1"use strict";(self.webpackChunkwiki=self.webpackChunkwiki||[]).push([["492"],{4930(s,e,a){a.r(e),a.d(e,{metadata:()=>n,default:()=>d,frontMatter:()=>r,contentTitle:()=>t,toc:()=>c,assets:()=>m});var n=JSON.parse('{"id":"machine-learning/llm/llm-evaluation","title":"LLM Evaluation","description":"MMLU\u3001HumanEval\u3001GPQA\u3001Chatbot Arena\u3001LLM-as-a-Judge\u3001benchmark contamination \u3092\u6574\u7406\u3057\u307E\u3059\u3002","source":"@site/docs/machine-learning/llm/llm-evaluation.mdx","sourceDirName":"machine-learning/llm","slug":"/machine-learning/llm/llm-evaluation","permalink":"/wiki/machine-learning/llm/llm-evaluation","draft":false,"unlisted":false,"tags":[],"version":"current","sidebarPosition":17,"frontMatter":{"sidebar_position":17,"title":"LLM Evaluation","description":"MMLU\u3001HumanEval\u3001GPQA\u3001Chatbot Arena\u3001LLM-as-a-Judge\u3001benchmark contamination \u3092\u6574\u7406\u3057\u307E\u3059\u3002"},"sidebar":"tutorialSidebar","previous":{"title":"Model Merging","permalink":"/wiki/machine-learning/llm/model-merging"},"next":{"title":"Reinforcement Learning","permalink":"/wiki/category/reinforcement-learning"}}'),l=a(74848),i=a(28453);let r={sidebar_position:17,title:"LLM Evaluation",description:"MMLU\u3001HumanEval\u3001GPQA\u3001Chatbot Arena\u3001LLM-as-a-Judge\u3001benchmark contamination \u3092\u6574\u7406\u3057\u307E\u3059\u3002"},t="LLM Evaluation",m={},c=[{value:"\u8A55\u4FA1\u8EF8",id:"\u8A55\u4FA1\u8EF8",level:2},{value:"\u4EE3\u8868\u7684 benchmark",id:"\u4EE3\u8868\u7684-benchmark",level:2},{value:"LLM-as-a-Judge",id:"llm-as-a-judge",level:2},{value:"Chatbot Arena",id:"chatbot-arena",level:2},{value:"Benchmark contamination",id:"benchmark-contamination",level:2},{value:"\u8A55\u4FA1\u8A2D\u8A08\u306E\u843D\u3068\u3057\u7A74",id:"\u8A55\u4FA1\u8A2D\u8A08\u306E\u843D\u3068\u3057\u7A74",level:2},{value:"\u6570\u5F0F\u3067\u898B\u308B LLM-as-a-Judge \u3068 Arena rating",id:"\u6570\u5F0F\u3067\u898B\u308B-llm-as-a-judge-\u3068-arena-rating",level:2},{value:"\u95A2\u9023\u30DA\u30FC\u30B8",id:"\u95A2\u9023\u30DA\u30FC\u30B8",level:2},{value:"\u4E3B\u306A\u30BD\u30FC\u30B9",id:"\u4E3B\u306A\u30BD\u30FC\u30B9",level:2}];function h(s){let e={a:"a",annotation:"annotation",h1:"h1",h2:"h2",header:"header",li:"li",math:"math",mermaid:"mermaid",mfrac:"mfrac",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",msub:"msub",msup:"msup",p:"p",semantics:"semantics",span:"span",strong:"strong",table:"table",tbody:"tbody",td:"td",th:"th",thead:"thead",tr:"tr",ul:"ul",...(0,i.R)(),...s.components};return(0,l.jsxs)(l.Fragment,{children:[(0,l.jsx)(e.header,{children:(0,l.jsx)(e.h1,{id:"llm-evaluation",children:"LLM Evaluation"})}),"\n",(0,l.jsx)(e.p,{children:"LLM \u306E\u8A55\u4FA1\u306F\u3001generative model \u306E\u4E2D\u3067\u3082\u7279\u306B\u96E3\u3057\u3044\u554F\u984C\u3067\u3059\u3002\u300C\u6B63\u89E3\u304C\u4E00\u610F\u306B\u6C7A\u307E\u3089\u306A\u3044\u300D\u300Cbenchmark contamination \u304C\u3042\u308B\u300D\u300Cuser \u4F53\u9A13\u306F\u9759\u7684 metric \u3067\u306F\u6E2C\u308C\u306A\u3044\u300D\u306A\u3069\u3001\u8907\u6570\u306E\u8AB2\u984C\u3092\u540C\u6642\u306B\u62B1\u3048\u307E\u3059\u3002"}),"\n",(0,l.jsx)(e.h2,{id:"\u8A55\u4FA1\u8EF8",children:"\u8A55\u4FA1\u8EF8"}),"\n",(0,l.jsx)(e.mermaid,{value:"flowchart TB\n A[LLM Evaluation] --\x3e B[Knowledge]\n A --\x3e C[Reasoning]\n A --\x3e D[Coding]\n A --\x3e E[Math]\n A --\x3e F[Instruction following]\n A --\x3e G[Safety / alignment]\n A --\x3e H[Human preference]\n A --\x3e I[Agentic / tool use]"}),"\n",(0,l.jsx)(e.h2,{id:"\u4EE3\u8868\u7684-benchmark",children:"\u4EE3\u8868\u7684 benchmark"}),"\n",(0,l.jsxs)(e.table,{children:[(0,l.jsx)(e.thead,{children:(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.th,{children:"Benchmark"}),(0,l.jsx)(e.th,{children:"\u8A55\u4FA1\u5BFE\u8C61"})]})}),(0,l.jsxs)(e.tbody,{children:[(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"MMLU / MMLU-Pro"}),(0,l.jsx)(e.td,{children:"\u591A\u5206\u91CE\u77E5\u8B58"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"GPQA"}),(0,l.jsx)(e.td,{children:"\u5927\u5B66\u9662\u30EC\u30D9\u30EB\u79D1\u5B66"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"HumanEval / MBPP"}),(0,l.jsx)(e.td,{children:"\u30B3\u30FC\u30C9\u751F\u6210"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"LiveCodeBench"}),(0,l.jsx)(e.td,{children:"\u6C5A\u67D3\u3057\u306B\u304F\u3044\u30B3\u30FC\u30C9\u8A55\u4FA1"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"GSM8K / MATH"}),(0,l.jsx)(e.td,{children:"\u7B97\u6570\u30FB\u6570\u5B66"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"AIME / MATH-500"}),(0,l.jsx)(e.td,{children:"\u9AD8\u96E3\u5EA6\u6570\u5B66"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"IFEval"}),(0,l.jsx)(e.td,{children:"\u6307\u793A\u8FFD\u5F93\u306E\u7CBE\u5BC6\u8A55\u4FA1"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"MT-Bench"}),(0,l.jsx)(e.td,{children:"\u81EA\u7531\u5BFE\u8A71 (LLM-as-a-Judge)"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Chatbot Arena"}),(0,l.jsx)(e.td,{children:"\u4EBA\u9593 pairwise \u6295\u7968"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"SWE-Bench"}),(0,l.jsx)(e.td,{children:"\u5B9F GitHub issue \u89E3\u6C7A"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"GAIA / AgentBench"}),(0,l.jsx)(e.td,{children:"Agent \u7CFB task"})]})]})]}),"\n",(0,l.jsx)(e.h2,{id:"llm-as-a-judge",children:"LLM-as-a-Judge"}),"\n",(0,l.jsxs)(e.p,{children:["\u4EBA\u624B\u8A55\u4FA1\u304C\u9AD8\u30B3\u30B9\u30C8\u306A\u305F\u3081\u3001\u5F37\u3044 LLM (GPT-4 / Claude \u7CFB) \u3092 judge \u306B\u4F7F\u3046 ",(0,l.jsx)(e.strong,{children:"LLM-as-a-Judge"})," \u304C\u5E83\u307E\u308A\u307E\u3057\u305F\u3002"]}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsx)(e.li,{children:"Pairwise (A \u3068 B \u3069\u3061\u3089\u304C\u826F\u3044\u304B)"}),"\n",(0,l.jsx)(e.li,{children:"Pointwise (1\u301C10 \u3067\u8A55\u4FA1)"}),"\n",(0,l.jsx)(e.li,{children:"Reference-based (\u6B63\u89E3\u3068\u6BD4\u8F03)"}),"\n"]}),"\n",(0,l.jsxs)(e.p,{children:["\u5229\u70B9\u306F\u5B89\u4FA1\u3067\u518D\u73FE\u6027\u304C\u6BD4\u8F03\u7684\u9AD8\u3044\u3053\u3068\u3002\u6B20\u70B9\u306F ",(0,l.jsx)(e.strong,{children:"\u5224\u5B9A LLM \u306E bias"})," (verbosity bias\u3001position bias\u3001self-preference) \u304C\u3042\u308B\u3053\u3068\u3067\u3059\u3002"]}),"\n",(0,l.jsx)(e.h2,{id:"chatbot-arena",children:"Chatbot Arena"}),"\n",(0,l.jsxs)(e.p,{children:["Chatbot Arena \u306F\u3001",(0,l.jsx)(e.strong,{children:"\u30E6\u30FC\u30B6\u30FC\u304C\u533F\u540D 2 \u30E2\u30C7\u30EB\u306B\u540C\u3058\u8CEA\u554F\u3092\u6295\u3052\u3001\u52DD\u8005\u3092\u6295\u7968"})," \u3059\u308B\u4EBA\u9593\u8A55\u4FA1\u3067\u3059\u3002Elo / Bradley-Terry rating \u3067\u30E9\u30F3\u30AD\u30F3\u30B0\u3092\u4F5C\u308A\u307E\u3059\u3002\u5B9F\u5229\u7528\u306B\u8FD1\u3044\u3001\u3082\u3063\u3068\u3082\u4FE1\u983C\u6027\u304C\u9AD8\u3044 indicator \u306E\u4E00\u3064\u3068\u3057\u3066\u6271\u308F\u308C\u3066\u3044\u307E\u3059\u3002"]}),"\n",(0,l.jsx)(e.h2,{id:"benchmark-contamination",children:"Benchmark contamination"}),"\n",(0,l.jsx)(e.p,{children:"Pretrain corpus \u306B benchmark \u306E\u89E3\u7B54\u304C\u542B\u307E\u308C\u3066\u3044\u308B\u3068\u3001\u8A55\u4FA1\u304C\u7121\u610F\u5473\u5316\u3057\u307E\u3059\u3002\u6700\u8FD1\u306E\u5BFE\u7B56:"}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsxs)(e.li,{children:[(0,l.jsx)(e.strong,{children:"Held-out / \u65B0\u4F5C benchmark"})," (LiveCodeBench\u3001AIME\u3001GPQA Diamond)"]}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.strong,{children:"N-gram / fuzzy match \u3067 contamination \u691C\u67FB"})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.strong,{children:"Private holdout"})}),"\n",(0,l.jsxs)(e.li,{children:[(0,l.jsx)(e.strong,{children:"Process-level \u8A55\u4FA1"})," (\u4E2D\u9593\u30B9\u30C6\u30C3\u30D7\u3092\u898B\u308B)"]}),"\n"]}),"\n",(0,l.jsx)(e.h2,{id:"\u8A55\u4FA1\u8A2D\u8A08\u306E\u843D\u3068\u3057\u7A74",children:"\u8A55\u4FA1\u8A2D\u8A08\u306E\u843D\u3068\u3057\u7A74"}),"\n",(0,l.jsxs)(e.table,{children:[(0,l.jsx)(e.thead,{children:(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.th,{children:"\u843D\u3068\u3057\u7A74"}),(0,l.jsx)(e.th,{children:"\u5185\u5BB9"})]})}),(0,l.jsxs)(e.tbody,{children:[(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Few-shot \u6570\u306E\u9055\u3044"}),(0,l.jsx)(e.td,{children:"0-shot vs 5-shot \u3067\u9806\u4F4D\u304C\u5909\u308F\u308B"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Prompt \u306E\u9055\u3044"}),(0,l.jsx)(e.td,{children:"system prompt / format \u3067\u5DEE\u304C\u51FA\u308B"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Decoding \u8A2D\u5B9A"}),(0,l.jsx)(e.td,{children:"temperature / top-p \u3067\u5DEE\u304C\u51FA\u308B"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Judge model \u306E bias"}),(0,l.jsx)(e.td,{children:"LLM judge \u306E\u81EA\u5DF1\u9078\u597D"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"Cherry-picked tasks"}),(0,l.jsx)(e.td,{children:"\u516C\u958B task \u304C contamination \u6E08\u307F"})]}),(0,l.jsxs)(e.tr,{children:[(0,l.jsx)(e.td,{children:"\u5358\u4E00 benchmark \u3078\u306E\u904E\u9069\u5408"}),(0,l.jsx)(e.td,{children:'"MMLU \u304C\u9AD8\u3044 \u2260 \u5F37\u3044"'})]})]})]}),"\n",(0,l.jsx)(e.p,{children:"\u5B9F\u52D9\u3067\u306F\u3001\u8907\u6570 benchmark + Chatbot Arena + \u81EA\u793E dogfood \u306E\u7D44\u5408\u305B\u304C\u6A19\u6E96\u3067\u3059\u3002"}),"\n",(0,l.jsx)(e.h2,{id:"\u6570\u5F0F\u3067\u898B\u308B-llm-as-a-judge-\u3068-arena-rating",children:"\u6570\u5F0F\u3067\u898B\u308B LLM-as-a-Judge \u3068 Arena rating"}),"\n",(0,l.jsxs)(e.p,{children:["Pairwise evaluation \u3067\u306F\u3001\u540C\u3058 prompt ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"x"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"x"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.4306em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"x"})]})})]})," \u306B\u5BFE\u3059\u308B\u4E8C\u3064\u306E\u56DE\u7B54 ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"y"}),(0,l.jsx)(e.mi,{children:"A"})]}),(0,l.jsx)(e.mo,{separator:"true",children:","}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"y"}),(0,l.jsx)(e.mi,{children:"B"})]})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"y_A,y_B"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"y"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3283em"}
1,children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"A"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mpunct",children:","}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"y"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3283em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0502em"},children:"B"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})})]})," \u3092\u6BD4\u8F03\u3057\u3001\u3069\u3061\u3089\u304C\u826F\u3044\u304B\u3092\u5224\u5B9A\u3057\u307E\u3059\u3002Judge model \u306E score \u3092 ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"s"}),(0,l.jsx)(e.mi,{children:"\u03D5"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mo,{separator:"true",children:","}),(0,l.jsx)(e.mi,{children:"y"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"s_\\phi(x,y)"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1.0361em",verticalAlign:"-0.2861em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",children:"s"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3361em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"\u03D5"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.2861em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,l.jsx)(e.span,{className:"mpunct",children:","}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"y"}),(0,l.jsx)(e.span,{className:"mclose",children:")"})]})})]})," \u3068\u3059\u308B\u3068\u3001A \u304C B \u306B\u52DD\u3064\u78BA\u7387\u306F Bradley-Terry model \u3067\u6B21\u306E\u3088\u3046\u306B\u66F8\u3051\u307E\u3059\u3002"]}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"P"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"A"}),(0,l.jsx)(e.mo,{children:"\u227B"}),(0,l.jsx)(e.mi,{children:"B"}),(0,l.jsx)(e.mo,{children:"\u2223"}),(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsx)(e.mi,{children:"\u03C3"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"s"}),(0,l.jsx)(e.mi,{children:"\u03D5"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mo,{separator:"true",children:","}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"y"}),(0,l.jsx)(e.mi,{children:"A"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mo,{children:"\u2212"}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"s"}),(0,l.jsx)(e.mi,{children:"\u03D5"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"x"}),(0,l.jsx)(e.mo,{separator:"true",children:","}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"y"}),(0,l.jsx)(e.mi,{children:"B"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"P(A\\succ B\\mid x)=\\sigma(s_\\phi(x,y_A)-s_\\phi(x,y_B))"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.1389em"},children:"P"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"A"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"\u227B"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0502em"},children:"B"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"\u2223"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,l.jsx)(e.span,{className:"mclose",children:")"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1.0361em",verticalAlign:"-0.2861em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"\u03C3"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",children:"s"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3361em"}
1,children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"\u03D5"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.2861em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,l.jsx)(e.span,{className:"mpunct",children:","}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"y"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3283em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"A"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mclose",children:")"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,l.jsx)(e.span,{className:"mbin",children:"\u2212"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1.0361em",verticalAlign:"-0.2861em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",children:"s"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3361em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"0em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"\u03D5"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.2861em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"x"}),(0,l.jsx)(e.span,{className:"mpunct",children:","}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.1667em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0359em"},children:"y"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3283em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0502em"},children:"B"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mclose",children:"))"})]})]})]})}),"\n",(0,l.jsx)(e.p,{children:"\u3053\u306E\u5F0F\u306E\u6C17\u6301\u3061\u306F\u3001\u300C\u7D76\u5BFE\u70B9\u3067\u306F\u306A\u304F\u3001\u540C\u3058 prompt \u306B\u5BFE\u3057\u3066\u3069\u3061\u3089\u306E\u56DE\u7B54\u304C\u76F8\u5BFE\u7684\u306B\u826F\u3044\u304B\u3092\u6BD4\u8F03\u3059\u308B\u300D\u3068\u3044\u3046\u3082\u306E\u3067\u3059\u3002"}),"\n",(0,l.jsxs)(e.p,{children:["Chatbot Arena \u306E\u3088\u3046\u306A rating \u3067\u306F\u3001model ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"i"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"i"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6595em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"i"})]})})]})," \u306E rating \u3092 ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"r"}),(0,l.jsx)(e.mi,{children:"i"})]})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"r_i"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0278em"},children:"r"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.311
17em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0278em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"i"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})})]})," \u3068\u3057\u3066\u3001model ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"i"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"i"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6595em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"i"})]})})]})," \u304C model ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"j"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"j"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.854em",verticalAlign:"-0.1944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0572em"},children:"j"})]})})]})," \u306B\u52DD\u3064\u78BA\u7387\u3092\u6B21\u306E\u3088\u3046\u306B\u7F6E\u304D\u307E\u3059\u3002"]}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"P"}),(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsx)(e.mi,{children:"i"}),(0,l.jsx)(e.mo,{children:"\u227B"}),(0,l.jsx)(e.mi,{children:"j"}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mo,{children:"="}),(0,l.jsxs)(e.mfrac,{children:[(0,l.jsx)(e.mn,{children:"1"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mn,{children:"1"}),(0,l.jsx)(e.mo,{children:"+"}),(0,l.jsxs)(e.msup,{children:[(0,l.jsx)(e.mn,{children:"10"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mo,{stretchy:"false",children:"("}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"r"}),(0,l.jsx)(e.mi,{children:"j"})]}),(0,l.jsx)(e.mo,{children:"\u2212"}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{children:"r"}),(0,l.jsx)(e.mi,{children:"i"})]}),(0,l.jsx)(e.mo,{stretchy:"false",children:")"}),(0,l.jsx)(e.mi,{mathvariant:"normal",children:"/"}),(0,l.jsx)(e.mn,{children:"400"})]})]})]})]})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"P(i\\succ j)=\\frac{1}{1+10^{(r_j-r_i)/400}}"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.1389em"},children:"P"}),(0,l.jsx)(e.span,{className:"mopen",children:"("}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"i"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"\u227B"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",style:{marginRight:"0.0572em"},children:"j"}),(0,l.jsx)(e.span,{className:"mclose",children:")"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"="}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"2.1248em",verticalAlign:"-0.8034em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mopen nulldelimiter"}),(0,l.jsx)(e.span,{className:"mfrac",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsxs)(e.span,{className:"vlist",style:{height:"1.3214em"}
1,children:[(0,l.jsxs)(e.span,{style:{top:"-2.2799em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord",children:"1"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,l.jsx)(e.span,{className:"mbin",children:"+"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2222em"}}),(0,l.jsx)(e.span,{className:"mord",children:"1"}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord",children:"0"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsx)(e.span,{className:"vlist-t",children:(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.8301em"},children:(0,l.jsxs)(e.span,{style:{top:"-3.0051em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mopen mtight",children:"("}),(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0278em"},children:"r"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3281em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.357em",marginLeft:"-0.0278em",marginRight:"0.0714em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.5em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size3 size1 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0572em"},children:"j"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.2819em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mbin mtight",children:"\u2212"}),(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0278em"},children:"r"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3281em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.357em",marginLeft:"-0.0278em",marginRight:"0.0714em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.5em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size3 size1 mtight",children:(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"i"})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.143em"},children:(0,l.jsx)(e.span,{})})})]})})]}),(0,l.jsx)(e.span,{className:"mclose mtight",children:")"}),(0,l.jsx)(e.span,{className:"mord mtight",children:"/400"})]})})]})})})})})]})]})]}),(0,l.jsxs)(e.span,{style:{top:"-3.23em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"frac-line",style:{borderBottomWidth:"0.04em"}})]}),(0,l.jsxs)(e.span,{style:{top:"-3.677em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"3em"}}),(0,l.jsx)(e.span,{className:"mord",children:(0,l.jsx)(e.span,{className:"mord",children:"1"})})]})]}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.8034em"},children:(0,l.jsx)(e.span,{})})})]})}),(0,l.jsx)(e.span,{className:"mclose nulldelimiter"})]})]})]})]})}),"\n",(0,l.jsx)(e.p,{children:"\u3053\u306E\u5F0F\u306F Elo rating \u306E\u6A19\u6E96\u7684\u306A\u5F62\u3067\u3059\u3002\u5B9F\u5229\u7528\u306B\u8FD1\u3044 prompt \u3067\u4EBA\u9593\u304C pairwise \u306B\u6295\u7968\u3059\u308B\u305F\u3081\u3001static benchmark \u3088\u308A\u3082 user preference \u306B\u8FD1\u3044 signal \u3092\u5F97\u3089\u308C\u307E\u3059\u3002\u305F\u3060\u3057\u3001position bias\u3001verbosity bias\u3001style preference \u306A\u3069\u3092\u5236\u5FA1\u3059\u308B\u5FC5\u8981\u304C\u3042\u308A\u307E\u3059\u3002"}),"\n",(0,l.jsxs)(e.p,{children:["Benchmark contamination \u306F\u3001training corpus ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{mathvariant:"script",children:"D"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"t"}),(0,l.jsx)(e.mi,{children:"r"}),(0,l.jsx)(e.mi,{children:"a"}),(0,l.jsx)(e.mi,{children:"i"}),(0,l.jsx)(e.mi,{children:"n"})]})]})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"\\mathcal{D}_{train}"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.8333em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathcal",style:{marginRight:"0.0278em"},children:"D"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.311
17em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0278em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"t"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0278em"},children:"r"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"ain"})]})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})})]})," \u306B benchmark item ",(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsx)(e.mrow,{children:(0,l.jsx)(e.mi,{children:"b"})}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"b"})]})})}),(0,l.jsx)(e.span,{className:"katex-html","aria-hidden":"true",children:(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.6944em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"b"})]})})]})," \u304C\u542B\u307E\u308C\u308B\u554F\u984C\u3068\u3057\u3066\u66F8\u3051\u307E\u3059\u3002"]}),"\n",(0,l.jsx)(e.span,{className:"katex-display",children:(0,l.jsxs)(e.span,{className:"katex",children:[(0,l.jsx)(e.span,{className:"katex-mathml",children:(0,l.jsx)(e.math,{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block",children:(0,l.jsxs)(e.semantics,{children:[(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"b"}),(0,l.jsx)(e.mo,{children:"\u2208"}),(0,l.jsxs)(e.msub,{children:[(0,l.jsx)(e.mi,{mathvariant:"script",children:"D"}),(0,l.jsxs)(e.mrow,{children:[(0,l.jsx)(e.mi,{children:"t"}),(0,l.jsx)(e.mi,{children:"r"}),(0,l.jsx)(e.mi,{children:"a"}),(0,l.jsx)(e.mi,{children:"i"}),(0,l.jsx)(e.mi,{children:"n"})]})]})]}),(0,l.jsx)(e.annotation,{encoding:"application/x-tex",children:"b\\in\\mathcal{D}_{train}"})]})})}),(0,l.jsxs)(e.span,{className:"katex-html","aria-hidden":"true",children:[(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.7335em",verticalAlign:"-0.0391em"}}),(0,l.jsx)(e.span,{className:"mord mathnormal",children:"b"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}}),(0,l.jsx)(e.span,{className:"mrel",children:"\u2208"}),(0,l.jsx)(e.span,{className:"mspace",style:{marginRight:"0.2778em"}})]}),(0,l.jsxs)(e.span,{className:"base",children:[(0,l.jsx)(e.span,{className:"strut",style:{height:"0.8333em",verticalAlign:"-0.15em"}}),(0,l.jsxs)(e.span,{className:"mord",children:[(0,l.jsx)(e.span,{className:"mord mathcal",style:{marginRight:"0.0278em"},children:"D"}),(0,l.jsx)(e.span,{className:"msupsub",children:(0,l.jsxs)(e.span,{className:"vlist-t vlist-t2",children:[(0,l.jsxs)(e.span,{className:"vlist-r",children:[(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.3117em"},children:(0,l.jsxs)(e.span,{style:{top:"-2.55em",marginLeft:"-0.0278em",marginRight:"0.05em"},children:[(0,l.jsx)(e.span,{className:"pstrut",style:{height:"2.7em"}}),(0,l.jsx)(e.span,{className:"sizing reset-size6 size3 mtight",children:(0,l.jsxs)(e.span,{className:"mord mtight",children:[(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"t"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",style:{marginRight:"0.0278em"},children:"r"}),(0,l.jsx)(e.span,{className:"mord mathnormal mtight",children:"ain"})]})})]})}),(0,l.jsx)(e.span,{className:"vlist-s",children:"\u200B"})]}),(0,l.jsx)(e.span,{className:"vlist-r",children:(0,l.jsx)(e.span,{className:"vlist",style:{height:"0.15em"},children:(0,l.jsx)(e.span,{})})})]})})]})]})]})]})}),"\n",(0,l.jsx)(e.p,{children:"\u3053\u306E\u72B6\u614B\u3067\u306F\u3001model \u304C\u4E00\u822C\u5316\u3057\u3066\u89E3\u3044\u305F\u306E\u304B\u3001\u8A18\u61B6\u3057\u3066\u3044\u305F\u306E\u304B\u3092\u533A\u5225\u3057\u306B\u304F\u304F\u306A\u308A\u307E\u3059\u3002\u305D\u306E\u305F\u3081\u3001\u6642\u9593\u3067\u5207\u3063\u305F live benchmark \u3084\u3001\u65B0\u4F5C problem \u3092\u4F7F\u3046\u8A55\u4FA1\u304C\u91CD\u8981\u306B\u306A\u308A\u307E\u3059\u3002"}),"\n",(0,l.jsx)(e.h2,{id:"\u95A2\u9023\u30DA\u30FC\u30B8",children:"\u95A2\u9023\u30DA\u30FC\u30B8"}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.a,{href:"/wiki/machine-learning/llm/llm-overview",children:"LLM Overview"})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.a,{href:"/wiki/machine-learning/llm/reasoning-models",children:"Reasoning Models"})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.a,{href:"/wiki/machine-learning/rlhf-and-alignment/rlhf-overview",children:"RLHF Overview"})}),"\n",(0,l.jsx)(e.li,{children:(0,l.jsx)(e.a,{href:"/wiki/machine-learning/ai-agents/ai-agents-overview",children:"AI Agents Overview"})}),"\n"]}),"\n",(0,l.jsx)(e.h2,{id:"\u4E3B\u306A\u30BD\u30FC\u30B9",children:"\u4E3B\u306A\u30BD\u30FC\u30B9"}),"\n",(0,l.jsxs)(e.ul,{children:["\n",(0,l.jsxs)(e.li,{children:["MMLU: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2009.033
100",children:"https://arxiv.org/abs/2009.03300"})]}),"\n",(0,l.jsxs)(e.li,{children:["HumanEval: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2107.03374",children:"https://arxiv.org/abs/2107.03374"})]}),"\n",(0,l.jsxs)(e.li,{children:["GPQA: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2311.12022",children:"https://arxiv.org/abs/2311.12022"})]}),"\n",(0,l.jsxs)(e.li,{children:["IFEval: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2311.07911",children:"https://arxiv.org/abs/2311.07911"})]}),"\n",(0,l.jsxs)(e.li,{children:["MT-Bench / LLM-as-a-Judge: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2306.05685",children:"https://arxiv.org/abs/2306.05685"})]}),"\n",(0,l.jsxs)(e.li,{children:["Chatbot Arena: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2403.04132",children:"https://arxiv.org/abs/2403.04132"})]}),"\n",(0,l.jsxs)(e.li,{children:["SWE-Bench: ",(0,l.jsx)(e.a,{href:"https://arxiv.org/abs/2310.06770",children:"https://arxiv.org/abs/2310.06770"})]}),"\n"]})]})}function d(s={}){let{wrapper:e}={...(0,i.R)(),...s.components};return e?(0,l.jsx)(e,{...s,children:(0,l.jsx)(h,{...s})}):h(s)}},28453(s,e,a){a.d(e,{R:()=>r,x:()=>t});var n=a(96540);let l={},i=n.createContext(l);function r(s){let e=n.useContext(i);return n.useMemo(function(){return"function"==typeof s?s(e):{...e,...s}},[e,s])}function t(s){let e;return e=s.disableParentContext?"function"==typeof s.components?s.components(l):s.components||l:r(s.components),n.createElement(i.Provider,{value:e},s.children)}}}]);
Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.