{"id":3201,"date":"2025-08-19T09:04:53","date_gmt":"2025-08-19T01:04:53","guid":{"rendered":"https:\/\/www.leexinghai.com\/aic\/?p=3201"},"modified":"2025-08-19T09:10:56","modified_gmt":"2025-08-19T01:10:56","slug":"3-4%e4%ba%ba%e5%b7%a5%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e7%9a%84%e7%ac%ac%e4%b8%80%e6%ac%a1%e5%af%92%e5%86%ac","status":"publish","type":"post","link":"https:\/\/www.leexinghai.com\/aic\/3-4%e4%ba%ba%e5%b7%a5%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e7%9a%84%e7%ac%ac%e4%b8%80%e6%ac%a1%e5%af%92%e5%86%ac\/","title":{"rendered":"3.4\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u7684\u7b2c\u4e00\u6b21\u5bd2\u51ac"},"content":{"rendered":"\n<p>\u8bbey=+1\u8868\u793aX\u662f\u8fde\u901a\u56fe<\/p>\n\n\n\n<p>\u8bbey=-1\u8868\u793aX\u662f\u975e\u8fde\u901a\u56fe\u3002<\/p>\n\n\n\n<p>\u7528 \u53cd\u8bc1\u6cd5 \u8bc1\u660e \u8bc6\u522b\u8fde\u901a\u56fe\u95ee\u9898\u662f\u975e\u7ebf\u6027\u53ef\u5206\u7684\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\uff1a<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u95ee\u9898\u662f\u7ebf\u6027\u53ef\u5206\u7684\uff0c\u90a3\u4e48\u4e00\u5b9a\u5b58\u5728\uff08\u03c9\uff0cb\uff09\uff1a<\/p>\n\n\n\n<p>\u5f53y=+1\u65f6\uff0c\u03c9<sup>T<\/sup>x+b\u22650\uff1b<\/p>\n\n\n\n<p>\u5f53y=-1\u662f\uff0c\u03c9<sup>T<\/sup>x+b\uff1c0<\/p>\n\n\n\n<p>\u56fe1\u8fde\u901a\uff1ay=+1<\/p>\n\n\n\n<p>2\uff081\uff091+2+3+5+6+b\u22650<\/p>\n\n\n\n<p>5\uff082\uff091+2+3+4+7+b\u22650<\/p>\n\n\n\n<p>\u53e3-\uff083\uff091+2+3+4+5+b\uff1c0<\/p>\n\n\n\n<p>-\u53e3\uff084\uff091+2+3+6+7+b\uff1c0<\/p>\n\n\n\n<p>\u516c\u5f0f1+2\uff0c\u67092[1+2+3+b]+4+5+6+7\u22650<\/p>\n\n\n\n<p>\u516c\u5f0f3+4\uff0c\u67092[1+2+3+b]+4+5+6+7&lt;0<\/p>\n\n\n\n<p>\u90a3\u4e48\u4e24\u4e2a\u65b0\u516c\u5f0f\u76f8\u540c\uff0c\u4e0d\u53ef\u80fd\u540c\u65f6\uff1e0\uff0c\uff1c0.<\/p>\n\n\n\n<p>\u6240\u4ee5\u8bc6\u522b\u8fde\u901a\u56fe\u7684\u95ee\u9898\u662f\u975e\u7ebf\u6027\u53ef\u5206\u7684\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u601d\u8003\uff1a\u8bf7\u8bc1\u660e\u3010\u4e00\u7b14\u753b\u95ee\u9898\u3011\u662f\u3010\u975e\u7ebf\u6027\u53ef\u5206\u3011\u95ee\u9898\u3002\u5373\u533a\u5206\u4e24\u7c7b\u4e8c\u503c\u56fe\u50cf\uff0c\u4e00\u79cd\u53ef\u4ee5\u7528\u4e00\u7b14\u753b\u51fa\uff0c\u53e6\u4e00\u79cd\u4e0d\u80fd\u4e00\u7b14\u753b\u51fa\u3002\u8981\u8bc1\u660e\u8fd9\u4e2a\u95ee\u9898\u7684\u975e\u7ebf\u6027\u53ef\u5206\u95ee\u9898\u3002<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\">\u7ed3\u8bba<\/h2>\n\n\n\n<p>\u201c\u80fd\u5426\u4e00\u7b14\u753b\u5b8c\u201d\u7684\u5224\u5b9a <strong>\u4e0d\u662f\u7ebf\u6027\u53ef\u5206\u7684<\/strong>\u3002<br>\u4e0b\u9762\u7ed9\u51fa\u4e00\u79cd <strong>\u6784\u9020-\u53cd\u8bc1<\/strong>\uff1a\u628a\u7ecf\u5178\u7684 <strong>XOR\uff08\u5947\u5076\uff09\u95ee\u9898<\/strong> \u5d4c\u5165\u5230\u201c\u4e00\u7b14\u753b\u201d\u5224\u5b9a\u91cc\uff1b\u56e0\u4e3a XOR \u672c\u8eab\u5728\u4efb\u4f55\u539f\u59cb\u7279\u5f81\u7a7a\u95f4\u90fd\u4e0d\u53ef\u7ebf\u6027\u5206\u79bb\uff0c\u4e00\u65e6\u5b83\u662f\u201c\u4e00\u7b14\u753b\u201d\u95ee\u9898\u7684\u5b50\u95ee\u9898\uff0c\u5c31\u8bf4\u660e\u6574\u9898\u4e5f\u5fc5\u7136\u975e\u7ebf\u6027\u53ef\u5206\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1 \u9884\u5907\uff1a\u4e00\u7b14\u753b\u21d4\u9876\u70b9\u5947\u5076\u6027<\/h2>\n\n\n\n<p>\u5bf9\u65e0\u5411\u56fe G=(V,E) \u6765\u8bf4 <\/p>\n\n\n\n<p>G\u00a0\u53ef\u4e00\u7b14\u753b\u2005\u200a\u27fa\u2005\u200a\u2223{v\u2208V\u2223deg\u2061(v)\u00a0\u4e3a\u5947}\u2223\u2005\u200a=0\u00a0\u6216\u00a02.<\/p>\n\n\n\n<p>\u4e8e\u662f\u53ea\u8981\u6211\u4eec\u80fd\u6784\u9020\u4e00\u4e2a\u6781\u5c0f\u56fe\uff0c\u4f7f<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5076\u6570\u6761\u8fb9 \u21d2 \u5947\u70b9\u6570\u4e3a 0 \u6216 2 (\u9633\u6027)<\/strong><\/li>\n\n\n\n<li><strong>\u5947\u6570\u6761\u8fb9 \u21d2 \u5947\u70b9\u6570 > 2 (\u9634\u6027)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u5c31\u5f62\u6210\u4e86 \u201c\u8fb9\u6570\u5947\u5076\uff1d\u7c7b\u522b\u6807\u7b7e\u201d \u7684 <strong>\u5947\u5076\u5224\u5b9a<\/strong>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2 \u6784\u9020\u4e00\u4e2a 3 \u6761\u8fb9\u7684\u201c\u661f\u5f62\u201d\u5b50\u95ee\u9898<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>      A\n      |\n     x1\n      |\n      O \u2014\u2014 x2 \u2014\u2014 B\n      |\n     x3\n      |\n      C\n<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9876\u70b9\uff1a\u4e2d\u5fc3 O\u548c\u4e09\u4e2a\u7aef\u70b9 A,B,C\u3002<\/li>\n\n\n\n<li>\u53ef\u9009\u8fb9\uff08\u7279\u5f81\uff09 x<sub>1<\/sub>=OA,\u2005\u200ax<sub>2<\/sub>=OB,\u2005\u200ax<sub>3<\/sub>=OC \u2208{0,1}.<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u6570\u636e\u96c6 D<\/strong>\uff088 \u4e2a\u53ef\u80fd\u56fe\uff0c\u7528 (x1,x2,x3) \u8868\u793a\uff09<\/p>\n<\/blockquote>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u8fb9\u7684\u7ec4\u5408<\/th><th>\u5947\u70b9\u4e2a\u6570<\/th><th>\u662f\u5426\u4e00\u7b14\u753b<\/th><th>\u7c7b\u522b<\/th><\/tr><\/thead><tbody><tr><td>(0,0,0)<\/td><td>0<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(1,0,0)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(0,1,0)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(0,0,1)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(1,1,0)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(1,0,1)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td>(0,1,1)<\/td><td>2<\/td><td>\u2705<\/td><td>+1<\/td><\/tr><tr><td><strong>(1,1,1)<\/strong><\/td><td><strong>4<\/strong><\/td><td>\u274c<\/td><td>\u20131<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u89c2\u5bdf\u53ef\u77e5\uff1a <\/p>\n\n\n\n<p>\u7c7b\u522b\u2005\u200a=\u2005\u200a{<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>+1,\u82e5\u00a0x1+x2+x3\u00a0\u4e3a\u5076\u6570,<\/li>\n\n\n\n<li>\u22121,\u82e5\u00a0x1+x2+x3\u00a0\u4e3a\u5947\u6570<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u6b63\u662f\u4e09\u7ef4 <strong>\u5076\uff0f\u5947 (Parity)<\/strong> \u51fd\u6570\u2014\u2014\u5b83\u662f\u7ecf\u5178\u7684 <strong>XOR<\/strong> \u5728 3 \u7ef4\u7684\u63a8\u5e7f\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3 XOR \/ \u5947\u5076\u51fd\u6570\u4e3a\u4ec0\u4e48\u7ebf\u6027\u4e0d\u53ef\u5206\uff1f<\/h2>\n\n\n\n<p>\u7ed9\u51fa\u4e00\u79cd\u7b80\u6d01\u7684\u51e0\u4f55\u8bba\u8bc1\uff08Minsky &amp; Papert 1969 \u540c\u6b3e\uff09\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6b63\u6837\u672c\u96c6\u5408<br>P={(0,0,0),(1,1,0),(1,0,1),(0,1,1)} \u7684 <strong>\u51f8\u5305<\/strong><br>\u542b\u6709\u70b9 (1\/2,1\/2,1\/2)\u3002<\/li>\n\n\n\n<li>\u8d1f\u6837\u672c\u96c6\u5408<br>N={(1,0,0),(0,1,0),(0,0,1),(1,1,1)} \u7684\u51f8\u5305<br><strong>\u540c\u6837<\/strong> \u542b\u6709\u8be5\u70b9(1\/2,1\/2,1\/2)\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u82e5\u4e24\u7c7b\u80fd\u88ab\u4e00\u6761\u8d85\u5e73\u9762\u5206\u5f00\uff0c\u5219\u5176\u51f8\u5305\u5fc5\u987b\u4e92\u4e0d\u76f8\u4ea4\uff1b<br>\u4f46\u8fd9\u91cc\u4e24\u51f8\u5305 <strong>\u76f8\u4ea4<\/strong>\uff0c\u6545\u4e0d\u5b58\u5728\u4efb\u4f55\u7ebf\u6027\u5206\u5272\u9762\u3002<br>\u56e0\u6b64 Parity \/ XOR <strong>\u975e\u7ebf\u6027\u53ef\u5206<\/strong>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4 \u5f52\u7ed3\u5230\u4e00\u7b14\u753b\u95ee\u9898<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6211\u4eec\u5df2\u7ecf\u628a\u201c\u4e00\u7b14\u753b\u201d\u4e2d\u7684\u4e00\u4e2a\u5c0f\u5b50\u96c6 D\u6620\u5c04\u6210 <strong>Parity<\/strong>\uff1b<\/li>\n\n\n\n<li>\u82e5\u6574\u4f53\u95ee\u9898\u53ef\u88ab\u4e00\u4e2a\u8d85\u5e73\u9762\u5206\u5272\uff0c\u5219 D \u4e5f\u5fc5\u80fd\u88ab\u540c\u4e00\u8d85\u5e73\u9762\u5206\u5272\u2014\u2014\u4e0e\u4e0a\u4e00\u8282\u77db\u76fe\u3002<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u6240\u4ee5<\/strong>\uff1a\u533a\u5206\u201c\u4e00\u7b14\u753b\u56fe\u201d\u548c\u201c\u975e\u4e00\u7b14\u753b\u56fe\u201d\u7684\u6574\u4f53\u4e8c\u5206\u7c7b\u4efb\u52a1 <strong>\u4e0d\u5b58\u5728<\/strong> \u4efb\u4f55\u57fa\u4e8e\u539f\u59cb 0\/1 \u50cf\u7d20\uff08\u8fb9\u5b58\u5728\u4e0e\u5426\uff09\u7684\u7ebf\u6027\u5224\u522b\u51fd\u6570\uff1b\u5373\u5b83\u662f <strong>\u975e\u7ebf\u6027\u53ef\u5206\u95ee\u9898<\/strong>\u3002<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">5 \u7ed3\u8bba\u4e0e\u542f\u793a<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8bc1\u660e\u601d\u8def<\/strong>\uff1a\u628a\u5df2\u77e5\u7684 XOR \u96be\u9898\u5d4c\u5165\u76ee\u6807\u4efb\u52a1<br>\u2192 \u627e\u5230\u51f8\u5305\u76f8\u4ea4<br>\u2192 \u5426\u5b9a\u7ebf\u6027\u53ef\u5206\u6027\u3002<\/li>\n\n\n\n<li><strong>\u5de5\u7a0b\u610f\u4e49<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u60f3\u8981\u81ea\u52a8\u5224\u522b\u4e00\u7b14\u753b\u56fe\u7247\uff0c\u5fc5\u987b\u501f\u52a9 <strong>\u6838\u6280\u5de7 \/ \u6df1\u5ea6\u6a21\u578b \/ \u975e\u7ebf\u6027\u7279\u5f81<\/strong>\uff1b<\/li>\n\n\n\n<li>\u5355\u5c42\u611f\u77e5\u5668\u6216\u4efb\u4f55\u7eaf\u7ebf\u6027\u6a21\u578b\u90fd\u65e0\u6cd5\u5b8c\u6210\u8be5\u533a\u5206\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u8bbey=+1\u8868\u793aX\u662f\u8fde\u901a\u56fe \u8bbey=-1\u8868\u793aX\u662f\u975e\u8fde\u901a\u56fe\u3002 \u7528 \u53cd\u8bc1\u6cd5 \u8bc1\u660e \u8bc6\u522b\u8fde\u901a\u56fe\u95ee\u9898\u662f\u975e\u7ebf\u6027\u53ef\u5206\u7684\uff1a \u5047\u8bbe 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