This outline can be adjusted to your needs, but it gives you a basic framework for a PyTorch tutorial.<\/p>\n\n\n\n Please explain the introduction to PyTorch in detail<\/p>\n\n\n\n The previous model used in this conversation is unavailable. We\u2019ve switched you to the latest default model<\/p>\n\n\n\n PyTorch is an open source machine learning framework that was first released in 2016 by the Facebook Artificial Intelligence Research Institute (FAIR). It is a Python-based scientific computing package that enables the construction and training of deep neural networks on GPUs and CPUs.<\/p>\n\n\n\n PyTorch has the following characteristics:<\/p>\n\n\n\n In general, PyTorch is a powerful, easy-to-use, and rich ecosystem deep learning framework, which has become one of the mainstream research and application of deep learning.<\/p>\n\n\n\n 1 \/ 2<\/p>\n\n\n\n Please explain the installation and configuration in detail<\/p>\n\n\n\n Installing and configuring PyTorch requires the following steps:<\/p>\n\n\n\n In the process of installing and configuring PyTorch, you need to pay attention to the following issues:<\/p>\n\n\n\n In general, the installation and configuration of PyTorch needs to be selected and installed according to your own operating system, hardware environment and usage requirements. You need to read the official documents carefully and follow the instructions strictly.<\/p>\n\n\n\n Please explain in detail how PyTorch compares to other deep learning frameworks<\/p>\n\n\n\n Compared with other deep learning frameworks, PyTorch has the following advantages:<\/p>\n\n\n\n In general, PyTorch’s dynamic calculation graph, Pythonic syntax, fast iteration and experimentation, readability and debugging, huge community and ecosystem, and efficient GPU acceleration make it the mainstream of research and application of deep learning. one of the frames. At the same time, other frameworks also have their own advantages, which need to be selected and used according to specific needs.<\/p>\n\n\n\n Please explain in detail PyTorch tensor operations and basic mathematical operations to create tensors<\/p>\n\n\n\n A tensor in PyTorch is a multidimensional array, similar to an array in NumPy. Tensor supports various mathematical operations, such as addition, subtraction, multiplication and division, matrix multiplication, linear algebra operations, etc., and is the basis of deep learning calculations.<\/p>\n\n\n\n Create tensors: PyTorch can use the torch.tensor() function to create tensors. Here are a few ways to create tensors:<\/p>\n\n\n\n Basic mathematical operations: Tensors in PyTorch support various basic mathematical operations, such as addition, subtraction, multiplication and division, matrix multiplication, linear algebra operations, etc. The following are examples of several basic mathematical operations:<\/p>\n\n\n\n The above is an example of tensor creation and basic mathematical operations in PyTorch. PyTorch also supports more mathematical operations, such as square, square root, exponent, logarithm, etc. For details, please refer to the official documentation.<\/p>\n\n\n\n Please explain in detail the shape and dimension of PyTorch tensor operations and basic mathematical operations<\/p>\n\n\n\n Tensor in PyTorch is a multi-dimensional array with two important properties of shape and dimension. shape is a tuple of integers representing the size of the tensor in each dimension, where dimension is the number of axes in the tensor. The shape and dimensionality of tensors are very important for deep learning tasks and can be used to describe the shape and dimensionality of input data and model parameters.<\/p>\n\n\n\n The shape of a tensor: You can use the shape property of a tensor to get its shape. Here are a few ways to get the shape of a tensor:<\/p>\n\n\n\n Dimensions of a tensor: You can use the ndim attribute of a tensor to get its dimensions. Here are a few ways to get tensor dimensions:<\/p>\n\n\n\n Shape and dimensionality in basic mathematical operations: Shape and dimensionality are also very important in basic mathematical operations in PyTorch. Here are examples of shapes and dimensions in several basic mathematical operations:<\/p>\n\n\n\n please continue<\/p>\n\n\n\n In the above example, operations such as tensor addition, tensor multiplication, and tensor transpose all change the shape and dimension of the tensor. In deep learning tasks, appropriate mathematical operations need to be performed according to the shape and dimension of the data and the model to ensure correct and efficient calculations.<\/p>\n\n\n\n It should be noted that when performing basic mathematical operations, the shape and dimension of the tensor must meet certain conditions before the operation can be performed. For example, in tensor multiplication, the last dimension of the two tensors must be the same, otherwise the multiplication operation cannot take place. Therefore, when doing mathematical operations, you need to carefully check the shape and dimensions of tensors, and transform them as necessary.<\/p>\n\n\n\n Please explain PyTorch tensor operations and basic mathematical operations indexing and slicing in detail<\/p>\n\n\n\n The tensor (tensor) in PyTorch supports indexing and slicing operations, which can be used to obtain specific elements or subsets in the tensor. The following are examples of several common indexing and slicing operations:<\/p>\n\n\n\n Indexing: You can use tensor indexing operations to get specific elements in a tensor. Indexing operations use square brackets [], and specify the position of the element within the square brackets. The following are examples of several indexing operations:<\/p>\n\n\n\n Slicing: You can use the tensor slicing operation to obtain a subset of tensors. Slicing operations use a colon: , and specify the start and end positions of the slice before and after the colon. The following are examples of several slice operations:<\/p>\n\n\n\n It should be noted that when performing indexing and slicing operations, you need to follow the indexing and slicing rules in Python. For example, indexing returns a scalar or 1D tensor, and slicing returns a subtensor. At the same time, when performing slice operations, you can use the step parameter to specify the interval, or omit the start and end parameters, which means from the beginning to the end or from the beginning to the specified position.<\/p>\n\n\n\n Please explain PyTorch tensor operations and basic mathematical operations tensor operations in detail<\/p>\n\n\n\n In PyTorch, tensor supports various basic mathematical operations, such as addition, subtraction, multiplication and division, matrix multiplication, linear algebra operations, etc. The following are several common examples of tensor operations:<\/p>\n\n\n\n In the above example, operations such as tensor addition, tensor multiplication, tensor transpose, tensor square, tensor sum, and tensor normalization are common tensor operations that can be used for data processing and models in deep learning tasks calculate.<\/p>\n\n\n\n It should be noted that when performing tensor operations, it is necessary to ensure that the shape and dimension of the tensor meet the operation requirements. For example, when performing tensor multiplication, the last dimension of the two tensors must be the same, otherwise the multiplication operation cannot be performed. At the same time, when performing tensor operations, data types and devices also need to be considered, such as using float or double data types, using CPU or GPU devices, and so on.<\/p>\n\n\n\n Please explain in detail PyTorch tensor operations and basic mathematical operations linear algebra operations<\/p>\n\n\n\n In PyTorch, linear algebra operations are one of the important operations in deep learning. Linear algebra operations can be used in tasks such as model training, optimization, and evaluation. The following are examples of several common linear algebra operations:<\/p>\n\n\n\n In the above example, operations such as matrix multiplication, matrix inversion, eigenvalue decomposition, and singular value decomposition are common linear algebra operations. These operations can be used for model training, parameter optimization, and result evaluation in deep learning tasks.<\/p>\n\n\n\n It should be noted that when performing linear algebra operations, it is necessary to ensure that the shape and dimension of the tensor meet the requirements. For example, when doing matrix multiplication, the last dimension of the two tensors must be the same, otherwise the multiplication cannot be performed. At the same time, when performing linear algebra operations, data types and devices also need to be considered, such as using float or double data types, using CPU or GPU devices, and so on.<\/p>\n\n\n\n Please explain in detail the PyTorch tensor operation and basic mathematical operation broadcasting mechanism<\/p>\n\n\n\n In PyTorch, broadcasting is a very important tensor operation that can be used to adapt tensors of different shapes in mathematical operations. The broadcasting mechanism enables mathematical operations on tensors of different shapes without requiring explicit tensor shape transformations. Here are a few examples of common broadcast mechanisms:<\/p>\n\n\n\n In the above example, the broadcasting mechanism enables mathematical operations on tensors of different shapes, such as adding a 2D tensor with a 1D tensor, multiplying a 3D tensor with a 2D tensor, and multiplying a 1D tensor with a scalar Multiply etc. The broadcasting mechanism automatically expands the dimensions of tensors to match the dimensions of other tensors, allowing tensors to fit in mathematical operations. It should be noted that when performing the broadcasting mechanism, the rules of the broadcasting mechanism need to be followed. For example, the dimensions of the tensor must conform to certain rules to ensure the correctness and efficiency of mathematical operations.<\/p>\n\n\n\n Please explain in detail PyTorch automatic derivation and optimization calculation graph and automatic derivation<\/p>\n\n\n\n In PyTorch, automatic derivation and optimization are one of the important operations in deep learning, which can be used in tasks such as model training and parameter optimization. Here are several common examples of automatic differentiation and optimization:<\/p>\n\n\n\n please continue<\/p>\n\n\n\n The above are several common examples of automatic derivation and optimization. The functions of automatic derivation and optimization in PyTorch are very powerful and flexible, and can meet the needs of various deep learning tasks. At the same time, it should be noted that the correctness and efficiency of automatic derivation and optimization depend on factors such as the construction of the calculation graph and the selection of the optimizer, which need to be continuously explored and optimized in practice.<\/p>\n\n\n\n Please explain in detail PyTorch automatic derivation and optimization backpropagation and gradient<\/p>\n\n\n\n In PyTorch, automatic derivation and optimization are one of the important operations in deep learning, which can be used in tasks such as model training and parameter optimization. Backpropagation and gradient are one of the core concepts of automatic derivation and optimization, which are used to calculate the gradient of the model and update the parameters of the model. Here is an example of backpropagation and gradient computation:<\/p>\n\n\n\n It should be noted that when performing backpropagation and gradient calculation, you need to ensure that the requires_grad attribute of the tensor is True, and when building the calculation graph, you need to set the requires_grad attribute of the node to True. At the same time, it is also necessary to pay attention to the correctness and efficiency of backpropagation and gradient calculation, such as avoiding problems such as gradient explosion and disappearance, and selecting an appropriate optimizer.<\/p>\n\n\n\n Please explain in detail the introduction of PyTorch automatic derivation and optimization optimizer<\/p>\n\n\n\n In PyTorch, the optimizer is one of the core components of model parameter optimization. It implements model training and optimization by performing gradient calculation and updating of model parameters. PyTorch provides a variety of optimizers, such as SGD, Adam, RMSprop, etc. Here are several common optimizer examples:<\/p>\n\n\n\n It should be noted that when selecting an optimizer, it is necessary to select the appropriate optimizer and hyperparameters, such as learning rate, momentum, weight decay, etc., according to the specific task and model. At the same time, it is also necessary to pay attention to the correctness and efficiency of the optimizer, such as avoiding problems such as gradient explosion and disappearance, and choosing an appropriate learning rate and other hyperparameters.<\/p>\n\n\n\n Please explain in detail the use and comparison of common optimizers for PyTorch automatic derivation and optimization<\/p>\n\n\n\n In PyTorch, common optimizers include SGD, Adam, RMSprop, etc. Different optimizers have different advantages and disadvantages and applicable scenarios in the process of optimizing model parameters. The following is the use and comparison of commonly used optimizers:<\/p>\n\n\n\n When using an optimizer, it is necessary to select an appropriate optimizer and hyperparameters, such as learning rate, momentum, weight decay, etc., according to specific tasks and models. At the same time, it is also necessary to pay attention to the correctness and efficiency of the optimizer, such as avoiding problems such as gradient explosion and disappearance, and choosing an appropriate learning rate and other hyperparameters.<\/p>\n\n\n\n In addition, in practical applications, it is usually necessary to compare and adjust optimizers. The most appropriate optimizer and hyperparameters can be selected by comparing the performance of different optimizers on the same task. Here is an example of training on the same task with different optimizers:<\/p>\n\n\n\n please continue<\/p>\n\n\n\n class MLP(nn.Module): def init<\/strong>(self): super().init<\/strong>() self.fc1 = nn.Linear(784, 256) self.fc2 = nn.Linear(256, 128) self.fc3 = nn.Linear(128, 10) self.relu = nn.ReLU()<\/p>\n\n\n\n def train(model, optimizer, criterion, train_loader, device): model.train() for batch_idx, (data, target) in enumerate(train_loader): data, target = data.to(device), target.to(device) optimizer.zero_grad() output = model(data) loss = criterion(output, target) loss.backward() optimizer.step()<\/p>\n\n\n\n def test(model, criterion, test_loader, device): model.eval() test_loss = 0 correct = 0 with torch.no_grad(): for data, target in test_loader: data, target = data.to(device), target.to(device) output = model(data) test_loss += criterion(output, target).item() pred = output.argmax(dim=1, keepdim=True) correct += pred.eq(target.view_as(pred)).sum().item()<\/p>\n\n\n\n device = torch.device(\u201ccuda\u201d if torch.cuda.is_available() else \u201ccpu\u201d) model = MLP().to(device) criterion = nn.CrossEntropyLoss() train_loader = DataLoader(train_dataset, batch_size=64, shuffle=True) test_loader = DataLoader(datasets.MNIST(\u2018.\/data\u2019, train=False, transform=transform), batch_size=1000, shuffle=True)<\/p>\n\n\n\n optimizer = torch.optim.SGD(model.parameters(), lr=0.01) for epoch in range(10): train(model, optimizer, criterion, train_loader, device) test(model, criterion, test_loader, device)<\/p>\n\n\n\n model = MLP().to(device) optimizer = torch.optim.Adam(model.parameters(), lr=0.001) for epoch in range(10): train(model, optimizer, criterion, train_loader, device) test(model, criterion, test_loader, device)<\/p>\n\n\n\n model = MLP().to(device) optimizer = torch.optim.RMSprop(model.parameters(), lr=0.001) for epoch in range(10): train(model, optimizer, criterion, train_loader, device) test(model, criterion, test_loader, device)<\/p>\n\n\n\n Please explain in detail how PyTorch builds a neural network model<\/p>\n\n\n\n In PyTorch, the torch.nn module can be used to build a neural network model, which provides a series of neural network layers and activation functions. By inheriting the nn.Module class and implementing the forward() method, you can build your own neural network model.<\/p>\n\n\n\n Here is an example of building a simple fully connected neural network model:<\/p>\n\n\n\n In the above example, a neural network model named Net is defined, which includes three fully connected layers and a ReLU activation function. In the initialization method __init__(), three fully connected layers are created using the nn.Linear() function, which are the input layer (784 dimensions) and two hidden layers (256 dimensions and 128 dimensions), and a ReLU activation is created at the same time function. In the forward propagation method forward(), the input is first reshaped, and then calculated through three fully connected layers and the ReLU activation function in turn, and finally the output result is obtained.<\/p>\n\n\n\n When using a neural network model, it is necessary to instantiate the model and pass the input data to the model for calculation, as in the following example:<\/p>\n\n\n\n In the above example, the neural network model instance model is first created, and the input data x (64 1-channel, 28\u00d728 size images) is passed to the model for calculation, and the output result y is obtained. Finally, the output shape is (64, 10), which means that there are 64 samples, and each sample has 10 output features.<\/p>\n\n\n\n In addition to the fully connected layer, PyTorch also provides a variety of commonly used neural network layers, such as convolutional layers, pooling layers, and recurrent neural network layers. Different layers can be selected according to specific tasks and data types to build neural network models.<\/p>\n\n\n\n Please explain the PyTorch activation function and loss function in detail<\/p>\n\n\n\n PyTorch provides a variety of commonly used activation functions and loss functions, and different functions can be selected for calculation according to specific tasks and models.<\/p>\n\n\n\n When using activation functions and loss functions, it is usually necessary to select appropriate functions and set appropriate hyperparameters according to specific tasks and models. At the same time, it is also necessary to pay attention to the correctness and efficiency of the activation function and loss function, such as avoiding problems such as gradient explosion and disappearance, and choosing an appropriate learning rate and other hyperparameters.<\/p>\n\n\n\n Please explain PyTorch initialization weights and biases in detail<\/p>\n\n\n\n In neural networks, the initialization of weights and biases has a great impact on the training and performance of the model. PyTorch provides a variety of commonly used initialization methods, and different methods can be selected for initialization according to specific tasks and models.<\/p>\n\n\n\n When using an initialization method, it is usually necessary to select an appropriate method and set appropriate hyperparameters according to specific tasks and models. At the same time, it is also necessary to pay attention to the correctness and efficiency of the initialization method, such as avoiding problems such as gradient explosion and disappearance. Choosing an appropriate weight and bias initialization method can speed up model training and improve model performance.<\/p>\n\n\n\n Please explain the PyTorch training and validation datasets in detail<\/p>\n\n\n\n In the training process of deep learning models, it is usually necessary to divide the data set into three parts: training set, verification set and test set. The training set is used for model training and parameter update, and the verification set is used for model tuning and model selection. , the test set is used for the final evaluation and performance testing of the model.<\/p>\n\n\n\n In PyTorch, you can use the dataset classes provided by the torch.utils.data module and torchvision.datasets module to load and process datasets. Among them, the torch.utils.data module provides two classes, Dataset and DataLoader, which can be used to customize datasets and data loaders. The torchvision.datasets module provides multiple commonly used dataset classes, which can be directly loaded and used. Here is an example of loading a dataset using the torchvision.datasets module:<\/p>\n\n\n\n In the above example, a transform variable is first defined, which includes two preprocessing methods: the ToTensor() method converts the image data into tensor data and normalizes it to the range [0,1], Normalize( ) method to normalize the tensor data so that the mean value of the data is 0.5 and the variance is 0.5. Then, use the datasets.MNIST() method to load the training set and validation set data, and pass the transform variable to them for preprocessing. Finally, two data loaders are created using the DataLoader class, which are used for batch loading of training set and validation set data respectively.<\/p>\n\n\n\n When using a data loader for model training, it is usually necessary to divide the data set into batches for training in each training iteration, and record the loss value and accuracy of the training process. At the same time, when testing the model on the validation set, it is also necessary to use the data loader to load the validation set in batches, and record the loss and accuracy indicators during the test process. According to the recorded indicators and model performance, model tuning and model selection can be performed.<\/p>\n\n\n\n In short, PyTorch provides flexible and convenient data loading and processing methods, and can choose the appropriate method for loading and division according to specific tasks and data sets. At the same time, reasonably dividing the data set and recording the training and verification indicators of the model can speed up the training of the model and improve the performance of the model.<\/p>\n\n\n\n Please explain PyTorch model training and verification in detail<\/p>\n\n\n\n In PyTorch, model training and verification are usually divided into the following steps:<\/p>\n\n\n\n Here is a sample code for training and validating a simple fully connected neural network model:<\/p>\n\n\n\n please continue<\/p>\n\n\n\n def train(model, device, train_loader, optimizer, criterion, epoch): model.train() train_loss = 0 correct = 0 for batch_idx, (data, target) in enumerate(train_loader): data, target = data.to(device), target.to(device) optimizer.zero_grad() output = model(data) loss = criterion(output, target) loss.backward() optimizer.step() train_loss += loss.item() * data.size(0) pred = output.argmax(dim=1, keepdim=True) correct += pred.eq(target.view_as(pred)).sum().item() train_loss \/= len(train_loader.dataset)<\/p>\n\n\n\n def val(model, device, val_loader, criterion): model.eval() val_loss = 0 correct = 0 with torch.no_grad(): for data, target in val_loader: data, target = data.to(device), target.to(device) output = model(data) val_loss += criterion(output, target).item() * data.size(0) pred = output.argmax(dim=1, keepdim=True) correct += pred.eq(target.view_as(pred)).sum().item() val_loss \/= len(val_loader.dataset)<\/p>\n\n\n\n<\/figure>\n\n\n\n
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pip install torch torchvision <\/code>During the installation process, PyTorch will automatically detect the operating system and hardware environment, and install the corresponding precompiled version.<\/li>\n\n\n\nimport torch print(torch.__version__) <\/code>If the version number of PyTorch is output, it means that the installation is successful.<\/li>\n\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) print(x) <\/code>output: luaCopy codetensor([[1, 2], [3, 4]])<\/code><\/li>\n\n\n\nimport numpy as np import torch x = np.array([[1, 2], [3, 4]]) y = torch.tensor(x) print(y) <\/code>output: luaCopy codetensor([[1, 2], [3, 4]])<\/code><\/li>\n\n\n\nimport torch x = torch.zeros((2, 3)) y = torch.ones((3, 4)) print(x) print(y) <\/code>output: luaCopy codetensor([[0., 0., 0.], [0., 0., 0.]]) tensor([[1., 1., 1., 1.], [1., 1., 1., 1.], [1., 1., 1., 1.]])<\/code><\/li>\n<\/ol>\n\n\n\n\n
import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2, 2], [2, 2]]) z = x + y print(z) <\/code>Output: luaCopy codetensor([[3, 4], [5, 6]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2], [2]]) z = x.mm(y) print(z) <\/code>output: luaCopy codetensor([[ 6], [14]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) z = x.t() print(z) <\/code>output: luaCopy codetensor([[1, 3], [2, 4]])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) print(x.shape) <\/code>output: cssCopy codetorch.Size([2, 2])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) print(x.size()) <\/code>output: cssCopy codetorch.Size([2, 2])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) print(x.numpy().shape) <\/code>output: scssCopy code(2, 2)<\/code><\/li>\n<\/ol>\n\n\n\n\n
import torch x = torch.tensor([[1, 2], [3, 4]]) print(x.ndim) <\/code>output: Copy code2<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) print(x.dim()) <\/code>output: Copy code2<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) print(len(x.shape)) <\/code>output: Copy code2<\/code><\/li>\n<\/ol>\n\n\n\n\n
import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2, 2], [2, 2]]) z = x + y print(z.shape) <\/code>output: cssCopy codetorch.Size([2, 2])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2], [2]]) z = x.mm(y) print(z.shape) <\/code>output: cssCopy codetorch.Size([2, 1])<\/code><\/li>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) z = x.t() print(z.shape) <\/code>output: cssCopy codetorch.Size([2, 2])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) y = x[1, 0] print(y) <\/code>output: scssCopy codetensor(3)<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = x[0, :] z = x[:, 1] print(y) print(z) <\/code>output: scssCopy codetensor([1, 2]) tensor([2, 4])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) mask = x > 2 y = x[mask] print(y) <\/code>output: scssCopy codetensor([3, 4])<\/code><\/li>\n<\/ol>\n\n\n\n\n
import torch x = torch.tensor([[1, 2], [3, 4]]) y = x[0:1, 0:1] print(y) <\/code>output: luaCopy codetensor([[1]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = x[0:1, :] z = x[:, 1:2] print(y) print(z) <\/code>output: luaCopy codetensor([[1, 2]]) tensor([[2], [4]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = x[::2, ::2] print(y) <\/code>output: luaCopy codetensor([[1]])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2, 2], [2, 2]]) z = x + y print(z) <\/code>Output: luaCopy codetensor([[3, 4], [5, 6]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2], [2]]) z = x.mm(y) print(z) <\/code>output: luaCopy codetensor([[ 6], [14]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) z = x.t() print(z) <\/code>output: luaCopy codetensor([[1, 3], [2, 4]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = x**2 print(y) <\/code>output: luaCopy codetensor([[ 1, 4], [ 9, 16]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.sum(x) print(y) <\/code>output: scssCopy codetensor(10)<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float) y = torch.nn.functional.normalize(x, p=2, dim=1) print(y) <\/code>output: luaCopy codetensor([[0.4472, 0.8944], [0.6, 0.8]])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[2], [2]]) z = x.mm(y) print(z) <\/code>output: luaCopy codetensor([[ 6], [14]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float) y = torch.inverse(x) print(y) <\/code>output: luaCopy codetensor([[-2.0000, 1.0000], [ 1.5000, -0.5000]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float) y, z = torch.eig(x, eigenvectors=True) print(y) print(z) <\/code>output: luaCopy codetensor([[ 0.3723, 0.0000], [ 5.6277, 0.0000]]) tensor([[ 0.8246, -0.4163], [ 0.5658, 0.9094]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[1, 2], [3, 4]], dtype=torch.float) u, s, v = torch.svd(x) print(u) print(s) print(v) <\/code>output: luaCopy codetensor([[-0.4046, -0.9145], [-0.9145, 0.4046]]) tensor([5.4649, 0.3650]) tensor([[-0.5760, -0.8174], [ 0.8174, -0.5760]])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([1, 2]) z = x + y print(z) <\/code>output: luaCopy codetensor([[2, 4], [4, 6]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) y = torch.tensor([[1, 2], [3, 4]]) z = x.mm(y) print(z) <\/code>output: luaCopy codetensor([[[ 7, 10], [15, 22]], [[19, 22], [43, 50]]])<\/code><\/li>\n\n\n\nimport torch x = torch.tensor([1, 2, 3]) y = 2 z = x * y print(z) <\/code>output: scssCopy codetensor([2, 4, 6])<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float, requires_grad=True) z = x + y w = z.sum() print(w) <\/code>: scssCopy code tensor(6., grad_fn=<SumBackward0>) <\/code>In the above example, a simple computational graph is built, where x and y are two tensors, z is their sum, and w is the sum of z. Setting requires_grad=True enables the nodes in the computation graph to support automatic derivation.<\/li>\n\n\n\nimport torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float, requires_grad=True) z = x + y w = z.sum() w.backward() print(x.grad) print(y.grad) <\/code>output: scssCopy code tensor([1., 1.]) tensor([1., 1.]) <\/code>In the above example, the backward() function is called to calculate the derivative of the tensor, and the corresponding derivative value is obtained through x.grad and y.grad.<\/li>\n\n\n\nimport torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float, requires_grad=True) z = x + y w = z.sum() optimizer = torch.optim.SGD([x, y], lr=0.01) optimizer.zero_grad() w.backward() optimizer.step() print(x) print(y) <\/code>output: scssCopy codetensor([0.9800, 1.9800], requires_grad=True) tensor([1.9800, 1.9800], requires_grad=True) ``<\/code><\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float) z = x + y with torch.no_grad(): w = z.sum() print(w.requires_grad) <\/code>output: graphqlCopy code False <\/code>In the above example, the gradient calculation is stopped by setting the with torch.no_grad() statement block, so that w no longer supports automatic derivation.<\/li>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float, requires_grad=True) z = x + y w = z.sum() w.backward() print(x.grad) print(y.grad) <\/code>output: scssCopy code tensor([1., 1.]) tensor([1., 1.]) <\/code>In the above example, the derivative of the tensor is calculated by calling the backward() function, and the corresponding derivative value is obtained through x.grad and y.grad.<\/li>\n\n\n\nimport torch x = torch.tensor([1, 2], dtype=torch.float, requires_grad=True) y = torch.tensor([2, 2], dtype=torch.float, requires_grad=True) z = x + y w = z.sum() grad = torch.autograd.grad(w, [x, y]) print(grad[0]) print(grad[1]) <\/code>output: scssCopy code tensor([1., 1.]) tensor([1., 1.]) <\/code>In the above example, the gradient of the tensor x and y is calculated by calling the grad() function, and the corresponding gradient value is obtained through grad[0] and grad[1].<\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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import torch x = torch.randn(10, 5) y = torch.randn(10, 2) model = torch.nn.Linear(5, 2) criterion = torch.nn.MSELoss() optimizer = torch.optim.SGD(model.parameters(), lr=0.1) for epoch in range(100): y_pred = model(x) loss = criterion(y_pred, y) optimizer.zero_grad() loss.backward() optimizer.step() print('Epoch:', epoch, 'Loss:', loss.item()) <\/code>In the above example, the SGD optimizer is created through the torch.optim.SGD() function, and the learning rate is set to 0.1. Then in the training loop, the gradient calculation and update of the model parameters are performed using the optimizer.<\/li>\n\n\n\nimport torch x = torch.randn(10, 5) y = torch.randn(10, 2) model = torch.nn.Linear(5, 2) criterion = torch.nn.MSELoss() optimizer = torch.optim.Adam(model.parameters(), lr=0.1) for epoch in range(100): y_pred = model(x) loss = criterion(y_pred, y) optimizer.zero_grad() loss.backward() optimizer.step() print('Epoch:', epoch, 'Loss:', loss.item()) <\/code>In the above example, the Adam optimizer is created through the torch.optim.Adam() function, and the learning rate is set to 0.1. Then in the training loop, the gradient calculation and update of the model parameters are performed using the optimizer.<\/li>\n<\/ol>\n\n\n\n<\/figure>\n\n\n\n
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pythonCopy code
import torch\nfrom torch import nn\nfrom torch.utils.data import DataLoader\nfrom torchvision import datasets, transforms\n\ntransform = transforms.Compose([\n transforms.ToTensor(),\n transforms.Normalize((0.1307,), (0.3081,))\n])\n\ntrain_dataset = datasets.MNIST('.\/data', train=True, download=True, transform=transform)\ntrain_loader = DataLoader(train_dataset, batch_size=64, shuffle=True)\n\nclass MLP(nn.Module):\n def __init__(self):\n super().__init__()\n self.fc1 = nn.Linear(784, 256)\n self.fc2\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n
rubyCopy code
def forward(self, x):\n x = x.view(-1, 784)\n x = self.relu(self.fc1(x))\n x = self.relu(self.fc2(x))\n x = self.fc3(x)\n return x\n<\/code><\/pre>\n\n\n\nscssCopy code
test_loss \/= len(test_loader.dataset)\naccuracy = 100. * correct \/ len(test_loader.dataset)\nprint('Test set: Average loss: {:.4f}, Accuracy: {}\/{} ({:.2f}%)'.format(\n test_loss, correct, len(test_loader.dataset), accuracy))\n<\/code><\/pre>\n\n\n\nUse the SGD optimizer<\/h1>\n\n\n\n
Using the Adam optimizer<\/h1>\n\n\n\n
Use the RMSprop optimizer<\/h1>\n\n\n\n
Copy code
\n\u5728\u4ee5\u4e0a\u793a\u4f8b\u4e2d\uff0c\u4f7f\u7528\u4e86\u4e09\u79cd\u4e0d\u540c\u7684\u4f18\u5316\u5668\uff08SGD\u3001Adam\u3001RMSprop\uff09\u5bf9\u540c\u4e00\u4efb\u52a1\uff08MNIST\u624b\u5199\u6570\u5b57\u8bc6\u522b\uff09\u8fdb\u884c\u4e86\u8bad\u7ec3\uff0c\u5e76\u6bd4\u8f83\u4e86\u5b83\u4eec\u7684\u8868\u73b0\u3002\u901a\u8fc7\u6bd4\u8f83\u4e0d\u540c\u4f18\u5316\u5668\u5728\u540c\u4e00\u4efb\u52a1\u4e0a\u7684\u8868\u73b0\uff0c\u53ef\u4ee5\u9009\u62e9\u6700\u5408\u9002\u7684\u4f18\u5316\u5668\u548c\u8d85\u53c2\u6570\u3002\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n
pythonCopy code
import torch\nfrom torch import nn\n\nclass Net(nn.Module):\n def __init__(self):\n super().__init__()\n self.fc1 = nn.Linear(784, 256)\n self.fc2 = nn.Linear(256, 128)\n self.fc3 = nn.Linear(128, 10)\n self.relu = nn.ReLU()\n\n def forward(self, x):\n x = x.view(-1, 784)\n x = self.relu(self.fc1(x))\n x = self.relu(self.fc2(x))\n x = self.fc3(x)\n return x\n<\/code><\/pre>\n\n\n\nmakefileCopy code
# \u521b\u5efa\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5b9e\u4f8b\nmodel = Net()\n\n# \u8f93\u5165\u6570\u636e\nx = torch.randn(64, 1, 28, 28)\n\n# \u8ba1\u7b97\u8f93\u51fa\u7ed3\u679c\ny = model(x)\n\n# \u8f93\u51fa\u7ed3\u679c\u5f62\u72b6\nprint(y.shape) # \u8f93\u51fa(64, 10)\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n
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pythonCopy code
import torch\nfrom torchvision import datasets, transforms\n\n# \u5b9a\u4e49\u6570\u636e\u9884\u5904\u7406\u65b9\u6cd5\ntransform = transforms.Compose([\n transforms.ToTensor(),\n transforms.Normalize((0.5,), (0.5,))\n])\n\n# \u52a0\u8f7d\u8bad\u7ec3\u96c6\u548c\u9a8c\u8bc1\u96c6\u6570\u636e\ntrainset = datasets.MNIST('data\/', train=True, download=True, transform=transform)\nvalset = datasets.MNIST('data\/', train=False, download=True, transform=transform)\n\n# \u521b\u5efa\u6570\u636e\u52a0\u8f7d\u5668\ntrainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)\nvalloader = torch.utils.data.DataLoader(valset, batch_size=64, shuffle=False)\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n
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pythonCopy code
import torch\nimport torch.nn as nn\nimport torch.optim as optim\nfrom torchvision import datasets, transforms\n\n# \u5b9a\u4e49\u6a21\u578b\u7c7b\nclass Net(nn.Module):\n def __init__(self):\n super(Net, self).__init__()\n self.fc1 = nn.Linear(784, 512)\n self.fc2 = nn.Linear(512, 256)\n self.fc3 = nn.Linear(256, 10)\n\n def forward(self, x):\n x = x.view(-1, 784)\n x = nn.functional.relu(self.fc1(x))\n x = nn.functional.relu(self.fc2(x))\n x = self.fc3(x)\n return nn\n<\/code><\/pre>\n\n\n\n<\/figure>\n\n\n\n
Define the training function<\/h1>\n\n\n\n
cssCopy code
print('Train Epoch: {} \\tLoss: {:.6f} \\tAcc: {:.6f}'.format(\n epoch, train_loss, correct \/ len(train_loader.dataset)))\n<\/code><\/pre>\n\n\n\nDefine the validation function<\/h1>\n\n\n\n
luaCopy code