神经网络框架原理

Posted 2022-12-12 未来可期-2018

文章目录

• • 1.建立计算图
  • 2.拓扑排序
  • 3.前馈计算
  • 4.反向传播

想看详细代码请到-> 从零编写一个简单神经网络框架

1.建立计算图

定义变量和使用各种算子的过程就是一个建立一个计算图的过程

import networkx as nx
import random
import numpy
from matplotlib.animation import FuncAnimation
%matplotlib notebook

seed=1
random.seed(seed)
np.random.seed(seed)

sample_graph = 
    'x':["linear_01"],
    'k':["linear_01"],
    'b':["linear_01"],
    'linear_01':["sigmoid"],
    "sigmoid":["linear_02"],
    "k2":["linear_02"],
    "b2":["linear_02"],
    "linear_02":["yhat"],
    "yhat":["loss"]


graph = nx.DiGraph(sample_graph)

2.拓扑排序

1. 利用拓扑排序获得前馈计算和反馈传播顺序，通过前馈计算计算出loss, 反向传播计算出loss对k和b的偏导

2. 所有节点的求导法则
   $$\frac{\partial loss}{\partial self}=\frac{\partial loss}{\partial output}\ast \frac{\partial output}{\partial self}$$

valid_feedforward_order = list(nx.topological_sort(graph))

3.前馈计算

def forward(i):
    color_map = ("red", "green")
    pre_color, after_color = color_map

    changed = valid_feedforward_order[:i]
    color_order = [
        after_color if c in changed else pre_color for c in valid_feedforward_order]

    if i == len(valid_feedforward_order):
        ani.event_source.stop()

    nx.draw(graph, layout, node_color=color_order, with_labels=True)

fig = plt.gcf()
nx.draw(graph, layout, with_labels=True)
ani = FuncAnimation(fig, forward, frames=range(len(valid_feedforward_order)),interval=300)
plt.show()

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4.反向传播

def backward(i):
    color_map = ("red", "green")
    pre_color, after_color = color_map

    changed = valid_feedforward_order[:i]
    color_order = [
        after_color if c in changed else pre_color for c in valid_feedforward_order][::-1]

    if i == len(valid_feedforward_order):
        ani.event_source.stop()

    nx.draw(graph, layout, node_color=color_order, with_labels=True)

fig = plt.gcf()
nx.draw(graph, layout, with_labels=True)
ani = FuncAnimation(fig, backward, frames=range(len(valid_feedforward_order)),interval=300)
plt.show()

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FuncAnimation

ani = FuncAnimation(fig,update,frames,init_func,interval=1,blit)

• fig figure对象
• update 不断更新图像的函数，生成新的xdata和ydata
• frames list 不断提供frame给update用于生成xdata和ydata
• init_func 初始函数为init，自定义开始帧
• interval 时间间隔1ms