{"id":133,"date":"2026-04-08T00:37:20","date_gmt":"2026-04-07T16:37:20","guid":{"rendered":"https:\/\/kktljr.top\/?p=133"},"modified":"2026-04-08T00:44:23","modified_gmt":"2026-04-07T16:44:23","slug":"%e3%80%8a%e9%b1%bc%e4%b9%a6%e3%80%8b%e7%ac%94%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/kktljr.top\/index.php\/2026\/04\/08\/%e3%80%8a%e9%b1%bc%e4%b9%a6%e3%80%8b%e7%ac%94%e8%ae%b0\/","title":{"rendered":"\u300a\u9c7c\u4e66\u300b\u7b14\u8bb0"},"content":{"rendered":"\n

\u300a\u9c7c\u4e66\u300b\u7b14\u8bb0<\/h1>\n\n\n\n

1. python\u57fa\u7840<\/h2>\n\n\n\n

1.1 Numpy<\/h3>\n\n\n\n

Np\u7684\u5e7f\u64ad:<\/p>\n\n\n\n


>>> x = np.array([1.0, 2.0, 3.0])
>>> x \/ 2.0
array([ 0.5,  1. ,  1.5])<\/pre>\n\n\n\n
\u591a\u7ef4\u6570\u7ec4:<\/p>\n\n\n\n

>>> A = np.array([[1, 2], [3, 4]])
>>> print(A)
[[1 2]
 [3 4]]
>>> A.shape  #\u591a\u7ef4\u6570\u7ec4\u6bcf\u9879\u957f\u5ea6\u4e00\u6837\u5426\u5219\u62a5\u9519
(2, 2)
>>> A.dtype  #\u77e9\u9635\u5143\u7d20\u7684\u6570\u636e\u7c7b\u578b
dtype('int64')
\u200b
>>> B = np.array([[3, 0],[0, 6]])
>>> A + B
array([[ 4,  2],
       [ 3, 10]])
>>> A * B       # *\u53f7\u4e3a\u76f4\u63a5\u6570\u7ec4\u5bf9\u5e94\u5143\u7d20\u4e58\u79ef
array([[ 3,  0],
       [ 0, 24]])<\/pre>\n\n\n\n
\u8bbf\u95ee\u64cd\u4f5c:<\/p>\n\n\n\n
>>> X = np.array([[51, 55], [14, 19], [0, 4]])
>>> X = X.flatten()     # \u5c06X\u8f6c\u6362\u4e3a\u4e00\u7ef4\u6570\u7ec4, \u5373\u62c9\u5e73
>>> print(X)
[51 55 14 19  0  4]
>>> X[np.array([0, 2, 4])] # \u83b7\u53d6\u7d22\u5f15\u4e3a0\u30012\u30014\u7684\u5143\u7d20
array([51, 14,  0])<\/pre>\n\n\n\n
\u77e9\u9635\u4e58\u79ef(\u70b9\u4e58):<\/p>\n\n\n\n
>>> A = np.array([[1,2], [3,4]])
>>> A.shape
(2, 2)
>>> B = np.array([[5,6], [7,8]])
>>> B.shape
(2, 2)
>>> np.dot(A, B)
array([[19, 22],
       [43, 50]])<\/pre>\n\n\n\n
1.2 Matplotlib<\/h3>\n\n\n\n
import numpy as np
import matplotlib.pyplot as plt
# \u751f\u6210\u6570\u636e
x = np.arange(0, 6, 0.1) # \u4ee50.1\u4e3a\u5355\u4f4d\uff0c\u751f\u62100\u52306\u7684\u6570\u636e
y = np.sin(x)
# \u7ed8\u56fe
plt.plot(x, y)
plt.show()<\/pre>\n\n\n\n
x = np.arange(0, 6, 0.1) # \u4ee50.1\u4e3a\u5355\u4f4d\uff0c\u751f\u62100\u52306\u7684\u6570\u636e
y1 = np.sin(x)
y2 = np.cos(x)
# \u7ed8\u5236\u56fe\u5f62
plt.plot(x, y1, label=\"sin\")
plt.plot(x, y2, linestyle = \"--\", label=\"cos\") # \u7528\u865a\u7ebf\u7ed8\u5236
plt.xlabel(\"x\") # x\u8f74\u6807\u7b7e
plt.ylabel(\"y\") # y\u8f74\u6807\u7b7e
plt.title('sin & cos') # \u6807\u9898
plt.legend()    #\u56fe\u4f8b\u663e\u793a, \u6536\u96c6plot()\u4e2d\u7684label
plt.show()<\/pre>\n\n\n\n
\u663e\u793a\u56fe\u50cf:<\/p>\n\n\n\n
import matplotlib.pyplot as plt
from matplotlib.image import imread
img = imread('lena.png') # \u8bfb\u5165\u56fe\u50cf\uff08\u8bbe\u5b9a\u5408\u9002\u7684\u8def\u5f84\uff01\uff09
plt.imshow(img)
plt.show()<\/pre>\n\n\n\n
2. \u611f\u77e5\u673a<\/h1>\n\n\n\n
2.1 \u4ec0\u4e48\u662f\u611f\u77e5\u673a<\/h3>\n\n\n\n
\u611f\u77e5\u673a\u7b97\u6cd5\u662f\u7f8e\u56fd\u5b66\u8005Frank Rosenblatt<\/strong>\u57281957\u5e74\u63d0\u51fa\u6765\u7684, \u662f\u795e\u7ecf\u7f51\u7edc\u7684\u8d77\u6e90\u7b97\u6cd5.<\/p>\n\n\n\n
\u611f\u77e5\u673a\u63a5\u6536\u591a\u4e2a\u8f93\u5165\u4fe1\u53f7, \u8f93\u51fa\u4e00\u4e2a\u4fe1\u53f7. \u5728\u611f\u77e5\u673a\u4e2d, \u8f93\u51fa\u4fe1\u53f7<\/strong><\/em><\/mark>\u53ea\u6709 0\/1 \u4e24\u79cd\u53d6\u503c. \u4e3a\u65b9\u4fbf\u7406\u89e3, 0\u5bf9\u5e94\"\u4e0d\u4f20\u9012\u4fe1\u53f7\", 1\u5bf9\u5e94\"\u4f20\u9012\u4fe1\u53f7\".<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u5176\u4e2dx1<\/sub>, x2<\/sub>\u4e3a\u8f93\u5165\u4fe1\u53f7, w1<\/sub>, w2<\/sub>\u4e3a\u6743\u91cd. \u56fe\u4e2d\u5706\u5708\u79f0\u4e3a\"\u795e\u7ecf\u5143\"\u6216\u8005\"\u8282\u70b9\". \u8f93\u5165\u4fe1\u53f7\u88ab\u9001\u5f80\u795e\u7ecf\u5143\u65f6, \u4f1a\u5206\u522b\u4e58\u4ee5\u56fa\u5b9a\u7684\u6743\u91cd. \u8fd9\u4e9b\u4fe1\u53f7\u7684\u603b\u548c\u8d85\u8fc7\u9608\u503c \u03b8<\/strong><\/em> \u65f6, \u624d\u4f1a\u8f93\u51fa1, \u79f0\u4e4b\u4e3a\"\u795e\u7ecf\u5143\u88ab\u6fc0\u6d3b\". \u5373:<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u4ee4\u03b8 = -b, \u5219\u6709<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u628ab\u6210\u4e3a\u504f\u7f6e<\/strong>, \u628aw1<\/sub>, w2<\/sub>\u79f0\u4e3a\u6743\u91cd<\/p>\n\n\n\n
w1<\/sub>, w2<\/sub>\u4e3a\u63a7\u5236\u8f93\u5165\u4fe1\u53f7\u91cd\u8981\u6027\u7684\u53c2\u6570, \u504f\u7f6e\u662f\u8c03\u6574\u795e\u7ecf\u5143\u88ab\u6fc0\u6d3b\u7684\u5bb9\u6613\u7a0b\u5ea6\u7684\u53c2\u6570.<\/p>\n\n\n\n
2.2 \u611f\u77e5\u673a\u7684\u5c40\u9650\u6027<\/h3>\n\n\n\n
\u7528\u4e0a\u6587\u4e2d\u7684\u611f\u77e5\u673a\u6a21\u578b\u65e0\u6cd5\u5b9e\u73b0\u5f02\u6216\u95e8, (w1<\/sub>, w2<\/sub> + b> 0, \u4e0ew1<\/sub> + w2<\/sub> + b< 0\u77db\u76fe)<\/p>\n\n\n\n
2.2.1 \u7ebf\u6027\u4e0e\u975e\u7ebf\u6027<\/h4>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
2.3 \u591a\u5c42\u611f\u77e5\u673a (\u5f02\u6216\u95e8\u5b9e\u73b0)<\/h3>\n\n\n\n
\u611f\u77e5\u673a\u7684\u53e0\u52a0, \u4f7f\u5f97\u611f\u77e5\u673a\u80fd\u591f\u5b9e\u73b0\u66f4\u591a\u7684\u529f\u80fd, \u5982\u4e0b\u56fe: <\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
3.\u795e\u7ecf\u7f51\u7edc<\/h2>\n\n\n\n
\u795e\u7ecf\u7f51\u7edc\u7684\u51fa\u7ebf, \u53ef\u4ee5\u81ea\u52a8\u5730\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u5230\u5408\u9002\u7684\u6743\u91cd\u53c2\u6570.<\/p>\n\n\n\n
3.1 \u795e\u7ecf\u7f51\u7edc\u7684\u7ed3\u6784<\/h3>\n\n\n\n
\u8f93\u5165\u5c42 ---- \u9690\u85cf\u5c42(\u4e2d\u95f4\u5c42) ---- \u8f93\u51fa\u5c42<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
3.2 \u6fc0\u6d3b\u51fd\u6570<\/h3>\n\n\n\n
\u6fc0\u6d3b\u51fd\u6570<\/strong><\/em>: \u5c06\u8f93\u5165\u4fe1\u53f7\u603b\u548c\u8f6c\u5316\u4e3a\u8f93\u51fa\u4fe1\u53f7\u7684\u51fd\u6570. \u5373\u4e0b\u56fe\u4e2dh(x):<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
3.2.1 \u9636\u8dc3\u51fd\u6570<\/h4>\n\n\n\n
\u524d\u6587\u4e2d\u7684\u6fc0\u6d3b\u51fd\u6570\u79f0\u4e3a\u9636\u8dc3\u51fd\u6570<\/strong>, \u4e00\u65e6\u8f93\u5165\u8d85\u8fc7\u9608\u503c, \u5c31\u5207\u6362\u8f93\u51fa.<\/p>\n\n\n\n
3.2.2 sigmoid\u51fd\u6570<\/h4>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\n
\u6fc0\u6d3b\u51fd\u6570\u5fc5\u987b\u4f7f\u7528\u975e\u7ebf\u6027\u51fd\u6570, \u56e0\u4e3a\u5982\u679c\u4f7f\u7528\u7ebf\u6027\u51fd\u6570\u7684\u8bdd, \u90a3\u4e48\u53e0\u52a0\u5c42\u5c31\u6ca1\u6709\u610f\u4e49\u4e86<\/p>\n<\/blockquote>\n\n\n\n
3.2.3 ReLU(Rectified Linear Unit)\u51fd\u6570<\/h4>\n\n\n\n
ReLU\u51fd\u6570, \u8f93\u5165\u5927\u4e8e0, \u76f4\u63a5\u8f93\u51fa\u8be5\u503c; \u8f93\u5165\u5c0f\u4e8e\u7b49\u4e8e0\u65f6, \u8f93\u51fa0.<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
3.3 3\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u5b9e\u73b0<\/h3>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u7b2c\u4e00\u5c42\u7684\u52a0\u6743\u548c\u53ef\u4ee5\u8868\u793a\u4e3a:<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u4e0a\u8ff0\u64cd\u4f5c\u8ba1\u7b97\u51fa\u4e86\u52a0\u6743\u4fe1\u53f7\u4e0e\u504f\u7f6e\u4e4b\u548c, \u7136\u540e\u8fd8\u8981\u901a\u8fc7\u4e4b\u524d\u5b66\u4e60\u7684\u6fc0\u6d3b\u51fd\u6570\u8f6c\u6362\u4e3a\u8f93\u51fa\u4fe1\u53f7.<\/p>\n\n\n\n
\u4ee3\u7801\u5b9e\u73b0\u5982\u4e0b<\/strong>:<\/p>\n\n\n\n
def step_function(x):
    return np.array(x > 0, dtype=int)
\u200b
def sigmoid(x):
    return 1 \/ (1 + np.exp(-x))
\u200b
def relu(x):
    return np.maximum(0, x)
\u200b
def identity_function(x):   #\u6052\u7b49\u51fd\u6570
    return x
\u200b
\u200b
def init_network():     #\u4e09\u5c42\u795e\u7ecf\u7f51\u7edc
        network = {}
        network['W1'] = np.array([[0.1,0.3,0.5], [0.2, 0.4, 0.6]])
        network['b1'] = np.array([0.1, 0.2, 0.3])
        network['W2'] = np.array([[0.1,0.4], [0.2, 0.5], [0.3, 0.6]])
        network['b2'] = np.array([0.1, 0.2])
        network['W3'] = np.array([[0.1,0.3], [0.2, 0.4]])
        network['b3'] = np.array([0.1, 0.2])
\u200b
        return network
\u200b
def forward(network, x):
    W1, W2, W3 = network['W1'], network['W2'], network['W3']
    b1, b2, b3 = network['b1'], network['b2'], network['b3']
\u200b
    a1 = np.dot(x, W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1, W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2, W3) + b3
    y = identity_function(a3)
    return y
\u200b
network = init_network()
x = np.array([1.0, 0.5])
y = forward(network, x)
print(y)<\/pre>\n\n\n\n
3.4 \u8f93\u51fa\u5c42\u8bbe\u8ba1<\/h3>\n\n\n\n
\u4e00\u822c\u6765\u8bf4, \u56de\u5f52\u95ee\u9898\u7528\u6052\u7b49\u51fd\u6570, \u5206\u7c7b\u95ee\u9898\u7528softmax\u51fd\u6570<\/p>\n\n\n\n
3.4.1 softmax\u51fd\u6570<\/h4>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\n
\u7531\u4e8e\u5728\u8ba1\u7b97\u673a\u4e2d, exp\u5bb9\u6613\u6ea2\u51fa, \u6240\u4ee5\u9700\u8981\u5bf9softmax\u51fd\u6570\u8fdb\u884c\u6539\u8fdb<\/p>\n<\/blockquote>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u53ef\u4ee5\u89c2\u5bdf\u5230, yk<\/sub>\u7684\u548c\u4e3a1, \u6211\u4eec\u53ef\u4ee5\u628asoftmax\u7684\u8f93\u51fa\u89e3\u91ca\u4e3a\u6982\u7387, \u6240\u4ee5\u4e00\u822c\u7528\u4e8e\u5206\u7c7b\u6a21\u578b\u4e2d, \u4e00\u822c\u800c\u8a00, \u795e\u7ecf\u7f51\u7edc\u53ea\u628a\u8f93\u51fa\u503c\u6700\u5927\u7684\u795e\u7ecf\u5143\u5bf9\u5e94\u7684\u7c7b\u522b\u4f5c\u4e3a\u8bc6\u522b\u7ed3\u679c. \u4e14exp\u4e3a\u9012\u589e\u51fd\u6570, \u6545\u5728\u8fdb\u884c\u63a8\u7406\u9636\u6bb5\u65f6, softmax\u51fd\u6570\u53ef\u4ee5\u7701\u7565.<\/p>\n\n\n\n
3.5 MNIST\u6570\u5b57\u8bc6\u522b<\/h3>\n\n\n\n
\u7565<\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
\u300a\u9c7c\u4e66\u300b\u7b14\u8bb0 1. python\u57fa\u7840 1.1 Numpy Np\u7684\u5e7f\u64ad: >>> x = np.array([1. …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-133","post","type-post","status-publish","format-standard","hentry","category-7"],"_links":{"self":[{"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/posts\/133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/comments?post=133"}],"version-history":[{"count":3,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/posts\/133\/revisions"}],"predecessor-version":[{"id":156,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/posts\/133\/revisions\/156"}],"wp:attachment":[{"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/media?parent=133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/categories?post=133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kktljr.top\/index.php\/wp-json\/wp\/v2\/tags?post=133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}