Python implementation of deep learning series [forward propagation and back propagation]

python implementation deep learning series


Before you understand the deep learning framework , We need to understand and even realize a process of online learning and parameter adjustment , And then understand the mechanism of deep learning ;

So , Bloggers here provide an example of their own writing , Let's take a look at the process of forward and backward propagation of e-learning ;

besides , In order to achieve batch Read , I also designed and provided a simple DataLoader Class to simulate the sampling of data iterators in deep learning ; And provides the function of access model ;

It is worth noting that Only use python Realization , So the demand for the environment is not great , I hope you can have more star My blog and github, Learn more useful knowledge !!


One 、 Realization effect

Two 、 Overall code framework

3、 ... and 、 Detailed code description

1. Data processing

2. Network design

3. Activation function

4. Training

Four 、 Training demonstration

5、 ... and 、 summary


One 、 Realization effect

Implement one by more than one Linear Layer network to fit the function , Project address :, function :


The fitting function is y = \sin (2\pi x),0\leqslant x\leqslant 2

The following results, from left to right, are ( The learning rate is 0.03,batchsize by 90):

Epoch:400,1000, 2000, 10000 above

Two 、 Overall code framework

3、 ... and 、 Detailed code description

1. Data processing

x yes 0 To 2 Data between , In steps of 0.01, So it is 200 Data ;

y It's the objective function , The amplitude is 20;

length It's data length ;

_build_items() It's about building a dict Storage x and y;

_transform() It's right x and y Data transformation ;

import numpy as np
class Dataset:
def __init__(self):
self.x = np.arange(0.0, 2.0, 0.01)
self.y = 20 * np.sin(2 * np.pi * self.x)
self.length = len(list(self.x))
def _build_items(self):
self.items = [{
'x': list(self.x)[i],
'y': list(self.y)[i]
}for i in range(self.length)]
def _transform(self):
self.x = self.x.reshape(1, self.__len__())
self.y = self.y.reshape(1, self.__len__())
def __len__(self):
return self.length
def __getitem__(self, index):
return self.items[index]

Be similar to Pytorch Inside DataLoader, Bloggers here also pass in two parameters for initialization :dataset and batch_size

__next__() It's the function that each iteration performs , utilize __len__() obtain dataset The length of , utilize __getitem__() Get the data in the dataset ;

_concate() Is to take a batch To put together the data of ;

_transform() It's a conversion of batch Data form of ;

import numpy as np
class DataLoader:
def __init__(self, dataset, batch_size):
self.dataset = dataset
self.batch_size = batch_size
self.current = 0
def __next__(self):
if self.current < self.dataset.__len__():
if self.current + self.batch_size <= self.dataset.__len__():
item = self._concate([self.dataset.__getitem__(index) for index in range(self.current, self.current + self.batch_size)])
self.current += self.batch_size
item = self._concate([self.dataset.__getitem__(index) for index in range(self.current, self.dataset.__len__())])
self.current = self.dataset.__len__()
return item
self.current = 0
raise StopIteration
def _concate(self, dataset_items):
concated_item = {}
for item in dataset_items:
for k, v in item.items():
if k not in concated_item:
concated_item[k] = [v]
concated_item = self._transform(concated_item)
return concated_item
def _transform(self, concated_item):
for k, v in concated_item.items():
concated_item[k] = np.array(v).reshape(1, len(v))
return concated_item
def __iter__(self):
return self

2. Network design

Be similar to Pytorch Inside Linear, Bloggers here also pass in three parameters for initialization :in_features, out_features, bias

_init_parameters() It's the initialization weight weight And offset bias,weight Size is [out_features, in_features],bias Size is [out_features, 1]

forward It's forward propagation :y = wx+b

import numpy as np
class Linear:
def __init__(self, in_features, out_features, bias=False):
self.in_features = in_features
self.out_features = out_features
self.bias = bias
def _init_parameters(self):
self.weight = np.random.random([self.out_features, self.in_features])
if self.bias:
self.bias = np.zeros([self.out_features, 1])
self.bias = None
def forward(self, input):
return + self.bias


A simple multilayer Linear The Internet

_init_parameters() It's a Linear The weight and paranoia in the layer are placed in one dict Internal storage ;

forward() It's forward propagation , The last floor doesn't go through Sigmoid;

backward() It's back propagation , Using gradient descent to realize error transfer and parameter adjustment : For example, a two-layer Linear The back propagation of layers is as follows




dz^{[0]}=W^{[1]}^{T}dz^{[1]}\ast S^{[0]}'(z^{[0]}) }



update_grads() It's updating weights and offsets ;

# -*- coding: UTF-8 -*-
import numpy as np
from ..lib.Activation.Sigmoid import sigmoid_derivative, sigmoid
from ..lib.Module.Linear import Linear
class network:
def __init__(self, layers_dim):
self.layers_dim = layers_dim
self.linear_list = [Linear(layers_dim[i - 1], layers_dim[i], bias=True) for i in range(1, len(layers_dim))]
self.parameters = {}
def _init_parameters(self):
for i in range(len(self.layers_dim) - 1):
self.parameters["w" + str(i)] = self.linear_list[i].weight
self.parameters["b" + str(i)] = self.linear_list[i].bias
def forward(self, x):
a = []
z = []
caches = {}
layers = len(self.parameters) // 2
for i in range(layers):
z_temp = self.linear_list[i].forward(a[i])
self.parameters["w" + str(i)] = self.linear_list[i].weight
self.parameters["b" + str(i)] = self.linear_list[i].bias
if i == layers - 1:
caches["z"] = z
caches["a"] = a
return caches, a[layers]
def backward(self, caches, output, y):
layers = len(self.parameters) // 2
grads = {}
m = y.shape[1]
for i in reversed(range(layers)):
# Suppose the last layer doesn't go through the activation function
# It's written according to the formula in the picture above
if i == layers - 1:
grads["dz" + str(i)] = output - y
else: # The front is full of sigmoid Activate
grads["dz" + str(i)] = self.parameters["w" + str(i + 1)]
grads["dz" + str(i + 1)]) * sigmoid_derivative(
caches["z"][i + 1])
grads["dw" + str(i)] = grads["dz" + str(i)].dot(caches["a"][i].T) / m
grads["db" + str(i)] = np.sum(grads["dz" + str(i)], axis=1, keepdims=True) / m
return grads
# It is to update all its weight and paranoia
def update_grads(self, grads, learning_rate):
layers = len(self.parameters) // 2
for i in range(layers):
self.parameters["w" + str(i)] -= learning_rate * grads["dw" + str(i)]
self.parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]

3. Activation function

Formula definition :S(x)=\frac{1}{1+e^{-x}}

The derivative can be represented by itself :S'(x)=\frac{e^{-x}}{(1+e^{-x})^2}=S(x)(1-S(x))

import numpy as np
def sigmoid(x):
return 1.0 / (1.0 + np.exp(-x))
def sigmoid_derivative(x):
return sigmoid(x) * (1 - sigmoid(x))

4. Training

Entry file of training model , contain Training test and The storage model

from code.scripts.trainer import Trainer
from code.config.default_config import _C
if __name__ == '__main__':
trainer = Trainer(cfg=_C)

The configuration file

layers_dim representative Linear The input and output dimensions of the layer ;

batch_size yes batch Size ;

total_epochs It's the total training time , Train once x For one epoch;

resume It's judgment. Keep training ;

result_img_path Is the path to the result store ;

ckpt_path It's the path to model storage ;

from easydict import EasyDict
_C = EasyDict()
_C.layers_dim = [1, 25, 1] # [1, 30, 10, 1]
_C.batch_size = 90
_C.total_epochs = 40000
_C.resume = True # False means retraining
_C.result_img_path = "D:/project/Pycharm/HJLNet/result.png"
_C.ckpt_path = 'D:/project/Pycharm/HJLNet/ckpt.npy'

I won't go into more details here , Mainly used train() This function trains ,test() To test

from ..lib.Data.DataLoader import DataLoader
from ..scripts.Dataset import Dataset
from import network
import matplotlib.pyplot as plt
import numpy as np
class Trainer:
def __init__(self, cfg):
self.ckpt_path = cfg.ckpt_path
self.result_img_path = cfg.result_img_path
self.layers_dim = cfg.layers_dim = network(self.layers_dim)
if cfg.resume:
self.dataset = Dataset()
self.dataloader = DataLoader(dataset=self.dataset, batch_size=cfg.batch_size)
self.total_epochs = cfg.total_epochs
self.iterations = 0
self.x = self.dataset.x
self.y = self.dataset.y
self.draw_data(self.x, self.y)
def train(self):
for i in range(self.total_epochs):
for item in self.dataloader:
caches, output =['x'])
grads =, output, item['y']), learning_rate=0.03)
if i % 100 == 0:
print("Epoch: {}/{} Iteration: {} Loss: {}".format(i + 1,
self.compute_loss(output, item['y'])))
self.iterations += 1
def test(self):
caches, output =
self.draw_data(self.x, output)
def save_models(self):
ckpt = {
}, ckpt)
print('Save models finish!!')
def load_models(self):
ckpt = np.load(self.ckpt_path).item() = ckpt["layers_dim"] = ckpt["parameters"]
print('load models finish!!')
def draw_data(self, x, y):
plt.scatter(x, y)
def show(self):
def save_results(self):
plt.savefig(fname=self.result_img_path, figsize=[10, 10])
# Calculate the error value
def compute_loss(self, output, y):
return np.mean(np.square(output - y))

Four 、 Training demonstration

Training time will be output during training , Number of iterations and loss changes , Store the model and results at the end of the training .

1. Start training

2. After training , Read the last model and continue training

3. Result display

5、 ... and 、 summary

In this way, we will know a basic network training process forward and backward propagation process , More detailed code and principles will be updated later , To help you learn the knowledge and concepts of deep learning ~

本文为[Sad love flowers, unintentional people]所创,转载请带上原文链接,感谢

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