此一章節 Michael Nielsen 先生開始說明手寫阿拉伯數字辨識的 Python 程式內容︰

Implementing our network to classify digits

Alright, let’s write a program that learns how to recognize handwritten digits, using stochastic gradient descent and the MNIST training data. We’ll do this with a short Python (2.7) program, just 74 lines of code! The first thing we need is to get the MNIST data. If you’re a git user then you can obtain the data by cloning the code repository for this book,

git clone https://github.com/mnielsen/neural-networks-and-deep-learning.git

If you don’t use git then you can download the data and code here.

Incidentally, when I described the MNIST data earlier, I said it was split into 60,000 training images, and 10,000 test images. That’s the official MNIST description. Actually, we’re going to split the data a little differently. We’ll leave the test images as is, but split the 60,000-image MNIST training set into two parts: a set of 50,000 images, which we’ll use to train our neural network, and a separate 10,000 image validation set. We won’t use the validation data in this chapter, but later in the book we’ll find it useful in figuring out how to set certain hyper-parameters of the neural network – things like the learning rate, and so on, which aren’t directly selected by our learning algorithm. Although the validation data isn’t part of the original MNIST specification, many people use MNIST in this fashion, and the use of validation data is common in neural networks. When I refer to the “MNIST training data” from now on, I’ll be referring to our 50,000 image data set, not the original 60,000 image data set* *As noted earlier, the MNIST data set is based on two data sets collected by NIST, the United States’ National Institute of Standards and Technology. To construct MNIST the NIST data sets were stripped down and put into a more convenient format by Yann LeCun, Corinna Cortes, and Christopher J. C. Burges. See this link for more details. The data set in my repository is in a form that makes it easy to load and manipulate the MNIST data in Python. I obtained this particular form of the data from the LISA machine learning laboratory at the University of Montreal (link)..

Apart from the MNIST data we also need a Python library called Numpy, for doing fast linear algebra. If you don’t already have Numpy installed, you can get it here.

Let me explain the core features of the neural networks code, before giving a full listing, below. The centerpiece is a Network class, which we use to represent a neural network. Here’s the code we use to initialize a Network object:

class Network(object):

    def __init__(self, sizes):
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        self.weights = [np.random.randn(y, x) 
                        for x, y in zip(sizes[:-1], sizes[1:])]

In this code, the list sizes contains the number of neurons in the respective layers. So, for example, if we want to create a Network object with 2 neurons in the first layer, 3 neurons in the second layer, and 1 neuron in the final layer, we’d do this with the code:

net = Network([2, 3, 1])

The biases and weights in the Network object are all initialized randomly, using the Numpy np.random.randn function to generate Gaussian distributions with mean 0 and standard deviation 1. This random initialization gives our stochastic gradient descent algorithm a place to start from. In later chapters we’ll find better ways of initializing the weights and biases, but this will do for now. Note that the Network initialization code assumes that the first layer of neurons is an input layer, and omits to set any biases for those neurons, since biases are only ever used in computing the outputs from later layers.

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打算深入理解者，對

NumPy

NumPy is the fundamental package for scientific computing with Python. It contains among other things:

• a powerful N-dimensional array object
• sophisticated (broadcasting) functions
• tools for integrating C/C++ and Fortran code
• useful linear algebra, Fourier transform, and random number capabilities

Besides its obvious scientific uses, NumPy can also be used as an efficient multi-dimensional container of generic data. Arbitrary data-types can be defined. This allows NumPy to seamlessly and speedily integrate with a wide variety of databases.

Numpy is licensed under the BSD license, enabling reuse with few restrictions.

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科學計算派生程式庫之了解大概不能少。

有志於此者，何不閱讀 Travis E. Oliphant 先生寫的

Guide to NumPy
Travis E. Oliphant, PhD
Dec 7, 2006
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etermined, Temporary, Distribution-Restriction (MDTDR) system (see http://www.trelgol.com) until October 31, 2010 at the latest. If you receive this book, you a re asked not to copy it in any form (electronic or paper) until the temporary distribution-restriction lapses. If you have multiple users at an institution, you should eith
er share a single copy using some form of digital library check-out, or buy multiple copies. The more copies purchased, the sooner the documentation can be released from this inconvenient distribution restriction. After October 31, 2010 this book may be freely
copied in any format and used as source material for other books as long as acknowledgement of the original author is given. Your support of this temporary distribution restriction plays an essential role in allowing the author and others like him to produce more quality books and software.

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指南耶！！總是用得着乎？？