{"id":3297,"date":"2025-01-10T17:14:29","date_gmt":"2025-01-10T09:14:29","guid":{"rendered":"https:\/\/www.ihub1.com\/?p=3297"},"modified":"2025-01-10T17:16:35","modified_gmt":"2025-01-10T09:16:35","slug":"%e8%ae%a9qwen2-5-7b%e8%b6%85%e8%b6%8ao1%ef%bc%8c%e5%be%ae%e8%bd%af%e5%b9%b2%e7%9a%84%ef%bc%81msra%e6%8e%a8%e5%87%ba%e5%b0%8f%e6%a8%a1%e5%9e%8b%e6%95%b0%e5%ad%a6%e6%8e%a8%e7%90%86%e8%87%aa%e6%88%91","status":"publish","type":"post","link":"https:\/\/www.ihub1.com\/index.php\/2025\/01\/10\/%e8%ae%a9qwen2-5-7b%e8%b6%85%e8%b6%8ao1%ef%bc%8c%e5%be%ae%e8%bd%af%e5%b9%b2%e7%9a%84%ef%bc%81msra%e6%8e%a8%e5%87%ba%e5%b0%8f%e6%a8%a1%e5%9e%8b%e6%95%b0%e5%ad%a6%e6%8e%a8%e7%90%86%e8%87%aa%e6%88%91\/","title":{"rendered":"\u8ba9Qwen2.5 7B\u8d85\u8d8ao1\uff0c\u5fae\u8f6f\u5e72\u7684\uff01MSRA\u63a8\u51fa\u5c0f\u6a21\u578b\u6570\u5b66\u63a8\u7406\u81ea\u6211\u8fdb\u5316\u65b0\u65b9\u6cd5"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"3297\" class=\"elementor elementor-3297\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b5e8702 e-flex e-con-boxed e-con e-parent\" data-id=\"b5e8702\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-676fd2b elementor-widget elementor-widget-text-editor\" data-id=\"676fd2b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p class=\"art_p\">7B\u53c2\u6570\u7684Qwen2.5\u6570\u5b66\u63a8\u7406\u8868\u73b0\u8d85\u8fc7o1-preview\uff0c\u8fd9\u662f\u600e\u4e48\u505a\u5230\u7684\uff1f\uff01<\/p><p class=\"art_p\">\u9760\u7684\u5c31\u662fMSRA\u6700\u65b0\u7684\u521b\u65b0\u7b97\u6cd5\uff0c<span>rStar-Math<\/span>\u3002<\/p><p class=\"art_p\">\u901a\u8fc7\u4ee3\u7801\u589e\u5f3aCoT\u3001\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22<span>\uff08MCTS\uff09<\/span>\u7b49\uff0c<span>rStar-Math\u80fd\u8ba9\u5c0f\u00b7\u5927\u6a21\u578b\u5728\u4e0d\u4f9d\u8d56\u84b8\u998f\u6559\u5e08\u6a21\u578b\u7684\u60c5\u51b5\u4e0b\uff0c\u901a\u8fc7\u591a\u8f6e\u81ea\u6211\u8fdb\u5316\u7684\u6df1\u5ea6\u601d\u7ef4\uff0c\u638c\u63e1\u6570\u5b66\u63a8\u7406\u3002<\/span><\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"0\" data-puid=\"0\"><img decoding=\"async\" id=\"0\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/218\/w730h288\/20250110\/30ca-fcb73236aa39258c1a3e9095ce08518d.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u5e76\u4e14\u6218\u529f\u8d6b\u8d6b\uff1a<\/p><p class=\"art_p\">\u5728\u7f8e\u56fd\u6570\u5b66\u7ade\u8d5bAIME 2024\u6d4b\u8bd5\u4e2d\uff0crStar-Math\u5e73\u5747\u89e3\u51b3\u4e8653.3%\u7684\u96be\u9898<span>\uff08OpenAI o1-preview\u4e3a44.6%\uff09<\/span>\uff0c<span>\u6253\u8d25\u6240\u6709\u5176\u5b83\u5f00\u6e90\u5927\u6a21\u578b<\/span>\uff0c\u4e00\u4e3e\u6210\u4e3a\u6700\u806a\u660e\u7684\u9ad8\u4e2d\u751f\u6570\u5b66top20%\u3002<\/p><p class=\"art_p\">\u5728MATH\u57fa\u51c6\u6d4b\u8bd5\u4e2d\uff0crStar-Math\u5c06<a target=\"app\" data-content=\"{&quot;ext&quot;:{&quot;word&quot;:&quot;\u963f\u91cc&quot;,&quot;market&quot;:&quot;us&quot;,&quot;symbol&quot;:&quot;baba&quot;,&quot;routeUri&quot;:&quot;sinanews:\\\/\\\/sina.cn\\\/finance\\\/stockDetail.pg?market=us&amp;symbol=BABA&amp;stockType=1&quot;},&quot;actionType&quot;:36,&quot;h5url&quot;:&quot;https:\\\/\\\/gu.sina.cn\\\/us\\\/hq\\\/quotes.php?code=BABA&quot;}\">\u963f\u91cc<\/a>\u5f00\u6e90\u5927\u6a21\u578bQwen2.5-Math-7B\u7684\u51c6\u786e\u7387\uff0c\u4ece58.8%\u62c9\u5347\u523090.0%\uff1bQwen2.5-Math-1.5B\u7684\u51c6\u786e\u7387\u4ece51.2%\u62c9\u5347\u523087.8%\uff1bPhi3-mini-3.8B\u7684\u51c6\u786e\u7387\u4ece41.4%\u63d0\u9ad8\u523086.4%<\/p><p class=\"art_p\"><span>\u2014\u2014\u8fd9\u4e9b\u6210\u7ee9\u5168\u90e8\u5168\u90e8\u8d85\u8fc7\u4e86OpenAI o1-preview\u3002<\/span><\/p><p class=\"art_p\">\u5c31\u8bf4\u725b\u4e0d\u725b\u5427\uff01<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"1\" data-puid=\"0\"><img decoding=\"async\" id=\"1\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/470\/w232h238\/20250110\/9999-ba8d0991d1c53c46b9769a99eb622ff0.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u5c0f\u58f0\u8bf4\uff0c<a target=\"app\" data-content=\"{&quot;ext&quot;:{&quot;word&quot;:&quot;\u5fae\u8f6f&quot;,&quot;market&quot;:&quot;us&quot;,&quot;symbol&quot;:&quot;msft&quot;,&quot;routeUri&quot;:&quot;sinanews:\\\/\\\/sina.cn\\\/finance\\\/stockDetail.pg?market=us&amp;symbol=MSFT&amp;stockType=1&quot;},&quot;actionType&quot;:36,&quot;h5url&quot;:&quot;https:\\\/\\\/gu.sina.cn\\\/us\\\/hq\\\/quotes.php?code=MSFT&quot;}\">\u5fae\u8f6f<\/a>\u6700\u8fd1\u6709\u4e00\u80a1\u5728\u5c0f\u00b7\u5927\u6a21\u578b<span>\u5708\u5b50\u91cc\u91cd\u62f3\u51fa\u51fb\u7684\u6001\u52bf\uff1a\u6628\u5929\u521a\u5f00\u6e90\u4e86\u76ee\u524d\u6700\u5f3a\u7684\u5c0f\u00b7\u5927\u6a21\u578b\uff0c14B\u7684phi-4\uff1b\u4eca\u5929\u53c8\u63a8\u51fa\u4e86rStar-Math\uff0c\u8bba\u6587\u4e2d\u76f4\u6307\u5176\u9762\u5411\u5c0f\u8bed\u8a00\u6a21\u578b<\/span><span>\uff08SLM\uff09<\/span>\u3002<\/p><p class=\"art_p\">\u8fd9\u4e2a\u8d8b\u52bf\u521a\u6709\u70b9\u82d7\u5934\uff0c\u7acb\u523b\u5f15\u5f97\u5168\u7f51\u8ba8\u8bba\u8fde\u8fde\u3002<\/p><p class=\"art_p\">\u6709\u7f51\u53cb\u4e0d\u7981\u5f00\u59cb\u731c\u6d4b\uff1a<\/p><blockquote><p class=\"art_p\">\u54b1\u5c31\u662f\u8bf4\uff0c\u6709\u6ca1\u6709\u4e00\u79cd\u53ef\u80fd\uff0c\u5728\u56fa\u5b9a\u8ba1\u7b97\u9884\u7b97\u7684\u60c5\u51b5\u4e0b\uff0c\u5c0f\u00b7\u5927\u6a21\u578b\u5176\u5b9e\u5728\u67d0\u4e9b\u63a8\u7406\u95ee\u9898\u4e0a\uff0c\u5b83\u5c31\u662f\u62a2\u8fc7\u5927\u6a21\u578b\u5462\uff1f<\/p><\/blockquote><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"2\" data-puid=\"0\"><img decoding=\"async\" id=\"2\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/29\/w1080h549\/20250110\/cb96-fb9af512912063935c9bf50bef993826.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">rStar &#8211; Math\u600e\u4e48\u505a\u5230\u7684\uff1f<\/p><p class=\"art_p\">Let\u2019s \u63d0\u95ee\uff1a<\/p><p class=\"art_p\">\u8ba9\u5c0f\u8bed\u8a00\u6a21\u578b\u80fd\u548co1\u7684\u6570\u5b66\u63a8\u7406\u80fd\u529b\u76f8\u5ab2\u7f8e\u751a\u81f3\u8d85\u8d8a\uff0c\u4e14\u65e0\u9700\u4ece\u9ad8\u7ea7\u6559\u5e08\u6a21\u578b\u4e2d\u84b8\u998f\uff0c\u5b83\u600e\u4e48\u505a\u5230\u7684\uff1f<\/p><p class=\"art_p\">MSRA\u5728\u8bba\u6587\u4e2d\u8868\u793a\uff0c\u8fd9\u662f\u901a\u8fc7\u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22<span>\uff08MCTS\uff09<\/span>\u8fdb\u884c\u6df1\u5ea6\u601d\u8003\u6765\u5b9e\u73b0\u7684\uff0c\u5e76\u4e14\uff0c\u5176\u4e2d\u4e00\u4e2a\u6570\u5b66\u7b56\u7565\u5c0f\u6a21\u578b\u5728\u57fa\u4e8e\u5c0f\u6a21\u578b\u7684\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u7684\u6307\u5bfc\u4e0b\u6267\u884c\u6d4b\u8bd5\u65f6\u641c\u7d22\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"3\" data-puid=\"0\"><img decoding=\"async\" id=\"3\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/660\/w1080h380\/20250110\/6920-c4eb9fc9fe28931c90b3e98346215b1f.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u76ee\u524d\uff0c\u4e1a\u754c\u666e\u904d\u4f9d\u8d56\u81ea\u7136\u8bed\u8a00\u751f\u6210\u7684\u63a8\u7406\u6b65\u9aa4\u6765\u63d0\u5347\u6570\u5b66\u63a8\u7406\u6a21\u578b\u7684\u80fd\u529b\u3002<\/p><p class=\"art_p\">\u8fd9\u79cd\u65b9\u6cd5\u5f88\u76f4\u7ed9\uff0c\u4f46\u5176\u5173\u952e\u5728\u4e8e\u8bad\u7ec3\u4e00\u4e2a\u5f3a\u5927\u7684\u7b56\u7565\u6a21\u578b\u6765\u751f\u6210\u89e3\u51b3\u65b9\u6848\u6b65\u9aa4\uff0c\u8fd8\u9700\u8981\u8bad\u7ec3\u4e00\u4e2a\u53ef\u9760\u7684\u5956\u52b1\u6a21\u578b\u6765\u8fdb\u884c\u51c6\u786e\u8bc4\u4f30\u3002<\/p><p class=\"art_p\">\u7136\u800c<span>\u4e0a\u8ff0\u4e24\u4e2a\u6a21\u578b\u90fd\u4f9d\u8d56\u4e8e\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e<\/span>\u3002<\/p><p class=\"art_p\">\u4f17\u6240\u5468\u77e5\u7684\u574f\u6d88\u606f\u662f\uff0c\u9ad8\u8d28\u91cf\u7684\u6570\u5b66\u63a8\u7406\u6570\u636e\u5728\u73b0\u5728\u662f\u975e\u5e38\u975e\u5e38\u7a00\u7f3a\u7684\uff0c\u540c\u65f6\u9ad8\u8d28\u91cf\u7684\u5408\u6210\u6570\u636e\u4e5f\u5b58\u5728\u4e00\u5b9abug\u3002<\/p><p class=\"art_p\">\u800c\u4e14\u5b9e\u9a8c\u8fc7\u7a0b\u8868\u660e\uff0c\u5b83\u5bb9\u6613\u9020\u6210\u8bb8\u591a\u4e0d\u76f8\u5173\u3001\u4e0d\u5fc5\u8981\u7684\u6b65\u9aa4\uff0c\u6216\u4ea7\u751f\u9519\u8bef\u3002<\/p><p class=\"art_p\">\u5f53\u8fd9\u79cd\u6d6a\u8d39\u548c\u5931\u8bef\u51fa\u73b0\u5728\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u4e2d\u65f6\uff0c<span>\u4e00\u822c\u5f88\u96be\u88ab\u5bdf\u89c9<\/span>\u3002<\/p><p class=\"art_p\">\u73b0\u6709\u7684\u529e\u6cd5\uff0c\u6bd4\u5982\u57fa\u4e8e\u84b8\u998f\u7684\u6570\u636e\u5408\u6210\u65b9\u6cd5\u6765\u8bad\u7ec3\u7b56\u7565\u6a21\u578b<span>\uff08\u5982\u6269\u5927GPT-4\u84b8\u998f\u7684CoT\u6570\u636e\uff09<\/span>\uff0c\u5df2\u7ecf\u660e\u663e\u7684\u51fa\u73b0\u56de\u62a5\u9012\u51cf\uff0c\u4e14\u6700\u7ec8\u5c55\u73b0\u7684\u80fd\u529b\u65e0\u6cd5\u8d85\u8fc7\u5176\u4ed6\u6559\u5e08\u6a21\u578b\u3002<\/p><p class=\"art_p\">\u4e0e\u6b64\u540c\u65f6\uff0c\u622a\u81f3\u4eca\u5929\uff0c\u8bad\u7ec3\u53ef\u9760\u7684PRM<span>\uff08Process Reward Model\uff0c\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\uff09<\/span>\u8fdb\u884c\u6570\u5b66\u63a8\u7406\u4ecd\u7136\u662f\u4e00\u4e2a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"4\" data-puid=\"0\"><img decoding=\"async\" id=\"4\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/468\/w236h232\/20250110\/46c7-cedb0c1d6c64bbe09d3d52d276b459d7.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">MSRA\u6b64\u6b21\u63a8\u51fa\u7684rStar-Math\uff0c\u5c31\u5f15\u5165\u4e86\u4e09\u9879\u521b\u65b0\u65b9\u6cd5\uff0c\u6765\u5e94\u5bf9\u8bad\u7ec3\u4e24\u4e2a\u5c0f\u6a21\u578b\u7684\u6311\u6218\uff1a<\/p><ul><li><p class=\"art_p\"><span>\u4ee3\u7801\u589e\u5f3aCoT\u6570\u636e\u5408\u6210\u65b9\u6cd5<\/span><\/p><\/li><li><p class=\"art_p\"><span>\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u8bad\u7ec3\u65b9\u6cd5<\/span><\/p><\/li><li><p class=\"art_p\"><span>\u56db\u8f6e\u81ea\u6211\u601d\u7ef4\u6df1\u5ea6\u8fdb\u5316<\/span><\/p><\/li><\/ul><p class=\"art_p\">\u54b1\u5c55\u5f00\u6765\u8bf4\u8bf4\uff5e<\/p><p class=\"art_p\">\u4ee3\u7801\u589e\u5f3aCoT\u6570\u636e\u5408\u6210\u65b9\u6cd5<\/p><p class=\"art_p\">rStar-Math\u9009\u62e9\u4f7f\u7528<span>\u4ee3\u7801\u589e\u5f3aCoT<\/span>\u6765\u89e3\u51b3\u4e0a\u8ff0\u96be\u9898\u3002<\/p><p class=\"art_p\">\u8be5\u65b9\u6cd5\u6267\u884c\u5e7f\u6cdb\u7684MCTS\u90e8\u7f72\uff0c\u4ece\u800c\u751f\u6210\u5177\u6709\u81ea\u6211\u6ce8\u91ca\u7684MCTS Q\u503c\u7684\u9010\u6b65\u9a8c\u8bc1\u63a8\u7406\u8f68\u8ff9\u3002<\/p><p class=\"art_p\">\u5177\u4f53\u6765\u8bf4\uff0c<span>\u4e00\u4e2a\u6570\u5b66\u95ee\u9898\u7684\u6c42\u89e3\uff0c\u4f1a\u5728MCTS\u5185\u88ab\u5206\u89e3\u4e3a\u591a\u6b65\u751f\u6210<\/span>\u3002<\/p><p class=\"art_p\">\u6a21\u578b\u5728\u751f\u6210\u6bcf\u4e00\u6b65\u63a8\u7406\u65f6\uff0c\u4f5c\u4e3a\u7b56\u7565\u6a21\u578b\u7684\u54ea\u4e2aSLM\u4f1a\u5bf9\u5019\u9009\u8282\u70b9\u8fdb\u884c\u91c7\u6837\uff0c\u4e0d\u4ec5\u751f\u6210\u8fd9\u4e00\u6b65\u7684CoT\u601d\u7ef4\u8138\u89e3\u91ca\uff0c\u8fd8\u751f\u6210\u76f8\u5bf9\u5e94\u7684Python\u4ee3\u7801\u3002<\/p><p class=\"art_p\">\u4e3a\u4e86\u9a8c\u8bc1\u751f\u6210\u8d28\u91cf\uff0c<span>\u53ea\u6709\u6210\u529f\u6267\u884cPython\u4ee3\u7801\u7684\u8282\u70b9\u624d\u4f1a\u88ab\u4fdd\u7559<\/span>\uff0c\u4ece\u800c\u51cf\u5c11\u4e2d\u95f4\u6b65\u9aa4\u7684\u9519\u8bef\uff0c\u786e\u4fdd\u6bcf\u4e00\u6b65\u63a8\u7406\u7684\u6b63\u786e\u6027\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"5\" data-puid=\"0\"><img decoding=\"async\" id=\"5\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/601\/w1080h321\/20250110\/cc78-92764d6dc01308bb2cddfaecb00c8b1a.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u5728\u6b64\u57fa\u7840\u4e0a\uff0c<span>\u4e3a\u4e86\u8fdb\u4e00\u6b65\u786e\u4fdd\u63a8\u7406\u6b65\u9aa4\u7684\u8d28\u91cf\uff0crStar-Math\u4f7f\u7528\u4e86MCTS\u6765\u751f\u6210\u9010\u6b65\u63a8\u7406\u8f68\u8ff9<\/span><span>\uff08\u7528\u6765\u5206\u89e3\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\u4e3a\u591a\u4e2a\u5355\u6b65\u751f\u6210\u4efb\u52a1\uff09<\/span>\u3002<\/p><p class=\"art_p\">\u5927\u91cf\u7684MCTS\u56de\u6eda\u4f1a\u6839\u636e\u6bcf\u4e2a\u4e2d\u95f4\u6b65\u9aa4\u5bf9\u6700\u7ec8\u6b63\u786e\u7b54\u6848\u7684\u8d21\u732e\uff0c\u81ea\u52a8\u4e3a\u5176\u5206\u914d\u4e00\u4e2aQ\u503c\u3002<\/p><p class=\"art_p\">\u6709\u52a9\u4e8e\u4ea7\u751f\u66f4\u591a\u5bfc\u81f4\u6b63\u786e\u7b54\u6848\u7684\u8f68\u8ff9\u7684\u6b65\u9aa4\u5c06\u88ab\u8d4b\u4e88\u66f4\u9ad8\u7684Q\u503c\uff0c\u5e76\u88ab\u8ba4\u4e3a\u5177\u6709\u66f4\u9ad8\u7684\u8d28\u91cf\u3002<\/p><p class=\"art_p\">\u8fd9\u786e\u4fdd\u4e86SLM\u751f\u6210\u7684\u63a8\u7406\u8f68\u8ff9\uff0c\u662f\u7531\u6b63\u786e\u3001\u9ad8\u8d28\u91cf\u7684\u4e2d\u95f4\u6b65\u9aa4\u7ec4\u6210\u7684\u3002<\/p><p class=\"art_p\">\u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u8bad\u7ec3\u65b9\u6cd5<\/p><p class=\"art_p\">\u73b0\u9636\u6bb5\uff0c\u591a\u6570\u5927\u6a21\u578b\u5728\u89e3\u51b3\u63a8\u7406\u6570\u5b66\u95ee\u9898\u65f6\uff0c\u90fd\u9762\u4e34\u4e00\u4e2a\u95ee\u9898\uff1a<\/p><p class=\"art_p\">\u65e0\u6cd5\u65e0\u6cd5\u63d0\u4f9b\u7ec6\u7c92\u5ea6\u7684\u6b65\u9aa4\u7ea7\u53cd\u9988\uff0c\u4ee5\u5e2e\u52a9\u5176\u5728\u63a8\u7406\u8fc7\u7a0b\u4e2d\u505a\u51fa\u66f4\u4f18\u7684\u9009\u62e9\u3002<\/p><p class=\"art_p\">\u5c3d\u7ba1\u4f7f\u7528\u4e86\u5e7f\u6cdb\u7684MCTS\u90e8\u7f72\uff0c\u4ecd\u4f1a\u51fa\u73b0Q\u503c\u4e0d\u591f\u7cbe\u786e\u7684\u60c5\u51b5\uff0c\u8fd9\u5c31\u5bfc\u81f4\u65e0\u6cd5\u5bf9\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u8fdb\u884c\u8bc4\u5206\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"6\" data-puid=\"0\"><img decoding=\"async\" id=\"6\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/73\/w1080h593\/20250110\/e37d-d0de1e08a1e2637cdd1e552ce9cb3ff2.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u4e3a\u6b64\uff0crStar-Math<span>\u901a\u8fc7\u5f15\u5165\u7528\u4e8e\u8bad\u7ec3\u5145\u5f53\u8fc7\u7a0b\u504f\u597d\u6a21\u578b<\/span><span>\uff08PPM\uff0cProcess Preference Model\uff09<\/span><span>\u7684SLM\uff0c\u6765\u53ef\u9760\u5730\u4e3a\u6bcf\u4e2a\u6570\u5b66\u63a8\u7406\u6b65\u9aa4\u9884\u6d4b\u5956\u52b1\u6807\u7b7e\u3002<\/span><\/p><p class=\"art_p\">PPM\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u662f\u901a\u8fc7\u6784\u5efa\u6b65\u9aa4\u7ea7\u7684\u6b63\u8d1f\u504f\u597d\u5bf9\u6765\u8bad\u7ec3\u6a21\u578b\uff0c\u800c\u4e0d\u662f\u76f4\u63a5\u4f9d\u8d56\u4e8e\u7cbe\u786e\u7684\u6b65\u9aa4\u7ea7\u8bc4\u5206\u3002<\/p><p class=\"art_p\">\u5b83\u6839\u636eQ\u503c\u4e3a\u6bcf\u4e2a\u6b65\u9aa4\u6784\u5efa\u504f\u597d\u5bf9\uff0c\u5e76\u4f7f\u7528\u6210\u5bf9\u6392\u540d\u635f\u5931\u6765\u4f18\u5316PPM\u5bf9\u6bcf\u4e2a\u63a8\u7406\u6b65\u9aa4\u7684\u5206\u6570\u9884\u6d4b\uff0c\u5b9e\u73b0\u53ef\u9760\u7684\u6807\u8bb0\u3002<\/p><p class=\"art_p\">\u5982\u4e0a\u6240\u8ff0\uff0c<span>Q\u503c\u867d\u7136\u4e0d\u7cbe\u51c6\u3001\u542b\u566a\u58f0\uff0c\u4f46PPM\u53ef\u4ee5\u5229\u7528\u5b83\uff0c\u53ef\u9760\u5730\u533a\u5206\u6b63<\/span><span>\uff08\u6b63\u786e\uff09<\/span><span>\u6b65\u9aa4\u548c\u8d1f<\/span><span>\uff08\u4e0d\u76f8\u5173 \/ \u9519\u8bef\uff09<\/span><span>\u6b65\u9aa4\u3002<\/span><\/p><p class=\"art_p\">\u56db\u8f6e\u81ea\u6211\u601d\u7ef4\u6df1\u5ea6\u8fdb\u5316<\/p><p class=\"art_p\">\u7531\u4e8eSLM\u80fd\u529b\u8f83\u5927\u6a21\u578b\u66f4\u5f31\uff0c\u56e2\u961f\u8bbe\u8ba1\u4e86<span>\u56db\u8f6e\u81ea\u6211\u601d\u7ef4\u6df1\u5ea6\u8fdb\u5316<\/span>\uff0c\u4ee5\u9010\u6b65\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u6570\u636e\uff0c\u5e76\u901a\u8fc7\u66f4\u5177\u6311\u6218\u6027\u7684\u6570\u5b66\u95ee\u9898\u6269\u5c55\u8bad\u7ec3\u96c6\u3002<\/p><p class=\"art_p\">\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u56e2\u961f\u9996\u5148\u9009\u62e9\u4e86\u4e00\u4e2a\u5305\u542b747k\u4e2a\u6570\u5b66\u95ee\u9898\u7684\u5f00\u6e90\u6570\u636e\u96c6\u3002<\/p><p class=\"art_p\">\u4f46\u5728\u6bcf\u4e00\u8f6e\u4e2d\uff0c\u7814\u7a76\u56e2\u961f\u6ca1\u6709\u4f7f\u7528747k\u6570\u5b66\u6570\u636e\u96c6\u4e2d\u7684\u539f\u59cb\u89e3\u51b3\u65b9\u6848\uff0c\u800c\u662f<span>\u8fdb\u884c\u4e86\u5e7f\u6cdb\u7684MCTS\u90e8\u7f72<\/span>\u2014\u2014<\/p><p class=\"art_p\">\u56db\u8f6e\u4e2d\u7684\u6bcf\u4e00\u8f6e\uff0c\u90fd\u4f7f\u7528MCTS\u751f\u6210\u9010\u6b65\u9a8c\u8bc1\u7684\u63a8\u7406\u8f68\u8ff9\uff0c\u7136\u540e\u5c06\u5176\u7528\u4e8e\u8bad\u7ec3\u65b0\u7b56\u7565SLM\u548cPPM\uff1b\u7136\u540e\u53c8\u5728\u4e0b\u4e00\u8f6e\u4e2d\u5e94\u7528\u65b0\u6a21\u578b\uff0c\u4ee5\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"7\" data-puid=\"0\"><img decoding=\"async\" id=\"7\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/546\/w1074h272\/20250110\/d444-9137e77d04d709449f64ae19226c0dec.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u56db\u8f6e\u81ea\u6211\u601d\u7ef4\u6df1\u5ea6\u8fdb\u5316\u5177\u4f53\u5982\u4e0b\u3002<\/p><p class=\"art_p\"><span>\u7b2c\u4e00\u8f6e\uff1a<\/span><\/p><p class=\"art_p\"><span>\u901a\u8fc7\u76d1\u7763\u5fae\u8c03\u5bf9\u57fa\u7840\u6a21\u578b\u8fdb\u884c\u521d\u6b65\u6539\u8fdb\uff0c\u4e3a\u540e\u7eed\u7684\u81ea\u6211\u8fdb\u5316\u5960\u5b9a\u57fa\u7840\u3002<\/span><\/p><p class=\"art_p\">\u6539\u8fdb\u540e\u7684\u6a21\u578b\u8868\u793a\u4e3aSLM-r1\u3002<\/p><p class=\"art_p\">\u5982\u88682\u6240\u793a\uff0c\u7814\u7a76\u4eba\u5458\u4f7f\u7528DeepSeek-Coder-V2-Instruct\u00a0<span>\uff08236B\uff09<\/span>\u8fd0\u884cMCTS\u6765\u6536\u96c6SFT\u6570\u636e\u3002<\/p><p class=\"art_p\">\u7531\u4e8e\u672c\u8f6e\u6ca1\u6709\u53ef\u7528\u7684\u5956\u52b1\u6a21\u578b\uff0c\u7814\u7a76\u8005\u5bf9Q\u503c\u4f7f\u7528\u7ec8\u7aef\u5f15\u5bfc\u7684\u6ce8\u91ca\uff0c\u5e76\u5c06MCTS\u9650\u5236\u4e3a8\u6b21\u63a8\u51fa\uff0c\u4ee5\u63d0\u9ad8\u6548\u7387\u3002<\/p><p class=\"art_p\">\u4e3a\u4e86\u83b7\u5f97\u6b63\u786e\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u56e2\u961f\u9009\u62e9\u5177\u6709\u6700\u9ad8\u5e73\u5747Q\u503c\u7684\u524d2\u6761\u8f68\u8ff9\u4f5c\u4e3aSFT\u6570\u636e\u3002<\/p><p class=\"art_p\">\u540c\u65f6\uff0c\u56e2\u961f\u5728\u8fd9\u4e00\u8f6e\u4e2d\u4e5f\u8bad\u7ec3\u4e86PPM-r1\u3002<\/p><p class=\"art_p\">\u8fd9\u4e00\u8f6e\u7684\u5173\u952e\u5728\u4e8e\u751f\u6210\u9ad8\u8d28\u91cf\u7684\u521d\u59cb\u8bad\u7ec3\u6570\u636e\uff0c\u5e76\u5229\u7528\u8fd9\u4e9b\u6570\u636e\u5bf9\u57fa\u7840\u6a21\u578b\u8fdb\u884c\u5fae\u8c03\u3002<\/p><p class=\"art_p\"><span>\u7b2c\u4e8c\u8f6e\uff1a<\/span><\/p><p class=\"art_p\"><span>\u8bad\u7ec3\u53ef\u9760\u7684PPM-r2\uff0c\u901a\u8fc7PPM\u663e\u8457\u63d0\u5347\u6a21\u578b\u63a8\u7406\u80fd\u529b\u3002<\/span><\/p><p class=\"art_p\">\u5728\u8fd9\u4e00\u8f6e\u4e2d\uff0c\u968f\u7740\u7b56\u7565\u6a21\u578b\u66f4\u65b0\u52307B SLM-r1\uff0c\u56e2\u961f\u8fdb\u884c\u4e86\u5e7f\u6cdb\u7684MCTS\u90e8\u7f72\uff0c\u4ee5\u83b7\u5f97\u66f4\u53ef\u9760\u7684Q\u503c\u6ce8\u91ca\uff1b\u9664\u6b64\u4e4b\u5916\uff0c\u8fd8\u8bad\u7ec3\u4e86\u7b2c\u4e00\u4e2a\u53ef\u9760\u7684\u5956\u52b1\u6a21\u578bPPM-r2\u3002<\/p><p class=\"art_p\">\u5177\u4f53\u6765\u8bf4\uff0c\u7814\u7a76\u56e2\u961f\u4e3a\u6bcf\u4e2a\u95ee\u9898\u6267\u884c16\u6b21MCTS\u90e8\u7f72\u3002\u7531\u6b64\u4ea7\u751f\u7684\u9010\u6b65\u9a8c\u8bc1\u63a8\u7406\u8f68\u8ff9\u8868\u660e\uff0c\u8d28\u91cf\u548cQ\u503c\u7cbe\u5ea6\u90fd\u6709\u4e86\u663e\u8457\u63d0\u9ad8\u3002<\/p><p class=\"art_p\">\u5982\u8868 4 \u6240\u793a\uff0cPPM-r2\u660e\u663e\u6bd4bootstrap\u8f6e\u6b21\u66f4\u6709\u6548\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"8\" data-puid=\"0\"><img decoding=\"async\" id=\"8\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/510\/w1080h230\/20250110\/a7a9-ca7899bfd7f8b94387cbdaf4c72800db.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u6b64\u5916\uff0c\u5982\u88683\u6240\u793a\uff0c\u7b56\u7565\u6a21\u578bSLM-r2\u4e5f\u5982\u9884\u671f\u7684\u90a3\u6837\u7ee7\u7eed\u6539\u8fdb\uff0c\u6307\u5bfc\u5176\u5728\u540e\u7eed\u7684\u63a8\u7406\u4e2d\u505a\u51fa\u66f4\u597d\u7684\u9009\u62e9\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"9\" data-puid=\"0\"><img decoding=\"async\" id=\"9\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/573\/w1080h293\/20250110\/fe81-ed16d4cd0f9c0fe2509e52819f86e33b.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\"><span>\u7b2c\u4e09\u8f6e\uff1a<\/span><\/p><p class=\"art_p\"><span>\u901a\u8fc7PPM\u589e\u5f3a\u7684MCTS\u751f\u6210\u66f4\u9ad8\u8d28\u91cf\u7684\u6570\u636e\uff0c\u8fdb\u4e00\u6b65\u63d0\u5347\u6a21\u578b\u7684\u63a8\u7406\u80fd\u529b\u3002<\/span><\/p><p class=\"art_p\">\u501f\u52a9\u53ef\u9760\u7684PPM-r2\uff0c\u7814\u7a76\u4eba\u5458\u5728\u8fd9\u4e00\u8f6e\u4e2d\u6267\u884cPPM\u589e\u5f3a\u7684MCTS\u4ee5\u751f\u6210\u6570\u636e\uff0c\u4ece\u800c\u83b7\u5f97\u66f4\u9ad8\u8d28\u91cf\u7684\u8f68\u8ff9\u3002\u6b64\u5904\u6db5\u76d6\u8bad\u7ec3\u96c6\u4e2d\u7684\u66f4\u591a\u6570\u5b66\u548c\u5965\u6797\u5339\u514b\u7ea7\u522b\u95ee\u9898<span>\uff08\u8be6\u7ec6\u53ef\u89c1\u88682\uff09<\/span>\u3002<\/p><p class=\"art_p\">\u7136\u540e\uff0c\u7814\u7a76\u8005\u4f7f\u7528\u751f\u6210\u7684\u63a8\u7406\u8f68\u8ff9\u548c\u81ea\u6211\u6ce8\u91ca\u7684Q\u503c\uff0c\u6765\u8bad\u7ec3\u65b0\u7b56\u7565SLM-r3\u548cPPM-r3\u2014\u2014\u8fd9\u4e24\u8005\u90fd\u663e\u793a\u51fa\u663e\u8457\u7684\u6539\u8fdb\u3002<\/p><p class=\"art_p\"><span>\u7b2c\u56db\u8f6e\uff1a<\/span><\/p><p class=\"art_p\"><span>\u901a\u8fc7\u589e\u52a0MCTS\u56de\u6eda\u6b21\u6570\uff0c\u89e3\u51b3\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u96be\u9898\u3002<\/span><\/p><p class=\"art_p\">\u524d\u7b2c\u4e09\u8f6e\u540e\uff0c\u867d\u7136rStar &#8211; Math\u5df2\u7ecf\u8ba9SLM\u5728\u5c0f\u5b66\u548cMATH\u9898\u76ee\u4e0a\u63d0\u9ad8\u6210\u529f\u7387\uff0c\u4f46\u5965\u8d5b\u7ea7\u522b\u9898\u76ee\u6210\u7ee9\u8fd8\u662f\u53ea\u670962.16%\u3002<\/p><p class=\"art_p\">\u4e3a\u6b64\uff0c\u56e2\u961f\u91c7\u7528\u4e86\u4e00\u79cd\u7b80\u5355\u7684\u7b56\u7565\uff0c\u5373\u5bf9\u4e8e\u572816\u6b21MCTS\u90e8\u7f72\u540e\u672a\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u4f1a\u989d\u5916\u6267\u884c64\u6b21\u90e8\u7f72\u3002<\/p><p class=\"art_p\">\u5982\u679c\u9700\u8981\uff0c\u8fd9\u4e2a\u6b21\u6570\u53ef\u4ee5\u589e\u52a0\u5230128\u6b21\u3002<\/p><p class=\"art_p\">\u6b64\u5916\uff0c\u7814\u7a76\u8005\u4eec\u8fd8\u4f7f\u7528\u4e0d\u540c\u7684\u968f\u673a\u79cd\u5b50\u8fdb\u884c\u591a\u4e2aMCTS\u6269\u5c55\uff0c\u6700\u540e\u5c06\u5965\u8d5b\u7ea7\u522b\u95ee\u9898\u7684\u6210\u529f\u7387\u63d0\u9ad8\u523080.58%\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"10\" data-puid=\"0\"><img decoding=\"async\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/546\/w1074h272\/20250110\/d444-9137e77d04d709449f64ae19226c0dec.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\u25b3\u6b64\u5904\u518d\u8d34\u4e00\u6b21\u88682\uff0c\u65b9\u4fbf\u5927\u5bb6\u67e5\u9605\" \/><h2 class=\"art_img_tit\">\u25b3\u6b64\u5904\u518d\u8d34\u4e00\u6b21\u88682\uff0c\u65b9\u4fbf\u5927\u5bb6\u67e5\u9605<\/h2><\/figure><p class=\"art_p\">\u7efc\u4e0a\uff0c\u7ecf\u8fc7\u56db\u8f6e\u81ea\u6211\u8fdb\u5316\uff0c747k\u6570\u5b66\u9898\u7684\u6210\u7ee9\u5df2\u7ecf\u6765\u5230\u4e8690.25%\u3002<\/p><p class=\"art_p\">\u5269\u4e0b\u7684\u672a\u89e3\u51b3\u7684\u95ee\u9898\u4e2d\uff0c\u5f88\u5927\u4e00\u90e8\u5206\u90fd\u662f\u7efc\u5408\u95ee\u9898\u3002<\/p><p class=\"art_p\">\u7814\u7a76\u8005\u4eba\u5de5\u624b\u52a8\u5ba1\u67e5\u4e8620\u4e2a\u95ee\u9898\u7684\u968f\u673a\u6837\u672c\uff0c\u53d1\u73b0\u5176\u4e2d19\u4e2a\u95ee\u9898\u88ab\u9519\u8bef\u5730\u6807\u8bb0\u4e3a\u9519\u8bef\u7b54\u6848\u3002<\/p><p class=\"art_p\"><span>\u57fa\u4e8e\u6b64\uff0c\u56e2\u961f\u5f97\u51fa\u7ed3\u8bba\uff1a\u5269\u4f59\u7684\u672a\u89e3\u51b3\u7684\u95ee\u9898\u8d28\u91cf\u8f83\u4f4e\uff0c\u56e0\u6b64\u81ea\u6211\u8fdb\u5316\u7684\u811a\u6b65\u7ec8\u6b62\u5728\u7b2c4\u8f6e\u3002<\/span><\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"11\" data-puid=\"0\"><img decoding=\"async\" id=\"11\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/553\/w1080h273\/20250110\/0572-cb89f526273929fffeb345a84bb04d7a.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u5b9e\u9a8c\u8bc4\u4f30\u4e0e\u53d1\u73b0<\/p><p class=\"art_p\">\u4e0b\u9762\u7684\u88685\uff0c\u663e\u793a\u4e86<span>rStar-Math\u4e0e\u6700\u5148\u8fdb\u7684\u63a8\u7406\u6a21\u578b\u8fdb\u884c\u6bd4\u8f83\u7684\u7ed3\u679c\u3002<\/span><\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"12\" data-puid=\"0\"><img decoding=\"async\" id=\"12\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/619\/w1080h1139\/20250110\/2f9c-791291b93f675c1e07d01d0fa9c56112.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u6709\u4e09\u4e2a\u503c\u5f97\u8bf4\u9053\u8bf4\u9053\u7684\u89c2\u5bdf\u53d1\u73b0\uff1a<\/p><p class=\"art_p\"><span>\u7b2c\u4e00\uff0crStar-Math \u663e\u8457\u63d0\u9ad8\u4e86SLM\u7684\u6570\u5b66\u63a8\u7406\u80fd\u529b\uff0c\u4ee5\u5c0f\u5f97\u591a\u7684\u6a21\u578b\u5c3a\u5bf8\uff0c\u5b9e\u73b0\u4e86\u4e0eOpenAI o1\u76f8\u5f53\uff0c\u751a\u81f3\u8d85\u8fc7o1\u7684\u6027\u80fd\u3002<\/span><\/p><p class=\"art_p\">\u4f8b\u5982\uff0cQwen2.5-Math-7B\u6700\u521d<span>\u5728MATH\u4e0a<\/span>\u7684\u51c6\u786e\u7387\u4e3a58.8%\uff0c\u4f7f\u7528rStar-Math\u540e\uff0c\u51c6\u786e\u7387\u663e\u8457\u63d0\u9ad8\u523090.0%\uff0c\u4f18\u4e8eo1-preview\u548cClaude 3.5 Sonnet\uff0c\u548co1-mini\u6253\u4e86\u4e2a\u5e73\u624b\u3002<\/p><p class=\"art_p\"><span>\u5728College Math\u57fa\u51c6\u6d4b\u8bd5\u4e2d<\/span>\uff0crStar-Math\u540eQwen2.5-Math-7B\u7684\u6bd4o1-mini\u9ad8\u51fa 2.7%\u3002<\/p><p class=\"art_p\"><span>\u5728AIME 2024\u4e0a<\/span>\uff0crStar-Math\u540e\u7684Qwen2.5-Math-7B\u5f97\u5206\u4e3a53.3%\uff0c\u4e0d\u53cao1-mini\u768456.7%\u3002\u4e0d\u8fc7\uff0c7B\u6a21\u578b\u5728AIME I \u548c II \u4e2d\u89e3\u51b3\u4e868\/15\u7684\u95ee\u9898\uff0c\u5728\u6700\u806a\u660e\u7684\u9ad8\u4e2d\u6570\u5b66\u5b66\u751f\u4e2d\u6392\u540d\u524d 20%\u3002<\/p><p class=\"art_p\">\u800c\u672a\u89e3\u51b3\u7684\u95ee\u9898\u4e2d\uff0c\u67098\u4e2a\u662f<span>\u9700\u8981\u89c6\u89c9\u91cc\u89c9\u7684\u51e0\u4f55\u56fe\u5f62\u9898\uff0c\u8fd9\u4e2a\u529f\u80fd\u76ee\u524drStar-Math\u8fd8\u4e0d\u652f\u6301\u3002<\/span><\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"13\" data-puid=\"0\"><img decoding=\"async\" id=\"13\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/792\/w1080h512\/20250110\/295c-9902de59c44d32fec5107d4914edb134.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\"><span>\u7b2c\u4e8c\uff0c\u5c3d\u7ba1\u4f7f\u7528\u8f83\u5c0f\u7684\u653f\u7b56\u6a21\u578b<\/span><span>\uff081.5B-7B\uff09<\/span><span>\u548c\u5956\u52b1\u6a21\u578b<\/span><span>\uff087B\uff09<\/span><span>\uff0c\u4f46rStar-Math\u7684\u6027\u80fd\u660e\u663e\u4f18\u4e8e\u6700\u5148\u8fdb\u7684System 2\u57fa\u7ebf\u3002<\/span><\/p><p class=\"art_p\">\u4e0e\u4f7f\u7528\u76f8\u540c\u7684\u57fa\u672c\u6a21\u578b<span>\uff08Qwen2-Math-7B\u3001Qwen2.5-Math-1.5B\/7B\uff09<\/span>\u4f46\u5956\u52b1\u6a21\u578b\u00a0<span>\uff08Qwen2.5-Math-RM-72B\uff09<\/span>\u00a0\u592710\u500d\u4ee5\u4e0a\u7684Qwen Best-of-N\u57fa\u7ebf\u76f8\u6bd4\uff0crStar-Math\u59cb\u7ec8\u5c06\u6240\u6709\u57fa\u672c\u6a21\u578b\u7684\u63a8\u7406\u51c6\u786e\u6027\u63d0\u9ad8\u5230\u6700\u5148\u8fdb\u7684\u6c34\u5e73\u3002<\/p><p class=\"art_p\">\u5373\u4f7f\u4e0eQwen2.5-Math-72B-Instruct\u7684\u7b56\u7565\u6a21\u578b\u592710\u500d\u4ee5\u4e0a\u7684N-Best-of-N\u5bf9\u6bd4\uff0c\u4f7f\u7528\u76f8\u540c\u6570\u91cf\u7684\u91c7\u6837\u89e3\u51b3\u65b9\u6848\uff0crStar-Math\u4e5f\u5728\u9664GSM8K\u4e4b\u5916\u7684\u6240\u6709\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u4e5f\u8d85\u8fc7\u4e86\u5b83\u3002<\/p><p class=\"art_p\"><span>\u7b2c\u4e09\uff0c\u9664\u4e86MATH\u3001GSM8K\u548cAIME\u7b49\u53ef\u80fd\u5b58\u5728\u8fc7\u5ea6\u4f18\u5316\u7684\u77e5\u540d\u57fa\u51c6\u6d4b\u8bd5\u4e4b\u5916\uff0crStar-Math\u5728\u5176\u5b83\u5177\u6709\u6311\u6218\u6027\u7684\u6570\u5b66\u57fa\u51c6\u6d4b\u8bd5\u4e2d\u8868\u73b0\u51fa\u5f88\u5f3a\u7684\u901a\u7528\u6027\u3002<\/span><\/p><p class=\"art_p\">\u5305\u62ec\u4f46\u4e0d\u9650\u4e8e\u5965\u8d5b\u57fa\u51c6\u3001\u5927\u5b66\u6570\u5b66\u548c\u4e2d\u56fd\u9ad8\u8003\u6570\u5b66\u8003\u8bd5\u00a0<span>\uff08Gaokao\uff09<\/span>\u3002<\/p><p class=\"art_p\">\u800c\u4e14\u9700\u8981\u5f3a\u8c03\u7684\u662f\uff0crStar-Math\u8bad\u7ec3\u96c6\u4e3b\u8981\u6765\u81ea\u516c\u5171\u6570\u636e\u96c6\uff0c<span>\u5e76\u6ca1\u6709\u9488\u5bf9\u8fd9\u4e9b\u57fa\u51c6\u6d4b\u8bd5\u8fdb\u884c\u7279\u5b9a\u7684\u4f18\u5316\u3002<\/span><\/p><p class=\"art_p\">\u603b\u7684\u6765\u8bf4\uff0c\u5b9e\u9a8c\u7ed3\u679c\u9a8c\u8bc1\u4e86\u81ea\u8fdb\u5316\u3001\u9010\u6b65\u9a8c\u8bc1\u63a8\u7406\u8f68\u8ff9\u548cPPM\u7684\u6709\u6548\u6027\u3002<\/p><p class=\"art_p\">One More Thing<\/p><p class=\"art_p\">\u672c\u7814\u7a76\u7684<span>\u5171\u540c\u4e00\u4f5c<\/span>\u5206\u522b\u662fMSRA\u7684Xinyu Guan\u548cLi Lyna Zhang\u3002<\/p><p class=\"art_p\"><span>Li Lyna Zhang<\/span>\u662f\u5de5\u4f5c\u7684\u9879\u76eeleader\uff0c\u672c\u535a\u90fd\u6bd5\u4e1a\u4e8e\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\uff0c\u76ee\u524d\u662fMSRA\u7cfb\u7edf\u4e0e\u7f51\u7edc\u7ec4\u7684\u9ad8\u7ea7\u7814\u7a76\u5458\u3002<\/p><figure class=\"art_img_mini j_p_gallery\" data-type=\"simple\" data-startindex=\"14\" data-puid=\"0\"><img decoding=\"async\" id=\"14\" class=\"art_img_mini_img j_fullppt_cover finpic\" src=\"https:\/\/k.sinaimg.cn\/n\/sinakd20250110s\/552\/w928h424\/20250110\/080b-7eb6aeda31b2887f3bd040085831a7ae.png\/w700d1q75cms.jpg?by=cms_fixed_width\" alt=\"\" \/><h2 class=\"art_img_tit\">\u00a0<\/h2><\/figure><p class=\"art_p\">\u53e6\u4e00\u4f4d\u5171\u540c\u4e00\u4f5c\uff0c<span>Xinyu Guan<\/span>\uff0c\u5728\u5b8c\u6210\u8fd9\u9879\u5de5\u4f5c\u7684\u65f6\u5019\u662f<span>MSRA\u7684\u5b9e\u4e60\u751f\uff0c\u8fd9\u4f4d\u540c\u5b66\u5f53\u65f6\u8fd8\u5728\u5317\u5927\u8bfb\u4e66\u3002<\/span><\/p><p class=\"art_p\">BTW\uff0c<span>\u8bba\u6587\u4e2d\u53e6\u4e00\u4f4d\u4f5c\u8005Youran Sun\u53c2\u4e0e\u9879\u76ee\u65f6\u4e5f\u662fMSRA\u5b9e\u4e60\u751f\uff0c\u8fd9\u4f4d\u540c\u5b66\u5219\u662f\u6e05\u534eer\u3002<\/span><\/p><p class=\"art_p\">\u554a\uff0c\u5e74\u8f7b\u4eba\u7684\u4e16\u754c\uff0c\u53c8\u662f\u5b9e\u4e60\u751f\u5462\uff5e<\/p><p class=\"art_p\">arXiv\uff1a<\/p><p class=\"art_p\">https:\/\/arxiv.org\/pdf\/2501.04519<\/p><p class=\"art_p\">\u4ee3\u7801\u548c\u6570\u636e\u8be6\u89c1GitHub\uff1a<\/p><p class=\"art_p\">https:\/\/github.com\/microsoft\/rStar<\/p><p class=\"art_p\">\u53c2\u8003\u94fe\u63a5\uff1a<\/p><p class=\"art_p\">[1]<span>https:\/\/x.com\/_akhaliq\/status\/1877206745652592763<\/span><\/p><p class=\"art_p\">[2]https:\/\/www.reddit.com\/r\/singularity\/comments\/1hxieic\/microsoft_says_with_rstarmath_it_has_demonstrated\/<\/p><p class=\"art_p\">[3]https:\/\/www.reddit.com\/r\/MachineLearning\/comments\/1hxk2ab\/r_rstarmath_small_llms_can_master_math_reasoning\/<\/p><p class=\"art_p\">[4]https:\/\/www.microsoft.com\/en-us\/research\/people\/lzhani\/<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u8861\u5b87 \u53d1\u81ea \u51f9\u975e\u5bfa<\/p>\n","protected":false},"author":1,"featured_media":3299,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3297","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/posts\/3297","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/comments?post=3297"}],"version-history":[{"count":10,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/posts\/3297\/revisions"}],"predecessor-version":[{"id":3308,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/posts\/3297\/revisions\/3308"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/media\/3299"}],"wp:attachment":[{"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/media?parent=3297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/categories?post=3297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ihub1.com\/index.php\/wp-json\/wp\/v2\/tags?post=3297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}