{"id":27720,"date":"2025-03-05T20:00:24","date_gmt":"2025-03-05T12:00:24","guid":{"rendered":"https:\/\/www.aisharenet.com\/?p=27720"},"modified":"2025-03-05T20:00:52","modified_gmt":"2025-03-05T12:00:52","slug":"damoxingruhebianbian","status":"publish","type":"post","link":"https:\/\/www.kdjingpai.com\/ja\/damoxingruhebianbian\/","title":{"rendered":"\u5927\u6a21\u578b\u5982\u4f55\u53d8\u5f97\u66f4\u201c\u806a\u660e\u201d\uff1f\u65af\u5766\u798f\u5927\u5b66\u63ed\u79d8\u81ea\u6211\u6539\u8fdb\u7684\u5173\u952e\uff1a\u56db\u79cd\u8ba4\u77e5\u884c\u4e3a"},"content":{"rendered":"<p>\u4eba\u5de5\u667a\u80fd\u9886\u57df\u8fd1\u5e74\u6765\u53d6\u5f97\u4e86\u4ee4\u4eba\u77a9\u76ee\u7684\u8fdb\u5c55\uff0c\u5c24\u5176\u662f\u5728\u5927\u8bed\u8a00\u6a21\u578b (LLM) \u65b9\u9762\u3002 \u8bb8\u591a\u6a21\u578b\uff0c\u4f8b\u5982 Qwen\uff0c\u5c55\u73b0\u51fa\u60ca\u4eba\u7684\u80fd\u529b\uff0c\u751a\u81f3\u80fd\u591f\u81ea\u6211\u68c0\u67e5\u7b54\u6848\u5e76\u7ea0\u6b63\u9519\u8bef\u3002 \u7136\u800c\uff0c\u5e76\u975e\u6240\u6709\u6a21\u578b\u90fd\u5177\u5907\u540c\u7b49\u7684\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u3002 \u540c\u6837\u662f\u7ed9\u4e88\u989d\u5916\u7684\u8ba1\u7b97\u8d44\u6e90\u548c \u201c\u601d\u8003\u201d \u65f6\u95f4\uff0c\u6709\u4e9b\u6a21\u578b\u80fd\u591f\u5145\u5206\u5229\u7528\u8fd9\u4e9b\u8d44\u6e90\uff0c\u6027\u80fd\u5927\u5e45\u63d0\u5347\uff0c\u800c\u53e6\u4e00\u4e9b\u6a21\u578b\u5374\u6536\u6548\u751a\u5fae\u3002 \u8fd9\u4e00\u73b0\u8c61\u5f15\u53d1\u4e86\u4eba\u4eec\u7684\u601d\u8003\uff1a \u7a76\u7adf\u662f\u4ec0\u4e48\u56e0\u7d20\u5bfc\u81f4\u4e86\u8fd9\u79cd\u5dee\u5f02\uff1f<\/p>\n<p>\u6b63\u5982\u4eba\u7c7b\u5728\u9762\u5bf9\u96be\u9898\u65f6\u4f1a\u82b1\u8d39\u66f4\u591a\u65f6\u95f4\u6df1\u5165\u601d\u8003\u4e00\u6837\uff0c\u4e00\u4e9b\u5148\u8fdb\u7684\u5927\u8bed\u8a00\u6a21\u578b\u5728\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u8fdb\u884c\u81ea\u6211\u6539\u8fdb\u8bad\u7ec3\u65f6\uff0c\u4e5f\u5f00\u59cb\u5c55\u73b0\u51fa\u7c7b\u4f3c\u7684\u63a8\u7406\u884c\u4e3a\u3002 \u7136\u800c\uff0c\u5728\u76f8\u540c\u7684\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u4e0b\uff0c\u4e0d\u540c\u6a21\u578b\u4e4b\u95f4\u7684\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u5374\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002 \u4f8b\u5982\uff0c\u5728 Countdown \u6e38\u620f\u4e2d\uff0cQwen-2.5-3B \u7684\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u5c31\u8fdc\u8d85 Llama-3.2-3B\u3002 \u5c3d\u7ba1\u4e24\u4e2a\u6a21\u578b\u5728\u521d\u59cb\u9636\u6bb5\u8868\u73b0\u90fd\u76f8\u5bf9\u8f83\u5f31\uff0c\u4f46\u5728\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u7ed3\u675f\u540e\uff0cQwen \u7684\u51c6\u786e\u7387\u8fbe\u5230\u4e86\u7ea6 60%\uff0c\u800c Llama \u4ec5\u4e3a 30% \u5de6\u53f3\u3002 \u8fd9\u79cd\u663e\u8457\u7684\u5dee\u8ddd\u80cc\u540e\u9690\u85cf\u7740\u600e\u6837\u7684\u673a\u5236\uff1f<\/p>\n<p>\u6700\u8fd1\uff0c\u65af\u5766\u798f\u5927\u5b66\u7684\u4e00\u9879\u7814\u7a76\u6df1\u5165\u6316\u6398\u4e86\u5927\u6a21\u578b\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u80cc\u540e\u7684\u673a\u5236\uff0c\u63ed\u793a\u4e86\u57fa\u7840\u8bed\u8a00\u6a21\u578b\u4e2d\u5173\u952e\u00a0<strong>\u8ba4\u77e5\u884c\u4e3a<\/strong>\u00a0\u7684\u91cd\u8981\u6027\u3002 \u8fd9\u9879\u7814\u7a76\u4e3a\u6211\u4eec\u7406\u89e3\u548c\u63d0\u5347 AI \u7cfb\u7edf\u7684\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u8fd9\u9879\u7814\u7a76\u4e00\u7ecf\u53d1\u5e03\u4fbf\u5f15\u8d77\u4e86\u5e7f\u6cdb\u8ba8\u8bba\u3002 Synth Labs \u7684 CEO \u5c31\u8ba4\u4e3a\uff0c\u8fd9\u9879\u53d1\u73b0\u4ee4\u4eba\u632f\u594b\uff0c\u56e0\u4e3a\u5b83\u6709\u671b\u88ab\u6574\u5408\u5230\u4efb\u4f55\u6a21\u578b\u4e2d\uff0c\u4ece\u800c\u63d0\u5347\u6a21\u578b\u7684\u6027\u80fd\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/49cb099792f4ba4.png\" alt=\"Synth Labs CEO \u8bc4\u8bba\" width=\"523\" height=\"296\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>\u56db\u79cd\u5173\u952e\u8ba4\u77e5\u884c\u4e3a<\/h2>\n<p>\u4e3a\u4e86\u63a2\u7a76\u4e0d\u540c\u6a21\u578b\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u5dee\u5f02\u7684\u539f\u56e0\uff0c\u7814\u7a76\u4eba\u5458\u5c06\u91cd\u70b9\u653e\u5728 Qwen-2.5-3B \u548c Llama-3.2-3B \u8fd9\u4e24\u6b3e\u57fa\u7840\u6a21\u578b\u4e0a\u3002 \u901a\u8fc7\u5728 Countdown \u6e38\u620f\u4e2d\u5bf9\u5b83\u4eec\u8fdb\u884c\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\uff0c\u7814\u7a76\u4eba\u5458\u89c2\u5bdf\u5230\u4e86\u660e\u663e\u7684\u5dee\u5f02\uff1a Qwen \u7684\u95ee\u9898\u89e3\u51b3\u80fd\u529b\u5f97\u5230\u663e\u8457\u63d0\u5347\uff0c\u800c Llama-3 \u5728\u76f8\u540c\u7684\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u63d0\u5347\u5374\u76f8\u5bf9\u6709\u9650\u3002 \u90a3\u4e48\uff0c\u7a76\u7adf\u662f\u54ea\u4e9b\u6a21\u578b\u5c5e\u6027\u5bfc\u81f4\u4e86\u8fd9\u79cd\u5dee\u5f02\uff1f<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/7067400db37f7e5.png\" alt=\"Qwen \u4e0e Llama-3 \u5bf9\u6bd4\" \/><\/p>\n<p>\u4e3a\u4e86\u7cfb\u7edf\u5730\u7814\u7a76\u8fd9\u4e2a\u95ee\u9898\uff0c\u7814\u7a76\u56e2\u961f\u5f00\u53d1\u4e86\u4e00\u4e2a\u6846\u67b6\uff0c\u7528\u4e8e\u5206\u6790\u5bf9\u89e3\u51b3\u95ee\u9898\u81f3\u5173\u91cd\u8981\u7684\u8ba4\u77e5\u884c\u4e3a\u3002 \u8be5\u6846\u67b6\u63cf\u8ff0\u4e86\u56db\u79cd\u5173\u952e\u7684\u8ba4\u77e5\u884c\u4e3a\uff1a<\/p>\n<ol>\n<li><strong>\u9a8c\u8bc1 (Verification)<\/strong>: \u7cfb\u7edf\u6027\u5730\u68c0\u67e5\u9519\u8bef\u3002<\/li>\n<li><strong>\u56de\u6eaf (Backtracking)<\/strong>: \u653e\u5f03\u5931\u8d25\u7684\u65b9\u6cd5\uff0c\u5e76\u5c1d\u8bd5\u65b0\u7684\u8def\u5f84\u3002<\/li>\n<li><strong>\u5b50\u76ee\u6807\u8bbe\u5b9a (Sub-goal Setting)<\/strong>: \u5c06\u590d\u6742\u95ee\u9898\u5206\u89e3\u4e3a\u53ef\u7ba1\u7406\u7684\u6b65\u9aa4\u3002<\/li>\n<li><strong>\u9006\u5411\u601d\u8003 (Reverse Thinking)<\/strong>: \u4ece\u671f\u671b\u7684\u7ed3\u679c\u53cd\u5411\u63a8\u5bfc\u81f3\u521d\u59cb\u8f93\u5165\u3002<\/li>\n<\/ol>\n<p>\u8fd9\u4e9b\u884c\u4e3a\u6a21\u5f0f\u4e0e\u4e13\u5bb6\u7ea7\u95ee\u9898\u89e3\u51b3\u8005\u5904\u7406\u590d\u6742\u4efb\u52a1\u7684\u65b9\u5f0f\u9ad8\u5ea6\u76f8\u4f3c\u3002 \u4f8b\u5982\uff0c\u6570\u5b66\u5bb6\u5728\u8fdb\u884c\u8bc1\u660e\u65f6\uff0c\u4f1a\u4ed4\u7ec6\u9a8c\u8bc1\u6bcf\u4e00\u6b65\u7684\u63a8\u5bfc\uff1b \u5f53\u9047\u5230\u77db\u76fe\u65f6\uff0c\u4f1a\u56de\u6eaf\u68c0\u67e5\u4e4b\u524d\u7684\u6b65\u9aa4\uff1b \u4e5f\u4f1a\u5c06\u590d\u6742\u7684\u5b9a\u7406\u62c6\u89e3\u4e3a\u66f4\u7b80\u5355\u7684\u5f15\u7406\u6765\u9010\u6b65\u8bc1\u660e\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/5da8540c22fdc6f.png\" alt=\"\u56db\u79cd\u8ba4\u77e5\u884c\u4e3a\" width=\"711\" height=\"727\" \/><\/p>\n<p>\u521d\u6b65\u5206\u6790\u8868\u660e\uff0cQwen \u6a21\u578b\u81ea\u7136\u5730\u5c55\u73b0\u51fa\u8fd9\u4e9b\u63a8\u7406\u884c\u4e3a\uff0c\u5c24\u5176\u662f\u5728\u9a8c\u8bc1\u548c\u56de\u6eaf\u65b9\u9762\uff0c\u800c Llama-3 \u6a21\u578b\u5219\u660e\u663e\u7f3a\u4e4f\u8fd9\u4e9b\u884c\u4e3a\u3002 \u57fa\u4e8e\u8fd9\u4e9b\u89c2\u5bdf\uff0c\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u4e86\u6838\u5fc3\u5047\u8bbe\uff1a\u00a0<strong>\u521d\u59cb\u7b56\u7565\u4e2d\u7684\u67d0\u4e9b\u63a8\u7406\u884c\u4e3a\uff0c\u5bf9\u4e8e\u6a21\u578b\u6709\u6548\u5229\u7528\u589e\u52a0\u7684\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\u81f3\u5173\u91cd\u8981\u3002 \u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c AI \u6a21\u578b\u60f3\u8981\u5728\u62e5\u6709\u66f4\u591a \u201c\u601d\u8003\u201d \u65f6\u95f4\u65f6\u53d8\u5f97\u66f4 \u201c\u806a\u660e\u201d\uff0c \u5fc5\u987b\u9996\u5148\u5177\u5907\u4e00\u4e9b\u57fa\u672c\u7684\u601d\u8003\u80fd\u529b\uff0c\u4f8b\u5982\u68c0\u67e5\u9519\u8bef\u3001\u9a8c\u8bc1\u7ed3\u679c\u7684\u4e60\u60ef\u3002 \u5982\u679c\u6a21\u578b\u4e00\u5f00\u59cb\u5c31\u7f3a\u4e4f\u8fd9\u4e9b\u57fa\u672c\u7684\u601d\u8003\u65b9\u6cd5\uff0c \u5373\u4f7f\u7ed9\u4e88\u518d\u591a\u7684\u601d\u8003\u65f6\u95f4\u548c\u8ba1\u7b97\u8d44\u6e90\uff0c\u4e5f\u65e0\u6cd5\u6709\u6548\u5730\u63d0\u5347\u5176\u6027\u80fd\u3002<\/strong>\u00a0\u8fd9\u4e0e\u4eba\u7c7b\u7684\u5b66\u4e60\u8fc7\u7a0b\u975e\u5e38\u76f8\u4f3c\u2014\u2014 \u5982\u679c\u5b66\u751f\u7f3a\u4e4f\u57fa\u672c\u7684\u81ea\u6211\u68c0\u67e5\u548c\u7ea0\u9519\u80fd\u529b\uff0c \u4ec5\u4ec5\u5ef6\u957f\u8003\u8bd5\u65f6\u95f4\u4e5f\u96be\u4ee5\u663e\u8457\u63d0\u9ad8\u5176\u6210\u7ee9\u3002<\/p>\n<p>&nbsp;<\/p>\n<h2>\u5b9e\u9a8c\u9a8c\u8bc1\uff1a\u8ba4\u77e5\u884c\u4e3a\u7684\u91cd\u8981\u6027<\/h2>\n<p>\u4e3a\u4e86\u9a8c\u8bc1\u4e0a\u8ff0\u5047\u8bbe\uff0c\u7814\u7a76\u4eba\u5458\u8fdb\u884c\u4e86\u4e00\u7cfb\u5217\u5de7\u5999\u7684\u5e72\u9884\u5b9e\u9a8c\u3002<\/p>\n<p>\u9996\u5148\uff0c\u4ed6\u4eec\u5c1d\u8bd5\u4f7f\u7528\u5305\u542b\u7279\u5b9a\u8ba4\u77e5\u884c\u4e3a (\u7279\u522b\u662f\u56de\u6eaf) \u7684\u4eba\u5de5\u5408\u6210\u63a8\u7406\u8f68\u8ff9\u6765\u5f15\u5bfc Llama-3 \u6a21\u578b\u3002 \u7ed3\u679c\u8868\u660e\uff0c\u7ecf\u8fc7\u8fd9\u79cd\u5f15\u5bfc\u7684 Llama-3 \u6a21\u578b\u5728\u5f3a\u5316\u5b66\u4e60\u8fc7\u7a0b\u4e2d\u8868\u73b0\u51fa\u663e\u8457\u7684\u6539\u5584\uff0c \u6027\u80fd\u63d0\u5347\u751a\u81f3\u53ef\u4ee5\u4e0e Qwen-2.5-3B \u76f8\u5ab2\u7f8e\u3002<\/p>\n<p>\u5176\u6b21\uff0c\u5373\u4f7f\u5f15\u5bfc\u6240\u7528\u7684\u63a8\u7406\u8f68\u8ff9\u5305\u542b\u9519\u8bef\u7684\u7b54\u6848\uff0c\u53ea\u8981\u8fd9\u4e9b\u8f68\u8ff9\u5c55\u73b0\u51fa\u6b63\u786e\u7684\u63a8\u7406\u6a21\u5f0f\uff0cLlama-3 \u6a21\u578b\u4f9d\u7136\u80fd\u591f\u53d6\u5f97\u8fdb\u6b65\u3002 \u8fd9\u4e00\u53d1\u73b0\u8868\u660e\uff0c\u00a0<strong>\u771f\u6b63\u9a71\u52a8\u6a21\u578b\u81ea\u6211\u6539\u8fdb\u7684\u5173\u952e\u56e0\u7d20\u662f\u63a8\u7406\u884c\u4e3a\u7684\u5b58\u5728\uff0c \u800c\u975e\u7b54\u6848\u672c\u8eab\u7684\u6b63\u786e\u6027\u3002<\/strong><\/p>\n<p>\u6700\u540e\uff0c\u7814\u7a76\u4eba\u5458\u4ece OpenWebMath \u6570\u636e\u96c6\u4e2d\u7b5b\u9009\u51fa\u5f3a\u8c03\u8fd9\u4e9b\u63a8\u7406\u884c\u4e3a\u7684\u5185\u5bb9\uff0c\u5e76\u5229\u7528\u8fd9\u4e9b\u6570\u636e\u5bf9 Llama-3 \u6a21\u578b\u8fdb\u884c\u4e86\u9884\u8bad\u7ec3\u3002 \u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c \u8fd9\u79cd\u6709\u9488\u5bf9\u6027\u7684\u9884\u8bad\u7ec3\u6570\u636e\u8c03\u6574\u80fd\u591f\u6709\u6548\u5730\u8bf1\u5bfc\u51fa\u6a21\u578b\u6709\u6548\u5229\u7528\u8ba1\u7b97\u8d44\u6e90\u6240\u9700\u7684\u63a8\u7406\u884c\u4e3a\u6a21\u5f0f\u3002 \u7ecf\u8fc7\u8c03\u6574\u9884\u8bad\u7ec3\u7684 Llama-3 \u6a21\u578b\uff0c\u5176\u6027\u80fd\u63d0\u5347\u8f68\u8ff9\u4e0e Qwen-2.5-3B \u6a21\u578b\u8868\u73b0\u51fa\u60ca\u4eba\u7684\u4e00\u81f4\u6027\u3002<\/p>\n<p>\u8fd9\u4e9b\u5b9e\u9a8c\u7ed3\u679c\u6709\u529b\u5730\u63ed\u793a\u4e86\u6a21\u578b\u7684\u521d\u59cb\u63a8\u7406\u884c\u4e3a\u4e0e\u5176\u81ea\u6211\u6539\u8fdb\u80fd\u529b\u4e4b\u95f4\u5b58\u5728\u7740\u7d27\u5bc6\u7684\u8054\u7cfb\u3002 \u8fd9\u79cd\u8054\u7cfb\u6709\u52a9\u4e8e\u89e3\u91ca\u4e3a\u4ec0\u4e48\u67d0\u4e9b\u8bed\u8a00\u6a21\u578b\u80fd\u591f\u6709\u6548\u5730\u5229\u7528\u989d\u5916\u7684\u8ba1\u7b97\u8d44\u6e90\uff0c \u800c\u53e6\u4e00\u4e9b\u6a21\u578b\u5219\u505c\u6ede\u4e0d\u524d\u3002 \u6df1\u5165\u7406\u89e3\u8fd9\u4e9b\u52a8\u6001\u53d8\u5316\uff0c\u5bf9\u4e8e\u5f00\u53d1\u80fd\u591f\u663e\u8457\u63d0\u5347\u95ee\u9898\u89e3\u51b3\u80fd\u529b\u7684 AI \u7cfb\u7edf\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<p>&nbsp;<\/p>\n<h2>Countdown \u6e38\u620f\u4e0e\u6a21\u578b\u9009\u62e9<\/h2>\n<p>\u8fd9\u9879\u7814\u7a76\u4ee5\u4e00\u4e2a\u4ee4\u4eba\u60ca\u8bb6\u7684\u89c2\u5bdf\u7ed3\u679c\u5f00\u7bc7\uff1a \u6765\u81ea\u4e0d\u540c\u6a21\u578b\u5bb6\u65cf\u3001\u89c4\u6a21\u76f8\u8fd1\u7684\u8bed\u8a00\u6a21\u578b\uff0c\u5728\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u8fdb\u884c\u8bad\u7ec3\u540e\uff0c\u5c55\u73b0\u51fa\u622a\u7136\u4e0d\u540c\u7684\u6027\u80fd\u63d0\u5347\u80fd\u529b\u3002 \u4e3a\u4e86\u6df1\u5165\u63a2\u7a76\u8fd9\u4e00\u73b0\u8c61\uff0c\u7814\u7a76\u4eba\u5458\u9009\u62e9\u4e86 Countdown \u6e38\u620f\u4f5c\u4e3a\u4e3b\u8981\u7684\u6d4b\u8bd5\u5e73\u53f0\u3002<\/p>\n<p>Countdown \u6e38\u620f\u662f\u4e00\u4e2a\u6570\u5b66\u96be\u9898\uff0c \u73a9\u5bb6\u9700\u8981\u4f7f\u7528\u52a0\u3001\u51cf\u3001\u4e58\u3001\u9664\u56db\u79cd\u57fa\u672c\u8fd0\u7b97\uff0c\u5c06\u4e00\u7ec4\u7ed9\u5b9a\u7684\u6570\u5b57\u7ec4\u5408\u8d77\u6765\uff0c\u4ee5\u8fbe\u5230\u76ee\u6807\u6570\u5b57\u3002 \u4f8b\u5982\uff0c\u7ed9\u5b9a\u6570\u5b57 25\u300130\u30013\u30014 \u548c\u76ee\u6807\u6570\u5b57 32\uff0c\u73a9\u5bb6\u9700\u8981\u901a\u8fc7\u4e00\u7cfb\u5217\u8fd0\u7b97\u5f97\u5230\u7cbe\u786e\u7684 32\uff0c\u4f8b\u5982\uff1a (30 \u2212 25 + 3) \u00d7 4 = 32\u3002<\/p>\n<p>\u4e4b\u6240\u4ee5\u9009\u62e9 Countdown \u6e38\u620f\u8fdb\u884c\u7814\u7a76\uff0c \u662f\u56e0\u4e3a\u5b83\u65e2\u80fd\u8003\u5bdf\u6a21\u578b\u7684\u6570\u5b66\u63a8\u7406\u3001\u89c4\u5212\u548c\u641c\u7d22\u7b56\u7565\u80fd\u529b\uff0c \u53c8\u63d0\u4f9b\u4e86\u4e00\u4e2a\u76f8\u5bf9\u53d7\u9650\u7684\u641c\u7d22\u7a7a\u95f4\uff0c \u4f7f\u5f97\u7814\u7a76\u4eba\u5458\u80fd\u591f\u8fdb\u884c\u6df1\u5165\u5206\u6790\u3002 \u4e0e\u66f4\u590d\u6742\u7684\u9886\u57df\u76f8\u6bd4\uff0c Countdown \u6e38\u620f\u964d\u4f4e\u4e86\u5206\u6790\u7684\u96be\u5ea6\uff0c \u540c\u65f6\u4ecd\u7136\u80fd\u591f\u6709\u6548\u8003\u5bdf\u590d\u6742\u7684\u63a8\u7406\u80fd\u529b\u3002 \u6b64\u5916\uff0c\u4e0e\u5176\u4ed6\u6570\u5b66\u4efb\u52a1\u76f8\u6bd4\uff0c Countdown \u6e38\u620f\u7684\u6210\u529f\u66f4\u591a\u5730\u4f9d\u8d56\u4e8e\u95ee\u9898\u89e3\u51b3\u80fd\u529b\uff0c \u800c\u975e\u5355\u7eaf\u7684\u6570\u5b66\u77e5\u8bc6\u3002<\/p>\n<p>\u7814\u7a76\u4eba\u5458\u9009\u62e9\u4e86 Qwen-2.5-3B \u548c Llama-3.2-3B \u8fd9\u4e24\u6b3e\u57fa\u7840\u6a21\u578b\uff0c \u4ee5\u5bf9\u6bd4\u4e0d\u540c\u6a21\u578b\u5bb6\u65cf\u4e4b\u95f4\u7684\u5b66\u4e60\u5dee\u5f02\u3002 \u5f3a\u5316\u5b66\u4e60\u5b9e\u9a8c\u57fa\u4e8e VERL \u5e93\uff0c \u5e76\u5229\u7528 TinyZero \u5b9e\u73b0\u3002 \u4ed6\u4eec\u4f7f\u7528 PPO (Proximal Policy Optimization) \u7b97\u6cd5\u8bad\u7ec3\u6a21\u578b 250 \u6b65\uff0c \u6bcf\u6b21\u63d0\u793a\u91c7\u6837 4 \u4e2a\u8f68\u8ff9\u3002 \u9009\u62e9 PPO \u7b97\u6cd5\u7684\u539f\u56e0\u662f\uff0c \u76f8\u8f83\u4e8e <a href=\"https:\/\/www.kdjingpai.com\/grpo-ruhezaishi\/\">GRPO<\/a> \u548c REINFORCE \u7b49\u5176\u4ed6\u5f3a\u5316\u5b66\u4e60\u7b97\u6cd5\uff0c PPO \u5728\u5404\u79cd\u8d85\u53c2\u6570\u8bbe\u7f6e\u4e0b\u8868\u73b0\u51fa\u66f4\u4f18\u7684\u7a33\u5b9a\u6027\uff0c \u5c3d\u7ba1\u4e0d\u540c\u7b97\u6cd5\u4e4b\u95f4\u7684\u6574\u4f53\u6027\u80fd\u5dee\u5f02\u5e76\u4e0d\u663e\u8457\u3002 (<em>\u7f16\u8005\u6ce8\uff1a \u7591\u4f3c\u539f\u6587 \u201cGRPO\u201d \u4e3a\u7b14\u8bef\uff0c\u5e94\u4e3a PPO\u3002<\/em>)<\/p>\n<p>\u5b9e\u9a8c\u7ed3\u679c\u63ed\u793a\u4e86\u4e24\u79cd\u6a21\u578b\u622a\u7136\u4e0d\u540c\u7684\u5b66\u4e60\u8f68\u8ff9\u3002 \u5c3d\u7ba1\u5728\u4efb\u52a1\u5f00\u59cb\u65f6\uff0c\u4e24\u8005\u7684\u8868\u73b0\u76f8\u8fd1\uff0c\u5f97\u5206\u90fd\u8f83\u4f4e\uff0c \u4f46 Qwen-2.5-3B \u5728\u8bad\u7ec3\u7684\u7b2c 30 \u6b65\u5de6\u53f3\u8868\u73b0\u51fa \u201c\u8d28\u7684\u98de\u8dc3\u201d\uff0c \u5177\u4f53\u8868\u73b0\u4e3a\u6a21\u578b\u751f\u6210\u7684\u56de\u590d\u660e\u663e\u53d8\u957f\uff0c \u4e14\u51c6\u786e\u6027\u663e\u8457\u63d0\u9ad8\u3002 \u8bad\u7ec3\u7ed3\u675f\u65f6\uff0cQwen-2.5-3B \u7684\u51c6\u786e\u7387\u8fbe\u5230\u4e86\u7ea6 60%\uff0c \u8fdc\u8d85 Llama-3.2-3B \u7684 30%\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/a32df3625a47287.png\" alt=\"Countdown \u6e38\u620f\u8bad\u7ec3\u7ed3\u679c\" \/><\/p>\n<p>\u5728\u8bad\u7ec3\u540e\u671f\uff0c\u7814\u7a76\u4eba\u5458\u89c2\u5bdf\u5230 Qwen-2.5-3B \u884c\u4e3a\u7684\u4e00\u4e2a\u6709\u8da3\u8f6c\u53d8\uff1a \u6a21\u578b\u9010\u6e10\u4ece\u4f7f\u7528\u663e\u5f0f\u7684\u9a8c\u8bc1\u8bed\u53e5 (\u4f8b\u5982 \u201c8*35 \u662f 280\uff0c\u592a\u9ad8\u4e86\u201d) \u8fc7\u6e21\u5230\u9690\u5f0f\u7684\u89e3\u51b3\u65b9\u6848\u68c0\u67e5\u3002 \u6a21\u578b\u4f1a \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e (\u4fc4\u8bed\uff0c\u8bd1\u4e3a \u201c \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u5730\u201d \u6216 \u201c \u4f9d\u5e8f\u5730\u201d) \u5c1d\u8bd5\u4e0d\u540c\u7684\u89e3\u6cd5\uff0c \u76f4\u5230\u627e\u5230\u6b63\u786e\u7684\u7b54\u6848\uff0c \u800c\u4e0d\u518d\u4f7f\u7528\u6587\u5b57\u6765\u8bc4\u4f30\u81ea\u8eab\u7684\u5de5\u4f5c\u3002 \u8fd9\u79cd\u5bf9\u6bd4\u9c9c\u660e\u5730\u5f15\u51fa\u4e86\u4e00\u4e2a\u6838\u5fc3\u95ee\u9898\uff1a \u7a76\u7adf\u662f\u54ea\u4e9b\u6f5c\u5728\u7684\u80fd\u529b\uff0c \u4f7f\u5f97\u6a21\u578b\u80fd\u591f\u6210\u529f\u5730\u5b9e\u73b0\u57fa\u4e8e\u63a8\u7406\u7684\u81ea\u6211\u6539\u8fdb\uff1f \u8981\u89e3\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c \u5c31\u9700\u8981\u6784\u5efa\u4e00\u4e2a\u7cfb\u7edf\u7684\u6846\u67b6\uff0c \u7528\u4e8e\u5206\u6790\u8ba4\u77e5\u884c\u4e3a\u3002<\/p>\n<p>&nbsp;<\/p>\n<h2>\u8ba4\u77e5\u884c\u4e3a\u5206\u6790\u6846\u67b6<\/h2>\n<p>\u4e3a\u4e86\u6df1\u5165\u7406\u89e3\u8fd9\u4e24\u79cd\u6a21\u578b\u8fe5\u5f02\u7684\u5b66\u4e60\u8f68\u8ff9\uff0c \u7814\u7a76\u4eba\u5458\u5f00\u53d1\u4e86\u4e00\u4e2a\u6846\u67b6\uff0c \u7528\u4e8e\u8bc6\u522b\u548c\u5206\u6790\u6a21\u578b\u8f93\u51fa\u4e2d\u7684\u5173\u952e\u8ba4\u77e5\u884c\u4e3a\u3002 \u8be5\u6846\u67b6\u91cd\u70b9\u5173\u6ce8\u4ee5\u4e0b\u56db\u79cd\u57fa\u672c\u884c\u4e3a\uff1a<\/p>\n<ol>\n<li><strong>\u56de\u6eaf (Backtracking)<\/strong>: \u5728\u68c0\u6d4b\u5230\u9519\u8bef\u65f6\uff0c \u663e\u5f0f\u5730\u4fee\u6539\u65b9\u6cd5 (\u4f8b\u5982\uff0c \u201c\u8fd9\u79cd\u65b9\u6cd5\u884c\u4e0d\u901a\uff0c \u56e0\u4e3a &#8230;\u201d)\u3002<\/li>\n<li><strong>\u9a8c\u8bc1 (Verification)<\/strong>: \u7cfb\u7edf\u5730\u68c0\u67e5\u4e2d\u95f4\u7ed3\u679c (\u4f8b\u5982\uff0c \u201c\u8ba9\u6211\u4eec\u901a\u8fc7 &#8230; \u6765\u9a8c\u8bc1\u8fd9\u4e2a\u7ed3\u679c\u201d)\u3002<\/li>\n<li><strong>\u5b50\u76ee\u6807\u8bbe\u5b9a (Sub-goal Setting)<\/strong>: \u5c06\u590d\u6742\u95ee\u9898\u5206\u89e3\u4e3a\u53ef\u7ba1\u7406\u7684\u6b65\u9aa4 (\u4f8b\u5982\uff0c \u201c\u8981\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c \u6211\u4eec\u9996\u5148\u9700\u8981 &#8230;\u201d)\u3002<\/li>\n<li><strong>\u9006\u5411\u601d\u8003 (Reverse Thinking)<\/strong>: \u5728\u76ee\u6807\u5bfc\u5411\u7684\u63a8\u7406\u95ee\u9898\u4e2d\uff0c \u4ece\u671f\u671b\u7684\u7ed3\u679c\u51fa\u53d1\uff0c \u9010\u6b65\u5411\u540e\u63a8\u5bfc\uff0c \u627e\u5230\u89e3\u51b3\u95ee\u9898\u7684\u8def\u5f84 (\u4f8b\u5982\uff0c \u201c\u8981\u8fbe\u5230 75 \u7684\u76ee\u6807\uff0c \u6211\u4eec\u9700\u8981\u4e00\u4e2a\u80fd\u88ab &#8230; \u6574\u9664\u7684\u6570\u5b57\u201d)\u3002<\/li>\n<\/ol>\n<p>\u9009\u62e9\u8fd9\u4e9b\u884c\u4e3a\u7684\u539f\u56e0\u5728\u4e8e\uff0c \u5b83\u4eec\u4ee3\u8868\u4e86\u4e0e\u8bed\u8a00\u6a21\u578b\u4e2d\u5e38\u89c1\u7684\u7ebf\u6027\u3001\u5355\u8c03\u63a8\u7406\u6a21\u5f0f\u622a\u7136\u4e0d\u540c\u7684\u95ee\u9898\u89e3\u51b3\u7b56\u7565\u3002 \u8fd9\u4e9b\u8ba4\u77e5\u884c\u4e3a\u4f7f\u5f97\u66f4\u52a0\u52a8\u6001\u3001\u7c7b\u4f3c\u641c\u7d22\u7684\u63a8\u7406\u8f68\u8ff9\u6210\u4e3a\u53ef\u80fd\uff0c \u89e3\u51b3\u65b9\u6848\u53ef\u4ee5\u4ee5\u975e\u7ebf\u6027\u7684\u65b9\u5f0f\u6f14\u8fdb\u3002 \u867d\u7136\u8fd9\u7ec4\u884c\u4e3a\u5e76\u975e\u8be6\u5c3d\u65e0\u9057\uff0c \u4f46\u7814\u7a76\u4eba\u5458\u9009\u62e9\u5b83\u4eec\u662f\u56e0\u4e3a\u5b83\u4eec\u6613\u4e8e\u8bc6\u522b\uff0c \u5e76\u4e14\u4e0e Countdown \u6e38\u620f\u4ee5\u53ca\u66f4\u5e7f\u6cdb\u7684\u6570\u5b66\u63a8\u7406\u4efb\u52a1 (\u4f8b\u5982\u6570\u5b66\u8bc1\u660e\u6784\u5efa) \u4e2d\u4eba\u7c7b\u7684\u95ee\u9898\u89e3\u51b3\u7b56\u7565\u81ea\u7136\u5951\u5408\u3002<\/p>\n<p>\u6bcf\u79cd\u8ba4\u77e5\u884c\u4e3a\u90fd\u53ef\u4ee5\u901a\u8fc7\u5176\u5728\u63a8\u7406 <a href=\"https:\/\/www.kdjingpai.com\/tokenization\/\">token<\/a> \u5e8f\u5217\u4e2d\u7684\u7279\u5b9a\u6a21\u5f0f\u6765\u8bc6\u522b\u3002 \u4f8b\u5982\uff0c \u56de\u6eaf\u8868\u73b0\u4e3a\u663e\u5f0f\u5426\u5b9a\u5e76\u66ff\u6362\u5148\u524d\u6b65\u9aa4\u7684 token \u5e8f\u5217\uff1b \u9a8c\u8bc1\u8868\u73b0\u4e3a\u751f\u6210\u5c06\u7ed3\u679c\u4e0e\u89e3\u51b3\u65b9\u6848\u6807\u51c6\u8fdb\u884c\u6bd4\u8f83\u7684 token\uff1b \u9006\u5411\u601d\u8003\u8868\u73b0\u4e3a\u4ece\u76ee\u6807\u51fa\u53d1\uff0c \u9010\u6b65\u6784\u5efa\u901a\u5f80\u521d\u59cb\u72b6\u6001\u7684\u89e3\u51b3\u65b9\u6848\u8def\u5f84\u7684 token\uff1b \u800c\u5b50\u76ee\u6807\u8bbe\u5b9a\u5219\u8868\u73b0\u4e3a\u663e\u5f0f\u5730\u63d0\u51fa\u5728\u901a\u5f80\u6700\u7ec8\u76ee\u6807\u7684\u8def\u5f84\u4e0a\u9700\u8981\u8fbe\u6210\u7684\u4e2d\u95f4\u6b65\u9aa4\u3002 \u7814\u7a76\u4eba\u5458\u5f00\u53d1\u4e86\u4e00\u4e2a\u4f7f\u7528 GPT-4o-mini \u6a21\u578b\u7684\u5206\u7c7b pipeline\uff0c \u80fd\u591f\u53ef\u9760\u5730\u8bc6\u522b\u6a21\u578b\u8f93\u51fa\u4e2d\u7684\u8fd9\u4e9b\u6a21\u5f0f\u3002<\/p>\n<p>&nbsp;<\/p>\n<h2>\u521d\u59cb\u884c\u4e3a\u5bf9\u81ea\u6211\u63d0\u5347\u7684\u5f71\u54cd<\/h2>\n<p>\u5c06\u4e0a\u8ff0\u5206\u6790\u6846\u67b6\u5e94\u7528\u4e8e\u521d\u59cb\u5b9e\u9a8c\uff0c \u5f97\u5230\u4e86\u4e00\u4e2a\u5173\u952e\u7684\u6d1e\u5bdf\uff1a\u00a0<strong>Qwen-2.5-3B \u6a21\u578b\u6027\u80fd\u7684\u663e\u8457\u63d0\u5347\uff0c \u4e0e\u8ba4\u77e5\u884c\u4e3a\u7684\u51fa\u73b0\u662f\u540c\u6b65\u53d1\u751f\u7684\uff0c \u7279\u522b\u662f\u9a8c\u8bc1\u548c\u56de\u6eaf\u884c\u4e3a\u3002<\/strong>\u00a0\u76f8\u6bd4\u4e4b\u4e0b\uff0c Llama-3.2-3B \u6a21\u578b\u5728\u6574\u4e2a\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0c \u51e0\u4e4e\u6ca1\u6709\u8868\u73b0\u51fa\u8fd9\u4e9b\u884c\u4e3a\u7684\u8ff9\u8c61\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/99056e0bf788185.png\" alt=\"\u8ba4\u77e5\u884c\u4e3a\u4e0e\u6a21\u578b\u6027\u80fd\" \/><\/p>\n<p>\u4e3a\u4e86\u66f4\u6df1\u5165\u5730\u7406\u89e3\u8fd9\u79cd\u5dee\u5f02\uff0c \u7814\u7a76\u4eba\u5458\u8fdb\u4e00\u6b65\u5206\u6790\u4e86\u4e09\u4e2a\u6a21\u578b\u7684\u57fa\u7ebf\u63a8\u7406\u6a21\u5f0f\uff1a Qwen-2.5-3B\u3001 Llama-3.2-3B \u548c Llama-3.1-70B\u3002 \u5206\u6790\u7ed3\u679c\u663e\u793a\uff0c \u76f8\u8f83\u4e8e Llama-3.2-3B \u548c Llama-3.1-70B \u8fd9\u4e24\u4e2a Llama \u6a21\u578b\u53d8\u4f53\uff0c Qwen-2.5-3B \u6a21\u578b\u4ea7\u751f\u5404\u79cd\u8ba4\u77e5\u884c\u4e3a\u7684\u6bd4\u4f8b\u90fd\u66f4\u9ad8\u3002 \u5c3d\u7ba1\u89c4\u6a21\u66f4\u5927\u7684 Llama-3.1-70B \u6a21\u578b\u5728\u8fd9\u4e9b\u884c\u4e3a\u7684\u6fc0\u6d3b\u9891\u7387\u4e0a\u666e\u904d\u9ad8\u4e8e Llama-3.2-3B \u6a21\u578b\uff0c \u4f46\u8fd9\u79cd\u63d0\u5347\u5e76\u4e0d\u5747\u8861\uff0c \u7279\u522b\u662f\u56de\u6eaf\u884c\u4e3a\uff0c \u5373\u4f7f\u5728\u66f4\u5927\u7684\u6a21\u578b\u4e2d\uff0c \u5176\u8868\u73b0\u4ecd\u7136\u6709\u9650\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/442ebeb8cf1693e.png\" alt=\"\u4e0d\u540c\u6a21\u578b\u7684\u8ba4\u77e5\u884c\u4e3a\" width=\"507\" height=\"482\" \/><\/p>\n<p>\u8fd9\u4e9b\u89c2\u5bdf\u7ed3\u679c\u63ed\u793a\u4e86\u4e24\u4e2a\u91cd\u8981\u7684\u6d1e\u5bdf\uff1a<\/p>\n<ol>\n<li><strong>\u521d\u59cb\u7b56\u7565\u4e2d\u5b58\u5728\u7684\u67d0\u4e9b\u8ba4\u77e5\u884c\u4e3a\uff0c \u53ef\u80fd\u662f\u6a21\u578b\u901a\u8fc7\u6269\u5c55\u63a8\u7406\u5e8f\u5217\uff0c \u6709\u6548\u5229\u7528\u589e\u52a0\u7684\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\u6240\u5fc5\u9700\u7684\u5148\u51b3\u6761\u4ef6\u3002<\/strong><\/li>\n<li><strong>\u589e\u52a0\u6a21\u578b\u89c4\u6a21\u53ef\u4ee5\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u6539\u5584\u8fd9\u4e9b\u8ba4\u77e5\u884c\u4e3a\u7684\u4e0a\u4e0b\u6587\u6fc0\u6d3b\u9891\u7387\u3002<\/strong><\/li>\n<\/ol>\n<p>\u8fd9\u79cd\u6a21\u5f0f\u81f3\u5173\u91cd\u8981\uff0c \u56e0\u4e3a\u5f3a\u5316\u5b66\u4e60\u53ea\u80fd\u653e\u5927\u5728\u6210\u529f\u8f68\u8ff9\u4e2d\u5df2\u7ecf\u51fa\u73b0\u7684\u884c\u4e3a\u3002 \u8fd9\u610f\u5473\u7740\uff0c \u521d\u59cb\u5177\u5907\u8fd9\u4e9b\u8ba4\u77e5\u884c\u4e3a\u80fd\u529b\uff0c \u662f\u6a21\u578b\u5b9e\u73b0\u6709\u6548\u5b66\u4e60\u7684\u5148\u51b3\u6761\u4ef6\u3002<\/p>\n<p>&nbsp;<\/p>\n<h2>\u5e72\u9884\u521d\u59cb\u884c\u4e3a\uff1a\u5f15\u5bfc\u6a21\u578b\u5b66\u4e60<\/h2>\n<p>\u5728\u786e\u7acb\u4e86\u57fa\u7840\u6a21\u578b\u4e2d\u8ba4\u77e5\u884c\u4e3a\u7684\u91cd\u8981\u6027\u4e4b\u540e\uff0c \u63a5\u4e0b\u6765\u7684\u95ee\u9898\u662f\uff1a \u662f\u5426\u53ef\u4ee5\u901a\u8fc7\u6709\u9488\u5bf9\u6027\u7684\u5e72\u9884\u624b\u6bb5\uff0c \u4eba\u4e3a\u5730\u8bf1\u5bfc\u6a21\u578b\u4ea7\u751f\u8fd9\u4e9b\u884c\u4e3a\uff1f \u7814\u7a76\u4eba\u5458\u63d0\u51fa\u7684\u5047\u8bbe\u662f\uff0c \u901a\u8fc7\u5728\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u4e4b\u524d\uff0c \u521b\u5efa\u9009\u62e9\u6027\u5730\u5c55\u73b0\u7279\u5b9a\u8ba4\u77e5\u884c\u4e3a\u7684\u57fa\u7840\u6a21\u578b\u53d8\u4f53\uff0c \u53ef\u4ee5\u66f4\u6df1\u5165\u5730\u7406\u89e3\u54ea\u4e9b\u884c\u4e3a\u6a21\u5f0f\u5bf9\u4e8e\u5b9e\u73b0\u6709\u6548\u7684\u5b66\u4e60\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<p>\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u5047\u8bbe\uff0c \u4ed6\u4eec\u9996\u5148\u4f7f\u7528 Countdown \u6e38\u620f\u8bbe\u8ba1\u4e86\u4e03\u4e2a\u4e0d\u540c\u7684\u542f\u52a8\u6570\u636e\u96c6\u3002 \u5176\u4e2d\u4e94\u4e2a\u6570\u636e\u96c6\u5206\u522b\u5f3a\u8c03\u4e0d\u540c\u7684\u884c\u4e3a\u7ec4\u5408\uff1a \u6240\u6709\u7b56\u7565\u7ec4\u5408\u3001 \u4ec5\u56de\u6eaf\u3001 \u56de\u6eaf\u4e0e\u9a8c\u8bc1\u3001 \u56de\u6eaf\u4e0e\u5b50\u76ee\u6807\u8bbe\u5b9a\uff0c \u4ee5\u53ca\u56de\u6eaf\u4e0e\u9006\u5411\u601d\u8003\u3002 \u4ed6\u4eec\u5229\u7528 Claude-3.5-Sonnet \u6a21\u578b\u751f\u6210\u8fd9\u4e9b\u6570\u636e\u96c6\uff0c \u56e0\u4e3a Claude-3.5-Sonnet \u5177\u5907\u751f\u6210\u5177\u6709\u7cbe\u786e\u6307\u5b9a\u884c\u4e3a\u7279\u5f81\u7684\u63a8\u7406\u8f68\u8ff9\u7684\u80fd\u529b\u3002<\/p>\n<p>\u4e3a\u4e86\u9a8c\u8bc1\u6027\u80fd\u7684\u63d0\u5347\u662f\u6e90\u4e8e\u7279\u5b9a\u7684\u8ba4\u77e5\u884c\u4e3a\uff0c \u800c\u975e\u7b80\u5355\u7684\u8ba1\u7b97\u65f6\u95f4\u589e\u52a0\uff0c \u7814\u7a76\u4eba\u5458\u8fd8\u5f15\u5165\u4e86\u4e24\u4e2a\u63a7\u5236\u6761\u4ef6\uff1a \u4e00\u4e2a\u7a7a\u7684\u601d\u7ef4\u94fe (Empty Chain of Thought)\uff0c \u4ee5\u53ca\u4e00\u4e2a\u586b\u5145\u4e86\u5360\u4f4d\u7b26 token \u94fe\uff0c \u4e14\u6570\u636e\u70b9\u957f\u5ea6\u4e0e \u201c\u6240\u6709\u7b56\u7565\u7ec4\u5408\u201d \u6570\u636e\u96c6\u76f8\u5339\u914d\u7684\u63a7\u5236\u6761\u4ef6\u3002 \u8fd9\u4e9b\u63a7\u5236\u6570\u636e\u96c6\u5e2e\u52a9\u7814\u7a76\u4eba\u5458\u9a8c\u8bc1\uff0c \u89c2\u5bdf\u5230\u7684\u4efb\u4f55\u6027\u80fd\u6539\u8fdb\u662f\u5426\u786e\u5b9e\u6e90\u4e8e\u7279\u5b9a\u7684\u8ba4\u77e5\u884c\u4e3a\uff0c \u800c\u975e\u4ec5\u4ec5\u662f\u8ba1\u7b97\u65f6\u95f4\u7684\u589e\u52a0\u3002<\/p>\n<p>\u6b64\u5916\uff0c \u7814\u7a76\u4eba\u5458\u8fd8\u521b\u5efa\u4e86 \u201c\u5168\u7b56\u7565\u7ec4\u5408\u201d \u6570\u636e\u96c6\u7684\u53d8\u4f53\uff0c \u5176\u4e2d\u4ec5\u5305\u542b\u4e0d\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff0c \u4f46\u4fdd\u7559\u4e86\u6240\u9700\u7684\u63a8\u7406\u6a21\u5f0f\u3002 \u8fd9\u4e2a\u53d8\u4f53\u7684\u76ee\u7684\u662f\u533a\u5206\u8ba4\u77e5\u884c\u4e3a\u7684\u91cd\u8981\u6027\u4e0e\u89e3\u51b3\u65b9\u6848\u51c6\u786e\u6027\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n<p>\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c \u5f53\u4f7f\u7528\u5305\u542b\u56de\u6eaf\u884c\u4e3a\u7684\u6570\u636e\u96c6\u8fdb\u884c\u521d\u59cb\u5316\u65f6\uff0c Llama-3 \u548c Qwen-2.5-3B \u6a21\u578b\u90fd\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u8868\u73b0\u51fa\u660e\u663e\u7684\u6027\u80fd\u6539\u8fdb\u3002 \u884c\u4e3a\u5206\u6790\u8fdb\u4e00\u6b65\u8868\u660e\uff0c\u00a0<strong>\u5f3a\u5316\u5b66\u4e60\u4f1a\u9009\u62e9\u6027\u5730\u653e\u5927\u5728\u7ecf\u9a8c\u4e0a\u88ab\u8bc1\u660e\u6709\u7528\u7684\u884c\u4e3a\uff0c \u540c\u65f6\u6291\u5236\u5176\u4ed6\u884c\u4e3a\u3002<\/strong>\u00a0\u4f8b\u5982\uff0c \u5728 \u201c\u5168\u7b56\u7565\u7ec4\u5408\u201d \u6761\u4ef6\u4e0b\uff0c \u6a21\u578b\u4f1a\u4fdd\u7559\u5e76\u52a0\u5f3a\u56de\u6eaf\u548c\u9a8c\u8bc1\u884c\u4e3a\uff0c \u540c\u65f6\u51cf\u5c11\u9006\u5411\u601d\u8003\u548c\u5b50\u76ee\u6807\u8bbe\u5b9a\u884c\u4e3a\u7684\u9891\u7387\u3002 \u7136\u800c\uff0c \u5f53\u4ec5\u4e0e\u56de\u6eaf\u884c\u4e3a\u914d\u5bf9\u65f6\uff0c \u88ab\u6291\u5236\u7684\u884c\u4e3a (\u4f8b\u5982\u9006\u5411\u601d\u8003\u548c\u5b50\u76ee\u6807\u8bbe\u5b9a) \u4f1a\u5728\u6574\u4e2a\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u6301\u7eed\u5b58\u5728\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/64f959e66bb36bb.png\" alt=\"\u4e0d\u540c\u542f\u52a8\u6570\u636e\u96c6\u7684\u8bad\u7ec3\u7ed3\u679c\" \/> \u00a0 <img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/41f22f8798ebddc.png\" alt=\"\u5f3a\u5316\u5b66\u4e60\u653e\u5927\u7684\u884c\u4e3a\" \/> \u00a0 <img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/f9f8b49cd149745.png\" alt=\"\u884c\u4e3a\u7ec4\u5408\u7684\u5f71\u54cd\" \/><\/p>\n<p>\u5f53\u4f7f\u7528\u7a7a\u7684\u601d\u7ef4\u94fe\u4f5c\u4e3a\u63a7\u5236\u6761\u4ef6\u8fdb\u884c\u542f\u52a8\u65f6\uff0c \u4e24\u79cd\u6a21\u578b\u7684\u6027\u80fd\u90fd\u4e0e\u57fa\u672c Llama-3 \u6a21\u578b\u76f8\u5f53 (\u51c6\u786e\u7387\u7ea6\u4e3a 30%-35%)\u3002 \u8fd9\u8868\u660e\uff0c \u4ec5\u4ec5\u5206\u914d\u989d\u5916\u7684 token\uff0c \u800c\u4e0d\u5305\u542b\u8ba4\u77e5\u884c\u4e3a\uff0c \u65e0\u6cd5\u6709\u6548\u5730\u5229\u7528\u6d4b\u8bd5\u65f6\u95f4\u8ba1\u7b97\u3002 \u66f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c \u4f7f\u7528\u7a7a\u7684\u601d\u7ef4\u94fe\u8fdb\u884c\u8bad\u7ec3\u751a\u81f3\u4f1a\u4ea7\u751f\u4e0d\u5229\u5f71\u54cd\uff0c Qwen-2.5-3B \u6a21\u578b\u4f1a\u505c\u6b62\u63a2\u7d22\u65b0\u7684\u884c\u4e3a\u6a21\u5f0f\u3002 \u8fd9\u8fdb\u4e00\u6b65\u5370\u8bc1\u4e86\u00a0<strong>\u8fd9\u4e9b\u8ba4\u77e5\u884c\u4e3a\u5bf9\u4e8e\u6a21\u578b\u901a\u8fc7\u66f4\u957f\u7684\u63a8\u7406\u5e8f\u5217\uff0c \u6709\u6548\u5229\u7528\u6269\u5c55\u8ba1\u7b97\u8d44\u6e90\u81f3\u5173\u91cd\u8981\u3002<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/a2c6172a792aba4.png\" alt=\"\u7a7a\u601d\u7ef4\u94fe\u7684\u5f71\u54cd\" \/><\/p>\n<p>\u66f4\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c \u4f7f\u7528\u4e0d\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\u8fdb\u884c\u521d\u59cb\u5316\uff0c \u4f46\u5177\u6709\u6b63\u786e\u8ba4\u77e5\u884c\u4e3a\u7684\u6a21\u578b\uff0c \u4e0e\u5728\u5305\u542b\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u6570\u636e\u96c6\u4e0a\u8bad\u7ec3\u7684\u6a21\u578b\uff0c \u53d6\u5f97\u4e86\u51e0\u4e4e\u76f8\u540c\u7684\u6027\u80fd\u6c34\u5e73\u3002 \u8fd9\u4e00\u7ed3\u679c\u5f3a\u6709\u529b\u5730\u8868\u660e\uff0c\u00a0<strong>\u8ba4\u77e5\u884c\u4e3a\u7684\u5b58\u5728 (\u800c\u975e\u83b7\u5f97\u6b63\u786e\u7b54\u6848) \u662f\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u6210\u529f\u5b9e\u73b0\u81ea\u6211\u6539\u8fdb\u7684\u5173\u952e\u56e0\u7d20\u3002<\/strong>\u00a0\u56e0\u6b64\uff0c \u6765\u81ea\u76f8\u5bf9\u8f83\u5f31\u6a21\u578b\u7684\u63a8\u7406\u6a21\u5f0f\uff0c \u53ef\u4ee5\u6709\u6548\u5730\u5f15\u5bfc\u5b66\u4e60\u8fc7\u7a0b\uff0c \u4ece\u800c\u6784\u5efa\u66f4\u5f3a\u5927\u7684\u6a21\u578b\u3002 \u8fd9\u518d\u6b21\u8bc1\u660e\u4e86\u00a0<strong>\u8ba4\u77e5\u884c\u4e3a\u7684\u5b58\u5728\u6bd4\u7ed3\u679c\u7684\u6b63\u786e\u6027\u66f4\u4e3a\u91cd\u8981\u3002<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/de3ee3fb63e5697.png\" alt=\"\u4e0d\u6b63\u786e\u89e3\u51b3\u65b9\u6848\u7684\u5f71\u54cd\" \/><\/p>\n<p>&nbsp;<\/p>\n<h2>\u9884\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u884c\u4e3a\u9009\u62e9<\/h2>\n<p>\u4e0a\u8ff0\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c \u67d0\u4e9b\u8ba4\u77e5\u884c\u4e3a\u5bf9\u4e8e\u6a21\u578b\u7684\u81ea\u6211\u5b8c\u5584\u81f3\u5173\u91cd\u8981\u3002 \u7136\u800c\uff0c \u524d\u8ff0\u7814\u7a76\u4e2d\uff0c \u7814\u7a76\u4eba\u5458\u8bf1\u5bfc\u521d\u59cb\u6a21\u578b\u4ea7\u751f\u7279\u5b9a\u884c\u4e3a\u7684\u65b9\u6cd5\uff0c \u662f\u9886\u57df\u7279\u5b9a\u7684\uff0c \u5e76\u4e14\u4f9d\u8d56\u4e8e Countdown \u6e38\u620f\u3002 \u8fd9\u53ef\u80fd\u4f1a\u5bf9\u6700\u7ec8\u63a8\u7406\u7684\u6cdb\u5316\u80fd\u529b\u4ea7\u751f\u4e0d\u5229\u5f71\u54cd\u3002 \u90a3\u4e48\uff0c \u662f\u5426\u53ef\u4ee5\u901a\u8fc7\u4fee\u6539\u6a21\u578b\u7684\u9884\u8bad\u7ec3\u6570\u636e\u5206\u5e03\uff0c \u6765\u589e\u52a0\u6709\u76ca\u63a8\u7406\u884c\u4e3a\u7684\u9891\u7387\uff0c \u4ece\u800c\u5b9e\u73b0\u66f4\u901a\u7528\u7684\u81ea\u6211\u5b8c\u5584\u80fd\u529b\u5462\uff1f<\/p>\n<p>\u4e3a\u4e86\u63a2\u7a76\u9884\u8bad\u7ec3\u6570\u636e\u4e2d\u8ba4\u77e5\u884c\u4e3a\u7684\u9891\u7387\uff0c \u7814\u7a76\u4eba\u5458\u9996\u5148\u5206\u6790\u4e86\u9884\u8bad\u7ec3\u6570\u636e\u4e2d\u8ba4\u77e5\u884c\u4e3a\u7684\u81ea\u7136\u9891\u7387\u3002 \u4ed6\u4eec\u91cd\u70b9\u5173\u6ce8 OpenWebMath \u548c FineMath \u6570\u636e\u96c6\uff0c \u8fd9\u4e24\u4e2a\u6570\u636e\u96c6\u662f\u4e13\u95e8\u4e3a\u6570\u5b66\u63a8\u7406\u800c\u6784\u5efa\u7684\u3002 \u7814\u7a76\u4eba\u5458\u4f7f\u7528 Qwen-2.5-32B \u6a21\u578b\u4f5c\u4e3a\u5206\u7c7b\u5668\uff0c \u5206\u6790\u4e86\u4ece\u8fd9\u4e24\u4e2a\u6570\u636e\u96c6\u4e2d\u968f\u673a\u62bd\u53d6\u7684 20 \u4e07\u4efd\u6587\u6863\uff0c \u4ee5\u67e5\u627e\u76ee\u6807\u8ba4\u77e5\u884c\u4e3a\u7684\u5b58\u5728\u60c5\u51b5\u3002 \u5206\u6790\u7ed3\u679c\u663e\u793a\uff0c \u5373\u4f7f\u5728\u8fd9\u4e9b\u4ee5\u6570\u5b66\u4e3a\u91cd\u70b9\u7684\u8bed\u6599\u5e93\u4e2d\uff0c \u56de\u6eaf\u548c\u9a8c\u8bc1\u7b49\u8ba4\u77e5\u884c\u4e3a\u7684\u51fa\u73b0\u9891\u7387\u4ecd\u7136\u5f88\u4f4e\u3002 \u8fd9\u8868\u660e\uff0c \u6807\u51c6\u7684\u9884\u8bad\u7ec3\u8fc7\u7a0b\u5bf9\u8fd9\u4e9b\u5173\u952e\u884c\u4e3a\u6a21\u5f0f\u7684\u63a5\u89e6\u662f\u6709\u9650\u7684\u3002<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/68b8a4f1260937f.png\" alt=\"\u9884\u8bad\u7ec3\u6570\u636e\u4e2d\u7684\u8ba4\u77e5\u884c\u4e3a\" \/><\/p>\n<p>\u4e3a\u4e86\u6d4b\u8bd5\u4eba\u4e3a\u589e\u52a0\u8ba4\u77e5\u884c\u4e3a\u7684\u63a5\u89e6\u662f\u5426\u80fd\u591f\u589e\u5f3a\u6a21\u578b\u7684\u81ea\u6211\u63d0\u5347\u6f5c\u529b\uff0c \u7814\u7a76\u4eba\u5458\u4ece OpenWebMath \u6570\u636e\u96c6\u51fa\u53d1\uff0c \u5f00\u53d1\u4e86\u4e00\u4e2a\u6709\u9488\u5bf9\u6027\u7684\u6301\u7eed\u9884\u8bad\u7ec3\u6570\u636e\u96c6\u3002 \u4ed6\u4eec\u9996\u5148\u4f7f\u7528 Qwen-2.5-32B \u6a21\u578b\u4f5c\u4e3a\u5206\u7c7b\u5668\uff0c \u5206\u6790\u6765\u81ea\u9884\u8bad\u7ec3\u8bed\u6599\u5e93\u7684\u6570\u5b66\u6587\u6863\uff0c \u4ee5\u8bc6\u522b\u76ee\u6807\u63a8\u7406\u884c\u4e3a\u7684\u5b58\u5728\u60c5\u51b5\u3002 \u5728\u6b64\u57fa\u7840\u4e0a\uff0c \u4ed6\u4eec\u521b\u5efa\u4e86\u4e24\u4e2a\u5bf9\u6bd4\u6570\u636e\u96c6\uff1a \u4e00\u4e2a\u5305\u542b\u4e30\u5bcc\u7684\u8ba4\u77e5\u884c\u4e3a\uff0c \u53e6\u4e00\u4e2a\u662f\u6781\u5c11\u5305\u542b\u8ba4\u77e5\u5185\u5bb9\u7684\u63a7\u5236\u6570\u636e\u96c6\u3002 \u7136\u540e\uff0c \u4ed6\u4eec\u4f7f\u7528 Qwen-2.5-32B \u6a21\u578b\u5c06\u8fd9\u4e24\u4e2a\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e2a\u6587\u6863\u91cd\u5199\u4e3a\u7ed3\u6784\u5316\u7684\u95ee\u7b54\u683c\u5f0f\uff0c \u540c\u65f6\u4fdd\u7559\u6e90\u6587\u6863\u4e2d\u8ba4\u77e5\u884c\u4e3a\u7684\u81ea\u7136\u5b58\u5728\u6216\u7f3a\u5931\u72b6\u6001\u3002 \u6700\u7ec8\u7684\u9884\u8bad\u7ec3\u6570\u636e\u96c6\uff0c \u6bcf\u4e2a\u90fd\u5305\u542b\u4e86\u603b\u5171 830 \u4e07\u4e2a token\u3002 \u8fd9\u79cd\u65b9\u6cd5\u4f7f\u5f97\u7814\u7a76\u4eba\u5458\u80fd\u591f\u6709\u6548\u5730\u9694\u79bb\u63a8\u7406\u884c\u4e3a\u7684\u5f71\u54cd\uff0c \u540c\u65f6\u63a7\u5236\u9884\u8bad\u7ec3\u671f\u95f4\u6570\u5b66\u5185\u5bb9\u7684\u683c\u5f0f\u548c\u6570\u91cf\u3002<\/p>\n<p>\u5728\u8fd9\u4e9b\u6570\u636e\u96c6\u4e0a\u5bf9 Llama-3.2-3B \u6a21\u578b\u8fdb\u884c\u9884\u8bad\u7ec3\uff0c \u5e76\u5e94\u7528\u5f3a\u5316\u5b66\u4e60\u540e\uff0c \u7814\u7a76\u4eba\u5458\u89c2\u5bdf\u5230\uff1a<\/p>\n<ol>\n<li><strong>\u884c\u4e3a\u4e30\u5bcc\u7684\u9884\u8bad\u7ec3\u6a21\u578b\uff0c \u6700\u7ec8\u5b9e\u73b0\u4e86\u4e0e Qwen-2.5-3B \u6a21\u578b\u76f8\u5f53\u7684\u6027\u80fd\u6c34\u5e73\uff0c \u800c\u63a7\u5236\u6a21\u578b\u7684\u6027\u80fd\u6539\u8fdb\u5219\u76f8\u5bf9\u6709\u9650\u3002<\/strong><\/li>\n<li><strong>\u5bf9\u8bad\u7ec3\u540e\u6a21\u578b\u7684\u884c\u4e3a\u5206\u6790\u8868\u660e\uff0c \u884c\u4e3a\u4e30\u5bcc\u7684\u9884\u8bad\u7ec3\u6a21\u578b\u53d8\u4f53\uff0c \u5728\u6574\u4e2a\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u59cb\u7ec8\u4fdd\u6301\u7740\u63a8\u7406\u884c\u4e3a\u7684\u9ad8\u6fc0\u6d3b\u5ea6\uff0c \u800c\u63a7\u5236\u6a21\u578b\u5219\u8868\u73b0\u51fa\u4e0e\u57fa\u672c Llama-3 \u6a21\u578b\u76f8\u4f3c\u7684\u884c\u4e3a\u6a21\u5f0f\u3002<\/strong><\/li>\n<\/ol>\n<p><img decoding=\"async\" src=\"https:\/\/www.kdjingpai.com\/wp-content\/uploads\/2025\/03\/decf5590f5f2828.png\" 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