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深度学习

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UFLDL Tutorial

ver 201406

∗

1 Introduction

This tutorial will teach you the main ideas of Unsupervised Feature Learning and Deep Learning.

By working through it, you will also get to implement several feature learning/deep learning

algorithms, get to see them work for yourself, and learn how to apply/adapt these ideas to new

problems.

This tutorial assumes a basic knowledge of machine learning (speciﬁcally, familiarity with the

ideas of supervised learning, logistic regression, gradient descent). If you are not familiar with

these ideas, we suggest you go to this Machine Learning course and complete sections II, III, IV

(up to Logistic Regression) ﬁrst.

Material contributed by: Andrew Ng, Jiquan Ngiam, Chuan Yu Foo, Yifan Mai, Caroline Suen

∗

This document was formated base on the online UFLDL Tutorial 2014-06-11. You may update the latest version

from GitHub. Please don’t hesitate to leave message in the web site if you have any comments or suggestion. Yes,

the format of this document is not perfect, and you may adjust it by yourself if you want. Don’t forget to share

your version, and notify me to update this document. Thanks, have fun!

-1

-0.5

0.5

-4 -2 0 2 4

f(z)

1+exp(−z)

tanh(z)

•

Figure 1: Activation functions

In this ﬁgure, we have used circles to also denote the inputs to the network. The circles labeled

“+1" are called bias units, and correspond to the intercept term. The leftmost layer of the network

is called the input layer, and the rightmost layer the output layer (which, in this example, has

only one node). The middle layer of nodes is called the hidden layer, because its values are not

observed in the training set. We also say that our example neural network has 3 input units (not

counting the bias unit), 3 hidden units, and 1 output unit.

We will let n

denote the number of layers in our network; thus n

= 3 in our example. We label

layer l as L

, so layer L

is the input layer, and layer L

the output layer. Our neural network

has parameters (W, b) = (W

(1)

, b

(1)

, W

(2)

, b

(2)

), where we write W

(l)

to denote the parameter (or

weight) associated with the connection between unit j in layer l, and unit i in layer l + 1. (Note

the order of the indices.) Also, b

(l)

is the bias associated with unit i in layer l + 1. Thus, in

our example, we have W

(1)

∈ ℜ

3×3

, and W

(2)

∈ ℜ

1×3

. Note that bias units don’t have inputs or

connections going into them, since they always output the value +1. We also let s

denote the

number of nodes in layer l (not counting the bias unit).

We will write a

(l)

to denote the activation (meaning output value) of unit i in layer l. For

l = 1, we also use a

(1)

= x

to denote the i-th input. Given a ﬁxed setting of the parameters

W, b, our neural network deﬁnes a hypothesis h

W,b

(x) that outputs a real number. Speciﬁcally, the

computation that this neural network represents is given by:

(2)

= f (W

(1)

+ W

(1)

+ W

(1)

+ b

(1)

)

(2)

= f (W

(1)

+ W

(1)

+ W

(1)

+ b

(1)

)

(2)

= f (W

(1)

+ W

(1)

+ W

(1)

+ b

(1)

)

W,b

(x) = a

(3)

= f (W

(2)

+ W

(2)

+ W

(2)

+ b

(2)

)

In the sequel, we also let z

(l)

denote the total weighted sum of inputs to unit i in layer l,

including the bias term (e.g., z

(2)



j=1

(1)

+ b

(1)

), so that a

(l)

= f (z

(l)

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