{"id":1809,"date":"2023-02-15T10:10:48","date_gmt":"2023-02-15T02:10:48","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=1809"},"modified":"2023-02-15T11:57:35","modified_gmt":"2023-02-15T03:57:35","slug":"bp-network","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/bp-network\/","title":{"rendered":"BP\u795e\u7ecf\u7f51\u7edc"},"content":{"rendered":"\n

\u4e3a\u4e86\u9274\u522b\u8bcd\u6027\uff0c\u9700\u8981\u4f7f\u7528\u795e\u7ecf\u5143\u7f51\u7edc\u5bf9\u7ed3\u679c\u8fdb\u884c\u9009\u62e9\u3002\u8fd9\u91cc\u4ecb\u7ecd\u4ee5\u4e0b\u6bd4\u8f83\u6700\u5178\u578b\u7684BP\u795e\u7ecf\u7f51\u7edc\u3002
\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8fd9\u662f\u4e00\u4e2a\u5178\u578b\u7684\u4e09\u5c42\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\uff0c\u7b2c\u4e00\u5c42\u662f\u8f93\u5165\u5c42\uff0c\u7b2c\u4e8c\u5c42\u662f\u9690\u85cf\u5c42\uff0c\u7b2c\u4e09\u5c42\u662f\u8f93\u51fa\u5c42\u3002<\/p>\n\n\n\n

\"\"
\u56fe3 \u5178\u578b\u7684\u4e09\u5c42\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784<\/figcaption><\/figure>\n\n\n\n

\u8bad\u7ec3\u6a21\u578b\u7684\u6b65\u9aa4\u662f\uff1a
\uff081\uff09\u6b63\u5411\u4f20\u64ad\uff1a\u628a\u70b9\u7684\u5750\u6807\u6570\u636e\u8f93\u5165\u795e\u7ecf\u7f51\u7edc\uff0c\u7136\u540e\u5f00\u59cb\u4e00\u5c42\u4e00\u5c42\u7684\u4f20\u64ad\u4e0b\u53bb\uff0c\u76f4\u5230\u8f93\u51fa\u5c42\u8f93\u51fa\u7ed3\u679c\u3002
\uff082\uff09\u53cd\u5411\u4f20\u64ad\uff1a\u59cb\u6839\u636e\u6570\u636e\u8bef\u5dee\u8c03\u6574\u5404\u4e2a\u90e8\u5206\u7684\u6743\u91cd\\(w_i\\)\u548c\u504f\u7f6e\\(b_j\\)\u3002
\uff083\uff09\u5f53\u5b8c\u6210\u4e86\u4e00\u6b21\u6b63\u53cd\u5411\u4f20\u64ad\uff0c\u4e5f\u5c31\u5b8c\u6210\u4e86\u4e00\u6b21\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u8fed\u4ee3\u3002\u53cd\u590d\u8fed\u4ee3\uff0c\u8bef\u5dee\u8d8a\u6765\u8d8a\u5c0f\uff0c\u51fd\u6570\u7684\u5224\u65ad\u4e5f\u5c31\u8d8a\u6765\u8d8a\u7cbe\u51c6\u3002<\/p>\n\n\n\n

1 \u51fd\u6570<\/h3>\n\n\n\n

\u5728\u8c08\u5230\u795e\u7ecf\u7f51\u7edc\u7684\u65f6\u5019\uff0c\u9700\u8981\u7528\u5230\u4e24\u4e2a\u51fd\u6570\uff1aSigmoid\u51fd\u6570\u53ca\u5176\u5bfc\u6570\u51fd\u6570\u3002<\/p>\n\n\n\n

\"\"
\u56fe4 Sigmoid\u51fd\u6570\u56fe\u50cf<\/figcaption><\/figure>\n\n\n\n

\\[y(x)=\\frac {1}{e^{-x} + 1}\\]<\/p>\n\n\n\n

\\[y^{\u2018}=\\frac {d}{dx}(\\frac {1}{e^{-x} + 1})=y(x)\\cdot [1-y(x)]\\]<\/p>\n\n\n\n

\"\"
\u56fe5 Sigmoid\u51fd\u6570\u7684\u5bfc\u6570\u51fd\u6570\u56fe\u50cf<\/figcaption><\/figure>\n\n\n\n

2 \u6b63\u5411\u4f20\u8f93<\/h3>\n\n\n\n

\u6b63\u5411\u4f20\u8f93\u7684\u6b65\u9aa4\u76f8\u5bf9\u6bd4\u8f83\u5bb9\u6613\u7406\u89e3\u548c\u5b9e\u73b0\uff1a<\/p>\n\n\n\n

\\[in_{h_j} = \\sum \\limits_{i=1}^N w_i \\cdot i_i + b_j\\]<\/p>\n\n\n\n

\\[out_{h_j} = y(in_{h_j})=\\frac {1}{e^{-in_{h_j}}+1}\\]<\/p>\n\n\n\n

\u5176\u4e2d\\(j\\)\u4e3a\u9690\u85cf\u5c42\u7684\u7f16\u53f7\uff0c\\(in_{h_j}\\)\u4e3a\u9690\u85cf\u5c42\u7684\u8f93\u5165\u6570\u636e\u3002\\(N\\)\u4e3a\u8f93\u5165\u7aef\u4e2a\u6570\u3002<\/p>\n\n\n\n

\\[in_{O_k} = \\sum \\limits_{i=1}^M w_i \\cdot out_{h_j} + b_k\\]<\/p>\n\n\n\n

\\[out_{O_k} = y(in_{O_k})=\\frac {1}{e^{-in_{O_k}}+1}\\]<\/p>\n\n\n\n

\u5176\u4e2d\\(k\\)\u4e3a\u8f93\u51fa\u5c42\u7684\u7f16\u53f7\uff0c\\(in_{O_k}\\)\u4e3a\u8f93\u51fa\u5c42\u7684\u8f93\u5165\u6570\u636e\u3002\\(M\\)\u4e3a\u8f93\u5165\u7aef\u4e2a\u6570\u3002<\/p>\n\n\n\n

3 \u8bef\u5dee\u8ba1\u7b97<\/h3>\n\n\n\n

\\[E=\\sum \\limits_{i=1}^L E_{O_i} \\\\ = \\frac {1}{2}{ (e_{O_1}-out_{O_1})}^2 + \\frac {1}{2}{ (e_{O_2}-out_{O_2})}^2 + …… \\]<\/p>\n\n\n\n

\u5176\u4e2d\\(E\\)\u4e3a\u603b\u8bef\u5dee\u91cf\uff0c\u65f6\u7528\u6765\u68c0\u6d4b\u603b\u4f53\u6536\u655b\u60c5\u51b5\u3002\\((e_{O_i}-out_{O_i})\\)\u662f\u8bef\u5dee\u5206\u9879\u3002\\(e_{O_i}\\)\u4e3a\u671f\u671b\u503c\u7684\u5206\u9879\uff0c\\(L\\)\u4e3a\u8f93\u51fa\u5c42\u4e2a\u6570\u3002<\/p>\n\n\n\n

4 \u53cd\u5411\u4f20\u64ad<\/h3>\n\n\n\n

\u53cd\u5411\u4f20\u64ad\u7684\u6b65\u9aa4\u76f8\u5bf9\u6bd4\u8f83\u6709\u96be\u5ea6\uff0c\u9700\u8981\u6709\u4e00\u5b9a\u7684\u9ad8\u6570\u57fa\u7840\u3002\u4e3b\u8981\u662f\u7528\u5230\u4e86\u5bfc\u6570\uff0c\u4ee5\u53ca\u94fe\u5f0f\u6cd5\u5219\u3002<\/p>\n\n\n\n

\"\"
\u56fe6 \u8ba1\u7b97\u8f93\u51fa\u5c42\u53cd\u5411\u4f20\u64ad<\/figcaption><\/figure>\n\n\n\n

\u4ee5\\(w_5\\)\u4e3a\u4f8b\uff1a<\/p>\n\n\n\n

\\[\\frac {\\partial E }{ \\partial w_5 } = \\frac {\\partial E }{ \\partial out_{O_1}} \\cdot \\frac {\\partial out_{O_1}}{\\partial in_{O_1}} \\cdot \\frac {\\partial in_{O_1}}{\\partial w_5} \\]<\/p>\n\n\n\n

\uff081\uff09\u56e0<\/p>\n\n\n\n

\\[E=\\sum \\limits_{i=1}^L E_{O_i} \\\\ = \\frac {1}{2}{ (e_{O_1}-out_{O_1})}^2 + \\frac {1}{2}{ (e_{O_2}-out_{O_2})}^2 + …… \\]<\/p>\n\n\n\n

\u6240\u4ee5<\/p>\n\n\n\n

\\[ \\frac {\\partial E}{\\partial out_{O_1}} = 2 \\cdot \\frac {1}{2} \\cdot (e_{O_1} – out_{O_1}) \\cdot (-1) = – (e_{O_1} – out_{O_1}) \\]<\/p>\n\n\n\n

\uff082\uff09\u56e0<\/p>\n\n\n\n

\\[out_{O_1} = y(in_{O_1})=\\frac {1}{e^{-in_{O_1}} + 1}\\]<\/p>\n\n\n\n

\u6240\u4ee5<\/p>\n\n\n\n

\\[ \\frac {\\partial out_{O_1}}{\\partial in_{O_1}} = y^{‘} (in_{O_1}) = y(in_{O_1})[1-y(in_{O_1})] = out_{O_1}(1-out_{O_1})\\]<\/p>\n\n\n\n

\uff083\uff09\u56e0<\/p>\n\n\n\n

\\[in_{O_k} = \\sum \\limits_{i=1}^M w_i \\cdot out_{h_j} + b_k\\]<\/p>\n\n\n\n

\u6240\u4ee5<\/p>\n\n\n\n

\\[\\frac {\\partial in_{O_1}}{\\partial w_5}=out_{h_1}\\]<\/p>\n\n\n\n

\uff084\uff09\u4e8e\u662f<\/p>\n\n\n\n

\\[\\frac {\\partial E}{\\partial w_5} = \\frac {\\partial E}{\\partial out_{O_1}} \\cdot \\frac {\\partial out_{O_1}}{\\partial in_{O_1}} \\cdot \\frac {\\partial in_{O_1}}{\\partial w_5} \\\\ = -(e_{O_1} – out_{O_1})\\cdot out_{O_1}(1-out_{O_1})\\cdot out_{h_1} = \\sigma_{O_1} \\cdot out_{h_1} \\]<\/p>\n\n\n\n

\u5176\u4e2d\\(\\sigma = -(e_{O_1}-out_{O_1})\\cdot out_{O_1}(1-out_{O_1})\\)\u3002<\/p>\n\n\n\n

\u5219\u5bf9\u4e8e\\(b_3\\)\u540c\u6837\u53ef\u4ee5\u63a8\u5bfc\u51fa\uff1a<\/p>\n\n\n\n

\\[\\frac {\\partial E}{\\partial b_3} = \\frac {\\partial E}{\\partial out_{O_1}} \\cdot \\frac {\\partial out_{O_1}}{\\partial in_{O_1}} \\cdot \\frac {\\partial in_{O_1}}{\\partial b_3} = \\sigma_{O_1}\\]<\/p>\n\n\n\n

\u8bbe\u795e\u7ecf\u7f51\u7edc\u7684\u5b66\u4e60\u7387\u4e3a\\(\\alpha\\)\uff0c\u66f4\u65b0\u8f93\u51fa\u5c42\u7684\u6743\u91cd\u548c\u504f\u7f6e\uff1a<\/p>\n\n\n\n

\\[{w_i}^{‘}= w_i – \\alpha \\cdot \\frac {\\partial E}{\\partial w_i}\\]<\/p>\n\n\n\n

\\[{b_j}^{‘}= b_j – \\alpha \\cdot \\frac {\\partial E}{\\partial w_j}\\]<\/p>\n\n\n\n

\u5176\u4e2d\\(i\\)\u4e3a\u8f93\u51fa\u5c42\u7684\u6743\u91cd\u7f16\u53f7\uff0c\\({w_i}^{‘}\\)\u4e3a\u66f4\u65b0\u540e\u7684\u6743\u91cd\uff1b\\(j\\)\u4e3a\u8f93\u51fa\u5c42\u7684\u504f\u7f6e\u7f16\u53f7\uff0c\\({b_j}^{‘}\\)\u4e3a\u66f4\u65b0\u540e\u7684\u504f\u7f6e\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u4ec5\u5b8c\u6210\u4e86\u4ece\u8f93\u51fa\u5230\u9690\u85cf\u5c42\u7684\u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\uff0c\u4e0b\u9762\u8981\u5b8c\u6210\u4ece\u9690\u85cf\u5c42\u5230\u8f93\u5165\u5c42\u7684\u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\u3002<\/p>\n\n\n\n

\"\"
\u56fe7 \u8ba1\u7b97\u8f93\u5165\u5c42\u53cd\u5411\u4f20\u64ad<\/figcaption><\/figure>\n\n\n\n

\u4ee5\\(w_1\\)\u4e3a\u4f8b\uff1a<\/p>\n\n\n\n

\\[\\frac {\\partial E}{\\partial w_1} = \\frac {\\partial E}{\\partial out_{h_1}} \\cdot \\frac {\\partial out_{h_1}}{\\partial in_{h_1}} \\cdot \\frac {\\partial in_{h_1}}{\\partial w_1} \\\\ = (\\frac {\\partial E_{O_1}}{\\partial out_{h_1}}+\\frac {\\partial E_{O_2}}{\\partial out_{h_1}})\\cdot \\frac {\\partial out_{h_1}}{\\partial in_{h_1}} \\cdot \\frac {\\partial in_{h_1}}{\\partial w_1}\\]<\/p>\n\n\n\n

\uff081\uff09\u53ef\u4ee5\u5148\u8ba1\u7b97<\/p>\n\n\n\n

\\[\\frac {\\partial E_{O_1}}{\\partial out_{h_1}} = \\frac {\\partial E_{O_1}}{\\partial in_{O_1}} \\cdot \\frac {\\partial in_{O_1}}{\\partial out_{h_1}} \\\\ = (\\frac{\\partial E_{O_1}}{\\partial out_{O_1}} \\cdot \\frac{\\partial out_{O_1}}{\\partial in_{O_1}})\\cdot \\frac {\\partial in_{O_1}}{\\partial out_{h_1}} \\\\ = -(e_{O_1} – out_{O_1}) \\cdot (1-out_{O_1})\\cdot w_5 = \\sigma_{O_1} \\cdot w_5\\]<\/p>\n\n\n\n

\u540c\u7406\u53ef\u5f97<\/p>\n\n\n\n

\\[\\frac {\\partial E_{O_2}}{\\partial out_{h_1}}= \\sigma_{O_2} \\cdot w_7\\]<\/p>\n\n\n\n

\uff082\uff09\\(\\frac {\\partial out_{h_1}}{\\partial in_{h_1}}=out_{h_1}(1-out_{h_1})\\)<\/p>\n\n\n\n

\uff083\uff09\\(\\frac {\\partial in_{h_1}}{\\partial w_1} = \\frac {\\partial}{\\partial w_1}(\\sum \\limits_{i=1}^N w_i \\cdot i_i + b_j)=i_1\\)<\/p>\n\n\n\n

\u6240\u4ee5<\/p>\n\n\n\n

\\[\\frac {\\partial E}{\\partial w_i} = \\sum \\limits_{i=1}^N \\frac {\\partial E_{O_i}}{\\partial out_{h_i}} \\cdot \\frac {\\partial out_{h_1}}{\\partial in_{h_1}} \\cdot \\frac {\\partial in_{h_1}}{\\partial w_1} \\\\ = (\\sum \\sigma_O w_O) \\cdot out_{h_i} (1-out_{h_i})\\cdot i_i \\]<\/p>\n\n\n\n

\u4ee4\\(\\sigma_{h_i} = (\\sum \\sigma_O w_O) \\cdot out_{h_i} (1-out_{h_i})\\)\uff0c\u5219\\(\\frac {\\partial E}{\\partial w_i} = \\sigma_{h_1}\\cdot i_i\\)\u3002<\/p>\n\n\n\n

\u53ef\u4ee5\u63a8\u5bfc\u5f97\uff1a\\(\\frac {\\partial E}{\\partial b_i}=\\sigma_{h_1}\\)\u3002\u8bfb\u8005\u6bd4\u8f83\u4e24\u5c42\u7684\u53cd\u5411\u4f20\u64ad\u516c\u5f0f\uff0c\u5c31\u53ef\u4ee5\u770b\u51fa\u4e00\u4e9b\u76f8\u4f3c\u6027\u3002<\/p>\n\n\n\n

\u8fd9\u4e00\u6bb5\u7b26\u53f7\u6bd4\u8f83\u591a\uff0c\u6709\u70b9\u773c\u82b1\u7f2d\u4e71\u3002\u8bfb\u8005\u53ef\u4ee5\u8bd5\u7740\u8fd9\u6837\u7406\u89e3\uff1a
\uff081\uff09\u628a\u6574\u4e2a\u795e\u7ecf\u7f51\u7edc\u53cd\u5411\u8fd0\u884c\uff0c\u8f93\u5165\u770b\u4f5c\u8f93\u51fa\uff0c\u8f93\u51fa\u770b\u4f5c\u8f93\u5165\u3002
\uff082\uff09\u5728\u53cd\u5411\u8fd0\u884c\u72b6\u6001\u4e0b\uff0c\u8bef\u5dee\\(\\sigma\\)\u5c31\u662f\u8f93\u5165\u7aef\u7684\u539f\u59cb\u6570\u503c\u3002<\/p>\n\n\n\n

\u8f93\u5165\u8bef\u5dee\u7684\u516c\u5f0f\u4e3a\uff1a\\(\\sigma_{O_i}=-(e_{O_i}-out_{O_i})\\cdot out_{O_i}(1-out_{O_i})\\)\u3002\u8fd9\u91cc\u4e0d\u7528\u6267\u7740\u4e8e\u4e0b\u6807\uff0c\u6bcf\u4e2a\u539f\u795e\u7ecf\u7f51\u7edc\u7684\u8f93\u51fa\u7aef\u4ec5\u80fd\u5bf9\u5e94\u4e00\u4e2a\u8bef\u5dee\u3002\u8fd9\u4e2a\u662f\u201c\u4e00\u4e00\u5bf9\u5e94\u201d\u7684\u5173\u7cfb\uff0c\u4e0d\u4f1a\u51fa\u9519\u3002
\u6b64\u65f6\u53ef\u4ee5\u6839\u636e\u516c\u5f0f\uff08\u542b\u5b66\u4e60\u7387\uff09\u53ef\u4ee5\u66f4\u65b0\u6743\u91cd\u548c\u504f\u7f6e\u3002\u6743\u91cd\u7684\u66f4\u65b0\uff0c\u4e0e\u6743\u91cd\u6240\u5728\u7684\u8fde\u63a5\u6709\u5173\u3002\u5c06\u8bef\u5dee\\(\\sigma\\)\u4e0e\u6743\u91cd\u6240\u8fde\u63a5\u7684\u53e6\u5916\u4e00\u7aef\u8f93\u5165\u503c\u76f8\u4e58\u5373\u53ef\u3002\u504f\u7f6e\u4ec5\u4e0e\u8bef\u5dee\\(\\sigma\\)\u76f8\u5173\u3002<\/p>\n\n\n\n

\uff083\uff09\u5728\u53cd\u5411\u8fd0\u884c\u72b6\u6001\u4e0b\uff0c\u5c06\u8bef\u5dee\u4f20\u9012\u81f3\u9690\u85cf\u5c42\u3002
\u6b64\u65f6\uff0c\u5e94\u4ee5\u5404\u4e2a\u539f\u8f93\u51fa\u8282\u70b9\u7684\u8bef\u5dee\u4f5c\u4e3a\u8f93\u5165\uff0c\u5373\uff1a\u8bef\u5dee\\(\\sigma\\)\u4f5c\u4e3a\u9690\u85cf\u5c42\u7684\u8f93\u5165\u3002\u5404\u4e2a\u8bef\u5dee\u52a0\u6743\u6c42\u548c\u540e\uff0c\u4e58\u4e0a\u9690\u85cf\u5c42\u8282\u70b9\u7684\u5bfc\u6570\u6570\u503c\uff0c\u53ef\u4ee5\u6784\u6210\u65b0\u7684\u8bef\u5dee\u3002\u6b64\u65b0\u6784\u6210\u7684\u8bef\u5dee\u4e0e\u539f\u8f93\u5165\u8282\u70b9\u76f8\u4e58\uff0c\u5373\u53ef\u5f97\u5230\u4fee\u6b63\u5404\u6743\u91cd\u7684\u6570\u503c\u3002<\/p>\n\n\n\n

\\(w_2\\)\u4e24\u7aef\u8fde\u63a5\u7740\\(i_2\\)\u548c\\(h_1\\)\u3002\u6240\u4ee5\\(w_2\\)\u00a0\u7684\u8bef\u5dee\u8f93\u5165\u5c31\u4e0e\\(w_5\\)\u548c\\(w_7\\)\u76f8\u5173\u3002\u5f04\u6e05\u695a\u76f8\u5173\u5173\u7cfb\u540e\uff0c\u5c31\u53ef\u4ee5\u6309\u7167\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97\u3002<\/p>\n\n\n\n

\\(b_2\\)\u8fde\u7740\\(h_2\\)\uff0c\u8282\u70b9\\(h_2\\)\u53c8\u901a\u8fc7\\(w_6\\)\u548c\\(w_8\\)\u8fde\u63a5\u7740\u8f93\u51fa\u7aef\u3002\u8fd9\u6837\u5c31\u7406\u987a\u4e86\u8bef\u5dee\u4f20\u64ad\u7684\u9014\u5f84\u5173\u7cfb\uff0c\u7136\u540e\u6309\u7167\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97\u5373\u53ef\u3002<\/p>\n\n\n\n

\u5982\u679c\u8bfb\u8005\u8fd8\u6709\u7591\u95ee\uff0c\u53ef\u4ee5\u53c2\u8003\u66f4\u8be6\u7ec6\u7684\u6587\u7ae0\u300aBP\u795e\u7ecf\u7f51\u7edc\u7b97\u6cd5\u63a8\u5bfc\u53ca\u4ee3\u7801\u5b9e\u73b0\u7b14\u8bb0<\/a>\u300b\u3002<\/p>\n\n\n\n

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\nusing System;\nusing System.Diagnostics;\n\nnamespace NLP\n{\n    public class BPNetwork\n    {\n        \/\/ \u5b66\u4e60\u7387\n        public double LearningRate { get; set; } = 0.618f;\n\n        \/\/ \u8f93\u5165\u5c42\n        private int InputCount;\n#if _USE_CLR\n        private double[] Inputs;\n#elif _USE_CONSOLE\n        private double[]? Inputs;\n#endif\n        \/\/ \u9690\u85cf\u5c42\n        private int HiddenCount;\n#if _USE_CLR\n        private double[] Hiddens;\n#elif _USE_CONSOLE\n        private double[]? Hiddens;\n#endif\n        \/\/ \u8f93\u51fa\u5c42\n        private int OutputCount;\n#if _USE_CLR\n        private double[] Outputs;\n#elif _USE_CONSOLE\n        private double[]? Outputs;\n#endif\n\n        \/\/ \u8bef\u5dee\n#if _USE_CLR\n        private double[] Errors;\n#elif _USE_CONSOLE\n        private double[]? Errors;\n#endif\n        \/\/ \u504f\u7f6e\n#if _USE_CLR\n        private double[] InputBiases;\n        private double[] OutputBiases;\n#elif _USE_CONSOLE\n        private double[]? InputBiases;\n        private double[]? OutputBiases;\n#endif\n        \/\/ \u8bef\u5dee\n        \/\/ \u53cd\u5411\u4f20\u64ad\u8ba1\u7b97\n#if _USE_CLR\n        private double[] Deltas;\n#elif _USE_CONSOLE\n        private double[]? Deltas;\n#endif\n\n        \/\/ \u8f93\u5165\u5c42\u6743\u91cd\n#if _USE_CLR\n        private double[][] InputWeights;\n#elif _USE_CONSOLE\n        private double[][]? InputWeights;\n#endif\n        \/\/ \u8f93\u51fa\u5c42\u6743\u91cd\n#if _USE_CLR\n        private double[][] OutputWeights;\n#elif _USE_CONSOLE\n        private double[][]? OutputWeights;\n#endif\n\n        public BPNetwork()\n        {\n\n        }\n\n        public int GetInputCount()\n        {\n            return InputCount;\n        }\n\n        public int GetOutputCount()\n        {\n            return OutputCount;\n        }\n\n        public int GetHiddenCount()\n        {\n            return HiddenCount;\n        }\n\n        static double Sigmoid(double x)\n        {\n            \/\/ \u8fd4\u56de\u7ed3\u679c\n            return 1.0f \/ (1.0f + Math.Pow(Math.E, -x));\n        }\n\n        static double DeltaSigmoid(double x)\n        {\n            double value = Sigmoid(x);\n            \/\/ \u8fd4\u56de\u7ed3\u679c\n            return value * (1.0f - value);\n        }\n\n        public void Initialize(int InputCount, int OutputCount, int HiddenCount)\n        {\n#if DEBUG\n            Debug.Assert(InputCount > 1);\n            Debug.Assert(OutputCount > 0);\n            Debug.Assert(HiddenCount > 1);\n#endif\n            \/\/ \u8bbe\u7f6e\u8f93\u5165\u5c42\n            this.InputCount = InputCount;\n            \/\/ \u8bbe\u7f6e\u8f93\u51fa\u5c42\n            this.OutputCount = OutputCount;\n            \/\/ \u8bbe\u7f6e\u9690\u85cf\u5c42\n            this.HiddenCount = HiddenCount;\n\n            \/\/ \u521b\u5efa\u8f93\u5165\u6570\u636e\n            Inputs = new double[InputCount];\n            \/\/ \u521b\u5efa\u8f93\u51fa\u6570\u636e\n            Outputs = new double[OutputCount];\n            \/\/ \u521b\u5efa\u9690\u85cf\u5c42\u6570\u636e\n            Hiddens = new double[HiddenCount];\n\n            \/\/ \u521b\u5efa\u8bef\u5dee\u6570\u636e\n            Errors = new double[OutputCount];\n            \/\/ \u521b\u5efa\u8bef\u5dee\u6570\u636e\n            Deltas = new double[OutputCount];\n\n            \/\/ \u521b\u5efa\u504f\u7f6e\u6570\u636e\n            InputBiases = new double[HiddenCount];\n            \/\/ \u521b\u5efa\u8f93\u5165\u5c42\u6743\u91cd\n            InputWeights = new double[HiddenCount][];\n            for (int i = 0; i < HiddenCount; i++)\n            {\n                InputWeights[i] = new double[InputCount];\n            }\n\n            \/\/ \u521b\u5efa\u504f\u7f6e\u6570\u636e\n            OutputBiases = new double[OutputCount];\n            \/\/ \u521b\u5efa\u8f93\u51fa\u5c42\u6743\u91cd\n            OutputWeights = new double[OutputCount][];\n            for (int i = 0; i < OutputCount; i++)\n            {\n                OutputWeights[i] = new double[HiddenCount];\n            }\n\n            \/\/ \u7ed9\u5b9a\u4e00\u4e2a\u521d\u59cb\u503c\n            Random random = new Random((int)DateTime.Now.Ticks);\n            \/\/ \u968f\u673a\u7ed9\u5b9a\u6570\u503c\n            for (int i = 0; i < InputCount; i++)\n                Inputs[i] = random.NextDouble();\n            for (int i = 0; i < OutputCount; i++)\n                Outputs[i] = random.NextDouble();\n            for (int i = 0; i < HiddenCount; i++)\n                for (int j = 0; j < InputCount; j++)\n                    InputWeights[i][j] = random.NextDouble();\n            for (int i = 0; i < OutputCount; i++)\n                for (int j = 0; j < HiddenCount; j++)\n                    OutputWeights[i][j] = random.NextDouble();\n        }\n\n        public double[] GetOutputs()\n        {\n#if DEBUG\n            Debug.Assert(Outputs != null);\n#endif\n            return Outputs;\n        }\n\n        public void SetInputs(double[] Inputs)\n        {\n#if DEBUG\n            Debug.Assert(this.Inputs != null);\n            Debug.Assert(Inputs != null &&\n                Inputs.Length == this.InputCount);\n#endif\n            \/\/ \u62f7\u8d1d\u6570\u636e\n            Inputs.CopyTo(this.Inputs, 0);\n        }\n\n        public double GetError()\n        {\n#if DEBUG\n            Debug.Assert(Errors != null);\n#endif\n            \/\/ \u6570\u503c\n            double value = 0.0;\n            \/\/ \u5faa\u73af\u5904\u7406\n            for (int i = 0; i < OutputCount; i++)\n            {\n                \/\/ \u8bef\u5dee\u6c42\u548c\n                value += 0.5 * Errors[i] * Errors[i];\n            }\n            \/\/ \u8fd4\u56de\u7ed3\u679c\n            return value;\n        }\n\n        public void SetOutputs(double[] expects)\n        {\n#if DEBUG\n            Debug.Assert(Errors != null);\n            Debug.Assert(Outputs != null);\n            Debug.Assert(expects != null &&\n                expects.Length == this.OutputCount);\n#endif\n            \/\/ \u5faa\u73af\u5904\u7406\n            for (int i = 0; i < OutputCount; i++)\n            {\n                \/\/ \u8ba1\u7b97\u8bef\u5dee\n                Errors[i] = expects[i] - Outputs[i];\n            }\n        }\n\n        public void Forward()\n        {\n#if DEBUG\n            Debug.Assert(Inputs != null);\n            Debug.Assert(Outputs != null);\n            Debug.Assert(Hiddens != null);\n            Debug.Assert(InputBiases != null);\n            Debug.Assert(InputWeights != null);\n            Debug.Assert(OutputBiases != null);\n            Debug.Assert(OutputWeights != null);\n#endif\n            \/\/ \u8ba1\u7b97\u9690\u85cf\u5c42\u6570\u636e\n            for (int i = 0;i < HiddenCount;i ++)\n            {\n                \/\/ \u6570\u503c\n                double value = 0.0;\n                \/\/ \u5faa\u73af\u5904\u7406\n                for(int j = 0;j < InputCount;j ++)\n                {\n                    value += InputWeights[i][j] * Inputs[j];\n                }\n                \/\/ \u8bbe\u7f6e\u8f93\u51fa\u503c\n                Hiddens[i] = Sigmoid(value + InputBiases[i]);\n            }\n\n            \/\/ \u8ba1\u7b97\u8f93\u51fa\u5c42\u6570\u636e\n            for(int i = 0;i < OutputCount;i ++)\n            {\n                \/\/ \u6570\u503c\n                double value = 0.0;\n                \/\/ \u5faa\u73af\u5904\u7406\n                for (int j = 0; j < HiddenCount; j++)\n                {\n                    value += OutputWeights[i][j] * Hiddens[j];\n                }\n                \/\/ \u8bbe\u7f6e\u8f93\u51fa\u503c\n                Outputs[i] = Sigmoid(value + OutputBiases[i]);\n            }\n        }\n\n        public void Backword()\n        {\n#if DEBUG\n            Debug.Assert(Errors != null);\n            Debug.Assert(Deltas != null);\n            Debug.Assert(Inputs != null);\n            Debug.Assert(Outputs != null);\n            Debug.Assert(Hiddens != null);\n            Debug.Assert(InputBiases != null);\n            Debug.Assert(InputWeights != null);\n            Debug.Assert(OutputBiases != null);\n            Debug.Assert(OutputWeights != null);\n#endif\n            \/\/ \u8ba1\u7b97\u9690\u5c42\n            for (int i = 0;i < OutputCount;i ++)\n            {\n                \/\/ \u94fe\u5f0f\u53cd\u5e94\n                double delta = - Errors[i];\n                \/\/ \u94fe\u5f0f\u53cd\u5e94\n                delta *= DeltaSigmoid(Outputs[i]);\n                \/\/ \u8bbe\u7f6e\u8bef\u5dee\n                Deltas[i] = delta;\n                \/\/ \u8bbe\u7f6e\u65b0\u7684\u504f\u7f6e\n                \/\/ \u4e0e\u5b66\u4e60\u7387\u6709\u5173\n                OutputBiases[i] -= LearningRate * delta;\n                \/\/ \u5faa\u73af\u5904\u7406\n                for (int j = 0;j < HiddenCount;j ++)\n                {\n                    \/\/ \u8bbe\u7f6e\u65b0\u7684\u6743\u91cd\n                    \/\/ \u4e0e\u5b66\u4e60\u7387\u6709\u5173\n                    OutputWeights[i][j] -= LearningRate * delta * Hiddens[j];\n                }\n            }\n\n            \/\/ \u8ba1\u7b97\u8f93\u5165\u5c42\n            for(int i = 0;i < HiddenCount;i ++)\n            {\n                \/\/ \u94fe\u5f0f\u53cd\u5e94\n                double delta = 0.0f;\n                \/\/ \u5faa\u73af\u5904\u7406\n                for (int j = 0;j < OutputCount;j ++)\n                {\n                    \/\/ \u94fe\u5f0f\u53cd\u5e94\n                    delta += OutputWeights[j][i] * Deltas[j]; \n                }\n                \/\/ \u94fe\u5f0f\u53cd\u5e94\n                delta *= DeltaSigmoid(Hiddens[i]);\n                \/\/ \u4e0e\u5b66\u4e60\u7387\u6709\u5173\n                \/\/ \u8bbe\u7f6e\u65b0\u7684\u504f\u7f6e\n                InputBiases[i] -= LearningRate * delta;\n                \/\/ \u5faa\u73af\u5904\u7406\n                for(int j = 0;j < InputCount; j ++)\n                {\n                    \/\/ \u8bbe\u7f6e\u65b0\u7684\u6743\u91cd\n                    \/\/ \u4e0e\u5b66\u4e60\u7387\u6709\u5173\n                    InputWeights[i][j] -= LearningRate * delta * Inputs[j];\n                }\n            }\n        }\n\n        public bool ImportFile(string fileName)\n        {\n#if DEBUG\n            Debug.Assert(!string.IsNullOrEmpty(fileName));\n#endif\n            \/\/ \u8bb0\u5f55\u65e5\u5fd7\n            LogTool.LogMessage("BPNetwork", "ImportFile", "\u5f00\u59cb\u8f93\u5165\u6570\u636e\uff01");\n\n            try\n            {\n                \/\/ \u521b\u5efa\u6587\u4ef6\u6d41\n                FileStream fs = new FileStream(fileName, FileMode.Open);\n                \/\/ \u521b\u5efa\u8f93\u51fa\u6d41\n                BinaryReader br = new BinaryReader(fs);\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ImportFile", "\u6587\u4ef6\u6d41\u5df2\u5f00\u542f\uff01");\n\n                \/\/ \u8bfb\u53d6\u6807\u8bc6\u7b26\n                string version = br.ReadString();\n                \/\/ \u68c0\u67e5\u7ed3\u679c\n                if(string.IsNullOrEmpty(version) || !version.Equals("BPNetwork"))\n                {\n                    \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                    LogTool.LogMessage("BPNetwork", "ImportFile", "\u65e0\u6cd5\u8bc6\u522b\u7684\u6587\u4ef6\uff01");\n                    return false;\n                }\n\n                \/\/ \u8bfb\u53d6InputCount;\n                InputCount = br.ReadInt32();\n                \/\/ \u8bfb\u53d6OutputCount;\n                OutputCount = br.ReadInt32();\n                \/\/ \u8bfb\u53d6HiddenCount;\n                HiddenCount = br.ReadInt32();\n                \/\/ \u8bfb\u53d6LearningRate;\n                LearningRate = br.ReadDouble();\n\n                \/\/ \u521d\u59cb\u5316\n                Initialize(InputCount, OutputCount, HiddenCount);\n#if DEBUG\n                Debug.Assert(Errors != null);\n                Debug.Assert(Deltas != null);\n                Debug.Assert(Inputs != null);\n                Debug.Assert(Outputs != null);\n                Debug.Assert(Hiddens != null);\n                Debug.Assert(InputBiases != null);\n                Debug.Assert(InputWeights != null);\n                Debug.Assert(OutputBiases != null);\n                Debug.Assert(OutputWeights != null);\n#endif\n\n                \/\/ \u8f93\u5165\u6570\u636e\n                for (int i = 0; i < InputCount; i++)\n                {\n                    InputBiases[i] = br.ReadDouble();\n                }\n                \/\/ \u8f93\u5165\u6570\u636e\n                for (int i = 0; i < HiddenCount; i++)\n                    for (int j = 0; j < InputCount; j++)\n                {\n                    InputWeights[i][j] = br.ReadDouble();\n                }\n                \/\/ \u8f93\u5165\u6570\u636e\n                for (int i = 0; i < OutputCount; i++)\n                {\n                    OutputBiases[i] = br.ReadDouble();\n                }\n                \/\/ \u8f93\u5165\u6570\u636e\n                for (int i = 0; i < OutputCount; i++)\n                    for (int j = 0; j < HiddenCount; j++)\n                {\n                    OutputWeights[i][j] = br.ReadDouble();\n                }\n                \/\/ \u5173\u95ed\u6587\u4ef6\u6d41\n                fs.Close();\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ImportFile", "\u6587\u4ef6\u6d41\u5df2\u5173\u95ed\uff01");\n            }\n            catch (System.Exception ex)\n            {\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ImportFile", "unexpected exit !");\n                LogTool.LogMessage(string.Format("\\texception.message = {0}", ex.Message));\n                \/\/ \u8fd4\u56de\u7ed3\u679c\n                return false;\n            }\n            \/\/ \u8bb0\u5f55\u65e5\u5fd7\n            LogTool.LogMessage("BPNetwork", "ImportFile", "\u6570\u636e\u8f93\u51fa\u5b8c\u6bd5\uff01");\n            \/\/ \u8fd4\u56de\u7ed3\u679c\n            return true;\n        }\n\n        public void ExportFile(string fileName)\n        {\n#if DEBUG\n            Debug.Assert(!string.IsNullOrEmpty(fileName));\n#endif\n            \/\/ \u8bb0\u5f55\u65e5\u5fd7\n            LogTool.LogMessage("BPNetwork", "ExportFile", "\u5f00\u59cb\u8f93\u51fa\u6570\u636e\uff01");\n\n            try\n            {\n                \/\/ \u4fdd\u5b58\u81f3\u672c\u5730\u78c1\u76d8\n                \/\/ \u521b\u5efa\u6587\u4ef6\u6d41\n                FileStream fs = new FileStream(fileName, FileMode.Create);\n                \/\/ \u521b\u5efa\u8f93\u51fa\u6d41\n                BinaryWriter bw = new BinaryWriter(fs);\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ExportFile", "\u6587\u4ef6\u6d41\u5df2\u5f00\u542f\uff01");\n\n                \/\/ \u8f93\u51fa\u6570\u636e\n                bw.Write("BPNetwork");\n                bw.Write(InputCount);\n                bw.Write(OutputCount);\n                bw.Write(HiddenCount);\n                bw.Write(LearningRate);\n#if DEBUG\n                Debug.Assert(Errors != null);\n                Debug.Assert(Deltas != null);\n                Debug.Assert(Inputs != null);\n                Debug.Assert(Outputs != null);\n                Debug.Assert(Hiddens != null);\n                Debug.Assert(InputBiases != null);\n                Debug.Assert(InputWeights != null);\n                Debug.Assert(OutputBiases != null);\n                Debug.Assert(OutputWeights != null);\n#endif\n                \/\/ \u8f93\u51fa\u6570\u636e\n                for (int i = 0; i < InputCount; i++) bw.Write(InputBiases[i]);\n                for (int i = 0; i < HiddenCount; i++)\n                    for (int j = 0; j < InputCount; j++) bw.Write(InputWeights[i][j]);\n                \/\/ \u8f93\u51fa\u6570\u636e\n                for (int i = 0; i < OutputCount; i++) bw.Write(OutputBiases[i]);\n                for (int i = 0; i < OutputCount; i++)\n                    for (int j = 0; j < HiddenCount; j++) bw.Write(OutputWeights[i][j]);\n                \/\/ \u5237\u65b0\u6253\u5370\u6d41\n                bw.Flush();\n                \/\/ \u5173\u95ed\u6253\u5370\u6d41\n                bw.Close();\n                \/\/ \u5173\u95ed\u6587\u4ef6\u6d41\n                fs.Close();\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ExportFile", "\u6587\u4ef6\u6d41\u5df2\u5173\u95ed\uff01");\n            }\n            catch (System.Exception ex)\n            {\n                \/\/ \u8bb0\u5f55\u65e5\u5fd7\n                LogTool.LogMessage("BPNetwork", "ExportFile", "unexpected exit !");\n                LogTool.LogMessage(string.Format("\\texception.message = {0}", ex.Message));\n            }\n            \/\/ \u8bb0\u5f55\u65e5\u5fd7\n            LogTool.LogMessage("BPNetwork", "ExportFile", "\u6570\u636e\u8f93\u51fa\u5b8c\u6bd5\uff01");\n        }\n\n        public void Print()\n        {\n#if DEBUG\n            Debug.Assert(Errors != null);\n            Debug.Assert(Deltas != null);\n            Debug.Assert(Inputs != null);\n            Debug.Assert(Outputs != null);\n            Debug.Assert(Hiddens != null);\n            Debug.Assert(InputBiases != null);\n            Debug.Assert(InputWeights != null);\n            Debug.Assert(OutputBiases != null);\n            Debug.Assert(OutputWeights != null);\n#endif\n            LogTool.LogMessage("BPNetwork", "Print",\n                "\u6253\u5370\u6570\u636e\uff01");\n            LogTool.LogMessage("\\tInputCount = " + InputCount);\n            LogTool.LogMessage("\\tOutputCount = " + OutputCount);\n            LogTool.LogMessage("\\tHiddenCount = " + HiddenCount);\n            LogTool.LogMessage("\\tLearningRate = " + LearningRate);\n            \/\/ \u6253\u5370\u8f93\u5165\u7aef\u6570\u636e\n            for (int i = 0; i < HiddenCount; i++)\n                LogTool.LogMessage(\n                    string.Format("\\tInputBiases[{0}] = {1}", i, InputBiases[i]));\n            for (int i = 0; i < HiddenCount; i++)\n                for(int j = 0;j < InputCount; j ++)\n                    LogTool.LogMessage(\n                        string.Format("\\tInputWeights[{0}][{1}] = {2}", i,j, InputWeights[i][j]));\n            \/\/ \u6253\u5370\u8f93\u51fa\u7aef\u6570\u636e\n            for (int i = 0; i < OutputCount; i++)\n                LogTool.LogMessage(\n                    string.Format("\\tOutputBiases[{0}] = {1}", i, OutputBiases[i]));\n            for (int i = 0; i < OutputCount; i++)\n                for (int j = 0; j < HiddenCount; j++)\n                    LogTool.LogMessage(\n                        string.Format("\\tInputWeights[{0}][{1}] = {2}", i, j, OutputWeights[i][j]));\n        }\n\n#if _USE_CONSOLE\n        public static void Main(string[] args)\n        {\n            \/\/ \u5f00\u542f\u65e5\u5fd7\n            LogTool.SetLog(true);\n            \/\/ \u521b\u5efa\u8ba1\u65f6\u5668\n            Stopwatch watch = new Stopwatch();\n            \/\/ \u5f00\u542f\u8ba1\u65f6\u5668\n            watch.Start();\n            \/\/ \u751f\u6210\u795e\u7ecf\u7f51\u7edc\n            BPNetwork network = new BPNetwork();\n            \/\/ \u521d\u59cb\u5316\n            network.Initialize(2, 2, 2);\n            \/\/ \u8bbe\u7f6e\u5b66\u4e60\u7387\n            network.LearningRate = 0.5;\n            \/\/ \u8bbe\u7f6e\u6807\u5b9a\u7528\u503c\n            double[] Inputs = new double[2] { 0.1, 0.2 };\n            double[] expects = new double[2] { 0.01, 0.99 };\n            \/\/ \u8bbe\u7f6e\u8f93\u5165\u6743\u91cd\n            network.InputWeights = new double[][]\n                {\n                    \/\/ W1\u548cW2\n                    new double[] { 0.1, 0.2 },\n                    \/\/ W3\u548cW4\n                    new double[] { 0.3, 0.4 },\n                };\n            \/\/ \u8bbe\u7f6e\u8f93\u51fa\u6743\u91cd\n            network.OutputWeights = new double[][]\n                {\n                    \/\/ W5\u548cW6\n                    new double[] { 0.5, 0.6 },\n                    \/\/ W7\u548cW8\n                    new double[] { 0.7, 0.8 },\n                };\n            \/\/ \u8bbe\u7f6e\u8f93\u5165\u504f\u7f6e\n            network.InputBiases = new double[] { 0.55, 0.56 };\n            \/\/ \u8bbe\u7f6e\u8f93\u51fa\u504f\u7f6e\n            network.OutputBiases = new double[] { 0.66, 0.67 };\n\n            \/\/ \u8bbe\u7f6e\u8f93\u5165\u503c\n            network.SetInputs(Inputs);\n            \/\/ \u8ba1\u7b97\u4e00\u6b21\u6b63\u5411\u4f20\u64ad\n            network.Forward();\n            \/\/ \u83b7\u5f97\u8f93\u51fa\u503c\n            double[] Outputs = network.GetOutputs();\n            \/\/ \u6253\u5370\u8f93\u51fa\u503c\n            \/\/Outputs[0] = 0.7989476413779711\n            \/\/Outputs[1] = 0.8390480283342561\n            Console.WriteLine("\\toutputs[0] = " + Outputs[0]);\n            Console.WriteLine("\\toutputs[1] = " + Outputs[1]);\n            \/\/ \u8bbe\u7f6e\u9884\u671f\u6570\u503c\n            network.SetOutputs(expects);\n            \/\/ \u6253\u5370\u8bef\u5dee\n            \/\/error = 0.3226124392928197\n            Console.WriteLine("\\terror = " + network.GetError());\n            \/\/ \u8ba1\u7b97\u4e00\u6b21\u53cd\u5411\u4f20\u64ad\n            network.Backword();\n            \/\/ \u5173\u95ed\u8ba1\u65f6\u5668\n            watch.Stop();\n            \/\/ \u6253\u5370\u7ed3\u679c\n            Console.WriteLine(string.Format("Time elapsed : {0} ms ", watch.ElapsedMilliseconds));\n        }\n#endif\n    }\n}\n\n<\/pre><\/div>","protected":false},"excerpt":{"rendered":"
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