{"id":53789,"date":"2025-02-16T11:36:42","date_gmt":"2025-02-16T03:36:42","guid":{"rendered":"https:\/\/fwq.ai\/blog\/53789\/"},"modified":"2025-02-16T11:36:42","modified_gmt":"2025-02-16T03:36:42","slug":"deepseek-r1%e6%9e%b6%e6%9e%84%e5%92%8c%e8%ae%ad%e7%bb%83%e8%bf%87%e7%a8%8b%e5%9b%be%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/fwq.ai\/blog\/53789\/","title":{"rendered":"DeepSeek R1\u67b6\u6784\u548c\u8bad\u7ec3\u8fc7\u7a0b\u56fe\u89e3"},"content":{"rendered":"<p>\u5982\u679c\u4f60\u5bf9 AI \u611f\u5174\u8da3\uff0c\u53ef\u80fd\u542c\u8bf4\u8fc7 DeepSeek R1\u3002\u5b83\u76ee\u524d\u5728 LLM \u9886\u57df\u5f88\u6d41\u884c\uff0c\u5e76\u4e14\u8868\u73b0\u4f18\u4e8e\u5f00\u6e90\u548c\u95ed\u6e90\u6a21\u578b\u3002<\/p>\n<p>\u4e3a\u4e86\u8ba9\u4e00\u5207\u53d8\u5f97\u7b80\u5355\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u624b\u7ed8\u6d41\u7a0b\u56fe\u548c\u7b80\u5355\u7684\u8ba1\u7b97\u6765\u5e2e\u52a9\u4ece\u5934\u5f00\u59cb\u6f84\u6e05DeeoSeek-R1\u7684\u6838\u5fc3\u6982\u5ff5\u3002<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u5c06\u5728\u6574\u4e2a\u535a\u5ba2\u4e2d\u4f7f\u7528\u5b57\u7b26\u4e32 2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u4f5c\u4e3a\u793a\u4f8b\uff0c\u5f15\u5bfc\u4f60\u4e86\u89e3 DeepSeek \u6280\u672f\u62a5\u544a\u7684\u6bcf\u4e2a\u7ec4\u6210\u90e8\u5206\u3002<\/p>\n<h2>1\u3001\u5feb\u901f\u6982\u89c8<\/h2>\n<p>\u56e0\u6b64\uff0c\u5728\u4ecb\u7ecd\u6280\u672f\u7ec6\u8282\u4e4b\u524d\uff0c\u5feb\u901f\u6982\u89c8\u4e00\u4e0b\uff1aDeepSeek-R1 \u4e0d\u662f\u4ece\u5934\u5f00\u59cb\u8bad\u7ec3\u7684\uff0c\u5c31\u50cf\u4ece\u65e0\u5230\u6709\u4e00\u6837\u3002\u76f8\u53cd\uff0c\u4ed6\u4eec\u4ece\u4e00\u4e2a\u975e\u5e38\u806a\u660e\u7684 LLM \u5f00\u59cb\uff0c\u4ed6\u4eec\u5df2\u7ecf\u6709\u4e86 DeepSeek-V3\uff0c\u4f46\u4ed6\u4eec\u60f3\u8ba9\u5b83\u6210\u4e3a\u63a8\u7406\u8d85\u7ea7\u660e\u661f\u3002<\/p>\n<p>  DeepSeek \u5b9e\u65bd\u5feb\u901f\u6982\u89c8 <\/p>\n<p>\u4e3a\u6b64\uff0c\u4ed6\u4eec\u4f7f\u7528\u4e86\u5f3a\u5316\u5b66\u4e60\uff08\u7b80\u79f0 RL\uff09\uff0c\u5f53 LLM \u505a\u51fa\u6709\u5229\u4e8e\u63a8\u7406\u7684\u4e8b\u60c5\u65f6\uff0c\u4f60\u4f1a\u5956\u52b1\u5b83\uff0c\u5426\u5219\u4f1a\u60e9\u7f5a\u5b83\u3002<\/p>\n<p>\u4f46\u8fd9\u4e0d\u4ec5\u4ec5\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u8bad\u7ec3\u8bfe\u7a0b\u3002\u5b83\u5c31\u50cf\u662f\u4e00\u6574\u5957\u6b65\u9aa4\uff0c\u4ed6\u4eec\u79f0\u4e4b\u4e3a\u7ba1\u9053\u3002\u4ed6\u4eec\u9996\u5148\u5c1d\u8bd5\u4e86\u7eaf RL\uff0c\u770b\u770b\u63a8\u7406\u662f\u5426\u4f1a\u81ea\u884c\u51fa\u73b0\uff0c\u8fd9\u5c31\u662f DeepSeek-R1-Zero\uff0c\u6709\u70b9\u50cf\u4e00\u4e2a\u5b9e\u9a8c\u3002\u7136\u540e\u5bf9\u4e8e\u771f\u6b63\u7684 DeepSeek-R1\uff0c\u4ed6\u4eec\u901a\u8fc7\u4e0d\u540c\u7684\u9636\u6bb5\u4f7f\u5176\u66f4\u6709\u6761\u7406\u3002\u4ed6\u4eec\u7ed9\u5b83\u4e00\u4e9b\u8d77\u59cb\u6570\u636e\u6765\u542f\u52a8\u5b83\uff0c\u7136\u540e\u8fdb\u884c RL\uff0c\u7136\u540e\u662f\u66f4\u591a\u6570\u636e\uff0c\u7136\u540e\u662f\u66f4\u591a RL\u2026\u2026\u5c31\u50cf\u4e00\u6b65\u4e00\u6b65\u5347\u7ea7\u4e00\u6837\uff01<\/p>\n<p>\u6574\u4e2a\u91cd\u70b9\u662f\u8ba9\u8fd9\u4e9b\u8bed\u8a00\u6a21\u578b\u66f4\u597d\u5730\u601d\u8003\u95ee\u9898\u5e76\u4e3a\u4f60\u63d0\u4f9b\u660e\u667a\u7684\u7b54\u6848\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u5410\u51fa\u5355\u8bcd\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u662f\u7684\uff0c\u5728\u6211\u4eec\u7814\u7a76\u6bcf\u4e2a\u6b65\u9aa4\u7684\u75af\u72c2\u7ec6\u8282\u4e4b\u524d\uff0c\u8fd9\u662f\u8d85\u7b80\u77ed\u7684\u7248\u672c\u3002<\/p>\n<h2>2\u3001DeepSeek V3 (MOE) \u5982\u4f55\u601d\u8003\uff1f<\/h2>\n<p>\u6b63\u5982\u6211\u4e4b\u524d\u6240\u8bf4\uff0cDeepSeek R1 \u8bad\u7ec3\u4e0d\u662f\u4ece\u5934\u5f00\u59cb\u6784\u5efa\u7684\uff0c\u800c\u662f\u4f7f\u7528 DeepSeek V3 \u4f5c\u4e3a\u57fa\u7840\u6a21\u578b\u3002\u90a3\u4e48\u6211\u4eec\u9700\u8981\u4e86\u89e3 V3 \u7684\u5de5\u4f5c\u539f\u7406\u4ee5\u53ca\u5b83\u4e3a\u4ec0\u4e48\u88ab\u79f0\u4e3a MOE\uff1f<\/p>\n<p>  DeepSeek V3 \u67b6\u6784 <\/p>\n<p>DeepSeek V3 \u6709\u4e24\u6761\u4e3b\u8981\u8def\u5f84\u3002\u5f53\u4f60\u8f93\u5165\u95ee\u9898\u65f6\uff0c\u5b83\u9996\u5148\u4f1a\u7ecf\u8fc7\u4e00\u4e2a\u8bb0\u5fc6\u7cfb\u7edf\uff0c\u8be5\u7cfb\u7edf\u901a\u8fc7\u67e5\u627e\u76f8\u5173\u4fe1\u606f\u5feb\u901f\u6784\u5efa\u4e0a\u4e0b\u6587\u3002\u53ef\u4ee5\u5c06\u5176\u89c6\u4e3a\u5feb\u901f\u56de\u5fc6\u4f60\u4e4b\u524d\u9047\u5230\u8fc7\u7684\u7c7b\u4f3c\u60c5\u51b5\u3002<\/p>\n<p>\u5b83\u7684\u4e3b\u8981\u4f18\u52bf\u5728\u4e8e\u5176\u51b3\u7b56\u7cfb\u7edf\u3002\u5728\u7406\u89e3\u4f60\u7684\u8f93\u5165\u540e\uff0c\u5b83\u4f1a\u4f7f\u7528\u4e00\u4e2a\u667a\u80fd\u8def\u7531\u5668\u5728\u4e24\u6761\u8def\u5f84\u4e4b\u95f4\u505a\u51fa\u51b3\u5b9a\uff1a\u5feb\u901f\u5904\u7406\u5668\u7528\u4e8e\u7b80\u5355\u7684\u4efb\u52a1\uff08\u5982\u7b80\u5355\u95ee\u9898\u6216\u5e38\u89c1\u8bf7\u6c42\uff09\u548c\u4e13\u5bb6\u7cfb\u7edf\u7528\u4e8e\u590d\u6742\u7684\u95ee\u9898\uff08\u5982\u5206\u6790\u6216\u4e13\u4e1a\u77e5\u8bc6\uff09\u3002<\/p>\n<blockquote><p>\n  \u8fd9\u4e2a\u8def\u7531\u5668\u4f7f DeepSeek V3 \u6210\u4e3a\u4e13\u5bb6\u6df7\u5408\u6a21\u578b (MOE)\n<\/p><\/blockquote>\n<p>\u56e0\u4e3a\u5b83\u4f1a\u52a8\u6001\u5730\u5c06\u6bcf\u4e2a\u8bf7\u6c42\u5b9a\u5411\u5230\u6700\u5408\u9002\u7684\u4e13\u5bb6\u7ec4\u4ef6\u4ee5\u8fdb\u884c\u9ad8\u6548\u5904\u7406\u3002<\/p>\n<p>\u7b80\u5355\u7684\u95ee\u9898\u901a\u8fc7\u5feb\u901f\u8def\u5f84\u83b7\u5f97\u5feb\u901f\u3001\u76f4\u63a5\u7684\u7b54\u6848\uff0c\u800c\u590d\u6742\u7684\u67e5\u8be2\u5219\u901a\u8fc7\u4e13\u5bb6\u7cfb\u7edf\u5f97\u5230\u8be6\u7ec6\u5173\u6ce8\u3002\u6700\u540e\uff0c\u8fd9\u4e9b\u54cd\u5e94\u88ab\u7ec4\u5408\u6210\u6e05\u6670\u3001\u51c6\u786e\u7684\u8f93\u51fa\u3002<\/p>\n<h2>3\u3001DeepSeek V3 \u4f5c\u4e3a RL \u8bbe\u7f6e\u4e2d\u7684\u7b56\u7565\u6a21\u578b<\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86 DeepSeek v3 \u7684\u601d\u8003\u65b9\u5f0f\uff0c\u5b83\u662f DeepSeek R1 \u5b9e\u73b0\u7684\u8d77\u70b9\uff0c\u6211\u6240\u8bf4\u7684\u8d77\u70b9\u662f\u6307\u5b83\u5df2\u7ecf\u521b\u5efa\u4e86 DeepSeek R1 Zero\u7248\u672c\uff0c\u8fd9\u662f\u4e00\u4e2a\u5728\u521b\u5efa\u6700\u7ec8\u7248\u672c\u4e4b\u524d\u5b58\u5728\u4e00\u4e9b\u9519\u8bef\u7684\u521d\u59cb\u7248\u672c\u3002<\/p>\n<p>\u521d\u59cb\u7248\u672c\uff08R1 Zero\uff09\u662f\u4f7f\u7528\u5f3a\u5316\u5b66\u4e60\u521b\u5efa\u7684\uff0c\u5176\u4e2d DeepSeek v3 \u5145\u5f53 RL \u4ee3\u7406\uff08\u91c7\u53d6\u884c\u52a8\u7684\u53c2\u4e0e\u8005\uff09\u3002\u8ba9\u6211\u4eec\u9996\u5148\u76f4\u89c2\u5730\u4e86\u89e3\u5b83\u7684\u5de5\u4f5c\u539f\u7406\u3002<\/p>\n<p>  V3 \u4f5c\u4e3a\u4ee3\u7406\u5de5\u4f5c\u6d41\u7a0b <\/p>\n<p>RL \u4ee3\u7406\uff08DeepSeek V3\uff09\u9996\u5148\u91c7\u53d6\u884c\u52a8\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u4f1a\u4e3a\u653e\u5165\u5176\u73af\u5883\u4e2d\u7684\u7ed9\u5b9a\u95ee\u9898\u751f\u6210\u7b54\u6848\u548c\u4e00\u4e9b\u63a8\u7406\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u73af\u5883\u53ea\u662f\u63a8\u7406\u4efb\u52a1\u672c\u8eab\u3002<\/p>\n<p>\u91c7\u53d6\u884c\u52a8\u540e\uff0c\u73af\u5883\u4f1a\u7ed9\u4e88\u5956\u52b1\u3002\u8fd9\u4e2a\u5956\u52b1\u5c31\u50cf\u53cd\u9988\uff0c\u5b83\u544a\u8bc9 DeepSeek V3 \u57fa\u7840\u6a21\u578b\u5176\u884c\u52a8\u6709\u591a\u597d\u3002\u79ef\u6781\u7684\u5956\u52b1\u610f\u5473\u7740\u5b83\u505a\u5bf9\u4e86\u67d0\u4ef6\u4e8b\uff0c\u53ef\u80fd\u5f97\u5230\u4e86\u6b63\u786e\u7684\u7b54\u6848\u6216\u63a8\u7406\u5f97\u5f88\u597d\u3002\u7136\u540e\uff0c\u8fd9\u4e2a\u53cd\u9988\u4fe1\u53f7\u8fd4\u56de\u5230 DeepSeek-V3-Base\uff0c\u5e2e\u52a9\u5b83\u5b66\u4e60\u548c\u8c03\u6574\u672a\u6765\u5982\u4f55\u91c7\u53d6\u884c\u52a8\u4ee5\u83b7\u5f97\u66f4\u597d\u7684\u5956\u52b1\u3002<\/p>\n<p>\u5728\u63a5\u4e0b\u6765\u7684\u90e8\u5206\u4e2d\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u8fd9\u4e2a\u5e26\u6709\u5956\u52b1\u6a21\u578b\u7684 RL \u8bbe\u7f6e\u4ee5\u53ca\u5b83\u4eec\u4f7f\u7528\u7684 RL \u7b97\u6cd5\u5e76\u5c1d\u8bd5\u4f7f\u7528\u6211\u4eec\u7684\u6587\u672c\u8f93\u5165\u6765\u89e3\u51b3\u5b83\u3002<\/p>\n<h2>4\u3001GRPO \u7b97\u6cd5\u5982\u4f55\u5de5\u4f5c\uff1f<\/h2>\n<p>\u8bad\u7ec3 LLM \u7684\u8ba1\u7b97\u6210\u672c\u6781\u9ad8\uff0c\u800c RL \u5219\u589e\u52a0\u4e86\u66f4\u591a\u7684\u590d\u6742\u6027\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6709\u8bb8\u591a\u53ef\u7528\u7684 RL \u7b97\u6cd5\uff0c\u4f46\u4f20\u7edf\u7684 RL \u4f7f\u7528\u4e00\u79cd\u79f0\u4e3a\u201c\u6279\u8bc4\u5bb6\u201d\u7684\u4e1c\u897f\u6765\u5e2e\u52a9\u4e3b\u8981\u51b3\u7b56\u90e8\u5206\uff08\u201c\u53c2\u4e0e\u8005\u201d\uff0c\u5373 DeepSeek V3\uff09\uff0c\u6b63\u5982\u4f60\u5df2\u7ecf\u77e5\u9053\u7684\u90a3\u6837\u3002\u8fd9\u4e2a\u6279\u8bc4\u5bb6\u901a\u5e38\u548c\u53c2\u4e0e\u8005\u672c\u8eab\u4e00\u6837\u5927\u548c\u590d\u6742\uff0c\u8fd9\u57fa\u672c\u4e0a\u4f7f\u8ba1\u7b97\u6210\u672c\u7ffb\u500d\u3002<\/p>\n<p>\u7136\u800c\uff0cGRPO \u7684\u505a\u6cd5\u4e0d\u540c\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u4ece\u4e00\u7ec4\u52a8\u4f5c\u7684\u7ed3\u679c\u4e2d\u627e\u51fa\u57fa\u7ebf\uff0c\u5373\u4e00\u79cd\u826f\u597d\u52a8\u4f5c\u7684\u53c2\u8003\u70b9\u3002\u56e0\u6b64\uff0cGRPO \u6839\u672c\u4e0d\u9700\u8981\u5355\u72ec\u7684\u6279\u8bc4\u5bb6\u6a21\u578b\u3002\u8fd9\u8282\u7701\u4e86\u5927\u91cf\u8ba1\u7b97\u5e76\u4f7f\u4e8b\u60c5\u53d8\u5f97\u66f4\u6709\u6548\u7387\u3002<\/p>\n<p>  GRPO \u7b97\u6cd5 <\/p>\n<p>\u5b83\u4ece\u5411\u6a21\u578b\u63d0\u51fa\u4e00\u4e2a\u95ee\u9898\u6216\u63d0\u793a\u5f00\u59cb\uff0c\u79f0\u4e3a\u201c\u65e7\u7b56\u7565\u201d\u3002 GRPO \u4e0d\u4f1a\u53ea\u5f97\u5230\u4e00\u4e2a\u7b54\u6848\uff0c\u800c\u662f\u6307\u793a\u65e7\u7b56\u7565\u9488\u5bf9\u540c\u4e00\u95ee\u9898\u751f\u6210\u4e00\u7ec4\u4e0d\u540c\u7684\u7b54\u6848\u3002\u7136\u540e\u8bc4\u4f30\u6bcf\u4e2a\u7b54\u6848\u5e76\u7ed9\u51fa\u5956\u52b1\u5206\u6570\uff0c\u4ee5\u53cd\u6620\u5176\u597d\u574f\u7a0b\u5ea6\u6216\u53ef\u53d6\u6027\u3002<\/p>\n<p>GRPO \u901a\u8fc7\u5c06\u6bcf\u4e2a\u7b54\u6848\u4e0e\u5176\u7ec4\u4e2d\u5176\u4ed6\u7b54\u6848\u7684\u5e73\u5747\u8d28\u91cf\u8fdb\u884c\u6bd4\u8f83\u6765\u8ba1\u7b97\u6bcf\u4e2a\u7b54\u6848\u7684\u201c\u4f18\u52bf\u201d\u3002\u9ad8\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u7b54\u6848\u83b7\u5f97\u6b63\u4f18\u52bf\uff0c\u800c\u4f4e\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u7b54\u6848\u83b7\u5f97\u8d1f\u4f18\u52bf\u3002\u81f3\u5173\u91cd\u8981\u7684\u662f\uff0c\u8fd9\u65e0\u9700\u5355\u72ec\u7684\u6279\u8bc4\u6a21\u578b\u5373\u53ef\u5b8c\u6210\u3002<\/p>\n<p>\u7136\u540e\u4f7f\u7528\u8fd9\u4e9b\u4f18\u52bf\u5206\u6570\u6765\u66f4\u65b0\u65e7\u7b56\u7565\uff0c\u4f7f\u5176\u66f4\u6709\u53ef\u80fd\u5728\u672a\u6765\u4ea7\u751f\u9ad8\u4e8e\u5e73\u5747\u6c34\u5e73\u7684\u7b54\u6848\u3002\u8fd9\u4e2a\u66f4\u65b0\u7684\u6a21\u578b\u6210\u4e3a\u65b0\u7684\u201c\u65e7\u7b56\u7565\u201d\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u91cd\u590d\u8fdb\u884c\uff0c\u8fed\u4ee3\u5730\u6539\u8fdb\u6a21\u578b\u3002<\/p>\n<h2>5\u3001GRPO \u7684\u76ee\u6807\u51fd\u6570<\/h2>\n<p>\u663e\u7136\uff0c\u5728\u8fd9\u4e2a GRPO \u80cc\u540e\uff0c\u6709\u590d\u6742\u7684\u6570\u5b66\u603b\u4e4b\uff0c\u6211\u4eec\u53ef\u4ee5\u79f0\u4e4b\u4e3a GRPO \u80cc\u540e\u7684\u76ee\u6807\u51fd\u6570\u3002<\/p>\n<p>  GRPO \u76ee\u6807 <\/p>\n<p>GRPO \u7684\u76ee\u6807\u51fd\u6570\u6709\u4e24\u4e2a\u76ee\u6807\uff0c\u4e00\u4e2a\u662f\u7ed9\u51fa\u826f\u597d\u7684\u8f93\u51fa\uff08\u9ad8\u56de\u62a5\uff09\uff0c\u540c\u65f6\u786e\u4fdd\u8bad\u7ec3\u8fc7\u7a0b\u7a33\u5b9a\u4e14\u4e0d\u4f1a\u5931\u63a7\u3002\u539f\u59cb\u51fd\u6570\u5f88\u5413\u4eba\uff0c\u4f46\u6211\u4eec\u4f1a\u5c06\u5176\u91cd\u5199\u4e3a\u66f4\u7b80\u5355\u7684\u5f62\u5f0f\uff0c\u800c\u4e0d\u4f1a\u5931\u53bb\u5176\u5b9e\u9645\u610f\u4e49\u3002<\/p>\n<p>  \u76ee\u6807\u51fd\u6570\uff08\u539f\u59cb\u4e0e\u7b80\u5316\uff09 <\/p>\n<p>\u8ba9\u6211\u4eec\u9010\u4e00\u5206\u89e3\u3002\u9996\u5148\uff0c <code>AverageResult[\u2026]<\/code> \u6216 <code>1\/n[\u2026]<\/code> \u6307\u7684\u662f\u8bc4\u4f30\u5728\u8bb8\u591a\u4e0d\u540c\u60c5\u51b5\u4e0b\u5e73\u5747\u53d1\u751f\u7684\u60c5\u51b5\u3002\u6211\u4eec\u63d0\u51fa\u4e00\u4e2a\u5305\u542b\u5404\u79cd\u95ee\u9898\u7684\u6a21\u578b\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u95ee\u9898\uff0c\u6a21\u578b\u90fd\u4f1a\u751f\u6210\u4e00\u7ec4\u7b54\u6848\u3002\u901a\u8fc7\u67e5\u770b\u8bb8\u591a\u95ee\u9898\u53ca\u5176\u5404\u81ea\u7684\u7b54\u6848\u7ec4\u4e2d\u7684\u8fd9\u4e9b\u7b54\u6848\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa\u5e73\u5747\u7ed3\u679c\u3002<\/p>\n<p>  \u5e73\u5747\u7684\u542b\u4e49 <\/p>\n<p>\u5728\u6b64\u8fc7\u7a0b\u4e2d\uff0c\u95ee\u9898\u88ab\u8f93\u5165\u5230\u65e7\u6a21\u578b\u4e2d\uff0c\u8be5\u6a21\u578b\u4f1a\u4ea7\u751f\u591a\u4e2a\u7b54\u6848\uff08\u4f8b\u5982\uff0c\u7b54\u6848 1\u3001\u7b54\u6848 2\u3001&#8230;\u3001\u7b54\u6848 G\uff09\u3002\u8fd9\u4e9b\u7b54\u6848\u5f62\u6210\u4e00\u4e2a\u7ec4\uff0c\u901a\u8fc7\u8bc4\u4f30\u4e0d\u540c\u95ee\u9898\u4e2d\u7684\u8fd9\u4e2a\u7ec4\uff0c\u6211\u4eec\u5f97\u51fa\u5e73\u5747\u7ed3\u679c\u3002<\/p>\n<p><code>SumOf[..]<\/code> \u6216 <code>\u2211[\u2026]<\/code> \u6307\u7684\u662f\u5bf9\u4e00\u7ec4\u7b54\u6848\uff08\u4f8b\u5982\uff0c\u7b54\u6848 1\u3001\u7b54\u6848 2\u3001&#8230;\u3001\u7b54\u6848 G\uff09\u4e2d\u7684\u6bcf\u4e2a\u7b54\u6848\u8fdb\u884c\u8ba1\u7b97\uff0c\u7136\u540e\u5c06\u6240\u6709\u8fd9\u4e9b\u8ba1\u7b97\u7684\u7ed3\u679c\u52a0\u5728\u4e00\u8d77\u3002<\/p>\n<p>\u7136\u540e\u662f\u5956\u52b1\u90e8\u5206\u3002\u8fd9\u662f\u5bf9\u7ed9\u51fa\u826f\u597d\u7b54\u6848\u7684\u6a21\u578b\u8fdb\u884c\u5956\u52b1\u7684\u90e8\u5206\u3002\u5b83\u5185\u90e8\u6709\u70b9\u590d\u6742\uff0c\u8ba9\u6211\u4eec\u653e\u5927\u4e00\u4e0b\uff1a<\/p>\n<p>  \u516c\u5f0f <\/p>\n<p><code>ChangeRatio<\/code> \u544a\u8bc9\u6211\u4eec\u4f7f\u7528\u65b0\u6a21\u578b\u7ed9\u51fa\u6b64\u7b54\u6848\u7684\u51e0\u7387\u662f\u589e\u52a0\u8fd8\u662f\u51cf\u5c11\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u7740\u773c\u4e8e\uff1a<\/p>\n<ul>\n<li>\u4f7f\u7528\u65b0\u6a21\u578b\u7684\u7b54\u6848\u51e0\u7387\uff1a\u65b0\u6a21\u578b\u7ed9\u51fa\u7279\u5b9a\u7b54\u6848\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\u3002<\/li>\n<li>\u4f7f\u7528\u65e7\u6a21\u578b\u7684\u7b54\u6848\u51e0\u7387\uff1a\u65e7\u6a21\u578b\u7ed9\u51fa\u76f8\u540c\u7b54\u6848\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\u3002<\/li>\n<\/ul>\n<p>\u63a5\u4e0b\u6765\uff0c\u4f18\u52bf ( <code>Advantage<\/code>) \u5206\u6570\u8868\u660e\u4e0e\u540c\u4e00\u7ec4\u4e2d\u7684\u5176\u4ed6\u7b54\u6848\u76f8\u6bd4\uff0c\u7b54\u6848\u6709\u591a\u597d\u6216\u591a\u5dee\u3002\u5b83\u7684\u8ba1\u7b97\u65b9\u5f0f\u5982\u4e0b\uff1a<\/p>\n<p>  \u4f18\u52bf\u516c\u5f0f <\/p>\n<ul>\n<li>\u7b54\u6848\u7684\u5206\u6570\uff1a\u7ed9\u4e88\u7279\u5b9a\u7b54\u6848\u7684\u5956\u52b1\u3002<\/li>\n<li>\u7ec4\u7684\u5e73\u5747\u5206\u6570\uff1a\u7ec4\u4e2d\u6240\u6709\u7b54\u6848\u7684\u5e73\u5747\u5956\u52b1\u5206\u6570\u3002<\/li>\n<li>\u7ec4\u4e2d\u5206\u6570\u7684\u5206\u5e03\uff1a\u7ec4\u4e2d\u7b54\u6848\u5206\u6570\u7684\u5dee\u5f02\u6709\u591a\u5927\u3002<\/li>\n<\/ul>\n<p><code>Advantage<\/code> \u5206\u6570\u544a\u8bc9\u6211\u4eec\u7b54\u6848\u662f\u5426\u4f18\u4e8e\u8be5\u7ec4\u5185\u7684\u5e73\u5747\u6c34\u5e73\uff0c\u4ee5\u53ca\u597d\u591a\u5c11\u3002<\/p>\n<p>  LimitedChangeRatio \u516c\u5f0f\uff08 <\/p>\n<p><code>LimitedChangeRatio<\/code> \u662f <code>ChangeRatio<\/code> \u7684\u4fee\u6539\u7248\u672c\u3002\u5b83\u786e\u4fdd <code>ChangeRatio<\/code> \u4e0d\u4f1a\u6ce2\u52a8\u592a\u5927\uff0c\u4ece\u800c\u4fdd\u6301\u6a21\u578b\u7684\u5b66\u4e60\u7a33\u5b9a\u3002\u9650\u5236\u7531\u4e00\u4e2a\u79f0\u4e3a <code>Epsilon<\/code> \u7684\u5c0f\u503c\u51b3\u5b9a\uff0c <code>h<\/code> \u786e\u4fdd\u53d8\u5316\u4e0d\u4f1a\u592a\u5267\u70c8\u3002<\/p>\n<p>\u6700\u540e\uff0c <code>SmallerOf[ \u2026 ]<\/code> \u51fd\u6570\u5728\u4e24\u4e2a\u9009\u9879\u4e2d\u9009\u62e9\u8f83\u5c0f\u7684\u503c\uff1a<\/p>\n<ul>\n<li><code>ChangeRatio \u00d7 Advantage<\/code>\uff1a\u7b54\u6848\u53ef\u80fd\u6027\u7684\u53d8\u5316\uff0c\u4e58\u4ee5\u5176\u4f18\u52bf\u5206\u6570\u3002<\/li>\n<li><code>LimitedChangeRatio \u00d7 Advantage<\/code>\uff1a\u76f8\u540c\uff0c\u4f46\u53d8\u5316\u7387\u6709\u9650\u3002<\/li>\n<\/ul>\n<p>\u901a\u8fc7\u9009\u62e9\u8f83\u5c0f\u7684\u503c\uff0c\u6a21\u578b\u53ef\u786e\u4fdd\u5b66\u4e60\u8fc7\u7a0b\u4fdd\u6301\u5e73\u7a33\uff0c\u4e0d\u4f1a\u5bf9\u6027\u80fd\u7684\u5927\u5e45\u53d8\u5316\u53cd\u5e94\u8fc7\u5ea6\u3002\u7ed3\u679c\u662f\u201c\u597d\u7b54\u6848\u5956\u52b1\u201d\uff0c\u9f13\u52b1\u6a21\u578b\u6539\u8fdb\u800c\u4e0d\u4f1a\u8fc7\u5ea6\u8865\u507f\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u51cf\u53bb StayStablePart\u3002\u8fd9\u662f\u4e3a\u4e86\u9632\u6b62\u65b0\u6a21\u578b\u53d1\u751f\u592a\u5927\u7684\u53d8\u5316\u3002\u5b83\u4e0d\u662f\u5f88\u590d\u6742\uff0c\u4f46\u8ba9\u6211\u4eec\u653e\u5927\u5b83\uff1a<\/p>\n<p>  StayStable \u65b9\u7a0b <\/p>\n<p><code>DifferenceFromReferenceModel<\/code> \u6d4b\u91cf\u65b0\u6a21\u578b\u4e0e\u53c2\u8003\u6a21\u578b\uff08\u901a\u5e38\u662f\u65e7\u6a21\u578b\uff09\u7684\u5dee\u5f02\u3002\u672c\u8d28\u4e0a\uff0c\u5b83\u6709\u52a9\u4e8e\u8bc4\u4f30\u65b0\u6a21\u578b\u4e0e\u524d\u4e00\u4e2a\u6a21\u578b\u76f8\u6bd4\u6240\u505a\u7684\u66f4\u6539\u3002<\/p>\n<p><code>Beta<\/code> \u503c\u63a7\u5236\u6a21\u578b\u5e94\u4fdd\u6301\u4e0e\u53c2\u8003\u6a21\u578b\u7684\u63a5\u8fd1\u7a0b\u5ea6\u3002\u8f83\u5927\u7684 <code>Beta<\/code> \u610f\u5473\u7740\u6a21\u578b\u5c06\u4f18\u5148\u4fdd\u6301\u66f4\u63a5\u8fd1\u65e7\u6a21\u578b\u7684\u884c\u4e3a\u548c\u8f93\u51fa\uff0c\u4ee5\u9632\u6b62\u504f\u5dee\u592a\u5927\u3002\u8ba9\u6211\u4eec\u5c06\u5176\u53ef\u89c6\u5316\uff1a<\/p>\n<p>  StayStable \u7684\u89c6\u89c9\u8868\u793a <\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c <code>StayStablePart<\/code> \u786e\u4fdd\u6a21\u578b\u9010\u6e10\u5b66\u4e60\u5e76\u4e14\u4e0d\u4f1a\u75af\u72c2\u8df3\u8dc3\u3002<\/p>\n<h2>6\u3001DeepSeek R1 Zero \u7684\u5956\u52b1\u5efa\u6a21<\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u4e3b\u8981\u7684\u7406\u8bba\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u4f7f\u7528\u6211\u4eec\u7684\u6587\u672c\u8f93\u5165\u6765\u4e86\u89e3\u521b\u5efa R1 Zero \u7684\u5956\u52b1\u5efa\u6a21\u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5bf9\u4e8e R1 Zero\uff0c\u4ed6\u4eec\u4fdd\u6301\u7b80\u5355\u76f4\u63a5\u3002\u4ed6\u4eec\u6ca1\u6709\u4f7f\u7528\u82b1\u54e8\u7684\u795e\u7ecf\u7f51\u7edc\u6765\u5224\u65ad\u7b54\u6848\uff08\u5c31\u50cf\u4ed6\u4eec\u5728\u540e\u671f\u9636\u6bb5\u53ef\u80fd\u4f1a\u505a\u7684\u90a3\u6837\uff09\uff0c\u800c\u662f\u4f7f\u7528\u4e86\u57fa\u4e8e\u89c4\u5219\u7684\u5956\u52b1\u7cfb\u7edf\u3002<\/p>\n<p>\u5bf9\u4e8e\u6211\u4eec\u7684\u6570\u5b66\u95ee\u9898\uff1a\u201c2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u201d<\/p>\n<h3>6.1 \u57fa\u4e8e\u89c4\u5219\u7684\u68c0\u67e5<\/h3>\n<p>\u7cfb\u7edf\u77e5\u9053\u6b63\u786e\u7b54\u6848\u662f 14\u3002\u5b83\u5c06\u67e5\u770b DeepSeek V3\uff08\u6211\u4eec\u7684 RL \u4ee3\u7406\uff09\u751f\u6210\u7684\u8f93\u51fa\uff0c\u5e76\u4e13\u95e8\u68c0\u67e5 &nbsp;<code>&lt;answer&gt;<\/code>\u6807\u7b7e\u5185\u7684\u5185\u5bb9\u3002<\/p>\n<p>  \u57fa\u4e8e\u89c4\u5219\u7684\u68c0\u67e5 <\/p>\n<p>\u5982\u679c &nbsp;<code>&lt;answer&gt;<\/code>\u6807\u7b7e\u5305\u542b\u201c14\u201d\uff08\u6216\u6570\u5b57\u76f8\u540c\u7684\u5185\u5bb9\uff09\uff0c\u5b83\u4f1a\u5f97\u5230\u6b63\u5956\u52b1\uff0c\u6bd4\u5982\u8bf4 +1\u3002\u5982\u679c\u5b83\u9519\u4e86\uff0c\u5b83\u4f1a\u5f97\u5230 0 \u5956\u52b1\uff0c\u751a\u81f3\u53ef\u80fd\u662f\u8d1f\u5956\u52b1\uff08\u5c3d\u7ba1\u672c\u6587\u5728\u8fd9\u4e2a\u9636\u6bb5\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\u91cd\u70b9\u5173\u6ce8 0\uff09\u3002<\/p>\n<h3>6.2 \u683c\u5f0f\u5316\u5956\u52b1<\/h3>\n<p>\u4f46 DeepSeek R1 Zero \u8fd8\u9700\u8981\u5b66\u4e60\u6b63\u786e\u6784\u5efa\u5176\u63a8\u7406\uff0c\u5e76\u4e14\u53ef\u4ee5\u4f7f\u7528 <code>&lt;think&gt;<\/code> \u548c <code>&lt;answer&gt;<\/code> \u6807\u7b7e\uff0c\u6b63\u786e\u8bbe\u7f6e\u683c\u5f0f\u7684\u5956\u52b1\u8f83\u5c11\u3002<\/p>\n<p>  \u683c\u5f0f\u5956\u52b1\u8fc7\u7a0b <\/p>\n<p>\u68c0\u67e5\u6a21\u578b\u8f93\u51fa\u662f\u5426\u6b63\u786e\u5730\u5c06\u63a8\u7406\u8fc7\u7a0b\u5305\u542b\u5728 <code>&lt;think&gt; \u2026&lt;\/think&gt;<\/code> \u4e2d\uff0c\u5e76\u5c06\u6700\u7ec8\u7b54\u6848\u5305\u542b\u5728 <code>&lt;answer&gt;\u2026 &lt;\/answer&gt;<\/code>\u4e2d\u3002<\/p>\n<blockquote><p>\n  DeepSeek R1 \u8bba\u6587\u660e\u786e\u63d0\u5230\u907f\u514d\u4f7f\u7528 DeepSeek-R1-Zero \u7684\u795e\u7ecf\u5956\u52b1\u6a21\u578b\uff0c\u4ee5\u9632\u6b62\u5956\u52b1\u9ed1\u5ba2\u653b\u51fb\u5e76\u964d\u4f4e\u521d\u59cb\u63a2\u7d22\u9636\u6bb5\u7684\u590d\u6742\u6027\n<\/p><\/blockquote>\n<h2>7\u3001\u5956\u52b1\u8bad\u7ec3\u6a21\u677f<\/h2>\n<p>\u4e3a\u4e86\u4f7f\u5956\u52b1\u6a21\u578b\u6709\u6548\uff0c\u7814\u7a76\u4eba\u5458\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u7279\u5b9a\u7684\u8bad\u7ec3\u6a21\u677f\u3002\u8be5\u6a21\u677f\u5145\u5f53\u84dd\u56fe\uff0c\u6307\u5bfc DeepSeek-V3-Base \u5982\u4f55\u5728\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u6784\u5efa\u5176\u54cd\u5e94\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u770b\u539f\u59cb\u6a21\u677f\u5e76\u5c06\u5176\u9010\u4e00\u5206\u89e3\uff1a<\/p>\n<pre><code>A conversation between User and Assistant. The user asks a question, and \nthe Assistant solves it. The assistant first thinks about the reasoning \nprocess in the mind and then provides the user with the answer. The reasoning \nprocess and answer are enclosed within &lt;think&gt; &lt;\/think&gt; and &lt;answer&gt; &lt;\/answer&gt;\ntags respectively, i.e., &lt;think&gt; reasoning process here &lt;\/think&gt;\n&lt;answer&gt; answer here &lt;\/answer&gt;. User: {prompt}. Assistant:<\/code><\/pre>\n<blockquote><p>\n  \u7ffb\u8bd1\uff1a<br \/>\n <br \/>\u7528\u6237\u548c\u52a9\u624b\u4e4b\u95f4\u7684\u5bf9\u8bdd\u3002\u7528\u6237\u63d0\u51fa\u95ee\u9898\uff0c\u52a9\u624b\u89e3\u51b3\u8be5\u95ee\u9898\u3002\u52a9\u624b\u9996\u5148\u5728\u8111\u6d77\u4e2d\u601d\u8003\u63a8\u7406\u8fc7\u7a0b\uff0c\u7136\u540e\u4e3a\u7528\u6237\u63d0\u4f9b\u7b54\u6848\u3002\u63a8\u7406\u8fc7\u7a0b\u548c\u7b54\u6848\u5206\u522b\u5305\u542b\u5728 &nbsp;&lt;think&gt;&lt;\/think&gt; \u548c &lt;answer&gt;&lt;\/answer&gt; &nbsp;\u6807\u7b7e\u4e2d\uff0c\u5373 &nbsp;&lt;think&gt;\u63a8\u7406\u8fc7\u7a0b\u5728\u8fd9\u91cc&lt;\/think&gt; &nbsp;&lt;answer&gt;\u7b54\u6848\u5728\u8fd9\u91cc&lt;\/answer&gt; \u3002\u7528\u6237\uff1a{prompt}\u3002\u52a9\u624b\uff1a\n<\/p><\/blockquote>\n<p>\u6211\u4eec\u5728 <code>{prompt}<\/code> \u4e2d\u63d2\u5165\u6570\u5b66\u95ee\u9898\uff0c\u4f8b\u5982 <code>2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f<\/code>\u3002\u91cd\u8981\u7684\u662f\u90a3\u4e9b &nbsp;\u548c &nbsp;\u6807\u7b7e\u3002\u8fd9\u79cd\u7ed3\u6784\u5316\u8f93\u51fa\u5bf9\u4e8e\u7814\u7a76\u4eba\u5458\u4ee5\u540e\u7aa5\u89c6\u6a21\u578b\u7684\u63a8\u7406\u6b65\u9aa4\u975e\u5e38\u91cd\u8981\u3002<\/p>\n<p>\u5f53\u6211\u4eec\u8bad\u7ec3 DeepSeek-R1-Zero \u65f6\uff0c\u6211\u4eec\u4f7f\u7528\u6b64\u6a21\u677f\u4e3a\u5176\u63d0\u4f9b\u63d0\u793a\u3002\u5bf9\u4e8e\u6211\u4eec\u7684\u793a\u4f8b\u95ee\u9898\uff0c\u8f93\u5165\u5c06\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<pre><code>A conversation between User and Assistant. The user asks a question, and \nthe Assistant solves it. The assistant first thinks about the reasoning \nprocess in the mind and then provides the user with the answer. The reasoning \nprocess and answer are enclosed within &lt;think&gt; &lt;\/think&gt; and &lt;answer&gt; &lt;\/answer&gt;\ntags respectively, i.e., &lt;think&gt; reasoning process here &lt;\/think&gt;\n&lt;answer&gt; answer here &lt;\/answer&gt;. User: What is 2 + 3 * 4?. Assistant:<\/code><\/pre>\n<blockquote><p>\n  \u7ffb\u8bd1\uff1a<br \/>\n <br \/>\u7528\u6237\u548c\u52a9\u624b\u4e4b\u95f4\u7684\u5bf9\u8bdd\u3002\u7528\u6237\u63d0\u51fa\u95ee\u9898\uff0c\u52a9\u624b\u89e3\u51b3\u8be5\u95ee\u9898\u3002\u52a9\u624b\u9996\u5148\u5728\u8111\u6d77\u4e2d\u601d\u8003\u63a8\u7406\u8fc7\u7a0b\uff0c\u7136\u540e\u4e3a\u7528\u6237\u63d0\u4f9b\u7b54\u6848\u3002\u63a8\u7406\u8fc7\u7a0b\u548c\u7b54\u6848\u5206\u522b\u5305\u542b\u5728 &nbsp;&lt;think&gt;&lt;\/think&gt; \u548c &lt;answer&gt;&lt;\/answer&gt; &nbsp;\u6807\u7b7e\u4e2d\uff0c\u5373 &nbsp;&lt;think&gt;\u63a8\u7406\u8fc7\u7a0b\u5728\u8fd9\u91cc&lt;\/think&gt; &nbsp;&lt;answer&gt;\u7b54\u6848\u5728\u8fd9\u91cc&lt;\/answer&gt; \u3002\u7528\u6237\uff1a2+3*4\u7b49\u4e8e\u591a\u5c11\uff1f\u3002\u52a9\u624b\uff1a\n<\/p><\/blockquote>\n<p>\u6211\u4eec\u671f\u671b\u6a21\u578b\u751f\u6210\u7b26\u5408\u6a21\u677f\u7684\u8f93\u51fa\uff0c\u4f8b\u5982\uff1a<\/p>\n<pre><code>&lt;think&gt;\nOrder of operations:\nmultiply before add. 3 * 4 = 12. 2 + 12 = 14\n&lt;\/think&gt;\n&lt;answer&gt;\n14\n&lt;\/answer&gt;<\/code><\/pre>\n<blockquote><p>\n  \u7ffb\u8bd1\uff1a<br \/>\n <br \/>&lt;think&gt;<br \/>\n <br \/>\u8fd0\u7b97\u987a\u5e8f\uff1a\u5148\u4e58\u540e\u52a0\u30023 * 4 = 12\u30022 + 12 = 14 14<br \/>\n <br \/>&lt;think&gt;<br \/>\n <br \/>&lt;answer&gt;<br \/>\n <br \/>14<br \/>\n <br \/>&lt;\/answer&gt;\n<\/p><\/blockquote>\n<p>\u6709\u8da3\u7684\u662f\uff0cDeepSeek \u56e2\u961f\u6709\u610f\u4fdd\u6301\u8fd9\u4e2a\u6a21\u677f\u7b80\u5355\u5e76\u4e13\u6ce8\u4e8e\u7ed3\u6784\uff0c\u800c\u4e0d\u662f\u544a\u8bc9\u6a21\u578b\u5982\u4f55\u63a8\u7406\u3002<\/p>\n<h2>8\u3001DeepSeek R1 Zero \u7684\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u8fc7\u7a0b<\/h2>\n<p>\u5c3d\u7ba1\u672c\u6587\u6ca1\u6709\u6307\u5b9a\u5f3a\u5316\u5b66\u4e60\u9884\u8bad\u7ec3\u7684\u786e\u5207\u521d\u59cb\u6570\u636e\u96c6\uff0c\u4f46\u6211\u4eec\u5047\u8bbe\u5b83\u5e94\u8be5\u4ee5\u63a8\u7406\u4e3a\u91cd\u70b9\u3002<\/p>\n<p>\u4ed6\u4eec\u6240\u505a\u7684\u7b2c\u4e00\u6b65\u662f\u4f7f\u7528\u65e7\u7b56\u7565\uff08\u5373\u5f3a\u5316\u5b66\u4e60\u66f4\u65b0\u4e4b\u524d\u7684 DeepSeek-V3-Base \u6a21\u578b\uff09\u751f\u6210\u591a\u4e2a\u53ef\u80fd\u7684\u8f93\u51fa\u3002\u5728\u4e00\u6b21\u8bad\u7ec3\u8fed\u4ee3\u4e2d\uff0c\u6211\u4eec\u5047\u8bbe GRPO \u91c7\u6837\u4e00\u7ec4 G = 4 \u4e2a\u8f93\u51fa\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u8be5\u6a21\u578b\u4e3a\u6211\u4eec\u7684\u6587\u672c\u8f93\u5165\u751f\u6210\u4ee5\u4e0b\u56db\u4e2a\u8f93\u51fa 2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f<\/p>\n<ul>\n<li>o1\uff1a &nbsp;<code>&lt;think&gt;2 + 3 = 5, 5 * 4 = 20&lt;\/think&gt; &nbsp;&lt;answer&gt; 20&lt;\/answer&gt;<\/code> \uff08\u8fd0\u7b97\u987a\u5e8f\u4e0d\u6b63\u786e\uff09<\/li>\n<li>o2\uff1a <code>&lt;think&gt;3 * 4 = 12, 2 + 12 = 14&lt;\/think&gt; &lt;answer&gt;14&lt;\/answer&gt;<\/code> \uff08\u6b63\u786e\uff09<\/li>\n<li>o3\uff1a <code>&lt;answer&gt;14&lt;\/answer&gt;<\/code> \uff08\u6b63\u786e\uff0c\u4f46\u7f3a\u5c11 <code>&lt;think&gt;<\/code>\u6807\u7b7e\uff09<\/li>\n<li>o4\uff1a <code>&lt;think&gt;...\u4e00\u4e9b\u80e1\u8a00\u4e71\u8bed\u7684\u63a8\u7406...&lt;\/think&gt; &nbsp;&lt;answer&gt; 7&lt;answer&gt;<\/code> \uff08\u4e0d\u6b63\u786e\u4e14\u63a8\u7406\u4e0d\u4f73\uff09<\/li>\n<\/ul>\n<p>  \u751f\u6210\u8f93\u51fa <\/p>\n<p>\u6bcf\u4e2a\u8f93\u51fa\u5c06\u6839\u636e\u6b63\u786e\u6027\u548c\u63a8\u7406\u8d28\u91cf\u8fdb\u884c\u8bc4\u4f30\u5e76\u5206\u914d\u5956\u52b1\u3002<\/p>\n<p>\u4e3a\u4e86\u5f15\u5bfc\u6a21\u578b\u8fdb\u884c\u66f4\u597d\u7684\u63a8\u7406\uff0c\u57fa\u4e8e\u89c4\u5219\u7684\u5956\u52b1\u7cfb\u7edf\u5e94\u8fd0\u800c\u751f\u3002\u6bcf\u4e2a\u8f93\u51fa\u90fd\u6839\u636e\u4ee5\u4e0b\u6761\u4ef6\u5206\u914d\u5956\u52b1\uff1a<\/p>\n<ul>\n<li>\u51c6\u786e\u5ea6\u5956\u52b1\uff1a\u7b54\u6848\u662f\u5426\u6b63\u786e\u3002<\/li>\n<li>\u683c\u5f0f\u5956\u52b1\uff1a\u63a8\u7406\u6b65\u9aa4\u662f\u5426\u4f7f\u7528 &nbsp;\u6807\u7b7e\u6b63\u786e\u683c\u5f0f\u5316\u3002<\/li>\n<\/ul>\n<p>\u5047\u8bbe\u5956\u52b1\u5206\u914d\u5982\u4e0b\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u8f93\u51fa<\/th>\n<th>\u51c6\u786e\u7387\u5956\u52b1<\/th>\n<th>\u683c\u5f0f\u5956\u52b1<\/th>\n<th>\u603b\u5956\u52b1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>o1\uff08\u63a8\u7406\u9519\u8bef\uff09<\/td>\n<td>0<\/td>\n<td>0.1<\/td>\n<td>0.1<\/td>\n<\/tr>\n<tr>\n<td>o2\uff08\u63a8\u7406\u6b63\u786e\uff09<\/td>\n<td>1<\/td>\n<td>0.1<\/td>\n<td>1.1<\/td>\n<\/tr>\n<tr>\n<td>o3\uff08\u6b63\u786e\u4f46\u7f3a\u5c11\u6807\u7b7e\uff09<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<td>1.0<\/td>\n<\/tr>\n<tr>\n<td>o4\uff08\u63a8\u7406\u9519\u8bef\u4e14\u8f83\u5dee\uff09<\/td>\n<td>0<\/td>\n<td>0.1<\/td>\n<td>0.1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>  \u5956\u52b1\u7ec6\u5206 <\/p>\n<p>\u6a21\u578b\u5e94\u8be5\u5b66\u4f1a\u504f\u7231\u5956\u52b1\u66f4\u9ad8\u7684\u8f93\u51fa\uff0c\u540c\u65f6\u964d\u4f4e\u751f\u6210\u4e0d\u6b63\u786e\u6216\u4e0d\u5b8c\u6574\u8f93\u51fa\u7684\u6982\u7387\u3002<\/p>\n<p>\u4e3a\u4e86\u786e\u5b9a\u6bcf\u4e2a\u8f93\u51fa\u5bf9\u6a21\u578b\u6027\u80fd\u7684\u6539\u5584\u6216\u6076\u5316\u7a0b\u5ea6\uff0c\u6211\u4eec\u4f7f\u7528\u5956\u52b1\u503c\u8ba1\u7b97\u4f18\u52bf\u3002\u4f18\u52bf\u6709\u52a9\u4e8e\u901a\u8fc7\u5f3a\u5316\u66f4\u597d\u7684\u8f93\u51fa\u6765\u4f18\u5316\u7b56\u7565\u3002<\/p>\n<p>\u4e3a\u6b64\uff0c\u8ba9\u6211\u4eec\u8ba1\u7b97\u5e73\u5747\u7b2c\u4e00\u4e2a\u5956\u52b1\u3002<\/p>\n<p>  \u5e73\u5747\u5956\u52b1\u8ba1\u7b97 <\/p>\n<p>\u6807\u51c6\u5dee\uff08\u8fd1\u4f3c\u503c\uff09= 0.5\uff0c\u73b0\u5728\u8ba1\u7b97\u6bcf\u4e2a\u8f93\u51fa\u7684\u4f18\u52bf\u3002<\/p>\n<p>  \u8ba1\u7b97\u6bcf\u4e2a\u8f93\u51fa\u7684\u5956\u52b1  \u53ef\u89c6\u5316\u4f18\u52bf\u8ba1\u7b97 <\/p>\n<p>\u8f93\u51fa o2 \u548c o3 \u83b7\u5f97\u6b63\u4f18\u52bf\uff0c\u8fd9\u610f\u5473\u7740\u5e94\u8be5\u9f13\u52b1\u5b83\u4eec\u3002\u8f93\u51fa o1 \u548c o4 \u83b7\u5f97\u8d1f\u4f18\u52bf\uff0c\u8fd9\u610f\u5473\u7740\u5e94\u8be5\u963b\u6b62\u5b83\u4eec\u3002<\/p>\n<p>\u7136\u540e\uff0cGRPO \u4f7f\u7528\u8ba1\u7b97\u51fa\u7684\u4f18\u52bf\u6765\u66f4\u65b0\u7b56\u7565\u6a21\u578b (DeepSeek-V3-Base)\uff0c\u4ee5\u589e\u52a0\u751f\u6210\u5177\u6709\u9ad8\u4f18\u52bf\u7684\u8f93\u51fa\uff08\u5982 o2 \u548c o3\uff09\u7684\u6982\u7387\uff0c\u5e76\u964d\u4f4e\u5177\u6709\u4f4e\u4f18\u52bf\u6216\u8d1f\u4f18\u52bf\u7684\u8f93\u51fa\uff08\u5982 o1 \u548c o4\uff09\u7684\u6982\u7387\u3002<\/p>\n<p>\u66f4\u65b0\u6839\u636e\u4ee5\u4e0b\u5185\u5bb9\u8c03\u6574\u6a21\u578b\u6743\u91cd\uff1a<\/p>\n<ul>\n<li>\u7b56\u7565\u6bd4\u7387\uff1a\u5728\u65b0\u7b56\u7565\u4e0e\u65e7\u7b56\u7565\u4e0b\u751f\u6210\u8f93\u51fa\u7684\u6982\u7387\u3002<\/li>\n<li>\u88c1\u526a\u673a\u5236\uff1a\u9632\u6b62\u8fc7\u5927\u7684\u66f4\u65b0\uff0c\u8fd9\u53ef\u80fd\u4f1a\u7834\u574f\u8bad\u7ec3\u7684\u7a33\u5b9a\u6027\u3002<\/li>\n<li>KL \u53d1\u6563\u60e9\u7f5a\uff1a\u786e\u4fdd\u66f4\u65b0\u4e0d\u4f1a\u504f\u79bb\u539f\u59cb\u6a21\u578b\u592a\u8fdc\u3002<\/li>\n<\/ul>\n<p>  GRPO \u5de5\u4f5c <\/p>\n<p>\u8fd9\u786e\u4fdd\u5728\u4e0b\u4e00\u6b21\u8fed\u4ee3\u4e2d\uff0c\u6a21\u578b\u66f4\u6709\u53ef\u80fd\u751f\u6210\u6b63\u786e\u7684\u63a8\u7406\u6b65\u9aa4\uff0c\u540c\u65f6\u51cf\u5c11\u4e0d\u6b63\u786e\u6216\u4e0d\u5b8c\u6574\u7684\u54cd\u5e94\u3002<\/p>\n<p>\u56e0\u6b64\uff0cRL \u662f\u4e00\u4e2a\u8fed\u4ee3\u8fc7\u7a0b\u3002\u4f7f\u7528\u4e0d\u540c\u7684\u63a8\u7406\u95ee\u9898\u91cd\u590d\u4e0a\u8ff0\u6b65\u9aa4\u6570\u5343\u6b21\u3002\u6bcf\u6b21\u8fed\u4ee3\u90fd\u4f1a\u9010\u6e10\u63d0\u9ad8\u6a21\u578b\u7684\u80fd\u529b\uff1a<\/p>\n<ul>\n<li>\u6267\u884c\u6b63\u786e\u7684\u64cd\u4f5c\u987a\u5e8f<\/li>\n<li>\u63d0\u4f9b\u903b\u8f91\u63a8\u7406\u6b65\u9aa4<\/li>\n<li>\u59cb\u7ec8\u4f7f\u7528\u6b63\u786e\u7684\u683c\u5f0f<\/li>\n<\/ul>\n<p>\u6574\u4f53\u8bad\u7ec3\u5faa\u73af\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<p>  DeepSeek \u7b80\u5316\u8bad\u7ec3\u8fc7\u7a0b <\/p>\n<p>\u968f\u7740\u65f6\u95f4\u7684\u63a8\u79fb\uff0c\u6a21\u200b\u200b\u578b\u4f1a\u4ece\u9519\u8bef\u4e2d\u5438\u53d6\u6559\u8bad\uff0c\u5728\u89e3\u51b3\u63a8\u7406\u95ee\u9898\u65b9\u9762\u53d8\u5f97\u66f4\u52a0\u51c6\u786e\u548c\u6709\u6548\u3002 <\/p>\n<h2>9\u3001R1 Zero \u7684\u4e24\u4e2a\u4e3b\u8981\u95ee\u9898<\/h2>\n<p>\u5728 V3 \u6a21\u578b\u4e0a\u4f7f\u7528 RL \u8bad\u7ec3\u8fc7\u7a0b\u521b\u5efa DeepSeek-R1 Zero \u540e\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u8bad\u7ec3\u540e\u7684\u6a21\u578b\u5728\u63a8\u7406\u6d4b\u8bd5\u4e2d\u8868\u73b0\u975e\u5e38\u51fa\u8272\uff0c\u751a\u81f3\u5728 AIME 2024 \u7b49\u4efb\u52a1\u4e0a\u7684\u5f97\u5206\u4e0e OpenAI-01-0912 \u7b49\u66f4\u9ad8\u7ea7\u7684\u6a21\u578b\u76f8\u4f3c\u3002\u8fd9\u8868\u660e\u4f7f\u7528\u5f3a\u5316\u5b66\u4e60 (RL) \u6765\u9f13\u52b1\u8bed\u8a00\u6a21\u578b\u4e2d\u7684\u63a8\u7406\u662f\u4e00\u79cd\u5f88\u6709\u524d\u9014\u7684\u65b9\u6cd5\u3002<\/p>\n<p>\u4f46\u4ed6\u4eec\u4e5f\u6ce8\u610f\u5230 DeepSeek-R1-Zero \u6709\u4e00\u4e9b\u5173\u952e\u95ee\u9898\u9700\u8981\u89e3\u51b3\uff0c\u624d\u80fd\u5728\u73b0\u5b9e\u4e16\u754c\u4e2d\u4f7f\u7528\u5e76\u8fdb\u884c\u66f4\u5e7f\u6cdb\u7684\u7814\u7a76\u3002<\/p>\n<p>  R1 Zero \u7684\u95ee\u9898\uff08 <\/p>\n<p>DeepSeek \u7684\u7814\u7a76\u4eba\u5458\u8868\u793a\uff0c\u8be5\u6a21\u677f\u6709\u610f\u7b80\u5355\u4e14\u7ed3\u6784\u96c6\u4e2d\u3002\u5b83\u907f\u514d\u5bf9\u63a8\u7406\u8fc7\u7a0b\u672c\u8eab\u65bd\u52a0\u4efb\u4f55\u7279\u5b9a\u4e8e\u5185\u5bb9\u7684\u9650\u5236\u3002\u4f8b\u5982\uff0c\u5b83\u6ca1\u6709\u8bf4\uff1a<\/p>\n<ul>\n<li>\u201c\u4f60\u5fc5\u987b\u4f7f\u7528\u5206\u6b65\u63a8\u7406\u201d\uff08\u5b83\u53ea\u662f\u8bf4\u201c\u63a8\u7406\u8fc7\u7a0b\u201d\uff0c\u8ba9\u6a21\u578b\u6765\u5b9a\u4e49\u5b83\u7684\u542b\u4e49\uff09\u3002<\/li>\n<li>\u201c\u4f60\u5fc5\u987b\u4f7f\u7528\u53cd\u601d\u6027\u63a8\u7406\u201d<\/li>\n<li>\u201c\u4f60\u5fc5\u987b\u4f7f\u7528\u7279\u5b9a\u7684\u95ee\u9898\u89e3\u51b3\u7b56\u7565\u201d<\/li>\n<\/ul>\n<p>\u4e3b\u8981\u95ee\u9898\u662f &nbsp;\u6807\u7b7e\u5185\u7684\u63a8\u7406\u8fc7\u7a0b\u96be\u4ee5\u9605\u8bfb\uff0c\u4f7f\u4eba\u7c7b\u96be\u4ee5\u7406\u89e3\u548c\u5206\u6790\u3002<\/p>\n<p>\u53e6\u4e00\u4e2a\u95ee\u9898\u662f\u8bed\u8a00\u6df7\u5408\uff0c\u5f53\u88ab\u95ee\u5230\u591a\u8bed\u8a00\u95ee\u9898\u65f6\uff0c\u6a21\u578b\u6709\u65f6\u4f1a\u5728\u540c\u4e00\u4e2a\u56de\u7b54\u4e2d\u6df7\u5408\u4f7f\u7528\u591a\u79cd\u8bed\u8a00\uff0c\u5bfc\u81f4\u8f93\u51fa\u4e0d\u4e00\u81f4\u548c\u6df7\u4e71\u3002\u5982\u679c\u4f60\u7528\u897f\u73ed\u7259\u8bed\u95ee\u5b83\u95ee\u9898\u3002\u7a81\u7136\u95f4\uff0c\u5b83\u7684\u201c\u601d\u7ef4\u201d\u5c31\u4f1a\u53d8\u6210\u82f1\u8bed\u548c\u897f\u73ed\u7259\u8bed\u7684\u6df7\u6742\uff0c\u4e0d\u592a\u5b8c\u7f8e\uff01\u8fd9\u4e9b\u95ee\u9898\uff0c\u6df7\u4e71\u7684\u63a8\u7406\u548c\u8bed\u8a00\u6df7\u4e71\uff0c\u662f\u660e\u663e\u7684\u969c\u788d\u3002<\/p>\n<blockquote><p>\n  \u8fd9\u662f\u4ed6\u4eec\u5c06\u6700\u521d\u7684 R1 Zero \u6a21\u578b\u8f6c\u53d8\u4e3a R1 \u7684\u4e24\u4e2a\u4e3b\u8981\u539f\u56e0\n<\/p><\/blockquote>\n<p>\u5728\u4e0b\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4ecb\u7ecd\u4ed6\u4eec\u5982\u4f55\u5c06 R1 zero \u6a21\u578b\u6539\u8fdb\u4e3a R1 \u6a21\u578b\uff0c\u4ece\u800c\u63d0\u9ad8\u5176\u6027\u80fd\u5e76\u5e2e\u52a9\u5176\u80dc\u8fc7\u6240\u6709\u5176\u4ed6\u6a21\u578b\uff08\u65e0\u8bba\u662f\u5f00\u6e90\u7684\u8fd8\u662f\u5c01\u95ed\u7684\uff09\u3002<\/p>\n<h2>10\u3001\u51b7\u542f\u52a8\u6570\u636e<\/h2>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u4fee\u590d R1 Zero \u95ee\u9898\u5e76\u771f\u6b63\u8ba9 DeepSeek \u63a8\u7406\u6b63\u786e\uff0c\u7814\u7a76\u4eba\u5458\u8fdb\u884c\u4e86\u51b7\u542f\u52a8\u6570\u636e\u6536\u96c6\u5e76\u5305\u62ec\u76d1\u7763\u5fae\u8c03\u3002<\/p>\n<p>\u4f60\u53ef\u4ee5\u5c06\u5176\u89c6\u4e3a\u5728\u771f\u6b63\u6fc0\u70c8\u7684 RL \u8bad\u7ec3\u4e4b\u524d\u4e3a\u6a21\u578b\u63d0\u4f9b\u826f\u597d\u7684\u63a8\u7406\u57fa\u7840\u3002\u57fa\u672c\u4e0a\uff0c\u4ed6\u4eec\u60f3\u6559 DeepSeek-V3 Base \u826f\u597d\u7684\u63a8\u7406\u662f\u4ec0\u4e48\u6837\u5b50\u4ee5\u53ca\u5982\u4f55\u6e05\u6670\u5730\u5448\u73b0\u5b83\u3002<\/p>\n<h3>10.1 \u4f7f\u7528\u957f CoT \u8fdb\u884c\u5c11\u91cf\u63d0\u793a<\/h3>\n<p>\u4ed6\u4eec\u4e3a DeepSeek-V3 Base \u63d0\u4f9b\u4e86\u4e00\u4e9b\u95ee\u9898\u793a\u4f8b\u4ee5\u53ca\u975e\u5e38\u8be6\u7ec6\u7684\u5206\u6b65\u89e3\u51b3\u65b9\u6848\uff0c\u79f0\u4e3a\u601d\u7ef4\u94fe (CoT)\u3002\u8fd9\u4e2a\u60f3\u6cd5\u662f\u8ba9\u6a21\u578b\u901a\u8fc7\u793a\u4f8b\u5b66\u4e60\u5e76\u5f00\u59cb\u6a21\u4eff\u8fd9\u79cd\u5206\u6b65\u63a8\u7406\u98ce\u683c\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u76f4\u89c2\u5730\u4e86\u89e3\u8fd9\u4e2a\u57fa\u4e8e\u793a\u4f8b\u7684\u5b66\u4e60\uff1a<\/p>\n<p>  \u57fa\u4e8e\u793a\u4f8b\u7684\u5b66\u4e60 <\/p>\n<p>\u5bf9\u4e8e\u6211\u4eec\u7684\u793a\u4f8b\u95ee\u9898 &nbsp;<code>2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f<\/code>\uff0c\u4ed6\u4eec\u53ef\u80fd\u4f1a\u663e\u793a\u5982\u4e0b\u63d0\u793a\uff1a<\/p>\n<pre><code>Problem Examples with Solutions:\n\nProblem: What's the square root of 9 plus 5?\nSolution: | special_token | First, find the square root of 9, which is 3. \nThen, add 5 to 3.  3 + 5 equals 8. | special_token | Summary: The answer is 8.\n\nProblem: Train travels at 60 mph for 2 hours, how far?\nSolution: | special_token | Use the formula: Distance = Speed times Time. \nSpeed is 60 mph, Time is 2 hours. Distance = 60 * 2 = 120 miles. \n| special_token | Summary: Train travels 120 miles.\n\nProblem: What is 2 + 3 * 4?\nSolution:<\/code><\/pre>\n<p>\u90a3\u4e9b <code>| special_token |<\/code> \u4e1c\u897f\u53ea\u662f\u5c06\u63a8\u7406\u6b65\u9aa4\u4e0e\u6458\u8981\u5206\u5f00\u7684\u6807\u8bb0\uff0c\u4f7f\u6a21\u578b\u53ef\u4ee5\u6e05\u695a\u5730\u5b66\u4e60\u7ed3\u6784\u3002<\/p>\n<p>\u770b\u5230\u8fd9\u4e9b\u793a\u4f8b\u540e\uff0c\u6a21\u578b\u5e94\u8be5\u5b66\u4f1a\u4ee5\u7c7b\u4f3c\u7684\u683c\u5f0f\u7ed9\u51fa\u7b54\u6848\uff0c\u4f8b\u5982 <code>2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f<\/code><\/p>\n<pre><code>| special_token |  Following order of operations (PEMDAS\/BODMAS), \ndo multiplication before addition.  So, first calculate 3 * 4 = 12. \nThen, add 2 to 12. 2 + 12 = 14. | special_token | Summary: The answer is 14.<\/code><\/pre>\n<h3>10.2 \u76f4\u63a5\u63d0\u793a<\/h3>\n<p>\u4ed6\u4eec\u6536\u96c6\u6570\u636e\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u76f4\u63a5\u63d0\u793a\u6a21\u578b\u4e0d\u4ec5\u89e3\u51b3\u95ee\u9898\uff0c\u800c\u4e14\u8fd8\u8981\u9010\u6b65\u660e\u786e\u5730\u5c55\u793a\u5176\u63a8\u7406\uff0c\u7136\u540e\u4ed4\u7ec6\u68c0\u67e5\u5176\u7b54\u6848\u3002<\/p>\n<p>  \u76f4\u63a5\u63d0\u793a <\/p>\n<p>\u8fd9\u662f\u4e3a\u4e86\u4fc3\u8fdb\u66f4\u4ed4\u7ec6\u548c\u5468\u5230\u7684\u95ee\u9898\u89e3\u51b3\u3002<\/p>\n<p>\u5bf9\u4e8e 2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\uff0c\u63d0\u793a\u53ef\u80fd\u662f\uff1a<\/p>\n<pre><code>Problem: Solve this, show reasoning step-by-step, and verify:\nWhat is 2 + 3 * 4?<\/code><\/pre>\n<p>\u4ed6\u4eec\u786e\u5b9e\u671f\u671b\u8f93\u51fa\u5305\u542b\u63a8\u7406\u6b65\u9aa4\u548c\u9a8c\u8bc1\u90e8\u5206\uff1a<\/p>\n<pre><code>| special_token | Reasoning: To solve 2 + 3 * 4, I need to use order of \noperations. Multiplication comes before addition.\nStep 1: Calculate 3 * 4 = 12.\nStep 2: Add 2 to the result from step 1: 2 + 12 = 14.\nVerification:  Checking order of operations again, yes, multiplication \nis before addition.  Calculation looks right.\n| special_token | Summary: The answer is 14.<\/code><\/pre>\n<h3>10.3 \u540e\u5904\u7406\u7ec6\u5316<\/h3>\n<p>\u4ed6\u4eec\u751a\u81f3\u4f7f\u7528\u4e86\u5df2\u7ecf\u8bad\u7ec3\u8fc7\u7684 R1 Zero \u6a21\u578b\u7684\u8f93\u51fa\u3002\u5c3d\u7ba1 R1 Zero \u5b58\u5728\u95ee\u9898\uff0c\u4f46\u5b83\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e9b\u63a8\u7406\u3002\u56e0\u6b64\uff0c\u4ed6\u4eec\u91c7\u7528\u4e86 R1 Zero \u7684\u8f93\u51fa\uff0c\u5e76\u8ba9\u4eba\u7c7b\u6807\u6ce8\u8005\u4f7f\u5176\u66f4\u6e05\u6670\u3001\u66f4\u7ed3\u6784\u5316\uff0c\u5e76\u7ea0\u6b63\u4efb\u4f55\u9519\u8bef\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6df7\u4e71\u7684 R1 Zero \u8f93\u51fa\u53ef\u80fd\u662f\uff1a<\/p>\n<pre><code>&lt;think&gt;  ummm... multiply 3 and 4... get 12... then add 2...&lt;\/think&gt;\n&lt;answer&gt; 14 &lt;\/answer&gt;<\/code><\/pre>\n<p>\u7136\u540e\u4eba\u7c7b\u4f1a\u5bf9\u5176\u8fdb\u884c\u6539\u8fdb\uff0c\u4f7f\u5176\u66f4\u6e05\u6670\u3001\u683c\u5f0f\u66f4\u597d\uff1a<\/p>\n<pre><code>| special_token | Reasoning: To solve this, we use order of operations,\ndoing multiplication before addition.\nStep 1: Multiply 3 by 4, which is 12.\nStep 2: Add 2 to the result: 2 + 12 = 14.\n| special_token | Summary: The answer is 14.<\/code><\/pre>\n<p>\u53ef\u89c6\u5316\u7ec6\u5316\u8fc7\u7a0b\u7684\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\uff1a<\/p>\n<p>  \u7ec6\u5316\u8fc7\u7a0b <\/p>\n<p>\u4ed6\u4eec\u6700\u7ec8\u83b7\u5f97\u7684\u51b7\u542f\u52a8\u6570\u636e\u975e\u5e38\u597d\uff0c\u56e0\u4e3a\uff1a<\/p>\n<ul>\n<li>\u9ad8\u8d28\u91cf\u63a8\u7406\u793a\u4f8b\uff1a\u6bcf\u4e2a\u793a\u4f8b\u90fd\u5c55\u793a\u4e86\u826f\u597d\u7684\u9010\u6b65\u63a8\u7406\u3002<\/li>\n<li>\u4e00\u81f4\u3001\u53ef\u8bfb\u7684\u683c\u5f0f\uff1a <code>| special_token |<\/code> \u683c\u5f0f\u4f7f\u6240\u6709\u5185\u5bb9\u7edf\u4e00\u4e14\u6613\u4e8e\u5904\u7406\u3002<\/li>\n<li>\u4eba\u5de5\u68c0\u67e5\uff1a\u4ed6\u4eec\u786e\u4fdd\u8fc7\u6ee4\u6389\u4efb\u4f55\u4e0d\u597d\u7684\u4f8b\u5b50\uff0c\u56e0\u6b64\u6570\u636e\u5e72\u51c0\u53ef\u9760\u3002<\/li>\n<\/ul>\n<p>\u83b7\u5f97\u6b64\u51b7\u542f\u52a8\u6570\u636e\u540e\uff0c\u4ed6\u4eec\u8fdb\u884c\u4e86\u76d1\u7763\u5fae\u8c03 (SFT)\u3002<\/p>\n<h2>11\u3001\u76d1\u7763\u5fae\u8c03<\/h2>\n<p>SFT \u7b2c 1 \u9636\u6bb5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u4f7f\u7528\u76d1\u7763\u5b66\u4e60\u6765\u6559 DeepSeek-V3-Base \u5982\u4f55\u4ea7\u751f\u9ad8\u8d28\u91cf\u3001\u7ed3\u6784\u5316\u7684\u63a8\u7406\u8f93\u51fa\u3002<\/p>\n<p>\u57fa\u672c\u4e0a\uff0c\u6211\u4eec\u5411\u6a21\u578b\u5c55\u793a\u4e86\u8bb8\u591a\u826f\u597d\u63a8\u7406\u7684\u4f8b\u5b50\uff0c\u5e76\u8981\u6c42\u5b83\u5b66\u4e60\u6a21\u4eff\u8fd9\u79cd\u98ce\u683c\u3002<\/p>\n<p>\u5bf9\u4e8e SFT\uff0c\u6211\u4eec\u9700\u8981\u5c06\u51b7\u542f\u52a8\u6570\u636e\u683c\u5f0f\u5316\u4e3a\u8f93\u5165-\u76ee\u6807\u5bf9\u3002\u5bf9\u4e8e\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u63a8\u7406\u95ee\u9898\uff0c\u6211\u4eec\u90fd\u4f1a\u521b\u5efa\u4e00\u4e2a\u8fd9\u6837\u7684\u5bf9\uff1a<\/p>\n<p>\u8f93\u5165 = \u63d0\u793a\u6216\u95ee\u9898\u63cf\u8ff0\u672c\u8eab<\/p>\n<pre><code>User: What is 2 + 3 * 4? Assistant:<\/code><\/pre>\n<p>\u8fd9\u662f\u6211\u4eec\u8f93\u5165\u5230\u6a21\u578b\u4e2d\u7684\u5185\u5bb9\uff0c\u6211\u4eec\u7684\u76ee\u6807\u662f\u76f8\u5e94\u7684\u7ed3\u6784\u826f\u597d\u7684\u63a8\u7406\u548c\u7b54\u6848<\/p>\n<pre><code>| special_token | According to the order of operations (PEMDAS\/BODMAS) ... \nSummary: The answer is 14.<\/code><\/pre>\n<p>\u8fd9\u662f\u6211\u4eec\u5e0c\u671b\u6a21\u578b\u5b66\u4e60\u751f\u6210\u7684\u7406\u60f3\u8f93\u51fa\u3002<\/p>\n<p>\u6211\u4eec\u544a\u8bc9\u6a21\u578b\uff1a<\/p>\n<blockquote><p>\n  \u5f53\u4f60\u770b\u5230\u6b64\u8f93\u5165\uff08\u95ee\u9898\uff09\u65f6\uff0c\u6211\u4eec\u5e0c\u671b\u4f60\u4ea7\u751f\u6b64\u76ee\u6807\u8f93\u51fa\uff08\u826f\u597d\u7684\u63a8\u7406\u548c\u7b54\u6848\uff09\n<\/p><\/blockquote>\n<p>\u4e0e\u5176\u7528\u8be6\u7ec6\u7684\u6587\u5b57\u89e3\u91ca\u5e76\u8ba9\u4f60\u96be\u4ee5\u7406\u89e3\uff0c\u4e0d\u5982\u5148\u5c06\u5176\u53ef\u89c6\u5316\uff0c\u4ee5\u4fbf\u66f4\u5bb9\u6613\u89e3\u91ca SFT<\/p>\n<p>  SFT \u6d41\u7a0b <\/p>\n<p>\u5fae\u8c03\u8fc7\u7a0b\u4ece\u8f93\u5165\u5f00\u59cb\uff1a\u63d0\u793a + \u76ee\u6807\u63a8\u7406\uff0c\u6211\u4eec\u5728\u6b64\u63d0\u4f9b\u4e00\u4e2a\u95ee\u9898\u548c\u4e00\u4e2a\u7ed3\u6784\u5316\u7684\u63a8\u7406\u793a\u4f8b\u3002\u8fd9\u4f1a\u8bad\u7ec3\u6a21\u578b\uff08DeepSeek-V3-Base \u6a21\u578b\uff09\u4ee5\u751f\u6210\u7ed3\u6784\u826f\u597d\u7684\u54cd\u5e94\u3002<\/p>\n<p>\u5728\u9884\u6d4b\u4e0b\u4e00\u4e2a\u6807\u8bb0\u4e2d\uff0c\u6a21\u578b\u4f1a\u751f\u6210\u63a8\u7406\u5e8f\u5217\u4e2d\u7684\u4e0b\u4e00\u4e2a\u5355\u8bcd\u3002\u4f7f\u7528\u635f\u5931\u51fd\u6570\u5c06\u5176\u4e0e\u6bd4\u8f83\u76ee\u6807\u6807\u8bb0\uff08\u8ba1\u7b97\u635f\u5931\uff09\u4e2d\u7684\u5b9e\u9645\u4e0b\u4e00\u4e2a\u6807\u8bb0\u8fdb\u884c\u6bd4\u8f83\u3002\u635f\u5931\u8d8a\u5927\uff0c\u610f\u5473\u7740\u9884\u6d4b\u8ddd\u79bb\u6b63\u786e\u6807\u8bb0\u8d8a\u8fdc\u3002<\/p>\n<p>\u5728\u66f4\u65b0\u6a21\u578b\u53c2\u6570\u4e2d\uff0c\u53cd\u5411\u4f20\u64ad\u548c\u4f18\u5316\u5668\u4f1a\u8c03\u6574\u6a21\u578b\u7684\u6743\u91cd\u4ee5<\/p>\n<p>\u6539\u8fdb\u5176\u9884\u6d4b\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u5faa\u73af\u5f80\u590d\uff0c\u91cd\u590d\u8bb8\u591a\u8f93\u5165\u76ee\u6807\u5bf9\uff0c\u6bcf\u6b21\u8fed\u4ee3\u9010\u6e10\u63d0\u9ad8\u6a21\u578b\u7ed3\u6784\u5316\u63a8\u7406\u80fd\u529b\u3002<\/p>\n<h2>12\u3001\u63a8\u7406\u5bfc\u5411\u5f3a\u5316\u5b66\u4e60<\/h2>\n<p>\u4ed6\u4eec\u5df2\u7ecf\u4e3a DeepSeek V3 \u63d0\u4f9b\u4e86 SFT \u63a8\u7406\u6559\u80b2\uff0c\u4f46\u4e3a\u4e86\u771f\u6b63\u63d0\u9ad8\u5176\u63a8\u7406\u80fd\u529b\uff0c\u7814\u7a76\u4eba\u5458\u5f15\u5165\u4e86\u63a8\u7406\u5bfc\u5411\u5b66\u4e60\uff01<\/p>\n<p>\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u91c7\u7528 SFT \u5fae\u8c03\u7684 DeepSeek-V3 \u6a21\u578b\uff0c\u5e76\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u63a8\u52a8\u5b83\u53d8\u5f97\u66f4\u597d\u3002<\/p>\n<p>\u4ed6\u4eec\u786e\u5b9e\u4f7f\u7528\u4e86\u76f8\u540c\u7684 GRPO \u7b97\u6cd5\uff0c\u4f46\u8fd9\u4e00\u9636\u6bb5\u771f\u6b63\u7684\u5347\u7ea7\u662f\u5956\u52b1\u7cfb\u7edf\u3002\u4ed6\u4eec\u6dfb\u52a0\u4e86\u4e00\u4e9b\u65b0\u7684\u3001\u975e\u5e38\u91cd\u8981\u7684\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\uff01<\/p>\n<p>\u8fd8\u8bb0\u5f97 R1 Zero \u6709\u65f6\u4f1a\u5bf9\u8bed\u8a00\u611f\u5230\u56f0\u60d1\u5e76\u5f00\u59cb\u6df7\u6dc6\u5b83\u4eec\u5417\uff1f\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u4ed6\u4eec\u4e13\u95e8\u589e\u52a0\u4e86\u4fdd\u6301\u8bed\u8a00\u4e00\u81f4\u6027\u7684\u5956\u52b1\u3002\u8fd9\u4e2a\u60f3\u6cd5\u5f88\u7b80\u5355\uff0c\u5982\u679c\u4f60\u7528\u82f1\u8bed\u95ee\u95ee\u9898\uff0c\u6211\u4eec\u5e0c\u671b\u63a8\u7406\u548c\u7b54\u6848\u4e5f\u662f\u7528\u82f1\u8bed\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u76f4\u89c2\u5730\u4e86\u89e3\u4e00\u4e0b\u8fd9\u4e2a\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u8ba1\u7b97\uff1a<\/p>\n<p>  \u4e00\u81f4\u6027\u5956\u52b1\u8ba1\u7b97 <\/p>\n<p>\u4e3a\u4e86\u7406\u89e3\u4e0a\u9762\u7684\u56fe\u8868\uff0c\u8ba9\u6211\u4eec\u91cd\u65b0\u56de\u987e\u4e4b\u524d\u7684\u793a\u4f8b\u8f93\u51fa o1 \u548c o2\uff0c\u770b\u770b\u5956\u52b1\u5982\u4f55\u968f\u7740\u8fd9\u4e2a\u65b0\u7684\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u800c\u53d8\u5316\u3002\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u6211\u4eec\u5047\u8bbe\u76ee\u6807\u8bed\u8a00\u662f\u82f1\u8bed\u3002<\/p>\n<p>\u8ba9\u6211\u4eec\u770b\u770b\u8fd9\u4e9b\u5956\u52b1\u5982\u4f55\u4e0e\u6211\u4eec\u7684\u793a\u4f8b\u8f93\u51fa\u4e00\u8d77\u53d1\u6325\u4f5c\u7528\u3002\u8003\u8651\u7b2c\u4e00\u4e2a\u8f93\u51fa o1\uff0c\u5b83\u9519\u8bef\u5730\u8ba1\u7b97\u4e86\u201c2 + 3 * 4\u201d\uff0c\u4f46\u7528\u82f1\u8bed\u5448\u73b0\u4e86\u5176\u6709\u7f3a\u9677\u7684\u63a8\u7406\uff1a<\/p>\n<pre><code>&lt;think&gt; 2 + 3 = 5, 5 * 4 = 20 &lt;\/think&gt; &lt;answer&gt; 20 &lt;\/answer&gt;<\/code><\/pre>\n<p>\u5bf9\u4e8e\u8fd9\u4e2a\uff0c\u51c6\u786e\u5ea6\u5956\u52b1\u81ea\u7136\u662f 0\uff0c\u56e0\u4e3a\u7b54\u6848\u662f\u9519\u8bef\u7684\u3002\u4f46\u662f\uff0c\u7531\u4e8e\u5047\u8bbe\u63a8\u7406 100% \u4f7f\u7528\u76ee\u6807\u8bed\u8a00\uff08\u672c\u4f8b\u4e2d\u4e3a\u82f1\u8bed\uff09\uff0c\u56e0\u6b64\u5b83\u83b7\u5f97\u7684\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u4e3a 1\u3002<\/p>\n<p>\u5f53\u6211\u4eec\u8ba1\u7b97 RL \u9636\u6bb5\u7684\u603b\u5956\u52b1\u65f6\uff0c\u6211\u4eec\u4f1a\u5c06\u8fd9\u4e9b\u7ed3\u5408\u8d77\u6765\u3002\u5982\u679c\u6211\u4eec\u4e3a\u51c6\u786e\u5ea6\u5956\u52b1\u5206\u914d\u6743\u91cd 1\uff0c\u4e3a\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u5206\u914d\u8f83\u5c0f\u7684\u6743\u91cd\uff08\u4f8b\u5982 0.2\uff09\uff0c\u5219 o1 \u7684\u603b\u5956\u52b1\u53d8\u4e3a\uff1a<\/p>\n<pre><code>Total Reward = (1 * Accuracy Reward) + (0.2 * Language Consistency Reward)\n\n(1 * 0) + (0.2 * 1) = 0.2<\/code><\/pre>\n<p>\u73b0\u5728\u8003\u8651\u8f93\u51fa o2\uff0c\u5b83\u6b63\u786e\u89e3\u51b3\u4e86\u95ee\u9898\u5e76\u4e14\u8fd8\u7528\u82f1\u8bed\u8fdb\u884c\u63a8\u7406\uff1a<\/p>\n<pre><code>&lt;think&gt; 3 * 4 = 12, 2 + 12 = 14 &lt;\/think&gt; &lt;answer&gt; 14 &lt;\/answer&gt;<\/code><\/pre>\n<p>\u6b64\u8f93\u51fa\u56e0\u6b63\u786e\u7b54\u6848\u800c\u83b7\u5f97\u5b8c\u7f8e\u7684\u51c6\u786e\u5ea6\u5956\u52b1 1\u3002\u5047\u8bbe\u5b83\u7684\u63a8\u7406\u4e5f\u662f 100% \u82f1\u8bed\uff0c\u5b83\u4e5f\u4f1a\u83b7\u5f97 1 \u7684\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u3002\u4f7f\u7528\u4e0e\u4e4b\u524d\u76f8\u540c\u7684\u6743\u91cd\uff0co2 \u7684\u603b\u5956\u52b1\u4e3a\uff1a<\/p>\n<pre><code>(1 * 1) + (0.2 * 1) = 1.2<\/code><\/pre>\n<p>\u8bf7\u6ce8\u610f\uff0c\u8bed\u8a00\u4e00\u81f4\u6027\u5956\u52b1\u5982\u4f55\u7565\u5fae\u63d0\u9ad8\u6b63\u786e\u7b54\u6848\u7684\u603b\u5956\u52b1\uff0c\u751a\u81f3\u4e3a\u9519\u8bef\u7b54\u6848 o1 \u63d0\u4f9b\u5c0f\u5e45\u6b63\u5956\u52b1\uff0c\u53ea\u8981\u5b83\u4fdd\u6301\u8bed\u8a00\u4e00\u81f4\u6027\u3002<\/p>\n<p>\u6b64 RL \u8bad\u7ec3\u5faa\u73af\u9075\u5faa\u6211\u4eec\u4e4b\u524d\u770b\u5230\u7684\u76f8\u540c DeepSeek R1 Zero \u8bad\u7ec3\u5faa\u73af\uff1a<\/p>\n<p>  \u63a8\u7406\u5bfc\u5411\u5faa\u73af <\/p>\n<ul>\n<li>\u751f\u6210\u591a\u4e2a\u8f93\u51fa\u3002<\/li>\n<li>\u7ec6\u5316\u5956\u52b1\uff0c\u5305\u62ec\u8bed\u8a00\u4e00\u81f4\u6027\u3002<\/li>\n<li>\u4f7f\u7528 GRPO \u8fdb\u884c\u4f18\u52bf\u4f30\u8ba1\u3002<\/li>\n<li>\u8bad\u7ec3\u6a21\u578b\u4ee5\u652f\u6301\u9ad8\u4f18\u52bf\u8f93\u51fa\u3002<\/li>\n<li>\u91cd\u590d\u8be5\u8fc7\u7a0b\uff01<\/li>\n<\/ul>\n<h2>13\u3001\u62d2\u7edd\u62bd\u6837<\/h2>\n<p>\u5bf9\u4e8e\u63a8\u7406\u6570\u636e\uff0cDeepSeek \u56e2\u961f\u5e0c\u671b\u83b7\u5f97\u7edd\u5bf9\u6700\u4f73\u793a\u4f8b\u4ee5\u8fdb\u4e00\u6b65\u8bad\u7ec3\u6a21\u578b\u3002\u4e3a\u6b64\uff0c\u4ed6\u4eec\u4f7f\u7528\u4e86\u4e00\u79cd\u79f0\u4e3a\u62d2\u7edd\u62bd\u6837\u7684\u6280\u672f\u3002<\/p>\n<p>  \u62d2\u7edd\u62bd\u6837 <\/p>\n<p>\u4e3a\u4e86\u6539\u8fdb\u63a8\u7406\u6570\u636e\uff0cDeepSeek \u4f7f\u7528\u4e86\u62d2\u7edd\u62bd\u6837\u3002\u5bf9\u4e8e\u201c2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u201d\uff0c\u4ed6\u4eec\u4f1a\u4ece\u4e0a\u4e00\u9636\u6bb5\u6a21\u578b\u751f\u6210\u8bb8\u591a\u8f93\u51fa\u3002\u60f3\u8c61\u4e00\u4e0b\u5f97\u5230 20\uff08\u9519\u8bef\uff09\u548c 14 \u2026\uff08\u6b63\u786e\uff0c\u63a8\u7406\uff09\u8fd9\u6837\u7684\u8f93\u51fa\u3002<\/p>\n<p>\u7136\u540e\u4ed6\u4eec\u4f1a\u8bc4\u4f30\u6bcf\u4e2a\u8f93\u51fa\u7684\u6b63\u786e\u6027\uff08\u7b54\u6848\u201c14\u201d\uff09\u548c\u63a8\u7406\u7684\u53ef\u8bfb\u6027\u3002\u53ea\u6709\u6b63\u786e\u4e14\u63a8\u7406\u5145\u5206\u7684\u6700\u4f73\u8f93\u51fa\u624d\u4f1a\u88ab\u4fdd\u7559\uff0c\u800c\u5176\u4ed6\u8f93\u51fa\u5219\u88ab\u62d2\u7edd\u3002<\/p>\n<p>\u5bf9\u4e8e\u590d\u6742\u7684\u63a8\u7406\uff0c\u751f\u6210\u5956\u52b1\u6a21\u578b\u7528\u4e8e\u5224\u65ad\u63a8\u7406\u8d28\u91cf\u3002\u4e25\u683c\u7684\u8fc7\u6ee4\u5668\u4f1a\u5220\u9664\u6df7\u5408\u8bed\u8a00\u3001\u6f2b\u65e0\u8fb9\u9645\u7684\u63a8\u7406\u6216\u4e0d\u76f8\u5173\u7684\u4ee3\u7801\u3002\u6b64\u8fc7\u7a0b\u4f1a\u4ea7\u751f\u7ea6 600k \u4e2a\u9ad8\u8d28\u91cf\u63a8\u7406\u6837\u672c\u3002<\/p>\n<p>\u9664\u4e86\u7cbe\u70bc\u63a8\u7406\u6570\u636e\u5916\uff0c\u4ed6\u4eec\u8fd8\u6dfb\u52a0\u4e86\u975e\u63a8\u7406\u6570\u636e\uff08\u7ea6 20 \u4e07\u4e2a\u6837\u672c\uff09\uff0c\u7528\u4e8e\u4e00\u822c\u6280\u80fd\uff1a\u5199\u4f5c\u3001\u95ee\u7b54\u3001\u7ffb\u8bd1\u7b49\uff0c\u6709\u65f6\u8fd8\u4f1a\u4f7f\u7528\u601d\u7ef4\u94fe\u6765\u5b8c\u6210\u590d\u6742\u4efb\u52a1\u3002<\/p>\n<p>\u6700\u540e\uff0cSFT \u7b2c 2 \u9636\u6bb5\u4f7f\u7528\u4e0b\u4e00\u4e2a\u6807\u8bb0\u9884\u6d4b\u5728\u7ec4\u5408\u6570\u636e\u96c6\uff08\u7cbe\u70bc\u63a8\u7406 + \u975e\u63a8\u7406\uff09\u4e0a\u8bad\u7ec3\u524d\u4e00\u4e2a\u6a21\u578b\u68c0\u67e5\u70b9\u3002\u6b64\u9636\u6bb5\u4f7f\u7528\u6765\u81ea\u62d2\u7edd\u91c7\u6837\u7684\u9876\u7ea7\u793a\u4f8b\u8fdb\u4e00\u6b65\u6539\u8fdb\u63a8\u7406\uff0c\u5e76\u5c06\u6a21\u578b\u63a8\u5e7f\u5230\u66f4\u5e7f\u6cdb\u7684\u4efb\u52a1\uff0c\u540c\u65f6\u4fdd\u6301\u7528\u6237\u53cb\u597d\u6027\u3002<\/p>\n<p>\u201c2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u201d\u73b0\u5728\u662f\u4e00\u4e2a\u5b8c\u7f8e\u7cbe\u70bc\u7684\u63a8\u7406\u793a\u4f8b\uff0c\u6210\u4e3a\u6b64\u8bad\u7ec3\u6570\u636e\u7684\u4e00\u90e8\u5206\u3002<\/p>\n<blockquote><p>\n  \u8fd9\u662f\u62d2\u7edd\u91c7\u6837\uff0c\u6211\u4eec\u62d2\u7edd\u4f4e\u4e8e\u6807\u51c6\u7684\u6837\u672c\uff0c\u53ea\u4fdd\u7559\u6700\u597d\u7684\u6837\u672c\u4ee5\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e\n<\/p><\/blockquote>\n<h2>14\u3001\u9002\u7528\u4e8e\u6240\u6709\u573a\u666f\u7684 RL<\/h2>\n<p>\u5728 SFT \u7b2c 2 \u9636\u6bb5\u4e4b\u540e\uff0c\u6211\u4eec\u83b7\u5f97\u4e86 DeepSeek V3 \u63a8\u7406\u3001\u4e00\u81f4\u8bf4\u8bdd\uff0c\u751a\u81f3\u5f88\u597d\u5730\u5904\u7406\u4e86\u4e00\u822c\u4efb\u52a1\uff01\u4f46\u8981\u771f\u6b63\u4f7f\u5176\u6210\u4e3a\u9876\u7ea7\u7684\u4eba\u5de5\u667a\u80fd\u52a9\u624b\uff0c\u7814\u7a76\u4eba\u5458\u5fc5\u987b\u4e0e\u4eba\u7c7b\u4ef7\u503c\u89c2\u8fdb\u884c\u6700\u540e\u7684\u8c03\u6574\u3002\u8fd9\u5c31\u662f\u5f3a\u5316\u5b66\u4e60\u5728\u6240\u6709\u573a\u666f\u4e2d\u7684\u4f7f\u547d\uff08\u5f3a\u5316\u5b66\u4e60\u7b2c 2 \u9636\u6bb5\uff09\uff01\u628a\u5b83\u770b\u4f5c\u662f\u8ba9DeepSeek R1\u771f\u6b63\u5b89\u5168\u7684\u6700\u540e\u4e00\u9053\u5de5\u5e8f\u3002<\/p>\n<p>  \u6700\u7ec8 RL \u6b65\u9aa4 <\/p>\n<p>\u5bf9\u4e8e\u6211\u4eec\u7684\u793a\u4f8b\u201c2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u201d\u867d\u7136\u51c6\u786e\u5ea6\u5956\u52b1\u4ecd\u7136\u5f3a\u5316\u4e86\u6b63\u786e\u7b54\u6848\uff0c\u4f46\u5956\u52b1\u7cfb\u7edf\u73b0\u5728\u8fd8\u8003\u8651\uff1a<\/p>\n<ul>\n<li>\u6709\u7528\u6027\uff0c\u8bc4\u4f30\u6458\u8981\uff08\u5982\u679c\u751f\u6210\uff09\u662f\u5426\u63d0\u4f9b\u4e86\u9664\u7b54\u6848\u4e4b\u5916\u7684\u6709\u7528\u80cc\u666f\u3002<\/li>\n<li>\u65e0\u5bb3\u6027\uff0c\u68c0\u67e5\u6574\u4e2a\u8f93\u51fa\u662f\u5426\u5b89\u5168\u4e14\u65e0\u504f\u89c1\u3002\u8fd9\u4e9b\u901a\u5e38\u7531\u6839\u636e\u4eba\u7c7b\u504f\u597d\u8bad\u7ec3\u7684\u5355\u72ec\u5956\u52b1\u6a21\u578b\u8fdb\u884c\u8bc4\u4f30\u3002<\/li>\n<\/ul>\n<p>\u6700\u7ec8\u7684\u5956\u52b1\u4fe1\u53f7\u6210\u4e3a\u51c6\u786e\u5ea6\u3001\u6709\u7528\u6027\u548c\u65e0\u5bb3\u6027\u5206\u6570\u7684\u52a0\u6743\u7ec4\u5408\u3002<\/p>\n<p>\u73b0\u5728\uff0c\u8bad\u7ec3\u6570\u636e\u5305\u62ec<\/p>\n<ul>\n<li>\u591a\u6837\u5316\u7ec4\u5408\uff0c\u5305\u62ec\u63a8\u7406\u95ee\u9898<\/li>\n<li>\u4e00\u822c QA \u63d0\u793a<\/li>\n<li>\u5199\u4f5c\u4efb\u52a1<\/li>\n<li>\u548c\u504f\u597d\u5bf9\uff0c\u5176\u4e2d\u4eba\u7c7b\u6307\u51fa\u4e24\u4e2a\u6a21\u578b\u8f93\u51fa\u4e2d\u7684\u54ea\u4e00\u4e2a\u5728\u6709\u7528\u6027\u548c\u65e0\u5bb3\u6027\u65b9\u9762\u66f4\u597d\u3002<\/li>\n<\/ul>\n<p>\u8bad\u7ec3\u8fc7\u7a0b\u9075\u5faa\u8fed\u4ee3 RL \u5faa\u73af\uff08\u53ef\u80fd\u4f7f\u7528 GRPO\uff09\u4ee5\u6839\u636e\u6765\u81ea\u8fd9\u4e9b\u591a\u6837\u5316\u6570\u636e\u7684\u7ec4\u5408\u5956\u52b1\u4fe1\u53f7\u4f18\u5316\u6a21\u578b\u3002<\/p>\n<p>\u7ecf\u8fc7\u591a\u6b21\u8bad\u7ec3\u8fed\u4ee3\u540e\uff0c\u6a21\u578b\u5f97\u5230\u6539\u8fdb\uff0c\u5728\u63a8\u7406\u6027\u80fd\u548c\u4e00\u81f4\u6027\uff08\u6709\u7528\u6027\/\u65e0\u5bb3\u6027\uff09\u4e4b\u95f4\u53d6\u5f97\u826f\u597d\u5e73\u8861\u3002\u4e00\u65e6\u8fbe\u5230\u8fd9\u79cd\u5e73\u8861\uff0c\u6a21\u578b\u5c31\u4f1a\u5728\u6d41\u884c\u7684\u57fa\u51c6\u6570\u636e\u96c6\u4e0a\u8fdb\u884c\u8bc4\u4f30\uff0c\u5e76\u8d85\u8d8a\u5176\u4ed6\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n<blockquote><p>\n  \u4ed6\u4eec\u7684\u6700\u7ec8\u68c0\u67e5\u70b9\uff0c\u9ad8\u5ea6\u4f18\u5316\u7684\u7248\u672c\u88ab\u547d\u540d\u4e3a DeepSeek-R1\n<\/p><\/blockquote>\n<h2>15\u3001\u84b8\u998f<\/h2>\n<p>  R1 \u7684\u84b8\u998f <\/p>\n<p>\u5728 DeepSeek \u56e2\u961f\u80fd\u591f\u521b\u5efa\u6027\u80fd\u826f\u597d\u7684 DeepSeek R1 \u540e\uff0c\u4ed6\u4eec\u8fdb\u4e00\u6b65\u5c06\u66f4\u5927\u7684\u6a21\u578b\u63d0\u70bc\u4e3a\u6027\u80fd\u66f4\u9ad8\u7684\u5c0f\u578b\u6a21\u578b\uff0c\u4f9b\u793e\u533a\u4f7f\u7528\uff0c\u84b8\u998f\u8fc7\u7a0b\u7684\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u6570\u636e\u51c6\u5907\uff1a\u6536\u96c6 800k \u4e2a\u63a8\u7406\u6837\u672c\u3002<\/li>\n<li>DeepSeek-R1 \u8f93\u51fa\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u6837\u672c\uff0c\u6559\u5e08\u6a21\u578b\uff08DeepSeek-R1\uff09\u7684\u8f93\u51fa\u7528\u4f5c\u5b66\u751f\u6a21\u578b\u7684\u76ee\u6807\u3002<\/li>\n<li>\u76d1\u7763\u5f0f\u5fae\u8c03 (SFT)\uff1a\u5b66\u751f\u6a21\u578b\uff08\u4f8b\u5982 Qwen-1.5B\u3001Llama-14B\uff09\u57fa\u4e8e\u8fd9 800k \u4e2a\u6837\u672c\u8fdb\u884c\u5fae\u8c03\uff0c\u4ee5\u5339\u914d DeepSeek-R1 \u8f93\u51fa\u3002<\/li>\n<li>\u84b8\u998f\u6a21\u578b\uff1a\u5b66\u751f\u6a21\u578b\u73b0\u5728\u88ab\u7cbe\u70bc\u6210\u66f4\u5c0f\u7684\u7248\u672c\uff0c\u4f46\u4fdd\u7559\u4e86 DeepSeek-R1 \u7684\u5927\u90e8\u5206\u63a8\u7406\u80fd\u529b\u3002<\/li>\n<li>\u7ed3\u679c\uff1a\u4f60\u5c06\u83b7\u5f97\u66f4\u5c0f\u3001\u66f4\u5feb\u4e14\u5177\u6709\u826f\u597d\u63a8\u7406\u80fd\u529b\u7684\u6a21\u578b\uff0c\u968f\u65f6\u53ef\u4ee5\u90e8\u7f72\u3002<\/li>\n<\/ul>\n<hr>\n","protected":false},"excerpt":{"rendered":"<p>\u5982\u679c\u4f60\u5bf9 AI \u611f\u5174\u8da3\uff0c\u53ef\u80fd\u542c\u8bf4\u8fc7 DeepSeek R1\u3002\u5b83\u76ee\u524d\u5728 LLM \u9886\u57df\u5f88\u6d41\u884c\uff0c\u5e76\u4e14\u8868\u73b0\u4f18\u4e8e\u5f00\u6e90\u548c\u95ed\u6e90\u6a21\u578b\u3002 \u4e3a\u4e86\u8ba9\u4e00\u5207\u53d8\u5f97\u7b80\u5355\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u624b\u7ed8\u6d41\u7a0b\u56fe\u548c\u7b80\u5355\u7684\u8ba1\u7b97\u6765\u5e2e\u52a9\u4ece\u5934\u5f00\u59cb\u6f84\u6e05DeeoSeek-R1\u7684\u6838\u5fc3\u6982\u5ff5\u3002 \u4e8b\u5b9e\u4e0a\uff0c\u6211\u4eec\u5c06\u5728\u6574\u4e2a\u535a\u5ba2\u4e2d\u4f7f\u7528\u5b57\u7b26\u4e32 2 + 3 * 4 \u7b49\u4e8e\u591a\u5c11\uff1f\u4f5c\u4e3a\u793a\u4f8b\uff0c\u5f15\u5bfc\u4f60\u4e86\u89e3 DeepSeek \u6280\u672f\u62a5\u544a\u7684\u6bcf\u4e2a\u7ec4\u6210\u90e8\u5206\u3002 1\u3001\u5feb\u901f\u6982\u89c8 \u56e0\u6b64\uff0c\u5728\u4ecb\u7ecd\u6280\u672f\u7ec6\u8282\u4e4b\u524d\uff0c\u5feb\u901f\u6982\u89c8\u4e00\u4e0b\uff1aDeepSeek-R1 \u4e0d\u662f\u4ece\u5934\u5f00\u59cb\u8bad\u7ec3\u7684\uff0c\u5c31\u50cf\u4ece\u65e0\u5230\u6709\u4e00\u6837\u3002\u76f8\u53cd\uff0c\u4ed6\u4eec\u4ece\u4e00\u4e2a\u975e\u5e38\u806a\u660e\u7684 LLM \u5f00\u59cb\uff0c\u4ed6\u4eec\u5df2\u7ecf\u6709\u4e86 DeepSeek-V3\uff0c\u4f46\u4ed6\u4eec\u60f3\u8ba9\u5b83\u6210\u4e3a\u63a8\u7406\u8d85\u7ea7\u660e\u661f\u3002 DeepSeek \u5b9e\u65bd\u5feb\u901f\u6982\u89c8 \u4e3a\u6b64\uff0c\u4ed6\u4eec\u4f7f\u7528\u4e86\u5f3a\u5316\u5b66\u4e60\uff08\u7b80\u79f0 RL\uff09\uff0c\u5f53 LLM \u505a\u51fa\u6709\u5229\u4e8e\u63a8\u7406\u7684\u4e8b\u60c5\u65f6\uff0c\u4f60\u4f1a\u5956\u52b1\u5b83\uff0c\u5426\u5219\u4f1a\u60e9\u7f5a\u5b83\u3002 \u4f46\u8fd9\u4e0d\u4ec5\u4ec5\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u8bad\u7ec3\u8bfe\u7a0b\u3002\u5b83\u5c31\u50cf\u662f\u4e00\u6574\u5957\u6b65\u9aa4\uff0c\u4ed6\u4eec\u79f0\u4e4b\u4e3a\u7ba1\u9053\u3002\u4ed6\u4eec\u9996\u5148\u5c1d\u8bd5\u4e86\u7eaf RL\uff0c\u770b\u770b\u63a8\u7406\u662f\u5426\u4f1a\u81ea\u884c\u51fa\u73b0\uff0c\u8fd9\u5c31\u662f DeepSeek-R1-Zero\uff0c\u6709\u70b9\u50cf\u4e00\u4e2a\u5b9e\u9a8c\u3002\u7136\u540e\u5bf9\u4e8e\u771f\u6b63\u7684 DeepSeek-R1\uff0c\u4ed6\u4eec\u901a\u8fc7\u4e0d\u540c\u7684\u9636\u6bb5\u4f7f\u5176\u66f4\u6709\u6761\u7406\u3002\u4ed6\u4eec\u7ed9\u5b83\u4e00\u4e9b\u8d77\u59cb\u6570\u636e\u6765\u542f\u52a8\u5b83\uff0c\u7136\u540e\u8fdb\u884c RL\uff0c\u7136\u540e\u662f\u66f4\u591a\u6570\u636e\uff0c\u7136\u540e\u662f\u66f4\u591a RL\u2026\u2026\u5c31\u50cf\u4e00\u6b65\u4e00\u6b65\u5347\u7ea7\u4e00\u6837\uff01 \u6574\u4e2a\u91cd\u70b9\u662f\u8ba9\u8fd9\u4e9b\u8bed\u8a00\u6a21\u578b\u66f4\u597d\u5730\u601d\u8003\u95ee\u9898\u5e76\u4e3a\u4f60\u63d0\u4f9b\u660e\u667a\u7684\u7b54\u6848\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u5410\u51fa\u5355\u8bcd\u3002 \u6240\u4ee5\uff0c\u662f\u7684\uff0c\u5728\u6211\u4eec\u7814\u7a76\u6bcf\u4e2a\u6b65\u9aa4\u7684\u75af\u72c2\u7ec6\u8282\u4e4b\u524d\uff0c\u8fd9\u662f\u8d85\u7b80\u77ed\u7684\u7248\u672c\u3002 2\u3001DeepSeek V3 (MOE) \u5982\u4f55\u601d\u8003\uff1f \u6b63\u5982\u6211\u4e4b\u524d\u6240\u8bf4\uff0cDeepSeek R1 \u8bad\u7ec3\u4e0d\u662f\u4ece\u5934\u5f00\u59cb\u6784\u5efa\u7684\uff0c\u800c\u662f\u4f7f\u7528 DeepSeek V3 \u4f5c\u4e3a\u57fa\u7840\u6a21\u578b\u3002\u90a3\u4e48\u6211\u4eec\u9700\u8981\u4e86\u89e3 V3 \u7684\u5de5\u4f5c\u539f\u7406\u4ee5\u53ca\u5b83\u4e3a\u4ec0\u4e48\u88ab\u79f0\u4e3a MOE\uff1f DeepSeek V3 \u67b6\u6784 DeepSeek V3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-53789","post","type-post","status-publish","format-standard","hentry","category-ai"],"_links":{"self":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts\/53789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/comments?post=53789"}],"version-history":[{"count":0,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/posts\/53789\/revisions"}],"wp:attachment":[{"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/media?parent=53789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/categories?post=53789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fwq.ai\/blog\/wp-json\/wp\/v2\/tags?post=53789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}