li><dl class="simple">
<dt>๋งค๊ฐ ๋ณ์๊ฐ ์๋ ์ ๊ฒฝ๋ง ๊ณ์ธต(layer) ๋ง๋ค๊ธฐ</dt><dd><ul class="simple">
<li><p>์ด๋ ๊ตฌํ์ ์ผ๋ถ๋ก <strong>numpy</strong> ๋ฅผ ํธ์ถํฉ๋๋ค.</p></li>
</ul>
</dd>
</dl>
</li>
<li><dl class="simple">
<dt>ํ์ต ๊ฐ๋ฅํ ๊ฐ์ค์น๊ฐ ์๋ ์ ๊ฒฝ๋ง ๊ณ์ธต(layer) ๋ง๋ค๊ธฐ</dt><dd><ul class="simple">
<li><p>์ด๋ ๊ตฌํ์ ์ผ๋ถ๋ก <strong>Scipy</strong> ๋ฅผ ํธ์ถํฉ๋๋ค.</p></li>
</ul>
</dd>
</dl>
</li>
</ol>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span>
<span class="kn">from</span> <span class="nn">torch.autograd</span> <span class="kn">import</span> <span class="n">Function</span>
</pre></div>
</div>
<div class="section" id="parameter-less">
<h2>๋งค๊ฐ ๋ณ์๊ฐ ์๋(Parameter-less) ์์<a class="headerlink" href="#parameter-less" title="Permalink to this headline">ยถ</a></h2>
<p>์ด ๊ณ์ธต(layer)์ ํน๋ณํ ์ ์ฉํ๊ฑฐ๋ ์ํ์ ์ผ๋ก ์ฌ๋ฐ๋ฅธ ์์
์ ์ํํ์ง ์์ต๋๋ค.</p>
<p>์ด๋ฆ์ ๋์ถฉ BadFFTFunction์ผ๋ก ์ง์์ต๋๋ค.</p>
<p><strong>๊ณ์ธต(layer) ๊ตฌํ</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy.fft</span> <span class="kn">import</span> <span class="n">rfft2</span><span class="p">,</span> <span class="n">irfft2</span>
<span class="k">class</span> <span class="nc">BadFFTFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="n">numpy_input</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">rfft2</span><span class="p">(</span><span class="n">numpy_input</span><span class="p">))</span>
<span class="k">return</span> <span class="nb">input</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">numpy_go</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">irfft2</span><span class="p">(</span><span class="n">numpy_go</span><span class="p">)</span>
<span class="k">return</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="c1"># ์ด ๊ณ์ธต์๋ ๋งค๊ฐ ๋ณ์๊ฐ ์์ผ๋ฏ๋ก nn.Module ํด๋์ค๊ฐ ์๋ ํจ์๋ก ๊ฐ๋จํ ์ ์ธํ ์ ์์ต๋๋ค.</span>
<span class="k">def</span> <span class="nf">incorrect_fft</span><span class="p">(</span><span class="nb">input</span><span class="p">):</span>
<span class="k">return</span> <span class="n">BadFFTFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>์์ฑ๋ ๊ณ์ธต(layer)์ ์ฌ์ฉ ์์:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">input</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">8</span><span class="p">,</span> <span class="mi">8</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">result</span> <span class="o">=</span> <span class="n">incorrect_fft</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="n">result</span><span class="p">)</span>
<span class="n">result</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">size</span><span class="p">()))</span>
<span class="nb">print</span><span class="p">(</span><span class="nb">input</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([[ 0.1427, 5.5778, 11.1232, 17.8041, 12.2626],
[ 9.5936, 4.0079, 4.6988, 6.7813, 3.6823],
[ 6.5884, 14.3957, 10.7560, 8.2738, 19.2556],
[ 7.7234, 5.7786, 8.3944, 5.8846, 15.3141],
[ 2.0789, 5.2201, 4.7461, 2.9303, 3.4912],
[ 7.7234, 5.6180, 3.1562, 3.6815, 15.3141],
[ 6.5884, 6.1014, 7.9042, 6.9556, 19.2556],
[ 9.5936, 5.5033, 10.4785, 1.1310, 3.6823]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[-1.4709e+00, -6.3109e-01, 1.3298e+00, 2.3514e+00, 5.9798e-01,
-1.1601e+00, 2.5796e+00, -9.1742e-01],
[-5.1303e-01, -1.2454e-01, 9.4299e-01, 4.1181e-02, -1.0822e+00,
-6.6457e-01, 1.6514e+00, -4.5767e-01],
[ 1.1881e+00, -8.2682e-01, -6.6985e-01, -1.4528e+00, 5.1185e-01,
-8.0868e-01, 1.7740e-03, 1.1327e+00],
[-1.1642e+00, 3.2232e-02, -1.8744e+00, 8.7643e-01, -2.9207e-01,
-6.5755e-01, 5.5591e-01, -5.4848e-01],
[-9.3801e-01, 1.2927e+00, -8.1564e-01, 1.2620e+00, -6.6684e-02,
-5.5979e-02, 4.3299e-01, -1.2738e+00],
[ 1.3811e+00, -4.1654e-01, 1.2796e+00, -1.1521e+00, 2.3741e-01,
-2.0551e+00, 2.4323e+00, -2.3034e+00],
[-6.3560e-01, -1.0755e+00, -1.0727e+00, 1.5191e-02, -6.5398e-02,
7.0480e-02, 8.0156e-01, -5.9931e-01],
[ 1.1470e-01, 9.0640e-01, 2.5264e-01, 1.6878e+00, 1.3140e-01,
1.0867e+00, 4.4034e-01, 3.6620e-01]], requires_grad=True)
</pre></div>
</div>
</div>
<div class="section" id="parameterized">
<h2>๋งค๊ฐ ๋ณ์๊ฐ ์๋(Parameterized) ์์<a class="headerlink" href="#parameterized" title="Permalink to this headline">ยถ</a></h2>
<p>๋ฅ๋ฌ๋ ๋ฌธํ์์ ์ด ๊ณ์ธต(layer)์ ์ค์ ์ฐ์ฐ์ ์ํธ ์๊ด(cross-correlation)์ด์ง๋ง
ํฉ์ฑ๊ณฑ(convolution)์ด๋ผ๊ณ ํท๊ฐ๋ฆฌ๊ฒ ๋ถ๋ฅด๊ณ ์์ต๋๋ค.
(ํฉ์ฑ๊ณฑ์ ํํฐ๋ฅผ ๋ค์ง์ด์ ์ฐ์ฐ์ ํ๋ ๋ฐ๋ฉด, ์ํธ ์๊ด์ ๊ทธ๋ ์ง ์์ ์ฐจ์ด๊ฐ ์์ต๋๋ค)</p>
<p>ํ์ต ๊ฐ๋ฅํ ๊ฐ์ค์น๋ฅผ ๊ฐ๋ ํํฐ(์ปค๋)๋ฅผ ๊ฐ๋ ์ํธ ์๊ด ๊ณ์ธต์ ๊ตฌํํด๋ณด๊ฒ ์ต๋๋ค.</p>
<p>์ญ์ ํ ๋จ๊ณ(backward pass)์์๋ ์
๋ ฅ์ ๋ํ ๊ธฐ์ธ๊ธฐ(gradient)์ ํํฐ์ ๋ํ ๊ธฐ์ธ๊ธฐ๋ฅผ ๊ณ์ฐํฉ๋๋ค.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">flip</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">from</span> <span class="nn">scipy.signal</span> <span class="kn">import</span> <span class="n">convolve2d</span><span class="p">,</span> <span class="n">correlate2d</span>
<span class="kn">from</span> <span class="nn">torch.nn.modules.module</span> <span class="kn">import</span> <span class="n">Module</span>
<span class="kn">from</span> <span class="nn">torch.nn.parameter</span> <span class="kn">import</span> <span class="n">Parameter</span>
<span class="k">class</span> <span class="nc">ScipyConv2dFunction</span><span class="p">(</span><span class="n">Function</span><span class="p">):</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span><span class="p">):</span>
<span class="c1"># ๋ถ๋ฆฌ(detach)ํ์ฌ NumPy๋ก ๋ณํ(cast)ํ ์ ์์ต๋๋ค.</span>
<span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="nb">input</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="nb">filter</span><span class="o">.</span><span class="n">detach</span><span class="p">(),</span> <span class="n">bias</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span>
<span class="n">result</span> <span class="o">=</span> <span class="n">correlate2d</span><span class="p">(</span><span class="nb">input</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="nb">filter</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'valid'</span><span class="p">)</span>
<span class="n">result</span> <span class="o">+=</span> <span class="n">bias</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">ctx</span><span class="o">.</span><span class="n">save_for_backward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span><span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">as_tensor</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">input</span><span class="o">.</span><span class="n">dtype</span><span class="p">)</span>
<span class="nd">@staticmethod</span>
<span class="k">def</span> <span class="nf">backward</span><span class="p">(</span><span class="n">ctx</span><span class="p">,</span> <span class="n">grad_output</span><span class="p">):</span>
<span class="n">grad_output</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">detach</span><span class="p">()</span>
<span class="nb">input</span><span class="p">,</span> <span class="nb">filter</span><span class="p">,</span> <span class="n">bias</span> <span class="o">=</span> <span class="n">ctx</span><span class="o">.</span><span class="n">saved_tensors</span>
<span class="n">grad_output</span> <span class="o">=</span> <span class="n">grad_output</span><span class="o">.</span><span class="n">numpy</span><span class="p">()</span>
<span class="n">grad_bias</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">grad_output</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">grad_input</span> <span class="o">=</span> <span class="n">convolve2d</span><span class="p">(</span><span class="n">grad_output</span><span class="p">,</span> <span class="nb">filter</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'full'</span><span class="p">)</span>
<span class="c1"># ์์ค์ ๋ค์๊ณผ ๊ฐ์ด ํํํ ์๋ ์์ต๋๋ค:</span>
<span class="c1"># grad_input = correlate2d(grad_output, flip(flip(filter.numpy(), axis=0), axis=1), mode='full')</span>
<span class="n">grad_filter</span> <span class="o">=</span> <span class="n">correlate2d</span><span class="p">(</span><span class="nb">input</span><span class="o">.</span><span class="n">numpy</span><span class="p">(),</span> <span class="n">grad_output</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">'valid'</span><span class="p">)</span>
<span class="k">return</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_input</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_filter</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">float</span><span class="p">),</span> <span class="n">torch</span><span class="o">.</span><span class="n">from_numpy</span><span class="p">(</span><span class="n">grad_bias</span><span class="p">)</span><span class="o">.</span><span class="n">to</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">float</span><span class="p">)</span>
<span class="k">class</span> <span class="nc">ScipyConv2d</span><span class="p">(</span><span class="n">Module</span><span class="p">):</span>
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">filter_width</span><span class="p">,</span> <span class="n">filter_height</span><span class="p">):</span>
<span class="nb">super</span><span class="p">(</span><span class="n">ScipyConv2d</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
<span class="bp">self</span><span class="o">.</span><span class="n">filter</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">filter_width</span><span class="p">,</span> <span class="n">filter_height</span><span class="p">))</span>
<span class="bp">self</span><span class="o">.</span><span class="n">bias</span> <span class="o">=</span> <span class="n">Parameter</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
<span class="k">def</span> <span class="nf">forward</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
<span class="k">return</span> <span class="n">ScipyConv2dFunction</span><span class="o">.</span><span class="n">apply</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">filter</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bias</span><span class="p">)</span>
</pre></div>
</div>
<p><strong>์ฌ์ฉ ์์:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">module</span> <span class="o">=</span> <span class="n">ScipyConv2d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Filter and bias: "</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="n">module</span><span class="o">.</span><span class="n">parameters</span><span class="p">()))</span>
<span class="nb">input</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">10</span><span class="p">,</span> <span class="mi">10</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">output</span> <span class="o">=</span> <span class="n">module</span><span class="p">(</span><span class="nb">input</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Output from the convolution: "</span><span class="p">,</span> <span class="n">output</span><span class="p">)</span>
<span class="n">output</span><span class="o">.</span><span class="n">backward</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Gradient for the input map: "</span><span class="p">,</span> <span class="nb">input</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>Filter and bias: [Parameter containing:
tensor([[-0.1602, -1.3375, 0.4899],
[ 0.0117, -1.8393, -1.1161],
[-0.7189, -0.9802, 0.4517]], requires_grad=True), Parameter containing:
tensor([[-0.0199]], requires_grad=True)]
Output from the convolution: tensor([[-6.0479e-01, -6.6172e-01, 5.7668e-01, 7.3642e-01, -1.0404e+00,
-2.5380e+00, 7.0431e-01, -3.0432e+00],
[ 4.0189e+00, -2.9888e-01, 1.5170e-01, 6.8403e-01, 6.4340e-01,
-4.1355e-02, 2.0061e+00, -5.5426e+00],
[-9.2383e-01, 4.2150e+00, -7.7942e-01, -1.9131e+00, -1.5988e+00,
-3.0727e+00, -9.9906e-01, -6.2175e-01],
[ 2.4869e+00, -2.0382e+00, -1.2072e+00, -2.4638e+00, 3.3878e+00,
-2.5876e+00, -1.6984e+00, 1.0379e+00],
[ 3.3521e+00, 3.0190e+00, -1.6648e+00, -4.4991e-01, 6.2380e+00,
-5.3818e+00, -5.1706e-03, 1.8641e+00],
[ 8.3524e-01, 2.5572e+00, 3.0948e-01, 2.6738e+00, 3.0596e+00,
-4.1210e+00, -1.7525e+00, 9.5410e-01],
[-2.9451e+00, -1.7272e+00, -3.1038e+00, 1.2254e+00, 1.3403e+00,
-5.1629e-01, -2.3515e-01, 2.7382e+00],
[-9.9022e-01, 1.1924e+00, 9.4509e-01, 1.5043e-01, -4.1593e+00,
1.5421e+00, 2.0839e+00, 2.3023e+00]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[-6.6709e-03, -1.2434e-01, -4.5475e-01, 1.2874e+00, 2.0362e+00,
7.2406e-01, 5.3141e-01, 7.4434e-01, -9.8842e-01, 2.0831e-01],
[-8.3832e-03, -5.7282e-03, 4.0055e-01, 5.7226e-01, 3.2199e+00,
3.4890e+00, 6.4686e+00, -1.9396e+00, 8.0274e-01, -3.3750e-01],
[-6.3797e-02, -6.4219e-01, 2.7781e+00, 4.9925e+00, 2.8659e+00,
-8.8033e-01, 6.4537e+00, 2.1578e+00, -3.0852e+00, -6.1653e-01],
[ 1.1052e-01, 1.5087e+00, 2.4574e+00, 2.5282e+00, 5.0612e+00,
1.8256e+00, 2.7466e+00, -2.0636e+00, 4.6944e+00, 1.3905e+00],
[-2.0347e-01, 1.6992e+00, 4.6616e+00, 3.5024e+00, 5.6251e+00,
6.4188e-01, 7.2062e-01, -1.7522e+00, -1.1723e-01, -1.0297e+00],
[ 8.2716e-01, 2.2493e+00, -3.7179e-01, 2.7535e+00, 6.2322e+00,
8.2966e-01, -6.1872e-01, -7.0798e+00, -2.1370e+00, 1.3610e+00],
[-3.1513e-01, 6.0357e-01, 7.8525e-01, 2.5810e-01, 3.7759e+00,
-3.0246e+00, -2.6638e+00, -1.8082e+00, -2.2248e+00, -1.3668e+00],
[ 8.4025e-01, -4.3326e-02, -6.0940e+00, -3.8165e+00, -1.0286e+00,
2.7988e+00, -6.3584e-01, -3.4374e+00, -2.6719e+00, -9.0657e-02],
[-6.0745e-01, -2.9021e-01, -3.7362e+00, -1.6683e+00, -2.5320e-01,
-3.3608e+00, -3.0979e+00, -2.0743e+00, -8.8610e-01, 2.0207e-01],
[ 4.8142e-01, -4.5982e-01, -1.9266e+00, -5.4646e-01, -1.8311e+00,
-3.4494e-01, -6.9319e-01, -4.1617e-02, 7.0677e-02, 3.3832e-02]])
</pre></div>
</div>
<p><strong>๊ธฐ์ธ๊ธฐ(gradient) ํ์ธ:</strong></p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">torch.autograd.gradcheck</span> <span class="kn">import</span> <span class="n">gradcheck</span>
<span class="n">moduleConv</span> <span class="o">=</span> <span class="n">ScipyConv2d</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="nb">input</span> <span class="o">=</span> <span class="p">[</span><span class="n">torch</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">20</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">torch</span><span class="o">.</span><span class="n">double</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">test</span> <span class="o">=</span> <span class="n">gradcheck</span><span class="p">(</span><span class="n">moduleConv</span><span class="p">,</span> <span class="nb">input</span><span class="p">,</span> <span class="n">eps</span><span class="o">=</span><span class="mf">1e-6</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Are the gradients correct: "</span><span class="p">,</span> <span class="n">test</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>Are the gradients correct: True
</pre></div>
</div>
<p class="sphx-glr-timing"><strong>Total running time of the script:</strong> ( 0 minutes 0.308 seconds)</p>
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