求解机器学习问题的步骤可以分为“学习”和“推理”两个阶段。
本例假设“学习”阶段已经完成，并将学习到的权重和偏置参数保存在pickle文件sample_weight.pkl中。至于是如何学习的，斋藤康毅指出会在后续章节详述。之后，使用学习到的权重和偏置参数，进行“推理”阶段的操作。
在“手写数字识别”项目中，所谓“推理”，即使用学习到的权重和偏置参数，对输入数据进行分类。

“手写数字识别”项目的代码含 mnist.py、neuralnet_mnist.py 及 sample_weight.pkl 等3个文件，它们位于同一文件夹下。项目创建及执行主要有两步，如下所示。
一、首先，在任一文件夹中新建 mnist.py 文件，内容如下：

try:import urllib.request
except ImportError:raise ImportError('You should use Python 3.x')
import os.path
import gzip
import pickle
import os
import numpy as npurl_base = 'http://yann.lecun.com/exdb/mnist/'
key_file = {'train_img':'train-images-idx3-ubyte.gz','train_label':'train-labels-idx1-ubyte.gz','test_img':'t10k-images-idx3-ubyte.gz','test_label':'t10k-labels-idx1-ubyte.gz'
}dataset_dir = os.path.dirname(os.path.abspath('__file__'))
save_file = dataset_dir + "/mnist.pkl"train_num = 60000
test_num = 10000
img_dim = (1, 28, 28)
img_size = 784def _download(file_name):file_path = dataset_dir + "/" + file_nameif os.path.exists(file_path):returnprint("Downloading " + file_name + " ... ")urllib.request.urlretrieve(url_base + file_name, file_path)print("Done")def download_mnist():for v in key_file.values():_download(v)def _load_label(file_name):file_path = dataset_dir + "/" + file_nameprint("Converting " + file_name + " to NumPy Array ...")with gzip.open(file_path, 'rb') as f:labels = np.frombuffer(f.read(), np.uint8, offset=8)print("Done")return labelsdef _load_img(file_name):file_path = dataset_dir + "/" + file_nameprint("Converting " + file_name + " to NumPy Array ...")    with gzip.open(file_path, 'rb') as f:data = np.frombuffer(f.read(), np.uint8, offset=16)data = data.reshape(-1, img_size)print("Done")return datadef _convert_numpy():dataset = {}dataset['train_img'] =  _load_img(key_file['train_img'])dataset['train_label'] = _load_label(key_file['train_label'])    dataset['test_img'] = _load_img(key_file['test_img'])dataset['test_label'] = _load_label(key_file['test_label'])return datasetdef init_mnist():download_mnist()dataset = _convert_numpy()print("Creating pickle file ...")with open(save_file, 'wb') as f:pickle.dump(dataset, f, -1)print("Done!")def _change_one_hot_label(X):T = np.zeros((X.size, 10))for idx, row in enumerate(T):row[X[idx]] = 1return Tdef load_mnist(normalize=True, flatten=True, one_hot_label=False):"""读入MNIST数据集Parameters----------normalize : 将图像的像素值正规化为0.0~1.0one_hot_label : one_hot_label为True的情况下，标签作为one-hot数组返回one-hot数组是指[0,0,1,0,0,0,0,0,0,0]这样的数组flatten : 是否将图像展开为一维数组Returns-------(训练图像, 训练标签), (测试图像, 测试标签)"""if not os.path.exists(save_file):init_mnist()with open(save_file, 'rb') as f:dataset = pickle.load(f)if normalize:for key in ('train_img', 'test_img'):dataset[key] = dataset[key].astype(np.float32)dataset[key] /= 255.0if one_hot_label:dataset['train_label'] = _change_one_hot_label(dataset['train_label'])dataset['test_label'] = _change_one_hot_label(dataset['test_label'])if not flatten:for key in ('train_img', 'test_img'):dataset[key] = dataset[key].reshape(-1, 1, 28, 28)return (dataset['train_img'], dataset['train_label']), (dataset['test_img'], dataset['test_label']) if __name__ == '__main__':init_mnist()

初次运行 mnist.py 文件时，会下载 MNIST 数据集，所以需要保证网络畅通。
由于连接的是 MNIST handwritten digit database, Yann LeCun, Corinna Cortes and Chris Burges，经验表明一般早上下载时网速好一些。
执行 mnist.py 文件时，会有如下提示信息：

Downloading train-images-idx3-ubyte.gz ... 
Done
Downloading train-labels-idx1-ubyte.gz ... 
Done
Downloading t10k-images-idx3-ubyte.gz ... 
Done
Downloading t10k-labels-idx1-ubyte.gz ... 
Done
Converting train-images-idx3-ubyte.gz to NumPy Array ...
Done
Converting train-labels-idx1-ubyte.gz to NumPy Array ...
Done
Converting t10k-images-idx3-ubyte.gz to NumPy Array ...
Done
Converting t10k-labels-idx1-ubyte.gz to NumPy Array ...
Done
Creating pickle file ...
Done!

运行 mnist.py 文件后，会在mnist.py 文件所在的文件夹下看到 MNIST 数据集所含的 'train-images-idx3-ubyte.gz'、'train-labels-idx1-ubyte.gz'、't10k-images-idx3-ubyte.gz'、't10k-labels-idx1-ubyte.gz' 等四个文件，以及生成的 mnist.pkl 文件。

若想查看 mnist.pkl 文件的内容，可运行如下代码：

import pickle
f=open('mnist.pkl','rb')
data=pickle.load(f)
print(data)

之后，可看到 mnist.pkl 文件的内容如下：

{'train_img': array([[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],...,[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0]], dtype=uint8), 'train_label': array([5, 0, 4, ..., 5, 6, 8], dtype=uint8), 'test_img': array([[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],...,[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0],[0, 0, 0, ..., 0, 0, 0]], dtype=uint8), 'test_label': array([7, 2, 1, ..., 4, 5, 6], dtype=uint8)}

二、将 neuralnet_mnist.py 文件及 sample_weight.pkl 文件复制到 mnist.py 文件所在的文件夹下。其中，neuralnet_mnist.py 文件的内容如下：

import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import pickle
from mnist import load_mnistdef sigmoid(x):return 1 / (1 + np.exp(-x))def softmax(x):if x.ndim == 2:x = x.Tx = x - np.max(x, axis=0)y = np.exp(x) / np.sum(np.exp(x), axis=0)return y.T x = x - np.max(x)return np.exp(x) / np.sum(np.exp(x))def get_data():(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, flatten=True, one_hot_label=False)return x_test, t_testdef init_network():with open("sample_weight.pkl", 'rb') as f:network = pickle.load(f)return networkdef predict(network, x):W1, W2, W3 = network['W1'], network['W2'], network['W3']b1, b2, b3 = network['b1'], network['b2'], network['b3']a1 = np.dot(x, W1) + b1z1 = sigmoid(a1)a2 = np.dot(z1, W2) + b2z2 = sigmoid(a2)a3 = np.dot(z2, W3) + b3y = softmax(a3)return yx, t = get_data()
network = init_network()
accuracy_cnt = 0
for i in range(len(x)):y = predict(network, x[i])p= np.argmax(y) # 获取概率最高的元素的索引if p == t[i]:accuracy_cnt += 1print("Accuracy:" + str(float(accuracy_cnt) / len(x)))

运行 neuralnet_mnist.py 文件后，会得到运行结果：Accuracy:0.9352，表示有93.52%的数据被正确分类了。
至此，一个识别精度达到93.52%的“手写数字识别”的神经网络就构建完成了。

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● 若想显示 MNIST 图像，同时也确认一下数据，则可用下面的 mnist_show.py 进行。下面的 mnist_show.py 代码执行后将显示第一张训练图像。

import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
from mnist import load_mnist
from PIL import Imagedef img_show(img):pil_img = Image.fromarray(np.uint8(img))pil_img.show()(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True, normalize=False)img = x_train[0]
label = t_train[0]
print(label)  # 5print(img.shape)  # (784,)
img = img.reshape(28, 28)  # 把图像的形状变为原来的尺寸
print(img.shape)  # (28, 28)img_show(img)

● 若想实现高速运算，则可引入“批处理”技巧。下面的 neuralnet_mnist_batch.py 给出了对 MNIST 数据集进行“批处理”的代码。

import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import pickle
from mnist import load_mnistdef sigmoid(x):return 1 / (1 + np.exp(-x))def softmax(x):if x.ndim == 2:x = x.Tx = x - np.max(x, axis=0)y = np.exp(x) / np.sum(np.exp(x), axis=0)return y.T x = x - np.max(x)return np.exp(x) / np.sum(np.exp(x))def get_data():(x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, flatten=True, one_hot_label=False)return x_test, t_testdef init_network():with open("sample_weight.pkl", 'rb') as f:network = pickle.load(f)return networkdef predict(network, x):w1, w2, w3 = network['W1'], network['W2'], network['W3']b1, b2, b3 = network['b1'], network['b2'], network['b3']a1 = np.dot(x, w1) + b1z1 = sigmoid(a1)a2 = np.dot(z1, w2) + b2z2 = sigmoid(a2)a3 = np.dot(z2, w3) + b3y = softmax(a3)return yx, t = get_data()
network = init_network()batch_size = 100 # 批数量
accuracy_cnt = 0for i in range(0, len(x), batch_size):x_batch = x[i:i+batch_size]y_batch = predict(network, x_batch)p = np.argmax(y_batch, axis=1)accuracy_cnt += np.sum(p == t[i:i+batch_size])print("Accuracy:" + str(float(accuracy_cnt) / len(x)))