线性回归的PyTorch实现

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写在前面

今天将继续进行PyTorch学习系列的更新，本文将用线性回归的例子，使用PyTorch来搭建人工智能神经网络¹，主要讲解如何搭建用通用的模板来搭建一个完整的网络模型。【这是深度学习数学原理专题系列的第三篇文章】

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PyTorch的__call__()和__init__()方法

要灵活运用PyTorch来搭建神经网络模型，前提是知道python类中的__call__和__init__方法。其中，__init__是类的初始化函数，类似于C++的构造函数，__call__可以使得类对象具有类似函数的功能²。

大家都知道，nn.Module 是所有神经网络单元（neural network modules）的基类，PyTorch在nn.Module中，实现了__call__方法，而在__call__方法中调用了forward函数³。

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线性回归的PyTorch代码实现

具体的讲解尽在注释中：

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# @Time    : 2021/11/25 20:46
# @Author  : William Baker
# @FileName: lesson5_Linear_Regression_with_PyTorch.py
# @Software: PyCharm
# @Blog    : https://blog.csdn.net/weixin_43051346

import torch
import matplotlib.pyplot as plt
import os
os.environ['KMP_DUPLICATE_LIB_OK'] = 'TRUE'
import numpy as np

plt.rcParams['font.sans-serif'] = ['SimHei']  #显示中文标签
plt.rcParams['axes.unicode_minus'] = False
from mpl_toolkits.mplot3d import Axes3D    # 绘制3D立体图
# fig = plt.figure()
# ax = Axes3D(fig)
# 绘制线
plt.figure(2)
ax2 = plt.subplot(projection='3d')


"""
a = torch.tensor([1.0])
a.requires_grad = True      # 或者 a.requires_grad_()
print(a)    # tensor([1.], requires_grad=True)
print(a.data)    # tensor([1.])
print(a.type())    # torch.FloatTensor                # a的类型是tensor
print(a.data.type())     # torch.FloatTensor             # a.data的类型是tensor
print(a.grad)       # None
print(type(a.grad))      # 
"""

# Step1: 准备数据集
x_data = torch.tensor([[1.0], [2.0], [3.0]])    # 结构为(3,1)
# print(x_data.shape)   # torch.Size([3, 1])
y_data = torch.tensor([[2.0], [4.0], [6.0]])

# Step2: 用类设计模型，目的是为了前向传播forward，计算预测值 y_hat
class LinearModel(torch.nn.Module):
    def __init__(self):   # 构造函数，用于初始化对象
        super(LinearModel, self).__init__()
        self.linear = torch.nn.Linear(1, 1)    # (1,1)是指输入x和输出y的特征维度，
                                               # torch.nn.Linear是pytorch的一个类，类后面加括号此处是在构造对象，该对象包含w和b两个tensor
                                               # 自动进行w*x+b的计算，linear是继承自Module,能进行反向传播
    def forward(self, x):   # 前馈时候执行计算（nn.Module会根据计算图自动实现 Backward反向传播）
        y_pred = self.linear(x)     # 进行y_pred=wx+b，可调用对象后面加括号 linear(x), 意味着实现了一个__call__函数的对象
        return y_pred

model = LinearModel()    # 用自己定义的上述模型时，只需要将其实例化即可，model也是一个可调用对象

# Step3: 设计loss和optimizer，其中计算loss是为了进行反向传播，计算optimizer是为了更新梯度
# MSELoss类继承自Module，torch.nn.MSELoss，可调用，pytorch提供的MSE损失函数
# criterion = torch.nn.MSELoss(size_average=False)
criterion = torch.nn.MSELoss(reduction='sum')

# 实例化一个优化器对象，parameters是所有权重参数
# parameters会检查module里面的所有成员，如果成员里有相应的权重，那么都要加到训练的参数集合上
optimizer = torch.optim.SGD(model.parameters(), lr=0.01)

# 新建几个列表，用于储存数据以进行可视化展示
epoch_list = []
loss_list = []
w_list = []
b_list = []
# Step4: 开始训练 (理想情况的训练结果是w=2,b=0,预测值为8)
for epoch in range(1000):
    y_pred = model(x_data)
    loss = criterion(y_pred, y_data)
    # loss计算出来是一个标量，print的时候会自动调用__str()__，所以打印的时候就不会产生计算图
    # print(epoch, loss)        # 0 tensor(44.2999, grad_fn=)
    # print('Epoch:{}, Loss:{}'.format(epoch, loss.item()))       # 0 19.965293884277344
    print('Epoch:{}, Loss:{}, w:{}, b:{}'.format(epoch, loss.item(), model.linear.weight.item(), model.linear.bias.item()))

    # 将梯度值清0
    optimizer.zero_grad()
    # 反向传播求梯度
    # print(loss)
    loss.backward()
    # 优化器 自动更新权重
    optimizer.step()

    # print('Epoch:{}, w:{}, b:{}'.format(epoch, model.linear.weight.item(), model.linear.bias.item()))

    epoch_list.append(epoch)
    loss_list.append(loss)
    # loss_list.append(loss.item())
    w_list.append(model.linear.weight.item())
    b_list.append(model.linear.bias.item())


# 打印出最终的权重和偏置值
print('w = ', model.linear.weight.item())
"""
# print('w- = ', model.linear.weight)
w- =  Parameter containing:
tensor([[2.0472]], requires_grad=True)
"""
print('b = ', model.linear.bias.item())

x_test = torch.tensor([4.0])
y_test = model(x_test)
print('y_pred = ', y_test.data)

"""
# 绘图
plt.plot(epoch_list, loss_list)
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.show()
"""

# """
ax2.plot3D(xs=epoch_list, ys=loss_list, zs=w_list, color='blue')
# 设置标签、标题
ax2.set_xlabel('Epoch')
ax2.set_ylabel('Loss')
ax2.set_zlabel('Weight')
plt.title('三维曲线')
plt.show()
# """

结果输出为：

Epoch:0, Loss:39.90363693237305, w:0.12869513034820557, b:0.431010365486145
Epoch:1, Loss:18.02081298828125, w:0.6009392738342285, b:0.6297063231468201
Epoch:2, Loss:8.275513648986816, w:0.9171115159988403, b:0.7598112225532532
Epoch:3, Loss:3.933544874191284, w:1.1291429996490479, b:0.8441691398620605
Epoch:4, Loss:1.9970381259918213, w:1.271682620048523, b:0.8980218172073364
Epoch:5, Loss:1.1314250230789185, w:1.3678488731384277, b:0.9315385818481445
Epoch:6, Loss:0.7425949573516846, w:1.4330666065216064, b:0.9515044093132019
Epoch:7, Loss:0.5660653710365295, w:1.4776273965835571, b:0.9624461531639099
Epoch:8, Loss:0.4840957224369049, w:1.508398175239563, b:0.9673840999603271
Epoch:9, Loss:0.44426894187927246, w:1.5299606323242188, b:0.9683332443237305
Epoch:10, Loss:0.42325150966644287, w:1.545371651649475, b:0.9666379690170288
Epoch:11, Loss:0.41065478324890137, w:1.5566710233688354, b:0.9631950855255127
Epoch:12, Loss:0.4018533229827881, w:1.565219759941101, b:0.9586028456687927
Epoch:13, Loss:0.39478713274002075, w:1.5719258785247803, b:0.9532603025436401
Epoch:14, Loss:0.3885386884212494, w:1.5773954391479492, b:0.947433590888977
Epoch:15, Loss:0.38269922137260437, w:1.5820326805114746, b:0.9413001537322998
Epoch:16, Loss:0.3770848512649536, w:1.5861074924468994, b:0.9349782466888428
Epoch:17, Loss:0.3716154098510742, w:1.5898000001907349, b:0.928546667098999
Epoch:18, Loss:0.3662521243095398, w:1.5932303667068481, b:0.9220578670501709
Epoch:19, Loss:0.360978364944458, w:1.5964789390563965, b:0.9155467748641968
Epoch:20, Loss:0.35578593611717224, w:1.5995992422103882, b:0.9090365171432495
Epoch:21, Loss:0.35067054629325867, w:1.6026270389556885, b:0.9025424122810364
Epoch:22, Loss:0.3456299901008606, w:1.605586290359497, b:0.8960745930671692
Epoch:23, Loss:0.34066227078437805, w:1.6084930896759033, b:0.8896397352218628
Epoch:24, Loss:0.33576661348342896, w:1.6113582849502563, b:0.8832421898841858
Epoch:25, Loss:0.33094120025634766, w:1.6141889095306396, b:0.8768846392631531
Epoch:26, Loss:0.32618504762649536, w:1.6169898509979248, b:0.8705689311027527
Epoch:27, Loss:0.3214970529079437, w:1.6197644472122192, b:0.864296019077301
Epoch:28, Loss:0.3168763518333435, w:1.6225148439407349, b:0.8580664992332458
Epoch:29, Loss:0.3123226463794708, w:1.6252427101135254, b:0.8518807291984558
Epoch:30, Loss:0.3078339099884033, w:1.6279491186141968, b:0.8457387685775757
Epoch:31, Loss:0.3034098446369171, w:1.6306346654891968, b:0.8396405577659607
Epoch:32, Loss:0.2990494966506958, w:1.6333000659942627, b:0.8335859775543213
Epoch:33, Loss:0.2947518229484558, w:1.6359456777572632, b:0.8275747895240784
Epoch:34, Loss:0.29051560163497925, w:1.638571858406067, b:0.8216068148612976
Epoch:35, Loss:0.2863404154777527, w:1.6411789655685425, b:0.8156817555427551
Epoch:36, Loss:0.28222525119781494, w:1.64376699924469, b:0.8097993731498718
Epoch:37, Loss:0.2781693637371063, w:1.646336317062378, b:0.8039593696594238
Epoch:38, Loss:0.2741714119911194, w:1.648887038230896, b:0.7981614470481873
Epoch:39, Loss:0.2702312171459198, w:1.6514192819595337, b:0.7924053072929382
Epoch:40, Loss:0.2663477063179016, w:1.6539332866668701, b:0.7866906523704529
Epoch:41, Loss:0.262519896030426, w:1.6564290523529053, b:0.7810172438621521
Epoch:42, Loss:0.2587469220161438, w:1.6589068174362183, b:0.7753847241401672
Epoch:43, Loss:0.2550283670425415, w:1.6613667011260986, b:0.7697927951812744
Epoch:44, Loss:0.2513631582260132, w:1.663808822631836, b:0.7642412185668945
Epoch:45, Loss:0.24775053560733795, w:1.6662334203720093, b:0.7587296962738037
Epoch:46, Loss:0.24419023096561432, w:1.6686404943466187, b:0.7532579302787781
Epoch:47, Loss:0.24068056046962738, w:1.6710301637649536, b:0.7478256225585938
Epoch:48, Loss:0.23722177743911743, w:1.6734026670455933, b:0.7424324750900269
Epoch:49, Loss:0.23381243646144867, w:1.6757580041885376, b:0.7370781898498535
Epoch:50, Loss:0.2304522842168808, w:1.6780964136123657, b:0.7317625284194946
Epoch:51, Loss:0.22714026272296906, w:1.6804178953170776, b:0.7264851927757263
Epoch:52, Loss:0.22387593984603882, w:1.6827226877212524, b:0.7212459444999695
Epoch:53, Loss:0.22065865993499756, w:1.6850107908248901, b:0.7160444855690002
Epoch:54, Loss:0.2174871414899826, w:1.6872824430465698, b:0.7108805179595947
Epoch:55, Loss:0.2143615484237671, w:1.6895376443862915, b:0.7057538032531738
Epoch:56, Loss:0.21128106117248535, w:1.6917766332626343, b:0.7006640434265137
Epoch:57, Loss:0.20824439823627472, w:1.6939995288848877, b:0.6956110000610352
Epoch:58, Loss:0.20525166392326355, w:1.6962063312530518, b:0.6905943751335144
Epoch:59, Loss:0.2023017704486847, w:1.6983972787857056, b:0.6856139302253723
Epoch:60, Loss:0.1993946135044098, w:1.7005723714828491, b:0.6806694269180298
Epoch:61, Loss:0.19652879238128662, w:1.702731728553772, b:0.6757605671882629
Epoch:62, Loss:0.19370445609092712, w:1.7048755884170532, b:0.6708871126174927
Epoch:63, Loss:0.1909206062555313, w:1.7070039510726929, b:0.6660488247871399
Epoch:64, Loss:0.18817675113677979, w:1.7091169357299805, b:0.6612454056739807
Epoch:65, Loss:0.18547259271144867, w:1.7112147808074951, b:0.6564766764640808
Epoch:66, Loss:0.18280676007270813, w:1.7132974863052368, b:0.6517423391342163
Epoch:67, Loss:0.18017956614494324, w:1.7153650522232056, b:0.6470420956611633
Epoch:68, Loss:0.17759010195732117, w:1.7174177169799805, b:0.6423757672309875
Epoch:69, Loss:0.17503808438777924, w:1.719455599784851, b:0.6377431154251099
Epoch:70, Loss:0.17252236604690552, w:1.721478819847107, b:0.6331438422203064
Epoch:71, Loss:0.17004303634166718, w:1.7234874963760376, b:0.6285777688026428
Epoch:72, Loss:0.16759920120239258, w:1.725481629371643, b:0.6240445971488953
Epoch:73, Loss:0.16519056260585785, w:1.7274614572525024, b:0.6195441484451294
Epoch:74, Loss:0.16281653940677643, w:1.7294269800186157, b:0.6150761246681213
Epoch:75, Loss:0.16047650575637817, w:1.7313783168792725, b:0.610640287399292
Epoch:76, Loss:0.15817005932331085, w:1.7333155870437622, b:0.606236457824707
Epoch:77, Loss:0.15589718520641327, w:1.7352389097213745, b:0.6018643975257874
Epoch:78, Loss:0.15365666151046753, w:1.7371482849121094, b:0.5975238680839539
Epoch:79, Loss:0.15144845843315125, w:1.739043951034546, b:0.5932146310806274
Epoch:80, Loss:0.14927172660827637, w:1.740925908088684, b:0.5889365077018738
Epoch:81, Loss:0.14712634682655334, w:1.7427942752838135, b:0.584689199924469
Epoch:82, Loss:0.14501190185546875, w:1.7446491718292236, b:0.5804725289344788
Epoch:83, Loss:0.14292789995670319, w:1.746490716934204, b:0.576286256313324
Epoch:84, Loss:0.1408737748861313, w:1.7483189105987549, b:0.5721302032470703
Epoch:85, Loss:0.13884928822517395, w:1.750133991241455, b:0.5680041313171387
Epoch:86, Loss:0.136853888630867, w:1.7519359588623047, b:0.56390780210495
Epoch:87, Loss:0.13488700985908508, w:1.7537249326705933, b:0.5598410367965698
Epoch:88, Loss:0.13294830918312073, w:1.7555010318756104, b:0.5558035969734192
Epoch:89, Loss:0.13103775680065155, w:1.757264256477356, b:0.551795244216919
Epoch:90, Loss:0.12915465235710144, w:1.7590148448944092, b:0.5478157997131348
Epoch:91, Loss:0.12729832530021667, w:1.76075279712677, b:0.5438650846481323
Epoch:92, Loss:0.12546904385089874, w:1.762478232383728, b:0.5399428606033325
Epoch:93, Loss:0.12366576492786407, w:1.7641911506652832, b:0.5360488891601562
Epoch:94, Loss:0.12188848108053207, w:1.7658917903900146, b:0.5321829915046692
Epoch:95, Loss:0.12013664841651917, w:1.7675801515579224, b:0.528344988822937
Epoch:96, Loss:0.11841027438640594, w:1.769256353378296, b:0.5245346426963806
Epoch:97, Loss:0.11670834571123123, w:1.7709203958511353, b:0.5207517743110657
Epoch:98, Loss:0.11503114551305771, w:1.77257239818573, b:0.5169962048530579
Epoch:99, Loss:0.113378144800663, w:1.7742125988006592, b:0.5132677555084229
Epoch:100, Loss:0.1117483600974083, w:1.7758409976959229, b:0.5095661878585815
Epoch:101, Loss:0.11014248430728912, w:1.777457594871521, b:0.5058912634849548
Epoch:102, Loss:0.10855944454669952, w:1.7790625095367432, b:0.5022428631782532
Epoch:103, Loss:0.10699936747550964, w:1.780655860900879, b:0.49862077832221985
Epoch:104, Loss:0.10546168684959412, w:1.7822376489639282, b:0.49502483010292053
Epoch:105, Loss:0.10394608229398727, w:1.7838081121444702, b:0.4914548099040985
Epoch:106, Loss:0.10245201736688614, w:1.7853672504425049, b:0.48791056871414185
Epoch:107, Loss:0.1009797751903534, w:1.7869150638580322, b:0.48439186811447144
Epoch:108, Loss:0.09952855110168457, w:1.7884517908096313, b:0.48089855909347534
Epoch:109, Loss:0.0980982780456543, w:1.7899774312973022, b:0.47743043303489685
Epoch:110, Loss:0.09668833017349243, w:1.7914921045303345, b:0.47398731112480164
Epoch:111, Loss:0.09529877454042435, w:1.792995810508728, b:0.47056901454925537
Epoch:112, Loss:0.09392917901277542, w:1.7944886684417725, b:0.46717536449432373
Epoch:113, Loss:0.09257938712835312, w:1.7959707975387573, b:0.4638062119483948
Epoch:114, Loss:0.09124889969825745, w:1.7974421977996826, b:0.4604613482952118
Epoch:115, Loss:0.08993737399578094, w:1.7989031076431274, b:0.45714062452316284
Epoch:116, Loss:0.08864488452672958, w:1.8003534078598022, b:0.4538438022136688
Epoch:117, Loss:0.0873708575963974, w:1.8017932176589966, b:0.4505707621574402
Epoch:118, Loss:0.08611523360013962, w:1.80322265625, b:0.4473213255405426
Epoch:119, Loss:0.08487764745950699, w:1.8046417236328125, b:0.44409531354904175
Epoch:120, Loss:0.08365774154663086, w:1.8060506582260132, b:0.44089260697364807
Epoch:121, Loss:0.08245540410280228, w:1.8074493408203125, b:0.43771296739578247
Epoch:122, Loss:0.08127039670944214, w:1.8088380098342896, b:0.4345562756061554
Epoch:123, Loss:0.08010249584913254, w:1.8102165460586548, b:0.43142232298851013
Epoch:124, Loss:0.07895141839981079, w:1.8115851879119873, b:0.42831099033355713
Epoch:125, Loss:0.07781660556793213, w:1.8129440546035767, b:0.42522212862968445
Epoch:126, Loss:0.07669828832149506, w:1.8142930269241333, b:0.4221555292606354
Epoch:127, Loss:0.07559596002101898, w:1.8156323432922363, b:0.419111043214798
Epoch:128, Loss:0.07450950145721436, w:1.8169618844985962, b:0.4160884916782379
Epoch:129, Loss:0.073438860476017, w:1.818281888961792, b:0.41308775544166565
Epoch:130, Loss:0.07238329946994781, w:1.8195924758911133, b:0.41010865569114685
Epoch:131, Loss:0.07134295254945755, w:1.8208935260772705, b:0.4071510434150696
Epoch:132, Loss:0.07031768560409546, w:1.8221851587295532, b:0.4042147397994995
Epoch:133, Loss:0.06930718570947647, w:1.823467493057251, b:0.4012996256351471
Epoch:134, Loss:0.06831107288599014, w:1.8247406482696533, b:0.3984055519104004
Epoch:135, Loss:0.06732937693595886, w:1.8260046243667603, b:0.3955323398113251
Epoch:136, Loss:0.06636182963848114, w:1.8272594213485718, b:0.3926798403263092
Epoch:137, Loss:0.06540804356336594, w:1.8285051584243774, b:0.38984793424606323
Epoch:138, Loss:0.06446800380945206, w:1.8297419548034668, b:0.38703644275665283
Epoch:139, Loss:0.0635414719581604, w:1.8309698104858398, b:0.38424521684646606
Epoch:140, Loss:0.06262824684381485, w:1.8321888446807861, b:0.381474107503891
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Epoch:883, Loss:1.3352878340811003e-06, w:1.9992249011993408, b:0.0017617783742025495
Epoch:884, Loss:1.3168073564884253e-06, w:1.9992305040359497, b:0.0017490754835307598
Epoch:885, Loss:1.297462404181715e-06, w:1.9992361068725586, b:0.0017364631639793515
Epoch:886, Loss:1.279574917134596e-06, w:1.999241590499878, b:0.0017239366425201297
Epoch:887, Loss:1.2609632449311903e-06, w:1.9992470741271973, b:0.0017115197842940688
Epoch:888, Loss:1.242488224306726e-06, w:1.9992525577545166, b:0.0016991839511319995
Epoch:889, Loss:1.2246637197677046e-06, w:1.9992579221725464, b:0.0016869292594492435
Epoch:890, Loss:1.2069681361026596e-06, w:1.9992632865905762, b:0.001674765138886869
Epoch:891, Loss:1.1893384908034932e-06, w:1.999268651008606, b:0.0016626915894448757
Epoch:892, Loss:1.1723416264430853e-06, w:1.9992738962173462, b:0.001650694408454001
Epoch:893, Loss:1.1554670891200658e-06, w:1.9992791414260864, b:0.0016387830255553126
Epoch:894, Loss:1.1392107808205765e-06, w:1.999284267425537, b:0.0016269574407488108
Epoch:895, Loss:1.1230699783482123e-06, w:1.9992893934249878, b:0.0016152272000908852
Epoch:896, Loss:1.1064942100347253e-06, w:1.9992945194244385, b:0.0016035924199968576
Epoch:897, Loss:1.0905273484240752e-06, w:1.9992996454238892, b:0.0015920291189104319
Epoch:898, Loss:1.0751582522061653e-06, w:1.9993046522140503, b:0.0015805468428879976
Epoch:899, Loss:1.0594199011393357e-06, w:1.9993096590042114, b:0.0015691552544012666
Epoch:900, Loss:1.044867076416267e-06, w:1.9993146657943726, b:0.001557844690978527
Epoch:901, Loss:1.029352688419749e-06, w:1.9993196725845337, b:0.0015466103795915842
Epoch:902, Loss:1.0148326055059442e-06, w:1.9993245601654053, b:0.0015354572096839547
Epoch:903, Loss:9.999507710745092e-07, w:1.9993294477462769, b:0.0015243898378685117
Epoch:904, Loss:9.8575674201129e-07, w:1.9993343353271484, b:0.0015133987180888653
Epoch:905, Loss:9.71548388406518e-07, w:1.9993391036987305, b:0.0015024696476757526
Epoch:906, Loss:9.57443262450397e-07, w:1.9993438720703125, b:0.0014916263753548265
Epoch:907, Loss:9.435553351977433e-07, w:1.9993486404418945, b:0.0014808689011260867
Epoch:908, Loss:9.304962986789178e-07, w:1.999353289604187, b:0.0014701734762638807
Epoch:909, Loss:9.17083355034265e-07, w:1.9993579387664795, b:0.001459568622522056
Epoch:910, Loss:9.033260539581534e-07, w:1.999362587928772, b:0.001449044793844223
Epoch:911, Loss:8.905497566047416e-07, w:1.999367117881775, b:0.0014385925605893135
Epoch:912, Loss:8.77538525401178e-07, w:1.9993717670440674, b:0.0014282308984547853
Epoch:913, Loss:8.650554832456692e-07, w:1.9993762969970703, b:0.0014179263962432742
Epoch:914, Loss:8.529294177606062e-07, w:1.9993807077407837, b:0.0014076887164264917
Epoch:915, Loss:8.404629738834046e-07, w:1.999385118484497, b:0.0013975368347018957
Epoch:916, Loss:8.28511531381082e-07, w:1.9993895292282104, b:0.0013874613214284182
Epoch:917, Loss:8.167510259227129e-07, w:1.9993939399719238, b:0.001377471606247127
Epoch:918, Loss:8.045528829825344e-07, w:1.9993983507156372, b:0.0013675438240170479
Epoch:919, Loss:7.937410373415332e-07, w:1.9994027614593506, b:0.0013576924102380872
Epoch:920, Loss:7.818201197551389e-07, w:1.9994070529937744, b:0.0013479077024385333
Epoch:921, Loss:7.710598310950445e-07, w:1.9994113445281982, b:0.0013381754979491234
Epoch:922, Loss:7.593110353809607e-07, w:1.999415636062622, b:0.0013285338645800948
Epoch:923, Loss:7.488086453122378e-07, w:1.9994198083877563, b:0.0013189446181058884
Epoch:924, Loss:7.378794180112891e-07, w:1.9994239807128906, b:0.0013094221940264106
Epoch:925, Loss:7.275268671946833e-07, w:1.999428153038025, b:0.0012999807950109243
Epoch:926, Loss:7.16853946869378e-07, w:1.9994323253631592, b:0.0012906062183901668
Epoch:927, Loss:7.065034424158512e-07, w:1.999436378479004, b:0.0012812888016924262
Epoch:928, Loss:6.959865004318999e-07, w:1.9994404315948486, b:0.0012720477534458041
Epoch:929, Loss:6.865105319775466e-07, w:1.9994444847106934, b:0.001262863865122199
Epoch:930, Loss:6.768609637219924e-07, w:1.999448537826538, b:0.0012537610018625855
Epoch:931, Loss:6.669472440989921e-07, w:1.9994524717330933, b:0.0012447201879695058
Epoch:932, Loss:6.57059956665762e-07, w:1.9994564056396484, b:0.0012357460800558329
Epoch:933, Loss:6.47479737381218e-07, w:1.9994603395462036, b:0.0012268244754523039
Epoch:934, Loss:6.384348125720862e-07, w:1.9994642734527588, b:0.0012179743498563766
Epoch:935, Loss:6.291305112426926e-07, w:1.9994680881500244, b:0.0012091815005987883
Epoch:936, Loss:6.198945357027696e-07, w:1.99947190284729, b:0.0012004505842924118
Epoch:937, Loss:6.112716164352605e-07, w:1.9994757175445557, b:0.001191781717352569
Epoch:938, Loss:6.024840786267305e-07, w:1.9994795322418213, b:0.001183189102448523
Epoch:939, Loss:5.938046001574548e-07, w:1.9994832277297974, b:0.0011746537638828158
Epoch:940, Loss:5.851439368598221e-07, w:1.9994869232177734, b:0.0011661899043247104
Epoch:941, Loss:5.772092208644608e-07, w:1.9994906187057495, b:0.0011577833211049438
Epoch:942, Loss:5.686708846042166e-07, w:1.9994943141937256, b:0.001149438670836389
Epoch:943, Loss:5.605009505416092e-07, w:1.9994980096817017, b:0.0011411512969061732
Epoch:944, Loss:5.523032200471789e-07, w:1.9995015859603882, b:0.0011329163098707795
Epoch:945, Loss:5.442520887299906e-07, w:1.9995051622390747, b:0.0011247575748711824
Epoch:946, Loss:5.366005666473939e-07, w:1.9995087385177612, b:0.0011166513431817293
Epoch:947, Loss:5.286651685310062e-07, w:1.9995123147964478, b:0.0011086070444434881
Epoch:948, Loss:5.215445071371505e-07, w:1.9995158910751343, b:0.0011006152490153909
Epoch:949, Loss:5.139295922163001e-07, w:1.9995193481445312, b:0.0010926711838692427
Epoch:950, Loss:5.06164269609144e-07, w:1.9995228052139282, b:0.0010847985977306962
Epoch:951, Loss:4.988692126062233e-07, w:1.9995262622833252, b:0.0010769785149022937
Epoch:952, Loss:4.92359731651959e-07, w:1.9995296001434326, b:0.0010691964998841286
Epoch:953, Loss:4.851647190662334e-07, w:1.9995330572128296, b:0.0010615003993734717
Epoch:954, Loss:4.782234555023024e-07, w:1.999536395072937, b:0.0010538423666730523
Epoch:955, Loss:4.713322141469689e-07, w:1.9995397329330444, b:0.0010462416103109717
Epoch:956, Loss:4.6449099500023294e-07, w:1.9995430707931519, b:0.0010386980138719082
Epoch:957, Loss:4.576607466333371e-07, w:1.9995464086532593, b:0.0010312116937711835
Epoch:958, Loss:4.5123198333385517e-07, w:1.9995496273040771, b:0.001023768214508891
Epoch:959, Loss:4.44500301455264e-07, w:1.999552845954895, b:0.0010163915576413274
Epoch:960, Loss:4.381649887363892e-07, w:1.999556064605713, b:0.0010090578580275178
Epoch:961, Loss:4.318372361922229e-07, w:1.9995592832565308, b:0.001001790864393115
Epoch:962, Loss:4.2563198121570167e-07, w:1.9995625019073486, b:0.0009945763740688562
Epoch:963, Loss:4.194328653284174e-07, w:1.999565601348877, b:0.000987390405498445
Epoch:964, Loss:4.1380309312444297e-07, w:1.9995687007904053, b:0.0009802712593227625
Epoch:965, Loss:4.076543973496882e-07, w:1.9995718002319336, b:0.000973209273070097
Epoch:966, Loss:4.0180975702241994e-07, w:1.999574899673462, b:0.0009661997901275754
Epoch:967, Loss:3.958610363952175e-07, w:1.9995779991149902, b:0.000959237979259342
Epoch:968, Loss:3.903922447534569e-07, w:1.999580979347229, b:0.0009523190674372017
Epoch:969, Loss:3.8496165188917075e-07, w:1.9995839595794678, b:0.0009454573737457395
Epoch:970, Loss:3.7931863516860176e-07, w:1.9995869398117065, b:0.0009386528981849551
Epoch:971, Loss:3.7375235706349486e-07, w:1.9995900392532349, b:0.0009319104137830436
Epoch:972, Loss:3.684040166263003e-07, w:1.9995930194854736, b:0.0009251917945221066
Epoch:973, Loss:3.632342213677475e-07, w:1.9995959997177124, b:0.0009185160743072629
Epoch:974, Loss:3.5799644138023723e-07, w:1.9995988607406616, b:0.0009118880261667073
Epoch:975, Loss:3.527623562149529e-07, w:1.9996017217636108, b:0.0009053171961568296
Epoch:976, Loss:3.476009737823915e-07, w:1.99960458278656, b:0.000898789323400706
Epoch:977, Loss:3.4281811167602427e-07, w:1.9996074438095093, b:0.0008923186687752604
Epoch:978, Loss:3.3769657648008433e-07, w:1.9996103048324585, b:0.0008858909131959081
Epoch:979, Loss:3.329826085973764e-07, w:1.9996131658554077, b:0.0008795060566626489
Epoch:980, Loss:3.279354245933064e-07, w:1.9996159076690674, b:0.000873164099175483
Epoch:981, Loss:3.2319098863808904e-07, w:1.999618649482727, b:0.0008668650989420712
Epoch:982, Loss:3.1880949791229796e-07, w:1.9996213912963867, b:0.0008606185438111424
Epoch:983, Loss:3.141317961308232e-07, w:1.9996241331100464, b:0.000854410114698112
Epoch:984, Loss:3.098123784184281e-07, w:1.999626874923706, b:0.0008482541306875646
Epoch:985, Loss:3.0526626915161614e-07, w:1.9996296167373657, b:0.0008421363309025764
Epoch:986, Loss:3.009440661116969e-07, w:1.9996322393417358, b:0.0008360471110790968
Epoch:987, Loss:2.963683982670773e-07, w:1.999634861946106, b:0.00083001988241449
Epoch:988, Loss:2.924246018665144e-07, w:1.999637484550476, b:0.0008240307797677815
Epoch:989, Loss:2.8791441764042247e-07, w:1.9996401071548462, b:0.000818089407403022
Epoch:990, Loss:2.840274646587204e-07, w:1.9996427297592163, b:0.0008121861610561609
Epoch:991, Loss:2.795827640511561e-07, w:1.9996453523635864, b:0.0008063305867835879
Epoch:992, Loss:2.7596644258665037e-07, w:1.999647855758667, b:0.0008005131967365742
Epoch:993, Loss:2.7182778694623266e-07, w:1.9996503591537476, b:0.0007947387057356536
Epoch:994, Loss:2.678107762221771e-07, w:1.9996528625488281, b:0.0007890118868090212
Epoch:995, Loss:2.6394309315946884e-07, w:1.9996553659439087, b:0.0007833231939002872
Epoch:996, Loss:2.601926212264516e-07, w:1.9996578693389893, b:0.0007776774582453072
Epoch:997, Loss:2.567044248280581e-07, w:1.9996603727340698, b:0.0007720650755800307
Epoch:998, Loss:2.529180278543208e-07, w:1.9996628761291504, b:0.0007664955919608474
Epoch:999, Loss:2.49247023020871e-07, w:1.9996652603149414, b:0.0007609690655954182
w =  1.9996676445007324
b =  0.0007554758922196925
y_pred =  tensor([7.9994])

训练的预期目标是使得权重值w=2，偏置值b=0，预测值为8，通过输出结果可知显然做到了，说明本次训练是比较成功的。接下来使用Python的Matplotlib库绘图来记录训练的完整过程⁴，把损失值loss和权重值weight随着Epoch变化的过程可视化。

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写到这里，差不多本文也就要结束了，如有错误之处，敬请指正。如果我的这篇文章帮助到了你，那我也会感到很高兴，一个人能走多远，在于与谁同行。

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参考文章

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1. 《PyTorch深度学习实践》完结合集 - 05.用PyTorch实现线性回归
   ↩︎

2. pytorch 之 call, init,forward
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3. pytorch系列 ----暂时就叫5的番外吧： nn.Modlue及nn.Linear 源码理解
   ↩︎

4. Python学习-Matplotlib库绘制三维统计图（绘制点、线、面）
   ↩︎