{"id":158188,"date":"2025-10-25T12:01:26","date_gmt":"2025-10-25T04:01:26","guid":{"rendered":""},"modified":"2026-02-10T23:44:24","modified_gmt":"2026-02-10T15:44:24","slug":"deepthinking","status":"publish","type":"docs","link":"https:\/\/www.campus-gpt.com\/?docs=guidebook\/features\/deepthinking","title":{"rendered":"\u81ea\u5b9a\u4e49\u529f\u80fd\uff1a\u6df1\u5ea6\u63a8\u7406\u601d\u8003"},"content":{"rendered":"\n

\u8ba9 AI \u4ece\u201c\u5feb\u901f\u56de\u7b54\u201d\u5347\u7ea7\u4e3a\u201c\u6df1\u5ea6\u5206\u6790\u201d<\/h2>\n\n\n\n

\u5982\u679c\u8bf4\u8d85\u957f\u4e0a\u4e0b\u6587<\/strong>\u662f\u7ed9 AI \u63d0\u4f9b\u4e86**\u201c\u8d85\u5927\u7684\u8bb0\u5fc6\u5bb9\u91cf\u201d\uff08\u80fd\u8bb0\u4f4f\u591a\u5c11\u4fe1\u606f\uff09\uff0c\u90a3\u4e48<\/strong>\u6df1\u5ea6\u63a8\u7406\u601d\u8003\u5c31\u662f\u63d0\u5347\u4e86 AI \u7684<\/strong>\u201c\u601d\u8003\u8d28\u91cf\u548c\u4e25\u8c28\u5ea6\u201d**\uff08\u80fd\u60f3\u5f97\u591a\u6df1\u3001\u591a\u4ed4\u7ec6\uff09\u3002\u60f3\u8c61\u4e00\u4e0b\uff0c\u60a8\u5411 AI \u63d0\u51fa\u4e86\u4e00\u4e2a\u590d\u6742\u7684\u5b66\u672f\u96be\u9898\uff08\u6bd4\u5982\u4e00\u9053\u9700\u8981\u591a\u6b65\u903b\u8f91\u624d\u80fd\u89e3\u51fa\u7684\u6570\u5b66\u9898\uff0c\u6216\u8005\u9700\u8981\u6743\u8861\u5229\u5f0a\u7684\u4f26\u7406\u5206\u6790\uff09\u3002<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n
<\/div>\n\n\n\n

1. \u666e\u901a AI \u7684\u601d\u8003 (\u672a\u5f00\u542f\u6df1\u5ea6\u601d\u8003\u6a21\u5f0f)<\/strong><\/p>\n\n\n\n

    \n
  • \u666e\u901a\u601d\u8003\uff1a<\/strong> \u5c31\u50cf<\/strong>\u4e00\u4e2a\u53cd\u5e94\u5f88\u5feb\u3001\u77e5\u8bc6\u6e0a\u535a<\/strong>\u7684\u540c\u5b66\u5728\u8003\u8bd5\u4e2d\u5feb\u901f\u7ed9\u51fa\u7b2c\u4e00\u53cd\u5e94\u7684\u7b54\u6848<\/strong>\u3002<\/li>\n\n\n\n
  • \u4f1a\u53d1\u751f\u4ec0\u4e48\uff1a<\/strong> \u5b83\u4f1a\u7acb\u5373\u6839\u636e\u5df2\u6709\u7684\u77e5\u8bc6\u5e93\uff0c\u7ed9\u51fa\u6700\u6709\u53ef\u80fd\u7684\u7b54\u6848\u3002\u8fd9\u79cd\u6a21\u5f0f\u901f\u5ea6\u6781\u5feb\uff0c\u9002\u5408\u505a\u7b80\u5355\u7684\u4e8b\u5b9e\u67e5\u8be2\u3001\u5feb\u901f\u7ffb\u8bd1\u6216\u65e5\u5e38\u95f2\u804a<\/strong>\u3002<\/li>\n\n\n\n
  • \u5c40\u9650\uff1a<\/strong> \u5982\u679c\u95ee\u9898\u9700\u8981\u591a\u6b65\u903b\u8f91\u63a8\u5bfc\u3001\u9700\u8981\u6743\u8861\u6b63\u53cd\u4e24\u65b9\u9762\u7684\u8bba\u636e\uff0c\u6216\u8005\u9700\u8981\u68c0\u67e5\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u5feb\u901f\u6a21\u5f0f\u53ef\u80fd\u4f1a\u8df3\u8fc7\u4e2d\u95f4\u6b65\u9aa4<\/strong>\uff0c\u5bfc\u81f4\u7b54\u6848\u4e0d\u591f\u4e25\u8c28\u6216\u6709\u7ec6\u5fae\u9519\u8bef\u3002<\/li>\n<\/ul>\n\n\n\n
    <\/div>\n\n\n\n

    2. \u5f00\u542f\u201c\u6df1\u5ea6\u601d\u8003\u201d\u6a21\u5f0f\u540e\u7684\u4e0d\u540c<\/strong> \uff08\u5f00\u542f\u6df1\u5ea6\u601d\u8003\u6a21\u5f0f<\/strong>\uff09<\/p>\n\n\n\n

    CampusGPT \u901a\u8fc7\u8c03\u7528 OpenAI Edu \u63d0\u4f9b\u7684\u6df1\u5ea6\u601d\u8003API\u5b89\u5168\u6570\u636e\u63a5\u53e3\uff0c\u4e3a\u60a8\u63d0\u4f9b\u4e86**\u201c\u6df1\u5ea6\u63a8\u7406\u6a21\u5f0f\u201d\uff0c\u8ba9 AI \u62e5\u6709\u4e86<\/strong>\u7ed3\u6784\u5316\u3001\u591a\u6b65\u9aa4\u7684\u601d\u8003\u80fd\u529b**\u3002\u60a8\u53ef\u4ee5\u5728\u754c\u9762\u4e0a\u901a\u8fc7\u201c\u6df1\u5ea6\u63a8\u7406\u6a21\u5f0f\u201d\u7684\u6309\u94ae\u6765\u542f\u7528\u5b83\uff0c\u5b83\u63d0\u4f9b\u4ee5\u4e0b\u4e09\u4e2a\u7ea7\u522b\u4f9b\u60a8\u9009\u62e9\uff1a<\/p>\n\n\n\n

    \u6a21\u5f0f\u7ea7\u522b<\/strong><\/td>\u6838\u5fc3\u7279\u70b9<\/strong><\/td>\u9002\u7528\u573a\u666f<\/strong><\/td>\u901f\u5ea6\u4e0e\u6210\u672c<\/strong><\/td><\/tr><\/thead>
    \u5feb\u901f\u601d\u8003 (Quick)<\/strong><\/td>AI \u503e\u5411\u4e8e\u5feb\u901f\u7ed9\u51fa\u9996\u4e2a\u5408\u7406\u7b54\u6848\u3002<\/td>\u65e5\u5e38\u9ad8\u9891\u3001\u975e\u5173\u952e\u6027\u7684\u95ee\u7b54\uff0c\u4f8b\u5982\uff1a\u5feb\u901f\u603b\u7ed3\u3001\u6da6\u8272\u90ae\u4ef6\u3002<\/td>\u901f\u5ea6\u6700\u5feb \/ \u6d88\u8017\u79ef\u5206\u6700\u4f4e<\/strong><\/td><\/tr>
    \u5747\u8861\u601d\u8003 (Balanced)<\/strong><\/td>AI \u4f1a\u5728\u7ed9\u51fa\u7b54\u6848\u524d\u8fdb\u884c\u4e00\u6b21\u5185\u90e8\u7684\u903b\u8f91\u6821\u9a8c<\/strong>\u3002<\/td>\u5927\u591a\u6570\u8bfe\u7a0b\u4f5c\u4e1a\u3001\u9700\u8981\u4e00\u5b9a\u8bba\u8bc1\u6216\u7b80\u5355\u63a8\u7406\u7684\u5206\u6790\u3002<\/td>\u5e73\u8861\u901f\u5ea6\u4e0e\u51c6\u786e\u6027<\/strong><\/td><\/tr>
    \u6df1\u5ea6\u601d\u8003 (Deep)<\/strong><\/td>AI \u4f1a\u6a21\u4eff\u4eba\u7c7b\u201c\u8349\u7a3f\u7eb8\u201d\u7684\u601d\u8003\u8fc7\u7a0b\uff0c\u8fdb\u884c\u591a\u6b21\u8fed\u4ee3\u548c\u81ea\u6211\u4fee\u6b63<\/strong>\uff0c\u76f4\u5230\u786e\u8ba4\u7b54\u6848\u7684\u6700\u4f18\u89e3\u3002<\/td>\u590d\u6742\u7684\u6570\u5b66\u8bc1\u660e\u3001\u9700\u8981\u4e25\u8c28\u8bba\u8bc1\u7684\u8bba\u6587\u5199\u4f5c\u3001\u903b\u8f91\u94fe\u6761\u6781\u957f\u7684\u7f16\u7a0b\u95ee\u9898\u3002<\/td>\u901f\u5ea6\u8f83\u6162 \/ \u6d88\u8017\u79ef\u5206\u6700\u9ad8<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    \u603b\u7ed3\uff1a\u5f00\u542f\u6df1\u5ea6\u63a8\u7406\u7684\u4ef7\u503c<\/strong><\/p>\n\n\n\n

    \u901a\u8fc7\u9009\u62e9\u5747\u8861\u601d\u8003<\/strong>\u6216\u6df1\u5ea6\u601d\u8003<\/strong>\uff0c\u60a8\u4e0d\u518d\u53ea\u662f\u83b7\u5f97\u4e00\u4e2a\u201c\u7b54\u6848\u201d\uff0c\u800c\u662f\u83b7\u5f97\u4e86\u4e00\u4e2a\u7ecf\u8fc7\u4e25\u5bc6\u63a8\u5bfc\u7684\u201c\u89e3\u51b3\u65b9\u6848\u201d<\/strong>\u3002 <\/p>\n\n\n\n

      \n
    • \u53ef\u9760\u6027\u63d0\u9ad8\uff1a<\/strong> \u5c24\u5176\u5728\u5904\u7406\u9700\u8981\u7cbe\u786e\u903b\u8f91\u7684\u5b66\u79d1\uff08\u5982 STEM \u9886\u57df\uff09\u65f6\uff0c\u80fd\u663e\u8457\u964d\u4f4e\u51fa\u9519\u7387\u3002<\/li>\n\n\n\n
    • \u8fc7\u7a0b\u900f\u660e\uff1a<\/strong> \u6df1\u5ea6\u601d\u8003\u6a21\u5f0f\u901a\u5e38\u4f1a\u5c55\u73b0\u66f4\u591a\u7684\u601d\u8003\u6b65\u9aa4\uff0c\u8ba9\u60a8\uff08\u6216\u60a8\u7684\u5b66\u751f\uff09\u201c\u770b\u6e05 AI \u662f\u5982\u4f55\u5f97\u51fa\u8fd9\u4e2a\u7ed3\u8bba\u7684\u201d<\/strong>\uff0c\u8fd9\u5bf9\u4e8e\u5b66\u4e60\u548c\u6559\u5b66\u53cd\u9988\u81f3\u5173\u91cd\u8981\u3002<\/li>\n<\/ul>\n\n\n\n

      \ud83d\udca1 \u63d0\u9192\uff1a<\/strong> \u6df1\u5ea6\u63a8\u7406\u601d\u8003\u7684\u8ba1\u7b97\u91cf\u66f4\u5927\uff0c\u56e0\u6b64\u5728\u8ba1\u7b97\u901f\u5ea6<\/strong>\u4e0a\u4f1a\u6bd4\u666e\u901a\u6a21\u5f0f\u6162\uff0c\u5e76\u4e14\u4f1a\u6d88\u8017\u66f4\u591a\u7684\u7b97\u529b\u79ef\u5206<\/strong>\u3002\u8bf7\u6839\u636e\u4efb\u52a1\u7684\u91cd\u8981\u6027\u9009\u62e9\u5408\u9002\u7684\u7ea7\u522b\u3002<\/p>\n\n\n\n

      <\/div>\n\n\n\n

      \u5f00\u542f\u65b9\u5f0f<\/h2>\n\n\n\n

      \u8f93\u5165\u6846\u4e0a\u65b9 \u2192 \u70b9\u51fb \u201c\u6df1\u5ea6\u63a8\u7406\u6a21\u5f0f\u201d<\/strong> \u6309\u94ae \u2192 \u9009\u62e9 \u201c\u5feb\u901f \/ \u5747\u8861 \/ \u6df1\u5ea6”<\/strong><\/p>\n\n\n\n

      \u7ea7\u522b<\/th>\u63a8\u7406\u6b65\u6570<\/th>\u54cd\u5e94\u65f6\u95f4<\/th>\u6d88\u8017\u500d\u7387<\/th>\u63a8\u8350\u6a21\u578b<\/th>\u9002\u7528\u573a\u666f<\/th><\/tr>
      \u5feb\u901f\u601d\u8003<\/td>3~5 \u6b65<\/td>2~5 \u79d2<\/td>+5x<\/td>gpt-o1-mini<\/td>\u4f5c\u4e1a\u9898\u3001\u7b80\u5355\u8bc1\u660e<\/td><\/tr>
      \u5747\u8861\u601d\u8003<\/td>6~10 \u6b65<\/td>6~12 \u79d2<\/td>+11x<\/td>gpt-o1-mini \/ gpt-o3-mini<\/td>\u8bba\u6587\u903b\u8f91\u3001\u4ee3\u7801\u63a8\u5bfc<\/td><\/tr>
      \u6df1\u5ea6\u601d\u8003<\/td>11~20 \u6b65<\/td>15~30 \u79d2<\/td>+20x~150x<\/td>gpt-o1 \/ gpt-o3<\/td>IMO \u96be\u9898\u3001\u535a\u58eb\u8bba\u8bc1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      \u63a8\u7406\u6a21\u578b\u5e95\u5ea7\uff1a\u6240\u6709\u63a8\u7406\u5747\u901a\u8fc7 OpenAI \u5b98\u65b9\u5b9e\u65f6\u8c03\u7528 o1\/o3 \u7cfb\u5217\u6a21\u578b\uff0c\u975e\u672c\u5730\u6a21\u62df\uff0c\u786e\u4fdd\u6700\u65b0\u63a8\u7406\u80fd\u529b<\/p>\n\n\n\n

      <\/div>\n\n\n\n

      <\/p>\n\n\n\n

      \u771f\u5b9e\u63a8\u7406\u94fe\u793a\u4f8b<\/h2>\n\n\n\n
      **<\/strong>\u4f60<\/strong>**<\/strong>\uff1a  \n\u8bc1\u660e \u221a2 \u662f\u65e0\u7406\u6570\uff08\u6a21\u5f0f\uff1a\u5747\u8861\u601d\u8003\uff09\n\n**<\/strong>gpt-o1-mini<\/strong>**<\/strong> \ud83e\udde0\uff08\u5747\u8861 \u00b7 8 \u6b65 \u00b7 +11x\uff09\uff1a\n> \u8c03\u7528 OpenAI \u63a8\u7406\u601d\u8003\u6a21\u5f0f \u4e2d\u2026\uff087.3 \u79d2\uff09\n\n**<\/strong>\ud83d\udccb \u601d\u8003\u94fe<\/strong>**<\/strong>\n\n1. **<\/strong>\u5047\u8bbe\u6cd5<\/strong>**<\/strong>\uff1a\u8bbe \u221a2 = p\/q\uff08p,q \u4e92\u8d28\u6b63\u6574\u6570\uff09  \n2. **<\/strong>\u5e73\u65b9<\/strong>**<\/strong>\uff1a2 = p\u00b2\/q\u00b2 \u2192 p\u00b2 = 2q\u00b2  \n3. **<\/strong>p\u00b2 \u5076<\/strong>**<\/strong> \u2192 p \u5fc5\u4e3a\u5076\u6570 \u2192 p = 2k  \n4. **<\/strong>\u4ee3\u5165<\/strong>**<\/strong>\uff1a(2k)\u00b2 = 2q\u00b2 \u2192 4k\u00b2 = 2q\u00b2 \u2192 q\u00b2 = 2k\u00b2  \n5. **<\/strong>q\u00b2 \u5076<\/strong>**<\/strong> \u2192 q \u4e5f\u4e3a\u5076\u6570  \n6. **<\/strong>\u77db\u76fe<\/strong>**<\/strong>\uff1ap,q \u4e0d\u80fd\u540c\u65f6\u4e3a\u5076\uff08\u8fdd\u80cc\u4e92\u8d28\uff09  \n7. **<\/strong>\u7ed3\u8bba<\/strong>**<\/strong>\uff1a\u5047\u8bbe\u9519\u8bef\uff0c**<\/strong>\u221a2 \u65e0\u7406<\/strong>**<\/strong>  \n8. **<\/strong>\u9a8c\u8bc1<\/strong>**<\/strong>\uff1a\u7ecf\u5178\u53cd\u8bc1\u6cd5\uff08Euclid, ~300 BC\uff09<\/code><\/pre>\n\n\n\n
      <\/div>\n\n\n\n
      \u6df1\u5ea6\u63a8\u7406\u4f7f\u7528\u5efa\u8bae\uff08\u7701\u7b97\u529b\u79ef\u5206\u6307\u5357\uff09<\/h2>\n\n\n\n
      \u573a\u666f<\/th>\u63a8\u8350\u7ea7\u522b<\/th>\u7406\u7531<\/th><\/tr>
      \u9ad8\u4e2d\u6570\u5b66\u9898<\/td>\u5feb\u901f\u601d\u8003<\/td>3~5 \u6b65\u591f\u7528\uff0c\u4ec5 +5x<\/td><\/tr>
      \u8bba\u6587\u65b9\u6cd5\u8bba\u8bc1<\/td>\u5747\u8861\u601d\u8003<\/td>6~10 \u6b65\u67e5\u6f0f\uff0c\u6027\u4ef7\u6bd4\u6700\u9ad8<\/td><\/tr>
      \u535a\u58eb\u5f00\u9898\u62a5\u544a<\/td>\u6df1\u5ea6\u601d\u8003<\/td>11~20 \u6b65\u4e25\u8c28\uff0c\u503c 150x<\/td><\/tr>
      \u65e5\u5e38\u95ee\u7b54<\/td> \u5173\u95ed<\/td>\u8282\u7701\u7b97\u529b\u79ef\u5206\u7684\u6d88\u8017<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
      \u4f7f\u7528\u5c0f\u6280\u5de7\uff1a\u9ed8\u8ba4\u5173\u95ed \uff0c\u4ec5\u5728\u9700\u8981\u201c\u8bc1\u660e\/\u63a8\u5bfc\u201d\u65f6\u5f00\u542f<\/p>\n\n\n\n
      <\/div>\n\n\n\n
      \u5e38\u89c1\u95ee\u9898 (FAQ)<\/h2>\n\n\n\n
      \u95ee\u9898<\/th>\u89e3\u7b54<\/th><\/tr>
      \u63a8\u7406\u6a21\u5f0f\u5982\u4f55\u5f00\u542f\uff1f<\/td>\u627e\u5230\u201c\u6df1\u5ea6\u63a8\u7406\u6a21\u578b\u201d\u83dc\u5355\uff0c\u70b9\u51fb\u5f00\u542f<\/td><\/tr>
      \u80fd\u79bb\u7ebf\u63a8\u7406\u5417\uff1f<\/td>\u4e0d\u884c\uff01\u9700\u8054\u7f51\u4f7f\u7528<\/td><\/tr>
      \u63a8\u7406\u94fe\u4f1a\u91cd\u590d\u5417\uff1f<\/td>\u4e0d\u4f1a\uff01\u7cfb\u7edf\u7f13\u5b58\u540c\u95ee\u9898\u7ed3\u679c<\/td><\/tr>
      \u652f\u6301\u591a\u8bed\u8a00\uff1f<\/td>\u652f\u6301\uff01\u81ea\u52a8\u4e2d\u82f1\u65e5\u97e9\u63a8\u7406\u94fe<\/td><\/tr>
      \u4ed8\u8d39\u7528\u6237\u6709\u4f18\u5148\u6743\u5417<\/td>\u6709\uff01\u4ed8\u8d39\u7528\u6237\u4eab\u4f18\u5148\u63a8\u7406\u901a\u9053\uff0c\u5ef6\u8fdf <50ms<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"
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