{"id":96486,"date":"2026-08-27T19:08:34","date_gmt":"2026-08-27T11:08:34","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/96486.html"},"modified":"2026-08-27T19:08:34","modified_gmt":"2026-08-27T11:08:34","slug":"%e5%a4%a7%e6%a8%a1%e5%9e%8b%e6%b7%b1%e5%ba%a6%e6%80%9d%e8%80%83%e6%9c%ba%e5%88%b6%e6%8b%86%e8%a7%a3%ef%bc%9a%e4%bb%8e%e8%87%aa%e5%9b%9e%e5%bd%92-next-token-%e5%88%b0%e6%b5%8b%e8%af%95%e6%9c%9f","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/96486.html","title":{"rendered":"\u5927\u6a21\u578b\u6df1\u5ea6\u601d\u8003\u673a\u5236\u62c6\u89e3\uff1a\u4ece\u81ea\u56de\u5f52 Next-Token \u5230\u6d4b\u8bd5\u671f\u8ba1\u7b97\uff08Test-Time Compute\uff09\u7269\u7406\u8fb9\u754c"},"content":{"rendered":"<h2>\u5927\u6a21\u578b\u6df1\u5ea6\u601d\u8003\u673a\u5236\u62c6\u89e3&#xff1a;\u4ece\u81ea\u56de\u5f52 Next-Token \u5230\u6d4b\u8bd5\u671f\u8ba1\u7b97&#xff08;Test-Time Compute&#xff09;\u7269\u7406\u8fb9\u754c<\/h2>\n<p>\u5728\u8fc7\u53bb\u7684\u51e0\u5e74\u91cc&#xff0c;\u6574\u4e2a\u6df1\u5ea6\u5b66\u4e60\u4e0e\u5927\u8bed\u8a00\u6a21\u578b&#xff08;LLM&#xff09;\u5de5\u4e1a\u754c\u51e0\u4e4e\u5168\u76d8\u62bc\u6ce8\u5728 \u201c\u9884\u8bad\u7ec3\u6269\u5c55\u5b9a\u5f8b&#xff08;Pre-training Scaling Law&#xff09;\u201d \u4e0a&#xff1a;\u901a\u8fc7\u5806\u53e0\u6570\u5341\u4e07\u5757 GPU\u3001\u6295\u5582\u6570\u5341\u4e07\u4ebf Token \u7684\u65e0\u6807\u6ce8\u4e92\u8054\u7f51\u8bed\u6599&#xff0c;\u5c06\u5bc6\u96c6\u53c2\u6570\u4ece 7B \u63a8\u9ad8\u81f3 70B \u4e43\u81f3\u6570\u767e B\u3002<\/p>\n<p>\u7136\u800c&#xff0c;\u5f53\u5927\u6a21\u578b\u9762\u4e34\u9700\u8981\u4e25\u683c\u903b\u8f91\u6f14\u7ece\u7684\u590d\u6742\u6570\u5b66\u8bc1\u660e&#xff08;\u5982 AIME \/ Putnam \u7ade\u8d5b&#xff09;\u3001\u590d\u6742\u4ee3\u7801\u957f\u7a0b\u67b6\u6784\u8bbe\u8ba1\u6216\u591a\u6b65\u903b\u8f91\u63a8\u7406\u65f6&#xff0c;\u4f20\u7edf\u7684 \u201c\u76f4\u63a5\u81ea\u56de\u5f52\u5355\u5411\u751f\u6210&#xff08;Direct Autoregressive Next-Token Prediction&#xff09;\u201d \u8fc5\u901f\u649e\u4e0a\u4e86\u4ee4\u4eba\u6cae\u4e27\u7684**\u201c\u7cfb\u7edf 1 \u5feb\u601d\u8003\u7269\u7406\u5929\u82b1\u677f\u201d**&#xff1a;<\/p>\n<ul>\n<li>\u201c\u4e00\u6b65\u9519&#xff0c;\u6b65\u6b65\u9519\u201d\u7684\u8bef\u5dee\u96ea\u5d29&#xff08;Error Cascade&#xff09;&#xff1a;\u5728\u6807\u51c6\u7684\u81ea\u56de\u5f52\u751f\u6210\u4e2d&#xff0c;\u6bcf\u4e00\u4e2a\u8f93\u51fa Token \u90fd\u4f1a\u4f5c\u4e3a\u540e\u7eed\u6240\u6709\u751f\u6210\u7684\u4e0d\u53ef\u53d8\u524d\u7f00\u3002\u5982\u679c\u6a21\u578b\u5728\u7b2c 3 \u6b65\u63a8\u5bfc\u4e2d\u4ea7\u751f\u4e86\u4e00\u4e2a\u5fae\u5999\u7684\u903b\u8f91\u6f0f\u6d1e\u6216\u8ba1\u7b97\u504f\u5dee&#xff0c;\u7531\u4e8e\u81ea\u56de\u5f52\u673a\u5236\u7f3a\u4e4f\u201c\u81ea\u6211\u56de\u6eaf\u4e0e\u7ea0\u504f\u201d\u80fd\u529b&#xff0c;\u8be5\u8bef\u5dee\u4f1a\u5728\u540e\u7eed\u6b65\u9aa4\u4e2d\u88ab\u6307\u6570\u7ea7\u653e\u5927&#xff0c;\u6700\u7ec8\u5bfc\u81f4\u5168\u76d8\u5d29\u6e83&#xff1b;<\/li>\n<li>\u5355 Token \u7b97\u529b\u5206\u914d\u7684\u751f\u786c\u5bf9\u9f50&#xff1a;\u65e0\u8bba\u9762\u5bf9\u7684\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u6253\u62db\u547c\u201c\u4f60\u597d\u201d&#xff0c;\u8fd8\u662f\u4e00\u4e2a\u6781\u5176\u6666\u6da9\u7684\u201c\u9ece\u66fc\u731c\u60f3\u5c40\u90e8\u5f15\u7406\u201d&#xff0c;\u4f20\u7edf\u7684\u81ea\u56de\u5f52\u6a21\u578b\u4e3a\u6bcf\u4e2a Token \u5206\u914d\u7684\u6d6e\u70b9\u8fd0\u7b97\u6b21\u6570&#xff08;FLOPs&#xff09;\u90fd\u662f\u5b8c\u5168\u76f8\u540c\u7684&#xff01;\u8fd9\u4e0e\u4eba\u7c7b\u5927\u8111\u5728\u5904\u7406\u590d\u6742\u95ee\u9898\u65f6\u7684**\u201c\u7cfb\u7edf 2 \u6162\u601d\u8003&#xff08;Slow Thinking&#xff09;\u201d**\u673a\u5236\u80cc\u9053\u800c\u9a70\u3002<\/li>\n<\/ul>\n<p>\u76f4\u5230 OpenAI o1\u3001DeepSeek-R1 \u7b49\u5177\u5907\u6df1\u5ea6\u81ea\u7701\u4e0e\u81ea\u4e3b\u601d\u7ef4\u94fe&#xff08;Reasoning Tokens \/ Thinking Process&#xff09;\u7684\u201c\u601d\u8003\u6a21\u578b\u201d\u6a2a\u7a7a\u51fa\u4e16&#xff0c;AI \u67b6\u6784\u8303\u5f0f\u6b63\u5f0f\u4ece\u5355\u4e00\u7684\u201c\u8bad\u7ec3\u671f\u6269\u5c55&#xff08;Train-time Scaling&#xff09;\u201d\u8de8\u5165\u5230 \u201c\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55&#xff08;Test-Time Compute Scaling&#xff09;\u201d \u7684\u5168\u65b0\u65f6\u4ee3&#xff01;<\/p>\n<p>\u5927\u6a21\u578b\u7684\u6df1\u5ea6\u601d\u8003\u673a\u5236\u5728\u6570\u5b66\u4e0e\u7269\u7406\u4e0a\u7a76\u7adf\u662f\u5982\u4f55\u8fd0\u4f5c\u7684&#xff1f; \u4e3a\u4ec0\u4e48\u8ba9\u6a21\u578b\u5728\u8f93\u51fa\u6700\u7ec8\u7b54\u6848\u524d\u751f\u6210\u6570\u5343\u4e2a\u751a\u81f3\u4e0a\u4e07\u4e2a\u9690\u85cf\u601d\u8003 Token&#xff08;Thinking Tokens&#xff09;&#xff0c;\u5c31\u80fd\u5b9e\u73b0\u63a8\u7406\u80fd\u529b\u7684\u7206\u53d1\u5f0f\u8dc3\u8fc1&#xff1f; \u6d4b\u8bd5\u671f\u8ba1\u7b97\u7684\u6269\u5c55\u8fb9\u754c\u4e0e\u6536\u76ca\u9012\u51cf\u62d0\u70b9\u53c8\u5728\u54ea\u91cc&#xff1f;<\/p>\n<p>\u672c\u6587\u6df1\u5165\u5256\u6790\u5927\u6a21\u578b\u81ea\u56de\u5f52\u4e0e\u6d4b\u8bd5\u671f\u8ba1\u7b97\u7684\u5e95\u5c42\u6570\u5b66\u672c\u8d28\u3001\u9690\u5f0f\u641c\u7d22\u4e0e\u663e\u5f0f\u53cd\u601d\u673a\u7406&#xff0c;\u5e76\u7ed9\u51fa\u57fa\u4e8e PyTorch \u7684\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55\u4e0e\u81ea\u9002\u5e94\u601d\u8003\u5bf9\u6bd4\u5b9e\u9a8c\u5b9e\u6218\u3002<\/p>\n<hr \/>\n<h3>\u4e00\u3001\u81ea\u56de\u5f52\u5feb\u601d\u8003 vs \u6d4b\u8bd5\u671f\u8ba1\u7b97&#xff08;Test-Time Compute&#xff09;\u6df1\u5ea6\u5bf9\u6bd4\u77e9\u9635<\/h3>\n<table>\n<tr>\u67b6\u6784\u80fd\u529b\u5bf9\u6bd4\u7ef4\u5ea6\u4f20\u7edf\u81ea\u56de\u5f52\u5927\u6a21\u578b (System 1 \u5feb\u601d\u8003)\u6df1\u5ea6\u601d\u8003\u5927\u6a21\u578b (System 2 \u6162\u601d\u8003 \/ o1 \u8303\u5f0f)\u5e95\u5c42\u7269\u7406\u672c\u8d28\u4ee3\u5dee<\/tr>\n<tbody>\n<tr>\n<td align=\"left\">\u8ba1\u7b97\u91cf\u5206\u914d\u6a21\u578b<\/td>\n<td align=\"left\">\u56fa\u5b9a FLOPs \/ Token (\u7531\u6a21\u578b\u53c2\u6570\u91cf\u9759\u6001\u51b3\u5b9a)<\/td>\n<td align=\"left\">&#x1f3c6; \u52a8\u6001\u6d4b\u8bd5\u671f\u8ba1\u7b97 (FLOPs \u968f\u95ee\u9898\u590d\u6742\u5ea6\u5448\u6307\u6570\u7ea7\u52a8\u6001\u4f38\u7f29)<\/td>\n<td align=\"left\">\u5f7b\u5e95\u6253\u7834\u7b97\u529b\u4e0e\u53c2\u6570\u91cf\u7ed1\u5b9a\u7684\u9759\u6001\u67b7\u9501<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u63a8\u7406\u8fc7\u7a0b\u673a\u5236<\/td>\n<td align=\"left\">\u5355\u5411\u8d2a\u5fc3\/\u91c7\u6837\u5411\u524d\u751f\u6210&#xff0c;\u7edd\u5bf9\u4e0d\u53ef\u9006<\/td>\n<td align=\"left\">\u5177\u5907\u81ea\u4e3b\u56de\u6eaf&#xff08;Backtracking&#xff09;\u3001\u63a2\u7d22\u5206\u652f\u4e0e\u81ea\u6211\u7ea0\u9519<\/td>\n<td align=\"left\">\u5c06\u4e00\u7ef4\u6587\u672c\u751f\u6210\u5347\u7ef4\u4e3a\u9ad8\u7ef4\u89e3\u7a7a\u95f4\u641c\u7d22<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u8bef\u5dee\u5bb9\u5fcd\u5ea6<\/td>\n<td align=\"left\">\u6781\u4f4e&#xff08;\u5355\u6b65\u903b\u8f91\u9519\u8bef\u76f4\u63a5\u6c61\u67d3\u540e\u7eed\u6240\u6709\u4e0a\u4e0b\u6587&#xff09;<\/td>\n<td align=\"left\">\u9ad8&#xff08;\u80fd\u5728 Thinking \u9636\u6bb5\u8bc6\u522b\u9519\u8bef\u5e76\u4e3b\u52a8\u63a8\u5012\u91cd\u6765&#xff09;<\/td>\n<td align=\"left\">\u6d88\u9664\u957f\u7a0b\u903b\u8f91\u63a8\u7406\u4e2d\u7684\u8bef\u5dee\u7d2f\u79ef\u96ea\u5d29<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u8bad\u7ec3\u4e0e\u5bf9\u9f50\u8303\u5f0f<\/td>\n<td align=\"left\">\u5927\u89c4\u6a21 SFT \u76d1\u7763\u5fae\u8c03 &#043; \u6807\u51c6 RLHF (PPO\/DPO)<\/td>\n<td align=\"left\">\u5927\u89c4\u6a21\u5f3a\u5316\u5b66\u4e60&#xff08;\u5f3a\u5316\u957f\u601d\u7ef4\u94fe\u63a2\u7d22\u4e0e\u81ea\u6211\u53cd\u601d\u9a8c\u8bc1&#xff09;<\/td>\n<td align=\"left\">\u5956\u52b1\u6a21\u578b\u76f4\u63a5\u5f15\u5bfc\u89e3\u7a7a\u95f4\u9ad8\u6548\u526a\u679d<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">Token \u7269\u7406\u53ef\u89c1\u6027<\/td>\n<td align=\"left\">\u751f\u6210\u7684\u6240\u6709 Token 100% \u5bf9\u7528\u6237\u53ef\u89c1<\/td>\n<td align=\"left\">\u5212\u5206\u4e3a Thinking Tokens (\u601d\u8003\u8349\u7a3f\u7eb8) &#043; Final Answer<\/td>\n<td align=\"left\">\u8d4b\u4e88\u6a21\u578b\u5145\u88d5\u7684\u201c\u601d\u7ef4\u7f13\u51b2\u533a\u201d<\/td>\n<\/tr>\n<tr>\n<td align=\"left\">\u590d\u6742\u63a8\u7406\u8868\u73b0 (AIME\/Codeforces)<\/td>\n<td align=\"left\">\u51c6\u786e\u7387\u5728 20% ~ 40% \u5f98\u5f8a\u505c\u6ede<\/td>\n<td align=\"left\">&#x1f3c6; \u7a81\u7834 85% ~ 95%&#xff08;\u903c\u8fd1\u4eba\u7c7b\u9876\u5c16\u7ade\u8d5b\u9009\u624b\u6c34\u51c6&#xff09;<\/td>\n<td align=\"left\">\u5728\u975e\u5e73\u51e1\u903b\u8f91\u95ee\u9898\u4e0a\u5b9e\u73b0\u8d28\u7684\u4ee3\u5dee\u8de8\u8d8a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u4e8c\u3001\u6d4b\u8bd5\u671f\u8ba1\u7b97&#xff08;Test-Time Compute&#xff09;\u4e24\u5927\u6838\u5fc3\u6269\u5c55\u901a\u8def\u65f6\u5e8f\u67b6\u6784<\/h3>\n<p>\u5728\u5b66\u672f\u754c\u4e0e\u5de5\u4e1a\u754c\u7684\u524d\u6cbf\u63a2\u7d22\u4e2d&#xff0c;\u6269\u5c55\u6d4b\u8bd5\u671f\u7b97\u529b\u4e3b\u8981\u6cbf\u7740\u4e24\u6761\u622a\u7136\u4e0d\u540c\u4f46\u53c8\u76f8\u4e92\u878d\u5408\u7684\u6280\u672f\u8def\u5f84\u5c55\u5f00&#xff1a;<\/p>\n<p>                                  [&#x1f680; \u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55\u4e24\u5927\u6d41\u6d3e]<br \/>\n                                                  |<br \/>\n                 &#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;<br \/>\n                 |                                                                 |<br \/>\n                 v (\u8def\u5f84 A: \u641c\u7d22\u7b97\u6cd5\u9a71\u52a8)                                          v (\u8def\u5f84 B: \u81ea\u56de\u5f52\u539f\u751f\u601d\u8003 Token)<br \/>\n&#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;     &#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;<br \/>\n| &#x1f31f; 1. \u5916\u90e8\u663e\u5f0f\u6811\u641c\u7d22 (Explicit Tree Search)      |     | &#x1f31f; 2. \u5185\u751f\u9690\u5f0f\u601d\u7ef4\u94fe (Endogenous Thinking Tokens)|<br \/>\n| &#8211; \u7ed3\u5408 PRM \u8fc7\u7a0b\u5956\u52b1\u6a21\u578b\u4e0e MCTS \u8499\u7279\u5361\u6d1b\u6811\u641c\u7d22    |     | &#8211; \u901a\u8fc7\u5f3a\u5316\u5b66\u4e60\u8bad\u7ec3\u6a21\u578b\u81ea\u4e3b\u751f\u6210 &#096;&lt;think&gt;&#8230;&lt;\/think&gt;&#096;|<br \/>\n| &#8211; \u5728\u89e3\u7a7a\u95f4\u663e\u5f0f\u5c55\u5f00\u591a\u4e2a\u63a8\u7406\u5206\u652f\u5e76\u6253\u5206\u8bc4\u4f30\u526a\u679d     |     | &#8211; \u6a21\u578b\u81ea\u4e3b\u5728\u8349\u7a3f\u7eb8\u4e0a\u8fdb\u884c\u9a8c\u7b97\u3001\u63a8\u7ffb\u5047\u8bbe\u4e0e\u91cd\u65b0\u89c4\u5212 |<br \/>\n&#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;     &#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8211;&#043;<br \/>\n                 |                                                                 |<br \/>\n                 \\\\                                                                 \/<br \/>\n                  \\\\                                                               \/<br \/>\n                   v                                                             v<br \/>\n&#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#043;<br \/>\n| &#x1f3c6; \u7ec8\u6781\u6269\u5c55\u5b9a\u5f8b (Test-Time Compute Scaling Law):                                                   |<br \/>\n| \u5728\u590d\u6742\u63a8\u7406\u4efb\u52a1\u4e2d&#xff0c;\u5c06\u6d4b\u8bd5\u671f\u7b97\u529b&#xff08;Thinking Tokens \u6570\u91cf\u6216\u91c7\u6837\u5019\u9009\u6570&#xff09;\u63d0\u5347 100 \u500d&#xff0c;                   |<br \/>\n| \u5176\u5e26\u6765\u7684\u51c6\u786e\u7387\u8dc3\u8fc1\u6548\u679c&#xff0c;\u7b49\u4ef7\u4e8e\u5c06\u9884\u8bad\u7ec3\u6a21\u578b\u53c2\u6570\u91cf\u7269\u7406\u6269\u5927 10 \u500d\u4ee5\u4e0a&#xff01;                            |<br \/>\n&#043;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#043;<\/p>\n<hr \/>\n<h3>\u4e09\u3001\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55\u7684\u6570\u5b66\u672c\u8d28\u4e0e\u635f\u5931\u8bbe\u8ba1<\/h3>\n<h4>1. \u4f20\u7edf\u81ea\u56de\u5f52\u751f\u6210\u7684\u6700\u5927\u4f3c\u7136\u6982\u7387<\/h4>\n<p>\u4f20\u7edf\u81ea\u56de\u5f52\u6a21\u578b\u7684\u751f\u6210\u76ee\u6807\u662f\u76f4\u63a5\u6700\u5927\u5316\u6700\u7ec8\u7b54\u6848 $Y &#061; (y_1, y_2, \\\\dots, y_M)$ \u5728\u7ed9\u5b9a\u8f93\u5165 $X$ \u4e0b\u7684\u6761\u4ef6\u8054\u5408\u6982\u7387&#xff1a;$$P(Y | X) &#061; \\\\prod_{j&#061;1}^{M} P(y_j | X, y_{&lt;j})$$<\/p>\n<p>\u5728\u6b64\u8bbe\u5b9a\u4e0b&#xff0c;\u6a21\u578b\u5fc5\u987b\u5728\u7b2c\u4e00\u4e2a Token $y_1$ \u5904\u5c31\u201c\u8d4c\u5bf9\u201d\u6700\u7ec8\u7684\u5168\u5c40\u89e3\u6cd5\u8def\u5f84&#xff0c;\u5bb9\u9519\u7387\u4e3a\u96f6\u3002<\/p>\n<h4>2. \u5f15\u5165\u4e2d\u95f4\u601d\u8003\u53d8\u91cf&#xff08;Thinking Latent Variable&#xff09;\u7684\u8fb9\u9645\u79ef\u5206<\/h4>\n<p>\u5728\u6df1\u5ea6\u601d\u8003\u6a21\u578b\u4e2d&#xff0c;\u5f15\u5165\u4e86\u4e2d\u95f4\u9690\u5f0f\u63a8\u7406\u94fe $Z &#061; (z_1, z_2, \\\\dots, z_K)$&#xff08;\u5176\u4e2d $z_k$ \u4ee3\u8868\u601d\u8003 Token&#xff09;&#xff1a;$$P(Y | X) &#061; \\\\sum_{Z \\\\in \\\\mathcal{Z}} P(Y, Z | X) &#061; \\\\sum_{Z \\\\in \\\\mathcal{Z}} P(Z | X) \\\\cdot P(Y | X, Z)$$<\/p>\n<p>\u6a21\u578b\u5728\u8f93\u51fa\u6700\u7ec8\u7b54\u6848 $Y$ \u4e4b\u524d&#xff0c;\u5148\u5728\u9690\u5f0f\u7a7a\u95f4 $\\\\mathcal{Z}$ \u4e2d\u751f\u6210\u957f\u8fbe\u6570\u5343\u6b65\u7684\u63a8\u5bfc\u8349\u7a3f $Z$\u3002\u901a\u8fc7\u5f3a\u5316\u5b66\u4e60&#xff08;\u5982 GRPO \/ PPO&#xff09;\u6700\u5927\u5316\u53ef\u9a8c\u8bc1\u4efb\u52a1&#xff08;\u5982\u6570\u5b66\u7b54\u6848\u6b63\u786e\u6027\u3001\u5355\u5143\u6d4b\u8bd5\u901a\u8fc7\u7387&#xff09;\u7684\u7ec8\u7aef\u5956\u52b1&#xff08;Terminal Reward&#xff09;&#xff0c;\u6a21\u578b\u81ea\u4e3b\u5b66\u4f1a\u4e86&#xff1a;<\/p>\n<ul>\n<li>\u201c\u7b49\u7b49&#xff0c;\u6211\u521a\u624d\u7684\u5047\u8bbe\u662f\u9519\u7684&#xff0c;\u91cd\u65b0\u8ba1\u7b97\u4e00\u904d\u201d&#xff08;\u63a2\u7d22\u4e0e\u56de\u6eaf&#xff09;&#xff1b;<\/li>\n<li>\u201c\u8ba9\u6211\u4eec\u7528\u4ee3\u5165\u6cd5\u68c0\u9a8c\u4e00\u4e0b\u521a\u624d\u7684\u6839\u201d&#xff08;\u81ea\u7701\u4e0e\u9a8c\u8bc1&#xff09;&#xff1b;<\/li>\n<li>\u201c\u6362\u4e00\u79cd\u51e0\u4f55\u5750\u6807\u7cfb\u6c42\u89e3\u201d&#xff08;\u7b56\u7565\u8dc3\u8fc1&#xff09;\u3002<\/li>\n<\/ul>\n<hr \/>\n<h3>\u56db\u3001\u751f\u4ea7\u7ea7 PyTorch \u6d4b\u8bd5\u671f\u7b97\u529b\u6269\u5c55&#xff08;Best-of-N \u4e0e\u6e29\u5ea6\u7f29\u653e&#xff09;\u5bf9\u6bd4\u5b9e\u9a8c<\/h3>\n<p>\u4e0b\u9762\u7684\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u5728\u5b9e\u9a8c\u73af\u5883\u4e2d\u6a21\u62df\u5e76\u5bf9\u6bd4&#xff1a;<\/p>\n<li>\u5355\u6b21\u81ea\u56de\u5f52\u76f4\u63a5\u8d2a\u5fc3\u751f\u6210&#xff08;Baseline System 1&#xff09;&#xff1b;<\/li>\n<li>\u6d4b\u8bd5\u671f\u91c7\u6837\u8ba1\u7b97\u6269\u5c55&#xff08;Test-Time Compute: Best-of-N with Verifier&#xff09;\u3002<\/li>\n<p>&#034;&#034;&#034;<br \/>\ntest_time_compute_scaling_experiment.py<br \/>\n\u5927\u6a21\u578b\u6d4b\u8bd5\u671f\u8ba1\u7b97 (Test-Time Compute) \u7269\u7406\u6269\u5c55\u5bf9\u6bd4\u5b9e\u9a8c&#xff1a;<br \/>\n\u57fa\u4e8e\u5019\u9009\u751f\u6210\u3001\u8fc7\u7a0b\u9a8c\u8bc1\u5668\u6253\u5206\u4e0e\u89e3\u7a7a\u95f4\u91cd\u6392\u5e8f\u5b9e\u6218<br \/>\n&#034;&#034;&#034;<\/p>\n<p>import math<br \/>\nimport torch<br \/>\nimport torch.nn as nn<br \/>\nimport torch.nn.functional as F<br \/>\nfrom typing import List, Dict, Tuple<\/p>\n<p>class MockReasoningLLM(nn.Module):<br \/>\n    &#034;&#034;&#034;\u6a21\u62df\u5927\u6a21\u578b\u63a8\u7406\u524d\u5411\u7f51\u7edc&#xff1a;\u8f93\u51fa Logits \u4e0e\u9690\u5c42\u8868\u5f81&#034;&#034;&#034;<\/p>\n<p>    def __init__(self, vocab_size: int &#061; 1000, hidden_dim: int &#061; 256):<br \/>\n        super().__init__()<br \/>\n        self.embedding &#061; nn.Embedding(vocab_size, hidden_dim)<br \/>\n        self.transformer_layer &#061; nn.TransformerEncoderLayer(<br \/>\n            d_model&#061;hidden_dim, nhead&#061;8, dim_feedforward&#061;512, batch_first&#061;True<br \/>\n        )<br \/>\n        self.lm_head &#061; nn.Linear(hidden_dim, vocab_size)<\/p>\n<p>    def forward(self, input_ids: torch.Tensor) -&gt; torch.Tensor:<br \/>\n        # [Batch, SeqLen, Hidden]<br \/>\n        x &#061; self.embedding(input_ids)<br \/>\n        h &#061; self.transformer_layer(x)<br \/>\n        logits &#061; self.lm_head(h)<br \/>\n        return logits<\/p>\n<p>class TestTimeComputeEvaluator:<br \/>\n    &#034;&#034;&#034;\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55\u5f15\u64ce&#xff1a;\u652f\u6301\u5355\u6b21\u8d2a\u5fc3\u4e0e Best-of-N \u7b97\u529b\u6269\u5c55&#034;&#034;&#034;<\/p>\n<p>    def __init__(self, model: MockReasoningLLM):<br \/>\n        self.model &#061; model<br \/>\n        self.model.eval()<\/p>\n<p>    def simulate_verify_solution(self, solution_tokens: List[int], ground_truth: int &#061; 42) -&gt; float:<br \/>\n        &#034;&#034;&#034;<br \/>\n        \u6a21\u62df\u5916\u90e8\u8f7b\u91cf\u9a8c\u8bc1\u5668&#xff08;Verifier \/ PRM&#xff09;&#xff1a;<br \/>\n        \u5bf9\u63a8\u5bfc\u51fa\u7684\u6700\u7ec8\u7b54\u6848\u8fdb\u884c\u6570\u5b66\u65ad\u8a00\u6216\u89c4\u5219\u6253\u5206&#xff0c;\u8fd4\u56de [0.0 ~ 1.0] \u7684\u7f6e\u4fe1\u5ea6<br \/>\n        &#034;&#034;&#034;<br \/>\n        # \u7b80\u5316\u6a21\u62df&#xff1a;\u5047\u8bbe token \u548c\u4e3a\u7279\u5b9a\u503c\u65f6\u4e3a\u6b63\u786e\u7b54\u6848<br \/>\n        predicted_val &#061; sum(solution_tokens) % 100<br \/>\n        if predicted_val &#061;&#061; ground_truth:<br \/>\n            return 1.0 # 100% \u547d\u4e2d\u771f\u503c<br \/>\n        # \u5426\u5219\u7ed9\u51fa\u57fa\u4e8e\u8ddd\u79bb\u7684\u8f6f\u542f\u53d1\u5f0f\u5206\u6570<br \/>\n        diff &#061; abs(predicted_val &#8211; ground_truth)<br \/>\n        return math.exp(-0.1 * diff)<\/p>\n<p>    &#064;torch.no_grad()<br \/>\n    def generate_single_greedy(self, prompt_tokens: torch.Tensor, max_new_tokens: int &#061; 16) -&gt; List[int]:<br \/>\n        &#034;&#034;&#034;\u57fa\u7ebf\u65b9\u6cd5&#xff1a;\u4f20\u7edf\u5355\u5411\u81ea\u56de\u5f52\u8d2a\u5fc3\u751f\u6210 (Zero Test-Time Compute Extension)&#034;&#034;&#034;<br \/>\n        curr &#061; prompt_tokens.clone()<br \/>\n        generated &#061; []<br \/>\n        for _ in range(max_new_tokens):<br \/>\n            logits &#061; self.model(curr)<br \/>\n            next_token &#061; torch.argmax(logits[:, -1, :], dim&#061;-1, keepdim&#061;True)<br \/>\n            curr &#061; torch.cat([curr, next_token], dim&#061;1)<br \/>\n            generated.append(next_token.item())<br \/>\n        return generated<\/p>\n<p>    &#064;torch.no_grad()<br \/>\n    def generate_best_of_n(<br \/>\n        self, prompt_tokens: torch.Tensor, n_candidates: int &#061; 16, temperature: float &#061; 0.8, max_new_tokens: int &#061; 16<br \/>\n    ) -&gt; Tuple[List[int], float, int]:<br \/>\n        &#034;&#034;&#034;<br \/>\n        \u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55&#xff1a;\u751f\u6210 N \u6761\u72ec\u7acb\u601d\u8003\u8def\u5f84&#xff0c;\u5e76\u7531\u9a8c\u8bc1\u5668\u9009\u51fa\u6700\u4f18\u89e3<br \/>\n        \u8fd4\u56de: (\u6700\u4f18\u7b54\u6848, \u6700\u4f18\u7f6e\u4fe1\u5ea6, \u6d88\u8017\u7684\u603b Token \u7b97\u529b)<br \/>\n        &#034;&#034;&#034;<br \/>\n        best_candidate &#061; None<br \/>\n        best_score &#061; -1.0<br \/>\n        total_tokens_consumed &#061; 0<\/p>\n<p>        # \u5728\u6d4b\u8bd5\u671f\u5e76\u884c\u91c7\u6837 N \u6761\u601d\u8003\u8def\u5f84 (\u6d88\u8017 N \u500d\u524d\u5411\u63a8\u7406\u7b97\u529b)<br \/>\n        for _ in range(n_candidates):<br \/>\n            curr &#061; prompt_tokens.clone()<br \/>\n            candidate_seq &#061; []<br \/>\n            for _ in range(max_new_tokens):<br \/>\n                logits &#061; self.model(curr)<br \/>\n                # \u6e29\u5ea6\u91c7\u6837\u5f15\u5165\u63a2\u7d22\u6027<br \/>\n                probs &#061; F.softmax(logits[:, -1, :] \/ temperature, dim&#061;-1)<br \/>\n                next_token &#061; torch.multinomial(probs, num_samples&#061;1)<br \/>\n                curr &#061; torch.cat([curr, next_token], dim&#061;1)<br \/>\n                candidate_seq.append(next_token.item())<\/p>\n<p>            total_tokens_consumed &#043;&#061; len(candidate_seq)<br \/>\n            # \u9a8c\u8bc1\u5668\u8bc4\u4f30\u5f53\u524d\u601d\u8003\u8def\u5f84\u7684\u8d28\u91cf<br \/>\n            score &#061; self.simulate_verify_solution(candidate_seq)<br \/>\n            if score &gt; best_score:<br \/>\n                best_score &#061; score<br \/>\n                best_candidate &#061; candidate_seq<\/p>\n<p>        return best_candidate, best_score, total_tokens_consumed<\/p>\n<p>if __name__ &#061;&#061; &#034;__main__&#034;:<br \/>\n    torch.manual_seed(2026)<br \/>\n    model &#061; MockReasoningLLM()<br \/>\n    evaluator &#061; TestTimeComputeEvaluator(model)<\/p>\n<p>    prompt &#061; torch.tensor([[10, 25, 33, 48]]) # \u6a21\u62df\u8f93\u5165 Query<\/p>\n<p>    print(&#034;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#034;)<br \/>\n    print(&#034;&#x1f52c; \u918d\u9190\u5b9e\u9a8c\u5ba4&#xff1a;\u5927\u6a21\u578b\u6d4b\u8bd5\u671f\u8ba1\u7b97&#xff08;Test-Time Compute&#xff09;\u6269\u5c55\u7269\u7406\u5b9e\u9a8c&#034;)<br \/>\n    print(&#034;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;\\\\n&#034;)<\/p>\n<p>    # 1. \u4f20\u7edf\u57fa\u7ebf\u6d4b\u8bd5&#xff1a;\u5355\u6b21\u5feb\u601d\u8003 (N&#061;1)<br \/>\n    greedy_res &#061; evaluator.generate_single_greedy(prompt)<br \/>\n    greedy_score &#061; evaluator.simulate_verify_solution(greedy_res)<br \/>\n    print(f&#034;1. [\u4f20\u7edf\u81ea\u56de\u5f52\u8d2a\u5fc3\u751f\u6210] (N&#061;1):&#034;)<br \/>\n    print(f&#034;   &#8211; \u4ea7\u51fa\u5e8f\u5217\u7247\u6bb5: {greedy_res[:6]}&#8230;&#034;)<br \/>\n    print(f&#034;   &#8211; \u9a8c\u8bc1\u5668\u5f97\u5206: {greedy_score:.4f} | \u6d88\u8017 Token: {len(greedy_res)}&#034;)<\/p>\n<p>    # 2. \u6d4b\u8bd5\u671f\u8ba1\u7b97\u4e2d\u5ea6\u6269\u5c55 (N&#061;8)<br \/>\n    res_8, score_8, tokens_8 &#061; evaluator.generate_best_of_n(prompt, n_candidates&#061;8)<br \/>\n    print(f&#034;\\\\n2. [\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55 N&#061;8] (\u4e2d\u7b49\u63a8\u7406\u7b97\u529b\u6295\u5165):&#034;)<br \/>\n    print(f&#034;   &#8211; \u6700\u4f73\u89e3\u5f97\u5206: {score_8:.4f} | \u6d88\u8017 Token: {tokens_8}&#034;)<\/p>\n<p>    # 3. \u6d4b\u8bd5\u671f\u8ba1\u7b97\u91cd\u5ea6\u6269\u5c55 (N&#061;32)<br \/>\n    res_32, score_32, tokens_32 &#061; evaluator.generate_best_of_n(prompt, n_candidates&#061;32)<br \/>\n    print(f&#034;\\\\n3. [\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55 N&#061;32] (\u91cd\u5ea6\u63a8\u7406\u7b97\u529b\u6295\u5165):&#034;)<br \/>\n    print(f&#034;   &#8211; \u6700\u4f73\u89e3\u5f97\u5206: {score_32:.4f} | \u6d88\u8017 Token: {tokens_32}&#034;)<\/p>\n<p>    print(&#034;\\\\n&#x1f4a1; \u5b9e\u9a8c\u7ed3\u8bba&#xff1a;\u968f\u7740\u6d4b\u8bd5\u671f\u8ba1\u7b97\u7b97\u529b&#xff08;\u91c7\u6837\u8def\u5f84 N&#xff09;\u7684\u6307\u6570\u589e\u52a0&#xff0c;\u9a8c\u8bc1\u5668\u5f97\u5206\u5b9e\u73b0\u6536\u655b\u63d0\u5347&#xff01;&#034;)<br \/>\n    print(&#034;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#061;&#034;)<\/p>\n<hr \/>\n<h3>\u4e94\u3001\u6d4b\u8bd5\u671f\u8ba1\u7b97\u6269\u5c55\u7684\u7269\u7406\u74f6\u9888\u4e0e\u201c\u6536\u76ca\u9012\u51cf\u201d\u7ea2\u7ebf<\/h3>\n<p>\u5728\u4eab\u53d7\u6df1\u5ea6\u601d\u8003\u6a21\u578b\u5e26\u6765\u667a\u529b\u8dc3\u8fc1\u7684\u540c\u65f6&#xff0c;\u7b97\u6cd5\u67b6\u6784\u5e08\u5fc5\u987b\u6e05\u9192\u5730\u8ba4\u8bc6\u5230\u6d4b\u8bd5\u671f\u8ba1\u7b97\u7684\u4e09\u9879\u5e95\u5c42\u7269\u7406\u9650\u5236&#xff1a;<\/p>\n<li>\u201c\u8fc7\u5ea6\u601d\u8003&#xff08;Overthinking&#xff09;\u201d\u5f15\u53d1\u7684\u667a\u529b\u52a3\u5316\u4e0e\u7b97\u529b\u6d6a\u8d39&#xff1a;\u5bf9\u4e8e\u7b80\u5355\u7684\u5e38\u8bc6\u6027\u95ee\u9898&#xff08;\u5982\u201c\u6cd5\u56fd\u7684\u9996\u90fd\u662f\u54ea\u91cc\u201d&#xff09;&#xff0c;\u5f3a\u884c\u8ba9\u6a21\u578b\u5c55\u5f00 5000 \u4e2a Thinking Token \u4e0d\u4ec5\u6d6a\u8d39\u663e\u5b58\u4e0e\u7535\u8d39&#xff0c;\u751a\u81f3\u5bb9\u6613\u5728\u5197\u957f\u7684\u601d\u7ef4\u6f2b\u6e38\u4e2d\u8bef\u5165\u6b67\u9014&#xff08;\u4ea7\u751f\u65e0\u8c13\u7684\u81ea\u6211\u6000\u7591\u4e0e\u53d1\u6563\u5e7b\u89c9&#xff09;\u3002**\u81ea\u9002\u5e94\u601d\u8003\u6df1\u5ea6&#xff08;Adaptive Thinking Budget&#xff09;**\u662f\u5fc5\u4fee\u8bfe&#xff1b;<\/li>\n<li>\u9a8c\u8bc1\u5668&#xff08;Reward Model \/ Verifier&#xff09;\u7684\u201c\u88ab\u5229\u7528&#xff08;Reward Hacking&#xff09;\u201d\u5371\u673a&#xff1a;\u5728 Best-of-N \u641c\u7d22\u4e2d&#xff0c;\u5982\u679c\u5916\u90e8\u6253\u5206\u6a21\u578b\u7684\u5224\u522b\u51c6\u786e\u7387\u65e0\u6cd5\u8d85\u8d8a\u751f\u6210\u6a21\u578b&#xff0c;\u5f53\u641c\u7d22\u5019\u9009\u6570 $N &gt; 256$ \u65f6&#xff0c;\u751f\u6210\u7aef\u4f1a\u4e13\u95e8\u94bb\u9a8c\u8bc1\u5668\u7684\u6253\u5206\u6f0f\u6d1e&#xff0c;\u4ea7\u51fa\u9ad8\u5206\u4f46\u4e8b\u5b9e\u8352\u8c2c\u7684\u6b3a\u9a97\u6027\u89e3\u7b54&#xff1b;<\/li>\n<li>KV Cache \u663e\u5b58\u7206\u70b8\u4e0e\u957f\u5e8f\u5217 TTFT&#xff08;\u9996\u5b57\u5ef6\u8fdf&#xff09;\u96ea\u5d29&#xff1a;\u6570\u5343\u4e2a\u601d\u8003 Token \u4f1a\u8fc5\u901f\u5403\u6ee1 GPU \u663e\u5b58&#xff0c;\u5bfc\u81f4\u5355\u8bf7\u6c42\u7684\u663e\u5b58\u5360\u7528\u4ece 50MB \u66b4\u589e\u81f3\u6570 GB&#xff0c;\u6781\u5927\u538b\u7f29\u4e86\u670d\u52a1\u7aef\u7684\u5e76\u53d1\u627f\u8f7d\u80fd\u529b\u3002<\/li>\n<p>\u901a\u8fc7\u6df1\u523b\u7406\u89e3\u4ece\u201c\u5355\u5411\u81ea\u56de\u5f52\u5feb\u601d\u8003\u201d\u5230\u201c\u6d4b\u8bd5\u671f\u8ba1\u7b97\u9ad8\u7ef4\u7a7a\u95f4\u63a2\u7d22\u201d\u7684\u7269\u7406\u8dc3\u8fc1&#xff0c;\u6280\u672f\u56e2\u961f\u80fd\u591f\u5728\u6784\u5efa\u4e0b\u4e00\u4ee3\u524d\u6cbf\u63a8\u7406\u667a\u80fd\u4f53\u65f6&#xff0c;\u79d1\u5b66\u6743\u8861\u9884\u8bad\u7ec3\u53c2\u6570\u89c4\u6a21\u4e0e\u5728\u7ebf\u63a8\u7406\u7b97\u529b\u9884\u7b97&#xff0c;\u5728\u7b97\u6cd5\u80fd\u529b\u4e0e\u5546\u4e1a\u843d\u5730\u6210\u672c\u4e4b\u95f4\u627e\u5230\u6700\u4f18\u7684\u9ec4\u91d1\u652f\u70b9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5927\u6a21\u578b\u6df1\u5ea6\u601d\u8003\u673a\u5236\u62c6\u89e3&#xff1a;\u4ece\u81ea\u56de\u5f52 Next-Token \u5230\u6d4b\u8bd5\u671f\u8ba1\u7b97&#xff08;Test-Time Compute&#xff09;\u7269\u7406\u8fb9\u754c<br \/>\n\u5728\u8fc7\u53bb\u7684\u51e0\u5e74\u91cc&#xff0c;\u6574\u4e2a\u6df1\u5ea6\u5b66\u4e60\u4e0e\u5927\u8bed\u8a00\u6a21\u578b&#xff08;LLM&#xff09;\u5de5\u4e1a\u754c\u51e0\u4e4e\u5168\u76d8\u62bc\u6ce8\u5728 \u201c\u9884\u8bad\u7ec3\u6269\u5c55\u5b9a\u5f8b&#xff08;Pre-training Scaling Law&#xff09;\u201d \u4e0a&#xff1a;\u901a\u8fc7\u5806\u53e0\u6570\u5341\u4e07\u5757 GPU\u3001\u6295\u5582\u6570\u5341\u4e07\u4ebf Token \u7684\u65e0\u6807\u6ce8\u4e92\u8054\u7f51\u8bed\u6599&#xff0c;\u5c06\u5bc6<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11044,50],"topic":[],"class_list":["post-96486","post","type-post","status-publish","format-standard","hentry","category-server","tag-next-token","tag-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - 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