[{"data":1,"prerenderedAt":205},["ShallowReactive",2],{"DlFXI4Eibt_Bn9lrEZz1TYbHCWFZj3IvqwHQSEW-Exc":3,"pvbp48bAXHeIKWpa3p0PFqVQF3pw2wDLUCyN4Y5tUzY":194},{"code":4,"msg":5,"data":6},0,"",{"category":7,"tag":11,"hot":39,"new":78,"banner":118,"data":143,"cache":193},[8,9,10],"Agent","OpenAI","LLM",[12,14,17,20,23,25,27,30,33,36],{"title":8,"total":13},39,{"title":15,"total":16},"Google",44,{"title":18,"total":19},"Nvidia",13,{"title":21,"total":22},"Claude",11,{"title":9,"total":24},35,{"title":10,"total":26},85,{"title":28,"total":29},"DeepSeek",9,{"title":31,"total":32},"OCR",1,{"title":34,"total":35},"Chat",7,{"title":37,"total":38},"Generator",116,[40,48,55,64,71],{"id":41,"publish_date":42,"is_original":4,"collection":5,"cover_url":43,"cover_url_1_1":44,"title":45,"summary":46,"author":47},557,"2022-04-29","article_res/cover/7a9b1375ed9bb298154981bae42b794d.jpeg","article_res/cover/afa281dd52bc0454e6735daa8e6b0706.jpeg","Translation and summary of Messari Report [2.8 Kristin Smith, Blockchain Association and Katie Haun, a16z]","We need unity and speed right now.","Translation",{"id":49,"publish_date":50,"is_original":4,"collection":5,"cover_url":51,"cover_url_1_1":52,"title":53,"summary":54,"author":47},531,"2022-05-25","article_res/cover/e8362057f8fa189594c60afdfaaeb6e5.jpeg","article_res/cover/8ea08d0d6fa7eee6b57ed4ec61b61ad6.jpeg","Decentralized Society: Finding Web3’s Soul / Decentralized Society: Finding the Soul of Web3 -7","Decentralization through Pluralism When analyzing ecosystems, it's desirable to measure how decentralized it is.",{"id":56,"publish_date":57,"is_original":32,"collection":58,"cover_url":59,"cover_url_1_1":60,"title":61,"summary":62,"author":63},127,"2024-11-14","#Google #AI Game #World Model #AI Story","article_res/cover/0233a875b7ec2debf59779e311547569.jpeg","article_res/cover/6ffddb6ae4914b3c699493311aa9f198.jpeg","Google Launches \"Unbounded\": A Generative Infinite Character Life Simulation Game","Unbounded: A Generative Infinite Game of Character Life Simulation","Renee's Entrepreneurial Journey",{"id":13,"publish_date":65,"is_original":32,"collection":66,"cover_url":67,"cover_url_1_1":68,"title":69,"summary":70,"author":63},"2025-02-14","#Deep Dive into LLMs #Andrej Karpathy #LLM #Tool Use #Hallucination","article_res/cover/11e858ad6b74dfa80f923d549b62855c.jpeg","article_res/cover/615e1b320f1fc163edc1d2d154a6de33.jpeg","Andrej Karpathy's in-depth explanation of LLM (Part 4): Hallucinations","hallucinations, tool use, knowledge/working memory",{"id":72,"publish_date":73,"is_original":4,"collection":5,"cover_url":74,"cover_url_1_1":75,"title":76,"summary":77,"author":47},579,"2022-04-07","article_res/cover/39387376ba28447af1eb40576b9df215.jpeg","article_res/cover/02727ede8551ed49901d0abe6d6305b7.jpeg","Messari Report Translation and Summary 【1-7 Surviving the Winter】","I’d be more cautious here: 10 year and 10 hour thinking only.",[79,87,95,103,111],{"id":80,"publish_date":81,"is_original":32,"collection":82,"cover_url":83,"cover_url_1_1":84,"title":85,"summary":86,"author":63},627,"2025-03-20","#AI Avatar #AI Video Generation","article_res/cover/d95481358f73924989f8c4ee9c75d1c8.jpeg","article_res/cover/b74bc0fab01f8b6a6aa87696c0c3ed8b.jpeg","DisPose: Generating Animated Videos by Driving Video with Reference Images","DisPose is a controllable human image animation method that enhances video generation.",{"id":88,"publish_date":89,"is_original":32,"collection":90,"cover_url":91,"cover_url_1_1":92,"title":93,"summary":94,"author":63},626,"2025-03-21","#Deep Dive into LLMs #LLM #RL #Andrej Karpathy #AlphaGo","article_res/cover/446553a5c8f8f2f07d97b20eaee84e56.jpeg","article_res/cover/e6c2823409c9b34624064b9acbaca6f1.jpeg","AlphaGo and the Power of Reinforcement Learning - Andrej Karpathy's Deep Dive on LLMs (Part 9)","Simply learning from humans will never surpass human capabilities.",{"id":96,"publish_date":97,"is_original":32,"collection":98,"cover_url":99,"cover_url_1_1":100,"title":101,"summary":102,"author":63},625,"2025-03-22","#Deep Dive into LLMs #LLM #RL #RLHF #Andrej Karpathy","article_res/cover/8da81d38b1e5cf558a164710fd8a5389.jpeg","article_res/cover/96f028d76c362a99a0dd56389e8f7a9b.jpeg","Reinforcement Learning from Human Feedback (RLHF) - Andrej Karpathy's Deep Dive on LLMs (Part 10)","Fine-Tuning Language Models from Human Preferences",{"id":104,"publish_date":105,"is_original":32,"collection":106,"cover_url":107,"cover_url_1_1":108,"title":109,"summary":110,"author":63},624,"2025-03-23","#Deep Dive into LLMs #LLM #Andrej Karpathy #AI Agent #MMM","article_res/cover/a5e7c3d48bb09109684d6513287c661d.jpeg","article_res/cover/d3f22b7c0ab8d82fd2da457a299e0773.jpeg","The Future of Large Language Models - Andrej Karpathy's In-Depth Explanation of LLM (Part 11)","preview of things to come",{"id":112,"publish_date":105,"is_original":32,"collection":113,"cover_url":114,"cover_url_1_1":115,"title":116,"summary":117,"author":63},623,"#Google #Voe #AI Video Generation","article_res/cover/c44062fea0f336c2b96b3928292392c2.jpeg","article_res/cover/a041041c69092ad3db191c5bf3ff981b.jpeg","Trial of Google's video generation model VOE2","Our state-of-the-art video generation model",[119,127,135],{"id":120,"publish_date":121,"is_original":32,"collection":122,"cover_url":123,"cover_url_1_1":124,"title":125,"summary":126,"author":63},160,"2024-10-04","#Philosophy","article_res/cover/496990c49211e8b7f996b7d39c18168e.jpeg","article_res/cover/14dbaa1ade9cb4316d5829423a900362.jpeg","Time","The fungus of the morning does not know the waxing and waning of the moon, and the cicada does not know the seasons; this is a short life. To the south of the state of Chu there is a dark spirit which regards five hundred years as spring and five hundred years as autumn. In ancient times there was a great tree called the Ming which regarded eight thousand years as spring and eight thousand years as autumn; this is a long life.",{"id":128,"publish_date":129,"is_original":32,"collection":130,"cover_url":131,"cover_url_1_1":132,"title":133,"summary":134,"author":63},98,"2024-12-17","#AI Video Generator #Sora #Pika","article_res/cover/3b86e85d03fff4f356a3e4cf2bb329c9.jpeg","article_res/cover/5fa5c20ad0b40f8f544d257c0ef02938.jpeg","Pika 2.0 video generation officially released: effect comparison with Sora","今天，我们推出了Pika 2.0模型。卓越的文字对齐效果。惊人的视觉表现。还有✨场景成分✨",{"id":136,"publish_date":137,"is_original":32,"collection":138,"cover_url":139,"cover_url_1_1":140,"title":141,"summary":142,"author":63},71,"2025-01-14","#Nvidia #World Foundation Model #Cosmos #Physical AI #Embodied AI","article_res/cover/feddf8c832dfb45d28804291f6a42a9e.jpeg","article_res/cover/d6bc2f1186d96b78228c2283a17a3645.jpeg","NVIDIA's Cosmos World Model","Cosmos World Foundation Model Platform for Physical AI",[144,163,188],{"title":8,"items":145},[146,147,155],{"id":104,"publish_date":105,"is_original":32,"collection":106,"cover_url":107,"cover_url_1_1":108,"title":109,"summary":110,"author":63},{"id":148,"publish_date":149,"is_original":32,"collection":150,"cover_url":151,"cover_url_1_1":152,"title":153,"summary":154,"author":63},622,"2025-03-24","#OWL #AI Agent #MAS #MCP #CUA","article_res/cover/cb50ca7f2bf4d1ed50202d7406e1c19a.jpeg","article_res/cover/4aa7aa3badfacf3cc84121334f1050dd.jpeg","OWL: Multi-agent collaboration","OWL: Optimized Workforce Learning for General Multi-Agent Assistance in Real-World Task Automation",{"id":156,"publish_date":157,"is_original":32,"collection":158,"cover_url":159,"cover_url_1_1":160,"title":161,"summary":162,"author":63},620,"2025-03-26","#LLM #Google #Gemini #AI Agent","article_res/cover/53751a6dbbe990b1eb0b63f3b062aed4.jpeg","article_res/cover/031344981f0a212ff82d1f3a64aa5756.jpeg","Gemini 2.5 Pro, claimed to be far ahead of the competition, has been released with great fanfare: comprehensively surpassing other LLMs and topping the global rankings","Gemini 2.5: Our most intelligent AI model",{"title":9,"items":164},[165,172,180],{"id":166,"publish_date":157,"is_original":32,"collection":167,"cover_url":168,"cover_url_1_1":169,"title":170,"summary":171,"author":63},619,"#OpenAI #AI Image Generator #4o #MMM #AR Transformer","article_res/cover/2faffc97fcecf3151552cb0fd3206d89.jpeg","article_res/cover/1133cb4948af44cee2e7fbe79efb69e5.jpeg","The native image function of GPT-4o is officially launched","Introducing 4o Image Generation",{"id":173,"publish_date":174,"is_original":4,"collection":175,"cover_url":176,"cover_url_1_1":177,"title":178,"summary":179,"author":63},434,"2023-07-15","#Anthropic #OpenAI #Google #AI Code Generator #Claude","article_res/cover/e1b6f600a2b9f262a4392684e5f2ce25.jpeg","article_res/cover/6e1772e83f78f9a351ab23d3e414adee.jpeg","Latest Updates on Google Bard /Anthropic Claude2 / ChatGPT Code Interpreter","We want our models to use their programming skills to provide more natural interfaces to the basic functions of our computers.  \n - OpenAI",{"id":181,"publish_date":182,"is_original":4,"collection":183,"cover_url":184,"cover_url_1_1":185,"title":186,"summary":187,"author":63},417,"2023-08-24","#OpenAI","article_res/cover/bccf897d50a88b18364e35f7466387e0.jpeg","article_res/cover/2f871085c1073717c1703ae86e18056f.jpeg","The GPT-3.5 Turbo fine-tuning (fine-tuning function) has been released～","Developers can now bring their own data to customize GPT-3.5 Turbo for their use cases.",{"title":10,"items":189},[190,191,192],{"id":88,"publish_date":89,"is_original":32,"collection":90,"cover_url":91,"cover_url_1_1":92,"title":93,"summary":94,"author":63},{"id":96,"publish_date":97,"is_original":32,"collection":98,"cover_url":99,"cover_url_1_1":100,"title":101,"summary":102,"author":63},{"id":104,"publish_date":105,"is_original":32,"collection":106,"cover_url":107,"cover_url_1_1":108,"title":109,"summary":110,"author":63},true,{"code":4,"msg":5,"data":195},{"id":196,"publish_date":197,"is_original":32,"collection":198,"articles_id":199,"cover_url":200,"cover_url_1_1":201,"title":202,"summary":203,"author":63,"content":204},33,"2025-02-20","#Deep Dive into LLMs #Andrej Karpathy #LLM #CoT #Tool Use","uItW4FCU_-QMZta8z4uXrg","article_res/cover/7a9e0e615787dd27b01e1d591b8a78f7.jpeg","article_res/cover/d7740cfd9742034123c2f8780eecab69.jpeg","Why Models Need \"Step-by-Step Thinking\" - Andrej Karpathy's In-Depth Explanation of LLMs (Part 6)","models need tokens to think","\u003Cdiv class=\"rich_media_content js_underline_content\n                       autoTypeSetting24psection\n            \" id=\"js_content\">\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">This chapter discusses the native computational capabilities of LLMs in problem-solving. It is quite enlightening to see how models \"think\" when analyzing many tricky problems.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">Previous chapter:\u003C/span>\u003C/p>\u003Cul style=\"list-style-type: disc;\" class=\"list-paddingleft-1\">\u003Cli>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Ca href=\"https://mp.weixin.qq.com/s?__biz=MzkwOTMzMzk0MQ==&mid=2247493745&idx=1&sn=a513e346af02bcbd673b6c069b3e96fa&scene=21#wechat_redirect\" textvalue=\"Andrej Karpathy 深度讲解大语言模型（LLM）技术（Part 1）-【预训练和推理】\" data-itemshowtype=\"0\" target=\"_blank\" linktype=\"text\" data-linktype=\"2\">Andrej Karpathy's In-Depth Explanation of Large Language Model (LLM) Technology (Part 1) - [Pre-training and Inference]\u003C/a>\u003C/span>\u003C/p>\u003C/li>\u003Cli>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Ca href=\"https://mp.weixin.qq.com/s?__biz=MzkwOTMzMzk0MQ==&mid=2247493774&idx=1&sn=082dfb34f746cd7c24154941055e89d4&scene=21#wechat_redirect\" textvalue=\"Andrej Karpathy 深度讲解LLM（Part 2）：通过 GPT-2和Llama 3.1理解训练和推理\" data-itemshowtype=\"0\" target=\"_blank\" linktype=\"text\" data-linktype=\"2\">Andrej Karpathy's In-Depth Explanation of LLM (Part 2): Understanding Training and Inference through GPT-2 and Llama 3.1\u003C/a>\u003C/span>\u003C/p>\u003C/li>\u003Cli>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Ca href=\"https://mp.weixin.qq.com/s?__biz=MzkwOTMzMzk0MQ==&mid=2247493792&idx=1&sn=8ffd4717f1b5532e3d91788dc462e590&scene=21#wechat_redirect\" textvalue=\"Andrej Karpathy 深度讲解LLM（Part 3）：Post-Training 后训练\" data-itemshowtype=\"0\" target=\"_blank\" linktype=\"text\" data-linktype=\"2\">Andrej Karpathy's In-Depth Explanation of LLM (Part 3): Post-Training\u003C/a>\u003C/span>\u003C/p>\u003C/li>\u003Cli>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Ca href=\"https://mp.weixin.qq.com/s?__biz=MzkwOTMzMzk0MQ==&mid=2247493806&idx=1&sn=a4c84ee0a0815c444735163725594c98&scene=21#wechat_redirect\" textvalue=\"Andrej Karpathy 深度讲解LLM（Part 4）：Hallucinations 幻觉\" data-itemshowtype=\"0\" target=\"_blank\" linktype=\"text\" data-linktype=\"2\">Andrej Karpathy Deep Dive on LLM (Part 4): Hallucinations\u003C/a>\u003C/span>\u003C/p>\u003C/li>\u003Cli>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Ca href=\"https://mp.weixin.qq.com/s?__biz=MzkwOTMzMzk0MQ==&mid=2247493816&idx=1&sn=57eb7a2346d39fb1993c2911c1ada552&scene=21#wechat_redirect\" textvalue=\"LLM 的“自我认知” - Andrej Karpathy 深度讲解LLM（Part 5）\" data-itemshowtype=\"0\" target=\"_blank\" linktype=\"text\" data-linktype=\"2\">LLM's \"Self-Awareness\" - Andrej Karpathy Deep Dive on LLM (Part 5)\u003C/a>\u003C/span>\u003C/p>\u003C/li>\u003C/ul>\u003Cp style='box-sizing:border-box;margin:0px;cursor:pointer;color:rgb(0, 0, 0);font-size:16px;line-height:1.8em;letter-spacing:normal;text-align:left;text-indent:0px;padding:8px 0px;font-family:Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;orphans:2;text-transform:none;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;white-space:normal;text-decoration-thickness:initial;text-decoration-style:initial;text-decoration-color:initial;'>\u003Cspan leaf=\"\">\u003Cbr>\u003C/span>\u003C/p>\u003Csection data-mpa-template=\"t\" mpa-from-tpl=\"t\" data-mpa-action-id=\"m78fz2gvk3f\">\u003Csection style=\"text-align: center;transform: translate3d(2px, 0px, 0px);margin: 10px 0%;padding:0 10px;\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;background-color: rgb(255, 202, 0);\" mpa-from-tpl=\"t\">\u003Csection style=\"margin: 5px 0% -5px;transform: translate3d(-5px, 0px, 0px);\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;border-style: solid;border-width: 8px 1px 1px;border-radius: 0px;border-color: rgb(62, 62, 62);background-color: rgb(255, 255, 255);padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Csection mpa-from-tpl=\"t\">\u003Csection style=\"text-align: left;padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Cp>\u003Cem>\u003Cstrong mpa-from-tpl=\"t\">\u003Cspan leaf=\"\">Example 1\u003C/span>\u003C/strong>\u003C/em>\u003C/p>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003Cblockquote style='box-sizing: border-box;margin: 20px 0px;;padding: 10px 10px 10px 20px;border-style: none none none solid;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0.05);width: auto;height: auto;box-shadow: rgba(0, 0, 0, 0) 0px 0px 0px 0px;display: block;overflow: auto;color: rgb(0, 0, 0);font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-size: 16px;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;letter-spacing: normal;orphans: 2;text-align: left;text-indent: 0px;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cp style=\"box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;text-indent: 0em;padding: 8px 0px;font-weight: normal;\">\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Emily bought 3 apples and 2 oranges. Each orange costs $2, and the total cost is $13. What is the price of the apples?\u003C/span>\u003C/strong>\u003C/p>\u003C/blockquote>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">This is a very simple math problem. Now, suppose the model gives two different answers as follows, located on the left and right sides respectively. Both answers arrive at the correct result, which is\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">3\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">However, one of the answers is clearly better for the assistant, while the other is an extremely poor response.\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010170\" data-ratio=\"0.3138888888888889\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770737040.7761611121789134.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">Data labelers need to select one as a training example; in this case, one answer would be considered very poor, and the other acceptable. If the wrong answer is used, the model may perform very poorly in mathematical calculations and could lead to undesirable results.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">The key to this question lies in recognizing and remembering that during model training and inference, they operate according to\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a unidirectional token sequence from left to right\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">for computation. The token sequence evolves from left to right, and each time the next token is generated, all existing tokens are fed into the neural network, which then calculates\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">The probability distribution of the next token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">。\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">During this computation process, the input tokens are fed into the neural network, which performs a series of calculations involving operations of multiple neurons, ultimately outputting the probability distribution of the next token.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">An important point to understand is that, mathematically speaking, the number of layers involved in these computations is finite. The following example has 3 layers; modern\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">state-of-the-art\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">neural networks may have\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">about 100 layers\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">However, no matter what, the number of computation layers performed to derive the probability of the next token from the previous token sequence is always finite.\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010171\" data-ratio=\"1.0472222222222223\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770738210.2769747769057418.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">The computational cost for each token is almost fixed, although this isn't entirely accurate. When the number of input tokens increases, the cost of the neural network's forward pass also increases, but this growth is not significant. Therefore,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a good way to understand it is: for each token in the sequence, there is roughly a fixed amount of computation.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">。\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">this computational cost cannot be too large because the number of layers in the model is limited. Looking vertically, the number of computation layers is not high, so\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">A single forward pass cannot perform any arbitrary complex computation.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">This means that the model's reasoning and computation process\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">must be distributed across multiple tokens\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, because a single token consumes only a limited amount of computational resources.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">We cannot expect the model to perform extensive computations while generating a specific token.\u003C/span>\u003Cspan leaf=\"\">Since the computation per token is fixed and constrained by the number of model layers. Therefore, we need\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">to distribute the computational burden among multiple tokens\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, allowing the model to perform reasoning step-by-step instead of expecting all computations to be completed on a single token. This is precisely why in the example above, one answer turns out to be much worse than the other\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">much worse\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">。\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-ratio=\"0.3138888888888889\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" data-imgfileid=\"100010172\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770737100.2581346911492717.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">Imagine that the model must generate tokens one by one from left to right. It needs to output sequentially\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">“The answer is ”\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">(The answer is), then is\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">“$”\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">(Dollar sign), following is\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">this critical position\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">needs\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">to compress the entire mathematical calculation process\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">to\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">(18 in the figure below), it directly outputs the correct answer \"3\".\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010198\" data-ratio=\"0.49166666666666664\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770738040.620860588896176.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">The problem is, once the model outputs\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">“3”\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">this token, the subsequent tokens are just\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Subsequent explanation of the answer\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, but this is not the actual calculation process; rather,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">it is a post hoc addition\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">. In other words,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">the answer was already determined when the model generated \"3\", and the subsequent text merely elaborates on the known answer\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">It will not affect how the model truly performs mathematical calculations.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">If the training data causes the model to directly output the final answer without going through a reasoning process, then it is actually\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">\u003Cspan textstyle=\"\" style=\"font-weight: normal;\">training the model to\u003C/span>\u003Cspan textstyle=\"\" style=\"font-weight: bold;\">guess\u003C/span>\u003Cspan textstyle=\"\" style=\"font-weight: normal;\">the answer, rather than\u003C/span>\u003Cspan textstyle=\"\" style=\"font-weight: bold;\">Calculate\u003C/span>\u003Cspan textstyle=\"\" style=\"font-weight: normal;\">Answer\u003C/span>\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">This doesn't work in the reasoning process because\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Each token can only use a limited amount of computation\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">。\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">This is why\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">The answer on the right is significantly better.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">— It distributes the computation process instead of compressing everything into a single token. In the answer on the right, the model derives the final answer step by step:\u003C/span>\u003C/p>\u003Cul style='box-sizing: border-box;margin: 8px 0px;;list-style-type: disc;padding: 0px 0px 0px 25px;color: rgb(0, 0, 0);font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-size: 16px;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;letter-spacing: normal;orphans: 2;text-align: left;text-indent: 0px;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;' class=\"list-paddingleft-1\">\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">The total price of oranges is $4.\u003C/span>\u003C/strong>\u003C/section>\u003C/li>\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Total price $13 - Price of oranges $4 = $9\u003C/span>\u003C/strong>\u003C/section>\u003C/li>\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">$9 divided by 3 apples, each apple costs $3.\u003C/span>\u003C/strong>\u003C/section>\u003C/li>\u003C/ul>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">This\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">step-by-step reasoning\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">approach allows each token to only perform relatively simple calculations, without needing to complete all reasoning at once. This not only aligns with the model's computational limitations but also makes it easier for the model to arrive at the correct answer during inference.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">If the model is guided during training to\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">calculate everything all at once\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, then it is likely unable to perform complex calculations during inference because\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">the amount of computation each token can perform is limited\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">. Therefore,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">the correct training approach is to have the model distribute the reasoning process across multiple tokens\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">; only in this way can it correctly perform calculations during inference.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">This is important when designing a Prompt, but in most cases, users don't need to explicitly consider this issue because OpenAI's annotators have already optimized it during data annotation, so ChatGPT will\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">slowly derive the answer\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">instead of giving the answer directly. For example, it will first\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">define variables, list equations, and solve step by step\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">not for explaining to humans, but for\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Help the model to conduct reasoning for itself\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">. If the model cannot generate these intermediate steps for itself, it will not be able to deduce the correct answer \"3\".\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Cbr>\u003C/span>\u003C/p>\u003Csection data-mpa-template=\"t\" mpa-from-tpl=\"t\" data-mpa-action-id=\"m78fztjc1jlq\">\u003Csection style=\"text-align: center;transform: translate3d(2px, 0px, 0px);margin: 10px 0%;padding:0 10px;\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;background-color: rgb(255, 202, 0);\" mpa-from-tpl=\"t\">\u003Csection style=\"margin: 5px 0% -5px;transform: translate3d(-5px, 0px, 0px);\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;border-style: solid;border-width: 8px 1px 1px;border-radius: 0px;border-color: rgb(62, 62, 62);background-color: rgb(255, 255, 255);padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Csection mpa-from-tpl=\"t\">\u003Csection style=\"text-align: left;padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Cp>\u003Cem>\u003Cstrong mpa-from-tpl=\"t\">\u003Cspan leaf=\"\">Example 2\u003C/span>\u003C/strong>\u003C/em>\u003C/p>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">If you directly ask the LLM to provide an answer without allowing it to reason. For instance, the same math problem is provided, but the model is required\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">to answer within a single token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">That is, directly output the answer without performing any extra calculations.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">On this simple question, the model\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">succeeded in\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">giving the correct answer in one forward pass. However, this answer actually consists of two tokens because the dollar sign\u003C/span>\u003Ccode style=\"box-sizing: border-box;font-family: Consolas, Monaco, Menlo, monospace;font-size: 14px;;color: rgb(30, 107, 184);line-height: 1.8em;letter-spacing: 0em;background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(27, 31, 35, 0.05);width: auto;height: auto;margin: 0px 2px;padding: 2px 4px;border-style: none;border-width: 3px;border-color: rgb(0, 0, 0) rgba(0, 0, 0, 0.4) rgba(0, 0, 0, 0.4);border-radius: 4px;overflow-wrap: break-word;word-break: break-all;\">\u003Cspan leaf=\"\">$\u003C/span>\u003C/code>\u003Cspan leaf=\"\">is also a separate token. Therefore, strictly speaking, it did not fully comply with the requirement to\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a single token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">is completed, but still within\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a single forward pass\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">the correct answer was derived.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">However, this result is limited to simple numbers. If we try to increase the difficulty, for example,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Emily bought 23 apples and 177 oranges\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, which increases the computational complexity of the problem. The model is asked again\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">to respond within a single token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, and it answered \"5\" — an answer\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">that is incorrect\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">。\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-ratio=\"0.325\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" data-imgfileid=\"100010203\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770738060.07748461132544548.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">Why is this? Because when the problem becomes complex, the model can no longer\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">complete all calculations in a single forward pass.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">In other words,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">it cannot finish all mathematical operations within a single token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, which ultimately leads to computational errors.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">When canceling\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">single token restriction\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, allowing the model to solve problems in a normal way, it begins to generate a series of\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">intermediate calculations\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, for example:\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010204\" data-ratio=\"1.0777777777777777\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770743720.7801154852855332.png\">\u003C/section>\u003Cul style='box-sizing: border-box;margin: 8px 0px;;list-style-type: disc;padding: 0px 0px 0px 25px;color: rgb(0, 0, 0);font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-size: 16px;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;letter-spacing: normal;orphans: 2;text-align: left;text-indent: 0px;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;' class=\"list-paddingleft-1\">\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cspan leaf=\"\">Calculate the total price of oranges\u003C/span>\u003C/section>\u003C/li>\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cspan leaf=\"\">Calculate the total price of apples\u003C/span>\u003C/section>\u003C/li>\u003Cli style=\"box-sizing: border-box;;\">\u003Csection style=\"box-sizing: border-box;;margin-top: 5px;margin-bottom: 5px;color: rgb(1, 1, 1);font-size: 16px;line-height: 1.8em;letter-spacing: 0em;text-align: left;font-weight: normal;\">\u003Cspan leaf=\"\">Calculate the price of a single apple\u003C/span>\u003C/section>\u003C/li>\u003C/ul>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">These\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Intermediate calculation steps\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">For the model,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">the computation for each token is relatively small\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">，so it can accurately arrive at the correct answer\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">7\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">. However, if it is required to do so in\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a single forward pass\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">to complete all calculations within it exceeds the model's capabilities, leading to computational errors.\u003C/span>\u003C/p>\u003Ch3 style='box-sizing: border-box;margin: 30px 0px 15px;color: rgba(0, 0, 0, 0.85);font-weight: 500;;padding: 0px;display: block;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;letter-spacing: normal;orphans: 2;text-align: left;text-indent: 0px;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan style=\"box-sizing: border-box;;font-size: 20px;color: rgb(0, 0, 0);line-height: 1.5em;letter-spacing: 0em;text-align: left;font-weight: bold;display: block;\">\u003Cspan leaf=\"\">Why is the model's mental arithmetic unreliable?\u003C/span>\u003C/span>\u003C/h3>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">In practical applications, we cannot fully trust the model's mental arithmetic abilities, especially when numbers become larger. Because\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">neural networks are inherently not suited for performing mathematical calculations\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">; they only approximate reasoning through pattern recognition.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">A more reliable approach is to have the model\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">call code\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">to complete the calculation. For example, the model could use Python code instead of relying on its mental arithmetic ability. The model can generate Python code to perform calculations, and the correctness of the code is more reliable than the model's \"mental arithmetic\".\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010205\" data-ratio=\"1.048148148148148\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770738080.5053989719100251.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">The model is essentially just a text prediction system, while the Python interpreter is a specialized tool for executing mathematical calculations. The LLM writes the program, the computer runs it, and then the LLM accesses the results of the computation.\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Rather than having the model calculate on its own, it should be made to call Python code.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">because this way the results will be more accurate.\u003C/span>\u003C/p>\u003Csection data-mpa-template=\"t\" mpa-from-tpl=\"t\" data-mpa-action-id=\"m78g1zz7133v\">\u003Csection style=\"text-align: center;transform: translate3d(2px, 0px, 0px);margin: 10px 0%;padding:0 10px;\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;background-color: rgb(255, 202, 0);\" mpa-from-tpl=\"t\">\u003Csection style=\"margin: 5px 0% -5px;transform: translate3d(-5px, 0px, 0px);\" mpa-from-tpl=\"t\">\u003Csection style=\"display: inline-block;min-width: 10%;vertical-align: top;border-style: solid;border-width: 8px 1px 1px;border-radius: 0px;border-color: rgb(62, 62, 62);background-color: rgb(255, 255, 255);padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Csection mpa-from-tpl=\"t\">\u003Csection style=\"text-align: left;padding-right: 8px;padding-left: 8px;\" mpa-from-tpl=\"t\">\u003Cp>\u003Cem>\u003Cstrong mpa-from-tpl=\"t\">\u003Cspan leaf=\"\">Example 3\u003C/span>\u003C/strong>\u003C/em>\u003C/p>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">For the same reason, the model performs poorly in\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">counting\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">as well.\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">For example, provide a sequence of dots (\".\"] to the model and ask: \"How many dots are below?\"\u003C/span>\u003Cspan leaf=\"\">\u003Cbr>\u003C/span>\u003Cspan leaf=\"\">The model tries to directly calculate within\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">a single token\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">the number of dots, but it often gives the wrong answer.\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-ratio=\"0.34629629629629627\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" data-imgfileid=\"100010206\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770747140.17198630298205164.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">Why? Because\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">It must complete all calculations in one forward pass.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">，but\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">the computational capacity within a single token is limited.\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">，and through these subsequent token IDs. Therefore, it cannot accurately count the number of points.\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010207\" data-ratio=\"0.46296296296296297\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770738060.2864300659527992.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">If we change the approach,\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">Let it use Python code\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">, the model will generate code like this:\u003C/span>\u003C/p>\u003Csection style=\"text-align: center;\" nodeleaf=\"\">\u003Cimg class=\"rich_pages wxw-img js_insertlocalimg\" data-imgfileid=\"100010208\" data-ratio=\"0.9296296296296296\" data-s=\"300,640\" data-type=\"png\" data-w=\"1080\" type=\"block\" style=\"height: auto !important;\" src=\"https://res.cooltool.vip/article_res/assets/17423770751220.8507447477767365.png\">\u003C/section>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">\u003Cbr>\u003C/span>\u003C/p>\u003Cp style='box-sizing: border-box;margin: 0px;;color: rgb(0, 0, 0);font-size: 16px;line-height: 1.8em;letter-spacing: normal;text-align: left;text-indent: 0px;padding: 8px 0px;font-family: Optima, \"Microsoft YaHei\", PingFangSC-regular, serif;font-style: normal;font-variant-ligatures: normal;font-variant-caps: normal;font-weight: 400;orphans: 2;text-transform: none;widows: 2;word-spacing: 0px;-webkit-text-stroke-width: 0px;white-space: normal;background-color: rgb(255, 255, 255);text-decoration-thickness: initial;text-decoration-style: initial;text-decoration-color: initial;'>\u003Cspan leaf=\"\">In this case, the model's task is just\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">to copy the input,\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">Then call the Python interpreter to execute\u003C/span>\u003Ccode style=\"box-sizing: border-box;font-family: Consolas, Monaco, Menlo, monospace;font-size: 14px;;color: rgb(30, 107, 184);line-height: 1.8em;letter-spacing: 0em;background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(27, 31, 35, 0.05);width: auto;height: auto;margin: 0px 2px;padding: 2px 4px;border-style: none;border-width: 3px;border-color: rgb(0, 0, 0) rgba(0, 0, 0, 0.4) rgba(0, 0, 0, 0.4);border-radius: 4px;overflow-wrap: break-word;word-break: break-all;\">\u003Cspan leaf=\"\">len(dots)\u003C/span>\u003C/code>\u003Cspan leaf=\"\">the calculation of the number of points. This is more\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">reliable\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">because the Python interpreter performs\u003C/span>\u003Cstrong style=\"box-sizing: border-box;font-weight: bold;;color: rgb(0, 0, 0);background: none 0% 0% / auto no-repeat scroll padding-box border-box rgba(0, 0, 0, 0);width: auto;height: auto;margin: 0px;padding: 0px;border-style: none;border-width: 3px;border-color: rgba(0, 0, 0, 0.4);border-radius: 0px;\">\u003Cspan leaf=\"\">deterministic calculations\u003C/span>\u003C/strong>\u003Cspan leaf=\"\">，while the neural network inference of the model is unstable.\u003C/span>\u003C/p>\u003Cp style=\"display: none;\">\u003Cmp-style-type data-value=\"3\">\u003C/mp-style-type>\u003C/p>\u003C/div>",1752585427388]