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<p class="caption" role="heading"><span class="caption-text">ํ์ดํ ์น(PyTorch) ๋ ์ํผ</span></p>
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<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" 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>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/transforms_tutorial.html">๋ณํ(Transform)</a></li>
<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>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/optimization_tutorial.html">๋ชจ๋ธ ๋งค๊ฐ๋ณ์ ์ต์ ํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/basics/saveloadrun_tutorial.html">๋ชจ๋ธ ์ ์ฅํ๊ณ ๋ถ๋ฌ์ค๊ธฐ</a></li>
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<p class="caption" role="heading"><span class="caption-text">Introduction to PyTorch on YouTube</span></p>
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<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt.html">PyTorch ์๊ฐ - YouTube ์๋ฆฌ์ฆ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/introyt1_tutorial.html">PyTorch ์๊ฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/tensors_deeper_tutorial.html">Pytorch Tensor ์๊ฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/autogradyt_tutorial.html">The Fundamentals of Autograd</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/modelsyt_tutorial.html">Building Models with PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/tensorboardyt_tutorial.html">PyTorch TensorBoard Support</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/trainingyt.html">Training with PyTorch</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/introyt/captumyt.html">Model Understanding with Captum</a></li>
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<p class="caption" role="heading"><span class="caption-text">ํ์ดํ ์น(PyTorch) ๋ฐฐ์ฐ๊ธฐ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/deep_learning_60min_blitz.html">PyTorch๋ก ๋ฅ๋ฌ๋ํ๊ธฐ: 60๋ถ๋ง์ ๋์ฅ๋ด๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/pytorch_with_examples.html">์์ ๋ก ๋ฐฐ์ฐ๋ ํ์ดํ ์น(PyTorch)</a></li>
<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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<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="../beginner/transfer_learning_tutorial.html">์ปดํจํฐ ๋น์ (Vision)์ ์ํ ์ ์ดํ์ต(Transfer Learning)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/fgsm_tutorial.html">์ ๋์ ์์ ์์ฑ(Adversarial Example Generation)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/dcgan_faces_tutorial.html">DCGAN ํํ ๋ฆฌ์ผ</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>
</ul>
<p class="caption" role="heading"><span class="caption-text">์ค๋์ค</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_io_tutorial.html">Audio I/O</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_resampling_tutorial.html">Audio Resampling</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/audio_data_augmentation_tutorial.html">Audio Data Augmentation</a></li>
<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>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/text_to_speech_with_torchaudio.html">Text-to-speech with Tacotron2</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/forced_alignment_with_torchaudio_tutorial.html">wav2vec2์ ์ด์ฉํ ๊ฐ์ ์ ๋ ฌ</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"><code class="docutils literal notranslate"><span class="pre">nn.Transformer</span></code> ์ torchtext๋ก ์ํ์ค-ํฌ-์ํ์ค(Sequence-to-Sequence) ๋ชจ๋ธ๋งํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/bettertransformer_tutorial.html">Fast Transformer Inference with Better Transformer</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"><code class="docutils literal notranslate"><span class="pre">nn.Transformer</span></code> ์ 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/reinforcement_ppo.html">Reinforcement Learning (PPO) with TorchRL Tutorial</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">Raspberry Pi 4 ์์ ์ค์๊ฐ ์ถ๋ก (Inference) (30fps!)</a></li>
</ul>
<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="../intermediate/jacobians_hessians.html">Jacobians, Hessians, hvp, vhp, and more: composing function transforms</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/ensembling.html">Model ensembling</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/per_sample_grads.html">Per-sample-gradients</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>
<li class="toctree-l1"><a class="reference internal" href="cpp_autograd.html">C++ ํ๋ก ํธ์๋์ ์๋ ๋ฏธ๋ถ (autograd)</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">PyTorch ํ์ฅํ๊ธฐ</span></p>
<ul>
<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>
<li class="toctree-l1"><a class="reference internal" href="cpp_extension.html">Custom C++ and CUDA Extensions</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_script_custom_ops.html">Extending TorchScript with Custom C++ Operators</a></li>
<li class="toctree-l1"><a class="reference internal" href="torch_script_custom_classes.html">์ปค์คํ
C++ ํด๋์ค๋ก TorchScript ํ์ฅํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="dispatcher.html">Registering a Dispatched Operator in C++</a></li>
<li class="toctree-l1"><a class="reference internal" href="extend_dispatcher.html">Extending dispatcher for a new backend in C++</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">๋ชจ๋ธ ์ต์ ํ</span></p>
<ul>
<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">ํ
์๋ณด๋๋ฅผ ์ด์ฉํ ํ์ดํ ์น ํ๋กํ์ผ๋ฌ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/hyperparameter_tuning_tutorial.html">Ray Tune์ ์ด์ฉํ ํ์ดํผํ๋ผ๋ฏธํฐ ํ๋</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>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/torchserve_with_ipex.html">Grokking PyTorch Intel CPU performance from first principles</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/torchserve_with_ipex_2.html">Grokking PyTorch Intel CPU performance from first principles (Part 2)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/nvfuser_intro_tutorial.html">Getting Started - Accelerate Your Scripts with nvFuser</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/ax_multiobjective_nas_tutorial.html">Multi-Objective NAS with Ax</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/torch_compile_tutorial.html">torch.compile Tutorial</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/scaled_dot_product_attention_tutorial.html">(Beta) Scaled Dot Product Attention (SDPA)๋ก ๊ณ ์ฑ๋ฅ ํธ๋์คํฌ๋จธ(Transformers) ๊ตฌํํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/scaled_dot_product_attention_tutorial.html#torch-compile-sdpa"><code class="docutils literal notranslate"><span class="pre">torch.compile</span></code> ๊ณผ ํจ๊ป SDPA ์ฌ์ฉํ๊ธฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/scaled_dot_product_attention_tutorial.html#id6">๊ฒฐ๋ก </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="../distributed/home.html">Distributed and Parallel Training Tutorials</a></li>
<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="../beginner/ddp_series_intro.html">Distributed Data Parallel in PyTorch - Video Tutorials</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>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/ddp_tutorial.html">๋ถ์ฐ ๋ฐ์ดํฐ ๋ณ๋ ฌ ์ฒ๋ฆฌ ์์ํ๊ธฐ</a></li>
<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/FSDP_adavnced_tutorial.html">Advanced Model Training with Fully Sharded Data Parallel (FSDP)</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/process_group_cpp_extension_tutorial.html">Cpp ํ์ฅ์ ์ฌ์ฉํ์ฌ ํ๋ก์ธ์ค ๊ทธ๋ฃน ๋ฐฑ์๋ ์ฌ์ฉ์ ์ ์</a></li>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/rpc_tutorial.html">Getting Started with Distributed RPC Framework</a></li>
<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>
</ul>
<p class="caption" role="heading"><span class="caption-text">๋ชจ๋ฐ์ผ</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/deeplabv3_on_ios.html">iOS์์์ ์ด๋ฏธ์ง ๋ถํ DeepLapV3</a></li>
<li class="toctree-l1"><a class="reference internal" href="../beginner/deeplabv3_on_android.html">์๋๋ก์ด๋์์์ ์ด๋ฏธ์ง ๋ถํ DeepLapV3</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">์ถ์ฒ ์์คํ
</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../intermediate/torchrec_tutorial.html">TorchRec ์๊ฐ</a></li>
<li class="toctree-l1"><a class="reference internal" href="sharding.html">Exploring TorchRec sharding</a></li>
</ul>
<p class="caption" role="heading"><span class="caption-text">Multimodality</span></p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="../beginner/flava_finetuning_tutorial.html">TorchMultimodal Tutorial: Finetuning FLAVA</a></li>
</ul>
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<p>Click <a class="reference internal" href="#sphx-glr-download-advanced-numpy-extensions-tutorial-py"><span class="std std-ref">here</span></a>
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<div class="sphx-glr-example-title section" id="numpy-scipy-extension">
<span id="sphx-glr-advanced-numpy-extensions-tutorial-py"></span><h1>NumPy์ SciPy๋ฅผ ์ฌ์ฉํ ํ์ฅ(Extension) ๋ง๋ค๊ธฐ<a class="headerlink" href="#numpy-scipy-extension" title="์ด ์ ๋ชฉ์ ๋ํ ํผ๋จธ๋งํฌ">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="์ด ์ ๋ชฉ์ ๋ํ ํผ๋จธ๋งํฌ">ยถ</a></h2>
<p>์ด ๊ณ์ธต(layer)์ ํน๋ณํ ์ ์ฉํ๊ฑฐ๋ ์ํ์ ์ผ๋ก ์ฌ๋ฐ๋ฅธ ์์
์ ์ํํ์ง ์์ต๋๋ค.</p>
<p>์ด๋ฆ์ ๋์ถฉ <code class="docutils literal notranslate"><span class="pre">BadFFTFunction</span></code> ์ผ๋ก ์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>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>tensor([[ 0.7493, 5.3761, 7.4498, 5.2065, 8.1245],
[10.7571, 9.3190, 13.9146, 6.2218, 1.9285],
[ 5.8930, 1.9813, 11.8968, 6.0770, 8.5321],
[17.1539, 9.4069, 11.7599, 1.9252, 11.2858],
[11.2505, 5.9365, 3.1825, 6.0164, 3.0514],
[17.1539, 7.1099, 3.6442, 8.3454, 11.2858],
[ 5.8930, 7.0157, 8.8019, 9.0743, 8.5321],
[10.7571, 5.9901, 3.6158, 5.7762, 1.9285]],
grad_fn=<BadFFTFunctionBackward>)
tensor([[ 0.0834, 0.0469, 0.2830, -1.0414, 2.5665, -0.2704, 0.5082, 0.7925],
[-0.3522, 0.4684, 0.2900, -0.9710, -0.6960, 0.5306, -1.6445, 0.8292],
[-0.0250, -1.1805, -1.3117, 0.5479, 0.7102, -1.0263, -0.9084, -0.5743],
[ 0.9343, -1.5087, 1.4279, 1.0486, 0.1963, -1.4240, 0.1408, -0.1087],
[ 0.0217, 1.1997, 0.1217, -1.1010, -2.2295, 0.1683, -0.2580, -0.7808],
[-0.2993, 0.9932, 0.6913, -0.8400, 0.4267, 0.2024, -2.1530, -2.0117],
[ 1.9086, 0.9026, 1.6754, 0.3198, 0.5785, 1.1717, 1.6946, 0.6565],
[ 1.1715, -0.9260, -1.4667, -0.3593, 0.1675, 0.1235, -0.5661, -0.3147]],
requires_grad=True)
</pre></div>
</div>
</div>
<div class="section" id="parameterized">
<h2>๋งค๊ฐ ๋ณ์๊ฐ ์๋(Parameterized) ์์<a class="headerlink" href="#parameterized" title="์ด ์ ๋ชฉ์ ๋ํ ํผ๋จธ๋งํฌ">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>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Filter and bias: [Parameter containing:
tensor([[-0.0685, 0.5146, -0.9103],
[-0.9190, 0.7659, 1.4033],
[-1.5628, -0.4356, 0.1513]], requires_grad=True), Parameter containing:
tensor([[0.0500]], requires_grad=True)]
Output from the convolution: tensor([[ 1.0434, 0.5532, 1.4637, 2.4000, -2.9941, -3.0063, -0.8389, -0.2737],
[-2.0167, 1.2345, -3.4750, 0.9726, 3.4054, -0.9997, 1.6345, -5.7391],
[ 0.8466, 1.3429, -4.8645, -1.8883, 2.5089, 0.6507, 5.4805, -0.4945],
[-0.6900, -0.4684, -1.6632, -1.6022, -1.6148, -4.8085, -1.3337, 3.9142],
[ 3.7322, -0.9291, 1.1793, 4.3954, 1.6756, -0.4551, 4.0487, -2.3517],
[ 1.3401, -0.4182, -2.7344, 2.6672, -1.1287, -1.3467, 2.7797, 10.2257],
[-1.6213, -0.9084, -1.0380, -0.1645, -2.4001, 0.8624, 0.8780, 5.1931],
[ 1.2913, 1.1509, -4.2846, 5.4657, -2.2595, 0.5128, -0.7484, -1.2321]],
grad_fn=<ScipyConv2dFunctionBackward>)
Gradient for the input map: tensor([[-0.0479, 0.5676, -2.0581, 1.6713, 2.2732, -1.0390, 0.6838, -0.7023,
1.2946, -0.6725],
[-0.7185, 3.9055, -0.6547, -6.2065, -1.9312, 1.2286, -0.0152, -2.3588,
0.4810, 1.5156],
[-2.0281, 5.0570, 6.3651, 0.0545, -0.4638, -0.4837, 4.1343, -3.3259,
-2.6426, -0.6377],
[-0.7372, 0.3809, -3.2023, 0.7439, -2.4857, 0.5112, 6.0474, 3.1520,
-0.3647, -0.7803],
[ 1.2595, 4.1878, -1.7010, -1.6706, -2.2941, -5.0591, -0.4691, 0.6966,
0.6100, 2.1561],
[-1.6727, 2.7531, 1.2086, 0.5137, -0.2360, 1.9270, 5.1387, -3.4446,
-2.6745, -0.9914],
[-2.4838, -1.5068, 1.6128, -0.5395, -1.3657, -1.3266, 3.4149, 0.5285,
-0.9051, 0.5061],
[-1.9095, -2.3272, 3.8304, -0.7444, 1.8315, -1.8599, 3.1576, 4.0086,
-2.1298, -2.1147],
[ 0.3715, -0.0954, 0.2900, -2.3744, -0.1899, -2.7285, 0.9018, 2.3479,
-1.1129, -0.5725],
[ 2.5708, 2.5453, 1.7140, 0.2467, 0.9614, 0.7750, 1.6201, 0.7669,
-0.0519, -0.0356]])
</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>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Are the gradients correct: True
</pre></div>
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