Deeply understand the core functions of Pytorch: automatic derivation!

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About the automatic derivation operation in pytorch, introduce the concept of automatic derivation in pytorch.

Automatic derivation is an important function of the deep learning framework, used to calculate gradients, implement parameter updates and optimization.

PyTorch is a commonly used deep learning framework that uses dynamic calculation graphs and automatic derivation mechanisms to simplify the gradient calculation process.

Automatic derivation

Automatic derivation is an important function of the machine learning framework. It can automatically calculate the derivative (gradient) of a function, thereby simplifying The process of training a deep learning model. In deep learning, models often contain a large number of parameters, and manually calculating gradients can become complex and error-prone. PyTorch provides an automatic derivation function, allowing users to easily calculate gradients and perform backpropagation to update model parameters. The introduction of this feature greatly improves the efficiency and ease of use of deep learning.

Some principles

PyTorch’s automatic derivation function is based on dynamic calculation graphs. A computation graph is a graph structure used to represent the function calculation process, in which nodes represent operations and edges represent data flow. Different from static calculation graphs, the structure of dynamic calculation graphs can be dynamically generated based on the actual execution process, rather than being defined in advance. This design makes PyTorch flexible and scalable to adapt to different computing needs. Through dynamic calculation graphs, PyTorch can record the history of operations, perform backpropagation and calculate gradients as needed. This makes PyTorch one of the widely used frameworks in the field of deep learning.

In PyTorch, every operation of the user is recorded to build the calculation graph. In this way, when the gradient needs to be calculated, PyTorch can perform backpropagation according to the calculation graph and automatically calculate the gradient of each parameter to the loss function. This automatic derivation mechanism based on dynamic calculation graphs makes PyTorch flexible and scalable, making it suitable for various complex neural network structures.

Basic operations for automatic derivation

1. Tensor(Tensor)

In PyTorch, tensor is the basic data structure for automatic derivation. Tensors are similar to multidimensional arrays in NumPy, but have additional features such as automatic derivation. Through the torch.Tensor class, users can create tensors and perform various operations on them.

import torch# 创建张量x = torch.tensor([2.0], requires_grad=True)

In the above example, requires_grad=True means that we want to automatically differentiate this tensor.

2. Computational graph construction

Each operation performed will create a node in the computational graph. PyTorch provides various tensor operations, such as addition, multiplication, activation functions, etc., which will leave traces in the calculation graph.

# 张量操作y = x ** 2z = 2 * y + 3

In the above example, the calculation processes of y and z are recorded in the calculation graph.

3. Gradient calculation and backpropagation

Once the calculation graph is constructed, backpropagation can be performed by calling the .backward() method to automatically calculate the gradient.

# 反向传播z.backward()

At this time, the gradient of x can be obtained by accessing x.grad.

# 获取梯度print(x.grad)

4. Disable gradient tracking

Sometimes, we want to disable gradient tracking for certain operations, we can use the torch.no_grad() context manager.

with torch.no_grad():# 在这个区域内的操作不会被记录在计算图中w = x + 1

5. Clear the gradient

In the training loop, it is usually necessary to clear the gradient before each backpropagation to avoid gradient accumulation.

# 清零梯度x.grad.zero_()

A complete case: automatic derivation of linear regression

In order to demonstrate the process of automatic derivation more specifically, let us consider a simple linear regression problem. We define a linear model and a mean square error loss function and use automatic derivation to optimize the model parameters.

import torch# 数据准备X = torch.tensor([[1.0], [2.0], [3.0]])y = torch.tensor([[2.0], [4.0], [6.0]])# 模型参数w = torch.tensor([[0.0]], requires_grad=True)b = torch.tensor([[0.0]], requires_grad=True)# 模型和损失函数def linear_model(X, w, b):return X @ w + bdef mean_squared_error(y_pred, y_true):return ((y_pred - y_true) ** 2).mean()# 训练循环learning_rate = 0.01epochs = 100for epoch in range(epochs):# 前向传播y_pred = linear_model(X, w, b)loss = mean_squared_error(y_pred, y)# 反向传播loss.backward()# 更新参数with torch.no_grad():w -= learning_rate * w.gradb -= learning_rate * b.grad# 清零梯度w.grad.zero_()b.grad.zero_()# 打印最终参数print("训练后的参数：")print("权重 w:", w)print("偏置 b:", b)

In this example, we define a simple linear model and mean square error loss function. Through multiple iterative training loops, the parameters w and b of the model will be optimized to minimize the loss function.

Finally

The automatic derivation in PyTorch provides powerful support for deep learning, making model training simpler and more efficient.

Through dynamic calculation graphs and gradient calculations, users can easily define complex neural network structures and implement optimization algorithms such as gradient descent through automatic derivation.

This allows deep learning researchers and engineers to focus more on model design and experiments without having to worry about the details of gradient calculations.

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