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−∞,+∞)(-\infty

w=[0,1]w

Time

Python

o1o_1o1

h1h_1h1

b=0b

MSE

w1w_1w1. How

ThenSince

x2x_2x2

backprop”.Phew

Male (000

3 Mar 2019Computer Science

Princeton University

ZERO

Python

0,1)(0

’d

We’ll

Nice

Alice

∂L∂w1\frac{\partial L}{\partial

L=(1−ypred)2L

∂L∂w1\frac{\partial L}{\partial w_1}∂w1∂L:Reminder

f′(x)=f(x)∗(1−f(x))f'(x

LLL

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SGD

We’ll

∂ypred∂w1\frac{\partial y_{pred}}{\partial

action!We’re

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Positivity 54.00%

Negativity 46.00%

SOURCE:
https://victorzhou.com/blog/intro-to-neural-networks/
##### Summary

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Write a review: Hacker News

Here’s what a simple neural network might look like:This network has 2 inputs, a hidden layer with 2 neurons (h1h_1h1 and h2h_2h2), and an output layer with 1 neuron (o1o_1o1). There can be multiple hidden layers!Let’s use the network pictured above and assume all neurons have the same weights w=[0,1]w = [0, 1]w=[0,1], the same bias b=0b = 0b=0, and the same sigmoid activation function. Let h1,h2,o1h_1, h_2, o_1h1,h2,o1 denote the outputs of the neurons they represent.What happens if we pass in the input x=[2,3]x = [2, 3]x=[2,3]?The output of the neural network for input x=[2,3]x = [2, 3]x=[2,3] is 0.72160.72160.7216. Let’s label each weight and bias in our network:Then, we can write loss as a multivariable function:Imagine we wanted to tweak w1w_1w1. All we’re doing is subtracting η∂L∂w1\eta \frac{\partial L}{\partial w_1}η∂w1∂L from w1w_1w1:If we do this for every weight and bias in the network, the loss will slowly decrease and our network will improve.Our training process will look like this:Let’s see it in action!It’s finally time to implement a complete neural network:You can run / play with this code yourself.

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