[{"data":1,"prerenderedAt":5296},["ShallowReactive",2],{"site-info":3,"post-gemini-for-workspace":99,"related-zh-TW-gemini-for-workspace":375},{"id":4,"company":5,"extension":16,"meta":17,"services":18,"social":96,"stem":97,"__hash__":98},"site\u002Fsite.yml",{"name":6,"nameEn":7,"email":8,"address":9,"addressEn":10,"lineUrl":11,"lineId":12,"duns":13,"youtube":14,"youtubeId":15},"銡策數位有限公司","Jecision Digital Co., Ltd.","contact@jecision.com","231 新北市新店區北新路二段 262 號 3 樓之 3","3F.-3, No. 262, Sec. 2, Beixin Rd., Xindian Dist., New Taipei City 231, Taiwan","https:\u002F\u002Fline.me\u002FR\u002Fti\u002Fp\u002F@374qnumi","@374qnumi","963905705","https:\u002F\u002Fwww.youtube.com\u002Fshorts\u002F6UE0WTmyjsg","6UE0WTmyjsg","yml",{},[19,43,69],{"key":20,"zh":21,"en":32},"audit",{"title":22,"tagline":23,"summary":24,"points":25,"deliverable":29,"detail":30,"duration":31},"企業 AI 導入健檢","先看清楚，再花錢","60 分鐘線上訪談，盤點最耗時、最依賴人力的營運環節；我們會告訴你哪些工作現在就能交給 AI、哪些還不成熟。",[26,27,28],"現況盤點：梳理日常營運中最耗時、最依賴人力的環節","痛點診斷：判斷哪些工作現在就能交給 AI，哪些建議先保留人力","可行性評估：依你的業務特性與預算，篩選適合的模型與工具","《企業 AI 導入建議報告書》（PDF）","含 1–2 個「開發成本最低、成效最明顯」的優先項目、技術棧建議、預期節省的人力時間與下一步","訪談 60 分鐘，報告書 3 個工作天內交付",{"title":33,"tagline":34,"summary":35,"points":36,"deliverable":40,"detail":41,"duration":42},"AI Readiness Audit","Look before you spend","A 60-minute remote audit of the workflows that eat the most time and people-power — and an honest answer on what AI can take over today, and what it cannot.",[37,38,39],"Audit the daily workflows that consume the most time and headcount","Triage which tasks AI can own today, and which should stay human","Shortlist the models and tools that fit your budget and constraints","AI Adoption Recommendation Report (PDF)","One or two highest-ROI entry points, a recommended tech stack, expected hours saved, and the concrete next step","60-minute call, report delivered within 3 business days",{"key":44,"zh":45,"en":56},"prompt",{"title":46,"tagline":47,"summary":48,"points":49,"deliverable":53,"detail":54,"duration":55},"提示詞工程","讓 AI 穩定產出，而不是碰運氣","針對你的實際任務設計提示詞與多步驟工作流，並做極限測試，確保換了資料、換了人操作也不會走鐘。",[50,51,52],"客製提示詞：ChatGPT、Claude、Gemini、Midjourney 等主流工具的專屬模板","除錯與優化：修掉幻覺、格式跑掉、時好時壞的問題","工作流建置：把複雜任務拆成多步驟提示詞與可重複的 SOP","提示詞文件或設定檔","附使用說明與範例，並提供 1 對 1 教學，確保你與團隊能自己維護","依任務複雜度報價，通常 3–7 個工作天",{"title":57,"tagline":58,"summary":59,"points":60,"deliverable":66,"detail":67,"duration":68},"Prompt Engineering","Make AI produce reliably, not by luck","Prompt sets and multi-step workflows designed for your actual tasks, stress-tested so they keep working when the data or the operator changes.",[61,62,64],"Custom prompts for ChatGPT, Claude, Gemini, Midjourney and friends",{"Debugging and tuning":63},"kill hallucinations, broken formats and flaky output",{"Workflow design":65},"break complex work into repeatable multi-step SOPs","Prompt library or exportable config","Ships with usage notes and examples, plus a 1:1 walkthrough so your team can maintain it","Quoted by complexity, typically 3–7 business days",{"key":70,"zh":71,"en":82},"poc",{"title":72,"tagline":73,"summary":74,"points":75,"deliverable":79,"detail":80,"duration":81},"極速 PoC","五天，看到能跑的東西","不談架構藍圖，直接做一個能動的雛形。五個工作天內交付線上可操作的智能體，用你真實的資料驗證。",[76,77,78],"Day 1：15 分鐘對焦，鎖定單一痛點與資料盤點","Day 2–4：模型串接、邏輯設計與雛形開發","Day 5：Demo 展示與 AI 擴展建議書","可線上操作的智能體雛形","交付範圍為概念驗證與展示，不含後續維運或大規模伺服器部署；要進階成完整系統會另行報價","5 個工作天",{"title":83,"tagline":84,"summary":85,"points":86,"deliverable":93,"detail":94,"duration":95},"Rapid PoC","Five days to something that runs","No architecture decks — a working prototype built in five business days, validated against your real data.",[87,89,91],{"Day 1":88},"15-minute scoping call, one pain point, data inventory",{"Day 2–4":90},"model integration, logic design, prototype build",{"Day 5":92},"live demo plus an AI expansion recommendation","A runnable online agent prototype","Proof of concept and demo scope only; ongoing operations and large-scale deployment are quoted separately","5 business days",[],"site","XTwARfVAOcrXNiKehsM6V6cdkd2HXy4d5yZVrSWrI3Q",{"zh":100,"en":373},{"id":101,"title":102,"author":103,"body":104,"cover":359,"coverAlt":102,"date":360,"description":361,"draft":362,"extension":363,"featured":362,"lang":364,"meta":365,"navigation":366,"path":367,"seo":368,"slug":369,"stem":370,"tags":371,"translationKey":369,"updated":373,"__hash__":374},"blog\u002Fblog\u002Fzh-TW\u002Fgemini-for-workspace.md","Gemini for Workspace 提示指南精要","Jecision",{"type":105,"value":106,"toc":344},"minimark",[107,111,115,166,169,208,211,215,229,232,246,249,263,266,280,283,297,300,335],[108,109,110],"p",{},"本文總結 Google Workspace 中 Gemini AI 的提示工程核心技巧與應用場景，幫助用戶高效利用生成式 AI 提升生產力。",[112,113,114],"h2",{"id":114},"有效提示四要素",[116,117,118,133,144,155],"ol",{},[119,120,121,125,126,129],"li",{},[122,123,124],"strong",{},"角色 (Persona)","：明確指定 AI 扮演的角色",[127,128],"br",{},[130,131,132],"code",{},"例：You are a program manager in tech industry...",[119,134,135,138,139,141],{},[122,136,137],{},"任務 (Task)","：使用動詞明確指令",[127,140],{},[130,142,143],{},"例：Draft an executive summary email...",[119,145,146,149,150,152],{},[122,147,148],{},"上下文 (Context)","：提供背景資訊",[127,151],{},[130,153,154],{},"例：based on project docs in Drive...",[119,156,157,160,161,163],{},[122,158,159],{},"格式 (Format)","：指定輸出結構",[127,162],{},[130,164,165],{},"例：Limit to bullet points",[112,167,168],{"id":168},"六大核心提示技巧",[170,171,172,178,184,190,196,202],"ul",{},[119,173,174,177],{},[122,175,176],{},"🗣️ 自然語言","：用完整句子表達，如日常對話",[119,179,180,183],{},[122,181,182],{},"🎯 具體明確","：提供充足上下文（可通過@引用文件）",[119,185,186,189],{},[122,187,188],{},"✂️ 簡潔清晰","：避免專業術語，平均有效提示約21詞",[119,191,192,195],{},[122,193,194],{},"🔁 迭代優化","：通過對話逐步精煉結果",[119,197,198,201],{},[122,199,200],{},"📂 活用文件","：整合 Google Drive\u002FDocs 內容",[119,203,204,207],{},[122,205,206],{},"✍️ 提示編輯","：用「Make this a power prompt:」優化原始提示",[112,209,210],{"id":210},"關鍵應用場景",[212,213,214],"h3",{"id":214},"行政支援",[170,216,217,223],{},[119,218,219,220],{},"會議議程：",[130,221,222],{},"Plan a 3-day offsite with team bonding activities",[119,224,225,226],{},"郵件管理：",[130,227,228],{},"Summarize emails from [manager] last week",[212,230,231],{"id":231},"客戶服務",[170,233,234,240],{},[119,235,236,237],{},"客訴處理：",[130,238,239],{},"Draft empathetic response for damaged goods complaint",[119,241,242,243],{},"自助資源：",[130,244,245],{},"Create \"Resolve Common Issues\" self-service guide",[212,247,248],{"id":248},"高管應用",[170,250,251,257],{},[119,252,253,254],{},"簡報製作：",[130,255,256],{},"Generate investor pitch outline for [product] launch",[119,258,259,260],{},"趨勢分析：",[130,261,262],{},"Summarize top 5 emerging tech trends in [industry]",[212,264,265],{"id":265},"行銷創作",[170,267,268,274],{},[119,269,270,271],{},"內容生成：",[130,272,273],{},"Write 3 social posts about [product] for [audience]",[119,275,276,277],{},"視覺設計：",[130,278,279],{},"Create retro-cool logo for coffee\u002Fgaming cafe",[212,281,282],{"id":282},"專案管理",[170,284,285,291],{},[119,286,287,288],{},"追蹤系統：",[130,289,290],{},"Create issue tracker with status\u002Fowner\u002Factions",[119,292,293,294],{},"會議摘要：",[130,295,296],{},"Extract action items from meeting transcript",[112,298,299],{"id":299},"進階提示技巧",[170,301,302,311,319,327],{},[119,303,304,307,308],{},[122,305,306],{},"角色扮演","：",[130,309,310],{},"You are head of creative at ad agency...",[119,312,313,307,316],{},[122,314,315],{},"輸出限制",[130,317,318],{},"Keep responses under 100 words",[119,320,321,307,324],{},[122,322,323],{},"語調控制",[130,325,326],{},"Use formal tone for executive communication",[119,328,329,307,332],{},[122,330,331],{},"迭代優化",[130,333,334],{},"Refine previous response to be more data-driven",[108,336,337],{},[338,339,343],"a",{"href":340,"rel":341},"https:\u002F\u002Fservices.google.com\u002Ffh\u002Ffiles\u002Fmisc\u002Fgemini-for-google-workspace-prompting-guide-101.pdf",[342],"nofollow","獲取完整指南",{"title":345,"searchDepth":346,"depth":346,"links":347},"",2,[348,349,350,358],{"id":114,"depth":346,"text":114},{"id":168,"depth":346,"text":168},{"id":210,"depth":346,"text":210,"children":351},[352,354,355,356,357],{"id":214,"depth":353,"text":214},3,{"id":231,"depth":353,"text":231},{"id":248,"depth":353,"text":248},{"id":265,"depth":353,"text":265},{"id":282,"depth":353,"text":282},{"id":299,"depth":346,"text":299},"\u002Fimages\u002Fblog\u002Fgemini-workspace-guide.webp","2025-06-05","把 Google Workspace 裡 Gemini 的提示技巧整理成可直接照抄的模板：角色設定、上下文邊界、輸出格式，以及最常見的四種失敗模式。",false,"md","zh-TW",{},true,"\u002Fblog\u002Fzh-tw\u002Fgemini-for-workspace",{"title":102,"description":361},"gemini-for-workspace","blog\u002Fzh-TW\u002Fgemini-for-workspace",[372,44],"gemini",null,"xKxfdHg5Nuv0-FjsDBBBi6RgOp7EQVs73rZI2Y_9aVQ",[376,600],{"id":377,"title":378,"author":103,"body":379,"cover":586,"coverAlt":587,"date":588,"description":589,"draft":362,"extension":363,"featured":366,"lang":364,"meta":590,"navigation":366,"path":591,"seo":592,"slug":593,"stem":594,"tags":595,"translationKey":593,"updated":373,"__hash__":599},"blog\u002Fblog\u002Fzh-TW\u002Fhello-jecision.md","搬家記：把部落格從一個沒人找得到的網域搬回來",{"type":105,"value":380,"toc":578},[381,384,387,405,411,414,417,424,439,442,445,466,484,490,493,505,515,518,532,538,541,566,569,575],[112,382,383],{"id":383},"起因是一行原始碼",[108,385,386],{},"前陣子要把一篇舊文章轉給同事看，順手抓了頁面原始碼，然後愣住。",[108,388,389,392,393,396,397,400,401,404],{},[130,390,391],{},"\u003Chtml>"," 沒有 ",[130,394,395],{},"lang","。沒有 ",[130,398,399],{},"\u003Ctitle>","。沒有 description，沒有 og，沒有 canonical，沒有一行 JSON-LD。公式的部分更妙——原始碼裡躺著的是 ",[130,402,403],{},"\\operatorname{Attention}"," 這串字，要等瀏覽器把 JavaScript 跑完，人才看得到排版好的數學。",[108,406,407,408],{},"也就是說：",[122,409,410],{},"對搜尋引擎來說，那篇文章從來沒有存在過。",[108,412,413],{},"文章寫得再好，放在一個沒有標題、沒有摘要、沒有結構化資料的頁面上，它就只是一段沒有人索引的文字。",[112,415,416],{"id":416},"當初為什麼會變這樣",[108,418,419,420,423],{},"不是不用心，是",[122,421,422],{},"工具用得比它設計的方式更用力","。",[108,425,426,427,430,431,434,435,438],{},"當時為了讓公式能顯示，我們在 Markdown 裡塞了 ",[130,428,429],{},"\u003Cdiv class=\"latex-block\">","，然後在 ",[130,432,433],{},"onMounted"," 裡用 KaTeX 把它的 ",[130,436,437],{},"textContent"," 換成公式。瀏覽器上看起來完全正常，所以也沒有人覺得有問題。",[108,440,441],{},"問題在於這個做法把兩件事綁在一起：內容要靠 JavaScript 才成立，而 SEO 需要的是「不跑 JavaScript 也成立」。",[112,443,444],{"id":444},"搬家的三個決定",[108,446,447,450,451,454,455,458,459,454,462,465],{},[122,448,449],{},"一、內容搬家，不是版面搬家。"," 12 篇文章全部重新轉換，公式改寫成 ",[130,452,453],{},"$...$"," 與 ",[130,456,457],{},"$$...$$","，交給 ",[130,460,461],{},"remark-math",[130,463,464],{},"rehype-katex"," 在 build 時處理。現在公式是 HTML 的一部分，不需要任何前端 JavaScript。",[108,467,468,471,472,475,476,479,480,483],{},[122,469,470],{},"二、網址由資料決定，不由檔名決定。"," 舊站的檔名是 ",[130,473,474],{},"2604.04921v1.md","，結果網址變成 ",[130,477,478],{},"\u002Fen\u002Fblog\u002F04921v1","——數字前綴被吃掉，檔名和網址永遠對不起來。新站改成 frontmatter 裡寫 ",[130,481,482],{},"slug","，檔名再亂都不影響網址。",[108,485,486,489],{},[122,487,488],{},"三、舊網址一條都不能斷。"," 已經被 Google 記住的東西，不該因為我們重寫而消失。28 條 301 對照全部列出來，包含尾斜線的版本。",[112,491,492],{"id":492},"三個差點讓上線失敗的意外",[108,494,495,498,499,501,502,504],{},[122,496,497],{},"第一個：slug 被吃掉。"," 這件事是在舊站發現的——",[130,500,474],{}," 變成 ",[130,503,478],{},"。如果沒有先抓一次線上頁面，我們會以為搬家只是複製檔案。",[108,506,507,510,511,514],{},[122,508,509],{},"第二個：hreflang 指到不存在的頁面。"," 新站預設會幫每個語系產生 alternate 連結，但只有中文版的文章，英文連結就是一個 404。跑 ",[130,512,513],{},"nuxt generate"," 的時候 prerender 直接掛掉，錯誤訊息長得像「Article not found，linked from \u002Fblog\u002Fxxx」。",[108,516,517],{},"解法不是關掉檢查，而是讓每一頁自己宣告「我實際有哪些語系版本」。只有真的存在的中英版本，才會出現在 hreflang 裡。",[108,519,520,527,528,531],{},[122,521,522,523,526],{},"第三個：",[130,524,525],{},"\u002Fsitemap.xml"," 是 HTML。"," 這件事最陰險。build 成功、檔案存在、打開也有內容——但它是一個 ",[130,529,530],{},"\u003Cmeta http-equiv=\"refresh\">"," 的轉址頁，不是 XML。Google 會直接判定 sitemap 無效。",[108,533,534,535,537],{},"後來在 build 後加了一步，把 sitemap index 的內容直接寫成 ",[130,536,525],{},"，才真的能提交。",[112,539,540],{"id":540},"現在的樣子",[170,542,543,546,553,560],{},[119,544,545],{},"公式在伺服器端就排版完成，原始碼裡有 MathML",[119,547,548,549,552],{},"每一頁都有 title、description、canonical、hreflang、og，文章另有 ",[130,550,551],{},"BlogPosting"," 結構化資料",[119,554,555,556,559],{},"RSS、",[130,557,558],{},"llms.txt","、sitemap、301 對照都有",[119,561,562,563,565],{},"還寫了一支 ",[130,564,20],{}," 腳本，build 完直接檢查 25 個頁面的 SEO 與壞連結。目前是 0 錯誤 0 警告",[112,567,568],{"id":568},"一句話總結",[108,570,571,572,423],{},"搬家最花時間的不是搬，是",[122,573,574],{},"確認搬過去的東西真的還在",[108,576,577],{},"我們的做法是：把「應該要有」的東西寫成檢查，讓它每次 build 都自己驗一遍。人會忘記，腳本不會。",{"title":345,"searchDepth":346,"depth":346,"links":579},[580,581,582,583,584,585],{"id":383,"depth":346,"text":383},{"id":416,"depth":346,"text":416},{"id":444,"depth":346,"text":444},{"id":492,"depth":346,"text":492},{"id":540,"depth":346,"text":540},{"id":568,"depth":346,"text":568},"\u002Fimages\u002Fblog\u002Fhello-jecision.svg","從臨時網域搬回品牌網域的示意圖","2026-10-23","舊站的每一篇文章，原始碼裡都沒有 title、沒有 description、沒有 canonical，公式還是純文字。這篇記錄我們把部落格搬回 jecision.com 的過程，以及三個差點讓上線失敗的意外。",{},"\u002Fblog\u002Fzh-tw\u002Fhello-jecision",{"title":378,"description":589},"hello-jecision","blog\u002Fzh-TW\u002Fhello-jecision",[596,597,598],"nuxt","seo","重構","eMzmxLsypk5GpqCf6q2_9_s4WWIcInwgrCKPRumQDZc",{"id":601,"title":602,"author":103,"body":603,"cover":5281,"coverAlt":5282,"date":5283,"description":5284,"draft":362,"extension":363,"featured":362,"lang":364,"meta":5285,"navigation":366,"path":5286,"seo":5287,"slug":5288,"stem":5289,"tags":5290,"translationKey":5288,"updated":5294,"__hash__":5295},"blog\u002Fblog\u002Fzh-TW\u002Fattention-as-kernel.md","Attention 其實是一個核平滑器",{"type":105,"value":604,"toc":5273},[605,608,611,614,617,1013,1370,1404,2345,2564,2780,3324,3327,3330,3333,3339,3524,4164,4284,4663,4666,4669,4675,5101,5104,5107,5222,5253,5256,5259,5266,5269],[112,606,607],{"id":607},"一句話讓我想了很久",[108,609,610],{},"「Attention 就是一個核平滑器。」",[108,612,613],{},"第一次看到這句話的時候我以為是某種比喻，畢竟「核方法」聽起來像是 SVM 那個年代的事，跟 Transformer 沒什麼關係。後來自己把公式展開一次，才發現它不是在打比方。",[112,615,616],{"id":616},"把公式拆開",[108,618,619,620,759,760,860,861,1012],{},"給定查詢矩陣 ",[621,622,625,670],"span",{"className":623},[624],"katex",[621,626,629],{"className":627},[628],"katex-mathml",[630,631,633],"math",{"xmlns":632},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[634,635,636,665],"semantics",{},[637,638,639,643,647],"mrow",{},[640,641,642],"mi",{},"Q",[644,645,646],"mo",{},"∈",[648,649,650,654],"msup",{},[640,651,653],{"mathvariant":652},"double-struck","R",[637,655,656,659,662],{},[640,657,658],{},"n",[644,660,661],{},"×",[640,663,664],{},"d",[666,667,669],"annotation",{"encoding":668},"application\u002Fx-tex","Q \\in \\mathbb{R}^{n \\times 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與值矩陣 ",[621,862,864,899],{"className":863},[624],[621,865,867],{"className":866},[628],[630,868,869],{"xmlns":632},[634,870,871,896],{},[637,872,873,876,878],{},[640,874,875],{},"V",[644,877,646],{},[648,879,880,882],{},[640,881,653],{"mathvariant":652},[637,883,884,886,888],{},[640,885,785],{},[644,887,661],{},[889,890,891,893],"msub",{},[640,892,664],{},[640,894,895],{},"v",[666,897,898],{"encoding":668},"V \\in \\mathbb{R}^{m \\times 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dot-product attention 是",[621,1014,1017],{"className":1015},[1016],"katex-display",[621,1018,1020,1100],{"className":1019},[624],[621,1021,1023],{"className":1022},[628],[630,1024,1026],{"xmlns":632,"display":1025},"block",[634,1027,1028,1097],{},[637,1029,1030,1034,1037,1041,1043,1046,1048,1050,1052,1055,1058,1061,1063,1067,1092,1094],{},[640,1031,1033],{"mathvariant":1032},"normal","Attn",[644,1035,1036],{},"⁡",[644,1038,1040],{"stretchy":1039},"false","(",[640,1042,642],{},[644,1044,1045],{"separator":674},",",[640,1047,774],{},[644,1049,1045],{"separator":674},[640,1051,875],{},[644,1053,1054],{"stretchy":1039},")",[644,1056,1057],{},"=",[640,1059,1060],{"mathvariant":1032},"softmax",[644,1062,1036],{},[1064,1065,1066],"mtext",{}," ⁣",[637,1068,1069,1071,1090],{},[644,1070,1040],{"fence":674},[1072,1073,1074,1085],"mfrac",{},[637,1075,1076,1078],{},[640,1077,642],{},[648,1079,1080,1082],{},[640,1081,774],{},[640,1083,1084],{"mathvariant":1032},"⊤",[1086,1087,1088],"msqrt",{},[640,1089,664],{},[644,1091,1054],{"fence":674},[640,1093,875],{},[640,1095,1096],{"mathvariant":1032},".",[666,1098,1099],{"encoding":668},"\\operatorname{Attn}(Q, 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",[621,1374,1376,1390],{"className":1375},[624],[621,1377,1379],{"className":1378},[628],[630,1380,1381],{"xmlns":632},[634,1382,1383,1388],{},[637,1384,1385],{},[640,1386,1387],{},"i",[666,1389,1387],{"encoding":668},[621,1391,1393],{"className":1392,"ariaHidden":674},[673],[621,1394,1396,1400],{"className":1395},[678],[621,1397],{"className":1398,"style":1399},[682],"height:0.6595em;",[621,1401,1387],{"className":1402},[687,688]," 個輸出向量是",[621,1405,1407],{"className":1406},[1016],[621,1408,1410,1550],{"className":1409},[624],[621,1411,1413],{"className":1412},[628],[630,1414,1415],{"xmlns":632,"display":1025},[634,1416,1417,1547],{},[637,1418,1419,1426,1428,1545],{},[889,1420,1421,1424],{},[640,1422,1423],{},"o",[640,1425,1387],{},[644,1427,1057],{},[1072,1429,1430,1495],{},[637,1431,1432,1451,1454,1456,1458,1489],{},[1433,1434,1435,1438,1449],"munderover",{},[644,1436,1437],{},"∑",[637,1439,1440,1443,1445],{},[640,1441,1442],{},"j",[644,1444,1057],{},[1446,1447,1448],"mn",{},"1",[640,1450,785],{},[640,1452,1453],{},"exp",[644,1455,1036],{},[1064,1457,1066],{},[637,1459,1460,1462,1487],{},[644,1461,1040],{"fence":674},[1072,1463,1464,1483],{},[637,1465,1466,1476],{},[1467,1468,1469,1472,1474],"msubsup",{},[640,1470,1471],{},"q",[640,1473,1387],{},[640,1475,1084],{"mathvariant":1032},[889,1477,1478,1481],{},[640,1479,1480],{},"k",[640,1482,1442],{},[1086,1484,1485],{},[640,1486,664],{},[644,1488,1054],{"fence":674},[889,1490,1491,1493],{},[640,1492,895],{},[640,1494,1442],{},[637,1496,1497,1511,1513,1515,1517],{},[1433,1498,1499,1501,1509],{},[644,1500,1437],{},[637,1502,1503,1505,1507],{},[640,1504,1442],{},[644,1506,1057],{},[1446,1508,1448],{},[640,1510,785],{},[640,1512,1453],{},[644,1514,1036],{},[1064,1516,1066],{},[637,1518,1519,1521,1543],{},[644,1520,1040],{"fence":674},[1072,1522,1523,1539],{},[637,1524,1525,1533],{},[1467,1526,1527,1529,1531],{},[640,1528,1471],{},[640,1530,1387],{},[640,1532,1084],{"mathvariant":1032},[889,1534,1535,1537],{},[640,1536,1480],{},[640,1538,1442],{},[1086,1540,1541],{},[640,1542,664],{},[644,1544,1054],{"fence":674},[640,1546,1096],{"mathvariant":1032},[666,1548,1549],{"encoding":668},"o_i = \\frac{\\sum_{j=1}^{m} \\exp\\!\\left(\\frac{q_i^{\\top} k_j}{\\sqrt{d}}\\right) v_j}{\\sum_{j=1}^{m} \\exp\\!\\left(\\frac{q_i^{\\top} k_j}{\\sqrt{d}}\\right)} 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",[621,2349,2351,2369],{"className":2350},[624],[621,2352,2354],{"className":2353},[628],[630,2355,2356],{"xmlns":632},[634,2357,2358,2366],{},[637,2359,2360],{},[889,2361,2362,2364],{},[640,2363,895],{},[640,2365,1442],{},[666,2367,2368],{"encoding":668},"v_j",[621,2370,2372],{"className":2371,"ariaHidden":674},[673],[621,2373,2375,2379],{"className":2374},[678],[621,2376],{"className":2377,"style":2378},[682],"height:0.7167em;vertical-align:-0.2861em;",[621,2380,2382,2385],{"className":2381},[687],[621,2383,895],{"className":2384,"style":997},[687,688],[621,2386,2388],{"className":2387},[718],[621,2389,2391,2411],{"className":2390},[722,974],[621,2392,2394,2408],{"className":2393},[726],[621,2395,2397],{"className":2396,"style":1578},[730],[621,2398,2399,2402],{"style":2305},[621,2400],{"className":2401,"style":738},[737],[621,2403,2405],{"className":2404},[742,743,744,745],[621,2406,1442],{"className":2407,"style":1685},[687,688,745],[621,2409,1002],{"className":2410},[1001],[621,2412,2414],{"className":2413},[726],[621,2415,2417],{"className":2416,"style":2324},[730],[621,2418],{}," 的加權和，權重是 ",[621,2421,2423,2441],{"className":2422},[624],[621,2424,2426],{"className":2425},[628],[630,2427,2428],{"xmlns":632},[634,2429,2430,2438],{},[637,2431,2432],{},[889,2433,2434,2436],{},[640,2435,1471],{},[640,2437,1387],{},[666,2439,2440],{"encoding":668},"q_i",[621,2442,2444],{"className":2443,"ariaHidden":674},[673],[621,2445,2447,2451],{"className":2446},[678],[621,2448],{"className":2449,"style":2450},[682],"height:0.625em;vertical-align:-0.1944em;",[621,2452,2454,2457],{"className":2453},[687],[621,2455,1471],{"className":2456,"style":997},[687,688],[621,2458,2460],{"className":2459},[718],[621,2461,2463,2483],{"className":2462},[722,974],[621,2464,2466,2480],{"className":2465},[726],[621,2467,2469],{"className":2468,"style":1578},[730],[621,2470,2471,2474],{"style":2305},[621,2472],{"className":2473,"style":738},[737],[621,2475,2477],{"className":2476},[742,743,744,745],[621,2478,1387],{"className":2479},[687,688,745],[621,2481,1002],{"className":2482},[1001],[621,2484,2486],{"className":2485},[726],[621,2487,2489],{"className":2488,"style":1600},[730],[621,2490],{},[621,2492,2494,2512],{"className":2493},[624],[621,2495,2497],{"className":2496},[628],[630,2498,2499],{"xmlns":632},[634,2500,2501,2509],{},[637,2502,2503],{},[889,2504,2505,2507],{},[640,2506,1480],{},[640,2508,1442],{},[666,2510,2511],{"encoding":668},"k_j",[621,2513,2515],{"className":2514,"ariaHidden":674},[673],[621,2516,2518,2522],{"className":2517},[678],[621,2519],{"className":2520,"style":2521},[682],"height:0.9805em;vertical-align:-0.2861em;",[621,2523,2525,2528],{"className":2524},[687],[621,2526,1480],{"className":2527,"style":1906},[687,688],[621,2529,2531],{"className":2530},[718],[621,2532,2534,2555],{"className":2533},[722,974],[621,2535,2537,2552],{"className":2536},[726],[621,2538,2540],{"className":2539,"style":1578},[730],[621,2541,2543,2546],{"style":2542},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[621,2544],{"className":2545,"style":738},[737],[621,2547,2549],{"className":2548},[742,743,744,745],[621,2550,1442],{"className":2551,"style":1685},[687,688,745],[621,2553,1002],{"className":2554},[1001],[621,2556,2558],{"className":2557},[726],[621,2559,2561],{"className":2560,"style":2324},[730],[621,2562],{}," 的相似度；左邊的分母只是把權重歸一化，讓它們加起來等於 1。",[108,2565,2566,2567,2779],{},"如果把 ",[621,2568,2570,2624],{"className":2569},[624],[621,2571,2573],{"className":2572},[628],[630,2574,2575],{"xmlns":632},[634,2576,2577,2621],{},[637,2578,2579,2582,2584,2586,2588,2590,2592,2594,2596,2598,2600],{},[640,2580,2581],{},"κ",[644,2583,1040],{"stretchy":1039},[640,2585,1471],{},[644,2587,1045],{"separator":674},[640,2589,1480],{},[644,2591,1054],{"stretchy":1039},[644,2593,1057],{},[640,2595,1453],{},[644,2597,1036],{},[1064,2599,1066],{},[637,2601,2602,2604,2610,2612,2615,2619],{},[644,2603,1040],{"fence":674},[648,2605,2606,2608],{},[640,2607,1471],{},[640,2609,1084],{"mathvariant":1032},[640,2611,1480],{},[640,2613,2614],{"mathvariant":1032},"\u002F",[1086,2616,2617],{},[640,2618,664],{},[644,2620,1054],{"fence":674},[666,2622,2623],{"encoding":668},"\\kappa(q, k) = \\exp\\!\\left(q^{\\top}k \u002F \\sqrt{d}\\right)",[621,2625,2627,2663],{"className":2626,"ariaHidden":674},[673],[621,2628,2630,2633,2636,2639,2642,2645,2648,2651,2654,2657,2660],{"className":2629},[678],[621,2631],{"className":2632,"style":1109},[682],[621,2634,2581],{"className":2635},[687,688],[621,2637,1040],{"className":2638},[1121],[621,2640,1471],{"className":2641,"style":997},[687,688],[621,2643,1045],{"className":2644},[1128],[621,2646],{"className":2647,"style":1132},[692],[621,2649,1480],{"className":2650,"style":1906},[687,688],[621,2652,1054],{"className":2653},[1148],[621,2655],{"className":2656,"style":693},[692],[621,2658,1057],{"className":2659},[697],[621,2661],{"className":2662,"style":693},[692],[621,2664,2666,2670,2673,2676,2679],{"className":2665},[678],[621,2667],{"className":2668,"style":2669},[682],"height:1.8em;vertical-align:-0.65em;",[621,2671,1453],{"className":2672},[1113],[621,2674],{"className":2675,"style":1174},[692],[621,2677],{"className":2678,"style":1132},[692],[621,2680,2682,2688,2720,2723,2726,2773],{"className":2681},[1181],[621,2683,2685],{"className":2684,"style":1186},[1121,1185],[621,2686,1040],{"className":2687},[1190,1740],[621,2689,2691,2694],{"className":2690},[687],[621,2692,1471],{"className":2693,"style":997},[687,688],[621,2695,2697],{"className":2696},[718],[621,2698,2700],{"className":2699},[722],[621,2701,2703],{"className":2702},[726],[621,2704,2706],{"className":2705,"style":707},[730],[621,2707,2708,2711],{"style":733},[621,2709],{"className":2710,"style":738},[737],[621,2712,2714],{"className":2713},[742,743,744,745],[621,2715,2717],{"className":2716},[687,745],[621,2718,1084],{"className":2719},[687,745],[621,2721,1480],{"className":2722,"style":1906},[687,688],[621,2724,2614],{"className":2725},[687],[621,2727,2729],{"className":2728},[687,1224],[621,2730,2732,2765],{"className":2731},[722,974],[621,2733,2735,2762],{"className":2734},[726],[621,2736,2738,2750],{"className":2737,"style":1234},[730],[621,2739,2741,2744],{"className":2740,"style":1239},[1238],[621,2742],{"className":2743,"style":1217},[737],[621,2745,2747],{"className":2746,"style":1246},[687],[621,2748,664],{"className":2749},[687,688],[621,2751,2752,2755],{"style":1252},[621,2753],{"className":2754,"style":1217},[737],[621,2756,2758],{"className":2757,"style":1260},[1259],[1262,2759,2760],{"xmlns":1264,"width":1265,"height":1266,"viewBox":1267,"preserveAspectRatio":1268},[1270,2761],{"d":1272},[621,2763,1002],{"className":2764},[1001],[621,2766,2768],{"className":2767},[726],[621,2769,2771],{"className":2770,"style":1282},[730],[621,2772],{},[621,2774,2776],{"className":2775,"style":1186},[1148,1185],[621,2777,1054],{"className":2778},[1190,1740]," 當成一個核函數，上面這一坨就是",[621,2781,2783],{"className":2782},[1016],[621,2784,2786,2876],{"className":2785},[624],[621,2787,2789],{"className":2788},[628],[630,2790,2791],{"xmlns":632,"display":1025},[634,2792,2793,2873],{},[637,2794,2795,2801,2803,2871],{},[889,2796,2797,2799],{},[640,2798,1423],{},[640,2800,1387],{},[644,2802,1057],{},[1072,2804,2805,2843],{},[637,2806,2807,2814,2816,2818,2824,2826,2832,2834,2837],{},[2808,2809,2810,2812],"munder",{},[644,2811,1437],{},[640,2813,1442],{},[640,2815,2581],{},[644,2817,1040],{"stretchy":1039},[889,2819,2820,2822],{},[640,2821,1471],{},[640,2823,1387],{},[644,2825,1045],{"separator":674},[889,2827,2828,2830],{},[640,2829,1480],{},[640,2831,1442],{},[644,2833,1054],{"stretchy":1039},[1064,2835,2836],{}," ",[889,2838,2839,2841],{},[640,2840,895],{},[640,2842,1442],{},[637,2844,2845,2851,2853,2855,2861,2863,2869],{},[2808,2846,2847,2849],{},[644,2848,1437],{},[640,2850,1442],{},[640,2852,2581],{},[644,2854,1040],{"stretchy":1039},[889,2856,2857,2859],{},[640,2858,1471],{},[640,2860,1387],{},[644,2862,1045],{"separator":674},[889,2864,2865,2867],{},[640,2866,1480],{},[640,2868,1442],{},[644,2870,1054],{"stretchy":1039},[644,2872,1045],{"separator":674},[666,2874,2875],{"encoding":668},"o_i = \\frac{\\sum_j \\kappa(q_i, k_j)\\, v_j}{\\sum_j \\kappa(q_i, k_j)} ,",[621,2877,2879,2934],{"className":2878,"ariaHidden":674},[673],[621,2880,2882,2885,2925,2928,2931],{"className":2881},[678],[621,2883],{"className":2884,"style":1559},[682],[621,2886,2888,2891],{"className":2887},[687],[621,2889,1423],{"className":2890},[687,688],[621,2892,2894],{"className":2893},[718],[621,2895,2897,2917],{"className":2896},[722,974],[621,2898,2900,2914],{"className":2899},[726],[621,2901,2903],{"className":2902,"style":1578},[730],[621,2904,2905,2908],{"style":1581},[621,2906],{"className":2907,"style":738},[737],[621,2909,2911],{"className":2910},[742,743,744,745],[621,2912,1387],{"className":2913},[687,688,745],[621,2915,1002],{"className":2916},[1001],[621,2918,2920],{"className":2919},[726],[621,2921,2923],{"className":2922,"style":1600},[730],[621,2924],{},[621,2926],{"className":2927,"style":693},[692],[621,2929,1057],{"className":2930},[697],[621,2932],{"className":2933,"style":693},[692],[621,2935,2937,2941,3321],{"className":2936},[678],[621,2938],{"className":2939,"style":2940},[682],"height:2.6976em;vertical-align:-1.1218em;",[621,2942,2944,2947,3318],{"className":2943},[687],[621,2945],{"className":2946},[1121,1197],[621,2948,2950],{"className":2949},[1072],[621,2951,2953,3309],{"className":2952},[722,974],[621,2954,2956,3306],{"className":2955},[726],[621,2957,2960,3108,3116],{"className":2958,"style":2959},[730],"height:1.5758em;",[621,2961,2963,2966],{"style":2962},"top:-2.314em;",[621,2964],{"className":2965,"style":1217},[737],[621,2967,2969,3010,3013,3016,3019,3059,3062,3065,3105],{"className":2968},[687],[621,2970,2972,2975],{"className":2971},[1113],[621,2973,1437],{"className":2974,"style":1656},[1113,1654,1655],[621,2976,2978],{"className":2977},[718],[621,2979,2981,3002],{"className":2980},[722,974],[621,2982,2984,2999],{"className":2983},[726],[621,2985,2988],{"className":2986,"style":2987},[730],"height:0.162em;",[621,2989,2990,2993],{"style":1672},[621,2991],{"className":2992,"style":738},[737],[621,2994,2996],{"className":2995},[742,743,744,745],[621,2997,1442],{"className":2998,"style":1685},[687,688,745],[621,3000,1002],{"className":3001},[1001],[621,3003,3005],{"className":3004},[726],[621,3006,3008],{"className":3007,"style":1716},[730],[621,3009],{},[621,3011],{"className":3012,"style":1132},[692],[621,3014,2581],{"className":3015},[687,688],[621,3017,1040],{"className":3018},[1121],[621,3020,3022,3025],{"className":3021},[687],[621,3023,1471],{"className":3024,"style":997},[687,688],[621,3026,3028],{"className":3027},[718],[621,3029,3031,3051],{"className":3030},[722,974],[621,3032,3034,3048],{"className":3033},[726],[621,3035,3037],{"className":3036,"style":1578},[730],[621,3038,3039,3042],{"style":2305},[621,3040],{"className":3041,"style":738},[737],[621,3043,3045],{"className":3044},[742,743,744,745],[621,3046,1387],{"className":3047},[687,688,745],[621,3049,1002],{"className":3050},[1001],[621,3052,3054],{"className":3053},[726],[621,3055,3057],{"className":3056,"style":1600},[730],[621,3058],{},[621,3060,1045],{"className":3061},[1128],[621,3063],{"className":3064,"style":1132},[692],[621,3066,3068,3071],{"className":3067},[687],[621,3069,1480],{"className":3070,"style":1906},[687,688],[621,3072,3074],{"className":3073},[718],[621,3075,3077,3097],{"className":3076},[722,974],[621,3078,3080,3094],{"className":3079},[726],[621,3081,3083],{"className":3082,"style":1578},[730],[621,3084,3085,3088],{"style":2542},[621,3086],{"className":3087,"style":738},[737],[621,3089,3091],{"className":3090},[742,743,744,745],[621,3092,1442],{"className":3093,"style":1685},[687,688,745],[621,3095,1002],{"className":3096},[1001],[621,3098,3100],{"className":3099},[726],[621,3101,3103],{"className":3102,"style":2324},[730],[621,3104],{},[621,3106,1054],{"className":3107},[1148],[621,3109,3110,3113],{"style":1287},[621,3111],{"className":3112,"style":1217},[737],[621,3114],{"className":3115,"style":1295},[1294],[621,3117,3119,3122],{"style":3118},"top:-3.8258em;",[621,3120],{"className":3121,"style":1217},[737],[621,3123,3125,3165,3168,3171,3174,3214,3217,3220,3260,3263,3266],{"className":3124},[687],[621,3126,3128,3131],{"className":3127},[1113],[621,3129,1437],{"className":3130,"style":1656},[1113,1654,1655],[621,3132,3134],{"className":3133},[718],[621,3135,3137,3157],{"className":3136},[722,974],[621,3138,3140,3154],{"className":3139},[726],[621,3141,3143],{"className":3142,"style":2987},[730],[621,3144,3145,3148],{"style":1672},[621,3146],{"className":3147,"style":738},[737],[621,3149,3151],{"className":3150},[742,743,744,745],[621,3152,1442],{"className":3153,"style":1685},[687,688,745],[621,3155,1002],{"className":3156},[1001],[621,3158,3160],{"className":3159},[726],[621,3161,3163],{"className":3162,"style":1716},[730],[621,3164],{},[621,3166],{"className":3167,"style":1132},[692],[621,3169,2581],{"className":3170},[687,688],[621,3172,1040],{"className":3173},[1121],[621,3175,3177,3180],{"className":3176},[687],[621,3178,1471],{"className":3179,"style":997},[687,688],[621,3181,3183],{"className":3182},[718],[621,3184,3186,3206],{"className":3185},[722,974],[621,3187,3189,3203],{"className":3188},[726],[621,3190,3192],{"className":3191,"style":1578},[730],[621,3193,3194,3197],{"style":2305},[621,3195],{"className":3196,"style":738},[737],[621,3198,3200],{"className":3199},[742,743,744,745],[621,3201,1387],{"className":3202},[687,688,745],[621,3204,1002],{"className":3205},[1001],[621,3207,3209],{"className":3208},[726],[621,3210,3212],{"className":3211,"style":1600},[730],[621,3213],{},[621,3215,1045],{"className":3216},[1128],[621,3218],{"className":3219,"style":1132},[692],[621,3221,3223,3226],{"className":3222},[687],[621,3224,1480],{"className":3225,"style":1906},[687,688],[621,3227,3229],{"className":3228},[718],[621,3230,3232,3252],{"className":3231},[722,974],[621,3233,3235,3249],{"className":3234},[726],[621,3236,3238],{"className":3237,"style":1578},[730],[621,3239,3240,3243],{"style":2542},[621,3241],{"className":3242,"style":738},[737],[621,3244,3246],{"className":3245},[742,743,744,745],[621,3247,1442],{"className":3248,"style":1685},[687,688,745],[621,3250,1002],{"className":3251},[1001],[621,3253,3255],{"className":3254},[726],[621,3256,3258],{"className":3257,"style":2324},[730],[621,3259],{},[621,3261,1054],{"className":3262},[1148],[621,3264],{"className":3265,"style":1132},[692],[621,3267,3269,3272],{"className":3268},[687],[621,3270,895],{"className":3271,"style":997},[687,688],[621,3273,3275],{"className":3274},[718],[621,3276,3278,3298],{"className":3277},[722,974],[621,3279,3281,3295],{"className":3280},[726],[621,3282,3284],{"className":3283,"style":1578},[730],[621,3285,3286,3289],{"style":2305},[621,3287],{"className":3288,"style":738},[737],[621,3290,3292],{"className":3291},[742,743,744,745],[621,3293,1442],{"className":3294,"style":1685},[687,688,745],[621,3296,1002],{"className":3297},[1001],[621,3299,3301],{"className":3300},[726],[621,3302,3304],{"className":3303,"style":2324},[730],[621,3305],{},[621,3307,1002],{"className":3308},[1001],[621,3310,3312],{"className":3311},[726],[621,3313,3316],{"className":3314,"style":3315},[730],"height:1.1218em;",[621,3317],{},[621,3319],{"className":3320},[1148,1197],[621,3322,1045],{"className":3323},[1128],[108,3325,3326],{},"——非參數回歸裡的 Nadaraya–Watson 估計。一模一樣。",[108,3328,3329],{},"差別只在於：這裡的「樣本」是模型自己學出來的，不是給定的資料集。",[112,3331,3332],{"id":3332},"知道這件事有什麼用",[108,3334,3335,3336,423],{},"不是為了數學上的優雅。是因為它會告訴你",[122,3337,3338],{},"哪裡可以砍",[108,3340,3341,3342,3372,3373,3523],{},"如果 ",[621,3343,3345,3359],{"className":3344},[624],[621,3346,3348],{"className":3347},[628],[630,3349,3350],{"xmlns":632},[634,3351,3352,3356],{},[637,3353,3354],{},[640,3355,2581],{},[666,3357,3358],{"encoding":668},"\\kappa",[621,3360,3362],{"className":3361,"ariaHidden":674},[673],[621,3363,3365,3369],{"className":3364},[678],[621,3366],{"className":3367,"style":3368},[682],"height:0.4306em;",[621,3370,2581],{"className":3371},[687,688]," 可以寫成有限維特徵映射的內積，也就是 ",[621,3374,3376,3424],{"className":3375},[624],[621,3377,3379],{"className":3378},[628],[630,3380,3381],{"xmlns":632},[634,3382,3383,3421],{},[637,3384,3385,3387,3389,3391,3393,3395,3397,3400,3403,3405,3407,3413,3415,3417,3419],{},[640,3386,2581],{},[644,3388,1040],{"stretchy":1039},[640,3390,1471],{},[644,3392,1045],{"separator":674},[640,3394,1480],{},[644,3396,1054],{"stretchy":1039},[644,3398,3399],{},"≈",[640,3401,3402],{},"ϕ",[644,3404,1040],{"stretchy":1039},[640,3406,1471],{},[648,3408,3409,3411],{},[644,3410,1054],{"stretchy":1039},[640,3412,1084],{"mathvariant":1032},[640,3414,3402],{},[644,3416,1040],{"stretchy":1039},[640,3418,1480],{},[644,3420,1054],{"stretchy":1039},[666,3422,3423],{"encoding":668},"\\kappa(q,k) \\approx \\phi(q)^{\\top}\\phi(k)",[621,3425,3427,3463],{"className":3426,"ariaHidden":674},[673],[621,3428,3430,3433,3436,3439,3442,3445,3448,3451,3454,3457,3460],{"className":3429},[678],[621,3431],{"className":3432,"style":1109},[682],[621,3434,2581],{"className":3435},[687,688],[621,3437,1040],{"className":3438},[1121],[621,3440,1471],{"className":3441,"style":997},[687,688],[621,3443,1045],{"className":3444},[1128],[621,3446],{"className":3447,"style":1132},[692],[621,3449,1480],{"className":3450,"style":1906},[687,688],[621,3452,1054],{"className":3453},[1148],[621,3455],{"className":3456,"style":693},[692],[621,3458,3399],{"className":3459},[697],[621,3461],{"className":3462,"style":693},[692],[621,3464,3466,3470,3473,3476,3479,3511,3514,3517,3520],{"className":3465},[678],[621,3467],{"className":3468,"style":3469},[682],"height:1.0991em;vertical-align:-0.25em;",[621,3471,3402],{"className":3472},[687,688],[621,3474,1040],{"className":3475},[1121],[621,3477,1471],{"className":3478,"style":997},[687,688],[621,3480,3482,3485],{"className":3481},[1148],[621,3483,1054],{"className":3484},[1148],[621,3486,3488],{"className":3487},[718],[621,3489,3491],{"className":3490},[722],[621,3492,3494],{"className":3493},[726],[621,3495,3497],{"className":3496,"style":707},[730],[621,3498,3499,3502],{"style":733},[621,3500],{"className":3501,"style":738},[737],[621,3503,3505],{"className":3504},[742,743,744,745],[621,3506,3508],{"className":3507},[687,745],[621,3509,1084],{"className":3510},[687,745],[621,3512,3402],{"className":3513},[687,688],[621,3515,1040],{"className":3516},[1121],[621,3518,1480],{"className":3519,"style":1906},[687,688],[621,3521,1054],{"className":3522},[1148],"，那麼",[621,3525,3527],{"className":3526},[1016],[621,3528,3530,3634],{"className":3529},[624],[621,3531,3533],{"className":3532},[628],[630,3534,3535],{"xmlns":632,"display":1025},[634,3536,3537,3631],{},[637,3538,3539,3545,3547,3629],{},[889,3540,3541,3543],{},[640,3542,1423],{},[640,3544,1387],{},[644,3546,3399],{},[1072,3548,3549,3593],{},[637,3550,3551,3553,3555,3561,3567,3573,3575,3577,3583,3585],{},[640,3552,3402],{},[644,3554,1040],{"stretchy":1039},[889,3556,3557,3559],{},[640,3558,1471],{},[640,3560,1387],{},[648,3562,3563,3565],{},[644,3564,1054],{"stretchy":1039},[640,3566,1084],{"mathvariant":1032},[2808,3568,3569,3571],{},[644,3570,1437],{},[640,3572,1442],{},[640,3574,3402],{},[644,3576,1040],{"stretchy":1039},[889,3578,3579,3581],{},[640,3580,1480],{},[640,3582,1442],{},[644,3584,1054],{"stretchy":1039},[1467,3586,3587,3589,3591],{},[640,3588,895],{},[640,3590,1442],{},[640,3592,1084],{"mathvariant":1032},[637,3594,3595,3597,3599,3605,3611,3617,3619,3621,3627],{},[640,3596,3402],{},[644,3598,1040],{"stretchy":1039},[889,3600,3601,3603],{},[640,3602,1471],{},[640,3604,1387],{},[648,3606,3607,3609],{},[644,3608,1054],{"stretchy":1039},[640,3610,1084],{"mathvariant":1032},[2808,3612,3613,3615],{},[644,3614,1437],{},[640,3616,1442],{},[640,3618,3402],{},[644,3620,1040],{"stretchy":1039},[889,3622,3623,3625],{},[640,3624,1480],{},[640,3626,1442],{},[644,3628,1054],{"stretchy":1039},[640,3630,1096],{"mathvariant":1032},[666,3632,3633],{"encoding":668},"o_i \\approx \\frac{\\phi(q_i)^{\\top} \\sum_j \\phi(k_j) v_j^{\\top}}{\\phi(q_i)^{\\top} \\sum_j \\phi(k_j)} .",[621,3635,3637,3693],{"className":3636,"ariaHidden":674},[673],[621,3638,3640,3644,3684,3687,3690],{"className":3639},[678],[621,3641],{"className":3642,"style":3643},[682],"height:0.6331em;vertical-align:-0.15em;",[621,3645,3647,3650],{"className":3646},[687],[621,3648,1423],{"className":3649},[687,688],[621,3651,3653],{"className":3652},[718],[621,3654,3656,3676],{"className":3655},[722,974],[621,3657,3659,3673],{"className":3658},[726],[621,3660,3662],{"className":3661,"style":1578},[730],[621,3663,3664,3667],{"style":1581},[621,3665],{"className":3666,"style":738},[737],[621,3668,3670],{"className":3669},[742,743,744,745],[621,3671,1387],{"className":3672},[687,688,745],[621,3674,1002],{"className":3675},[1001],[621,3677,3679],{"className":3678},[726],[621,3680,3682],{"className":3681,"style":1600},[730],[621,3683],{},[621,3685],{"className":3686,"style":693},[692],[621,3688,3399],{"className":3689},[697],[621,3691],{"className":3692,"style":693},[692],[621,3694,3696,3700,4161],{"className":3695},[678],[621,3697],{"className":3698,"style":3699},[682],"height:2.7967em;vertical-align:-1.1218em;",[621,3701,3703,3706,4158],{"className":3702},[687],[621,3704],{"className":3705},[1121,1197],[621,3707,3709],{"className":3708},[1072],[621,3710,3712,4150],{"className":3711},[722,974],[621,3713,3715,4147],{"className":3714},[726],[621,3716,3719,3902,3910],{"className":3717,"style":3718},[730],"height:1.6749em;",[621,3720,3721,3724],{"style":2962},[621,3722],{"className":3723,"style":1217},[737],[621,3725,3727,3730,3733,3773,3807,3810,3850,3853,3856,3859,3899],{"className":3726},[687],[621,3728,3402],{"className":3729},[687,688],[621,3731,1040],{"className":3732},[1121],[621,3734,3736,3739],{"className":3735},[687],[621,3737,1471],{"className":3738,"style":997},[687,688],[621,3740,3742],{"className":3741},[718],[621,3743,3745,3765],{"className":3744},[722,974],[621,3746,3748,3762],{"className":3747},[726],[621,3749,3751],{"className":3750,"style":1578},[730],[621,3752,3753,3756],{"style":2305},[621,3754],{"className":3755,"style":738},[737],[621,3757,3759],{"className":3758},[742,743,744,745],[621,3760,1387],{"className":3761},[687,688,745],[621,3763,1002],{"className":3764},[1001],[621,3766,3768],{"className":3767},[726],[621,3769,3771],{"className":3770,"style":1600},[730],[621,3772],{},[621,3774,3776,3779],{"className":3775},[1148],[621,3777,1054],{"className":3778},[1148],[621,3780,3782],{"className":3781},[718],[621,3783,3785],{"className":3784},[722],[621,3786,3788],{"className":3787},[726],[621,3789,3792],{"className":3790,"style":3791},[730],"height:0.7751em;",[621,3793,3795,3798],{"style":3794},"top:-2.989em;margin-right:0.05em;",[621,3796],{"className":3797,"style":738},[737],[621,3799,3801],{"className":3800},[742,743,744,745],[621,3802,3804],{"className":3803},[687,745],[621,3805,1084],{"className":3806},[687,745],[621,3808],{"className":3809,"style":1132},[692],[621,3811,3813,3816],{"className":3812},[1113],[621,3814,1437],{"className":3815,"style":1656},[1113,1654,1655],[621,3817,3819],{"className":3818},[718],[621,3820,3822,3842],{"className":3821},[722,974],[621,3823,3825,3839],{"className":3824},[726],[621,3826,3828],{"className":3827,"style":2987},[730],[621,3829,3830,3833],{"style":1672},[621,3831],{"className":3832,"style":738},[737],[621,3834,3836],{"className":3835},[742,743,744,745],[621,3837,1442],{"className":3838,"style":1685},[687,688,745],[621,3840,1002],{"className":3841},[1001],[621,3843,3845],{"className":3844},[726],[621,3846,3848],{"className":3847,"style":1716},[730],[621,3849],{},[621,3851],{"className":3852,"style":1132},[692],[621,3854,3402],{"className":3855},[687,688],[621,3857,1040],{"className":3858},[1121],[621,3860,3862,3865],{"className":3861},[687],[621,3863,1480],{"className":3864,"style":1906},[687,688],[621,3866,3868],{"className":3867},[718],[621,3869,3871,3891],{"className":3870},[722,974],[621,3872,3874,3888],{"className":3873},[726],[621,3875,3877],{"className":3876,"style":1578},[730],[621,3878,3879,3882],{"style":2542},[621,3880],{"className":3881,"style":738},[737],[621,3883,3885],{"className":3884},[742,743,744,745],[621,3886,1442],{"className":3887,"style":1685},[687,688,745],[621,3889,1002],{"className":3890},[1001],[621,3892,3894],{"className":3893},[726],[621,3895,3897],{"className":3896,"style":2324},[730],[621,3898],{},[621,3900,1054],{"className":3901},[1148],[621,3903,3904,3907],{"style":1287},[621,3905],{"className":3906,"style":1217},[737],[621,3908],{"className":3909,"style":1295},[1294],[621,3911,3912,3915],{"style":3118},[621,3913],{"className":3914,"style":1217},[737],[621,3916,3918,3921,3924,3964,3996,3999,4039,4042,4045,4048,4088,4091],{"className":3917},[687],[621,3919,3402],{"className":3920},[687,688],[621,3922,1040],{"className":3923},[1121],[621,3925,3927,3930],{"className":3926},[687],[621,3928,1471],{"className":3929,"style":997},[687,688],[621,3931,3933],{"className":3932},[718],[621,3934,3936,3956],{"className":3935},[722,974],[621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",[621,4168,4170,4193],{"className":4169},[624],[621,4171,4173],{"className":4172},[628],[630,4174,4175],{"xmlns":632},[634,4176,4177,4190],{},[637,4178,4179,4182,4184,4186,4188],{},[640,4180,4181],{},"O",[644,4183,1040],{"stretchy":1039},[640,4185,658],{},[640,4187,785],{},[644,4189,1054],{"stretchy":1039},[666,4191,4192],{"encoding":668},"O(nm)",[621,4194,4196],{"className":4195,"ariaHidden":674},[673],[621,4197,4199,4202,4206,4209,4213],{"className":4198},[678],[621,4200],{"className":4201,"style":1109},[682],[621,4203,4181],{"className":4204,"style":4205},[687,688],"margin-right:0.0278em;",[621,4207,1040],{"className":4208},[1121],[621,4210,4212],{"className":4211},[687,688],"nm",[621,4214,1054],{"className":4215},[1148]," 掉到 ",[621,4218,4220,4245],{"className":4219},[624],[621,4221,4223],{"className":4222},[628],[630,4224,4225],{"xmlns":632},[634,4226,4227,4242],{},[637,4228,4229,4231,4233,4235,4238,4240],{},[640,4230,4181],{},[644,4232,1040],{"stretchy":1039},[640,4234,658],{},[644,4236,4237],{},"+",[640,4239,785],{},[644,4241,1054],{"stretchy":1039},[666,4243,4244],{"encoding":668},"O(n + m)",[621,4246,4248,4272],{"className":4247,"ariaHidden":674},[673],[621,4249,4251,4254,4257,4260,4263,4266,4269],{"className":4250},[678],[621,4252],{"className":4253,"style":1109},[682],[621,4255,4181],{"className":4256,"style":4205},[687,688],[621,4258,1040],{"className":4259},[1121],[621,4261,658],{"className":4262},[687,688],[621,4264],{"className":4265,"style":911},[692],[621,4267,4237],{"className":4268},[755],[621,4270],{"className":4271,"style":911},[692],[621,4273,4275,4278,4281],{"className":4274},[678],[621,4276],{"className":4277,"style":1109},[682],[621,4279,785],{"className":4280},[687,688],[621,4282,1054],{"className":4283},[1148],[621,4285,4287],{"className":4286},[1016],[621,4288,4290,4395],{"className":4289},[624],[621,4291,4293],{"className":4292},[628],[630,4294,4295],{"xmlns":632,"display":1025},[634,4296,4297,4392],{},[4298,4299,4303,4342],"mtable",{"rowspacing":4300,"columnalign":4301,"columnspacing":4302},"0.25em","right left","0em",[4304,4305,4306,4316],"mtr",{},[4307,4308,4309],"mtd",{},[4310,4311,4313],"mstyle",{"scriptlevel":4312,"displaystyle":674},"0",[1064,4314,4315],{},"標準 attention",[4307,4317,4318],{},[4310,4319,4320],{"scriptlevel":4312,"displaystyle":674},[637,4321,4322,4324,4327,4330,4332,4334,4336,4338,4340],{},[637,4323],{},[644,4325,4326],{},":",[692,4328],{"width":4329},"1em",[640,4331,4181],{},[644,4333,1040],{"stretchy":1039},[640,4335,658],{},[640,4337,785],{},[640,4339,664],{},[644,4341,1054],{"stretchy":1039},[4304,4343,4344,4351],{},[4307,4345,4346],{},[4310,4347,4348],{"scriptlevel":4312,"displaystyle":674},[1064,4349,4350],{},"線性 attention",[4307,4352,4353],{},[4310,4354,4355],{"scriptlevel":4312,"displaystyle":674},[637,4356,4357,4359,4361,4363,4365,4367],{},[637,4358],{},[644,4360,4326],{},[692,4362],{"width":4329},[640,4364,4181],{},[1064,4366,1066],{},[637,4368,4369,4371,4373,4380,4382,4384,4390],{},[644,4370,1040],{"fence":674},[640,4372,658],{},[648,4374,4375,4377],{},[640,4376,664],{},[1446,4378,4379],{},"2",[644,4381,4237],{},[640,4383,785],{},[648,4385,4386,4388],{},[640,4387,664],{},[1446,4389,4379],{},[644,4391,1054],{"fence":674},[666,4393,4394],{"encoding":668},"\\begin{aligned}\n\\text{標準 attention} &: \\quad O(n m d) \\\\\n\\text{線性 attention} &: \\quad O\\!\\left(n d^2 + m d^2\\right)\n\\end{aligned}",[621,4396,4398],{"className":4397,"ariaHidden":674},[673],[621,4399,4401,4405],{"className":4400},[678],[621,4402],{"className":4403,"style":4404},[682],"height:2.7241em;vertical-align:-1.1121em;",[621,4406,4408],{"className":4407},[687],[621,4409,4411,4478],{"className":4410},[4298],[621,4412,4415],{"className":4413},[4414],"col-align-r",[621,4416,4418,4469],{"className":4417},[722,974],[621,4419,4421,4466],{"className":4420},[726],[621,4422,4425,4447],{"className":4423,"style":4424},[730],"height:1.6121em;",[621,4426,4428,4431],{"style":4427},"top:-3.7721em;",[621,4429],{"className":4430,"style":1217},[737],[621,4432,4434],{"className":4433},[687],[621,4435,4438,4443],{"className":4436},[687,4437],"text",[621,4439,4442],{"className":4440},[687,4441],"cjk_fallback","標準",[621,4444,4446],{"className":4445},[687]," attention",[621,4448,4450,4453],{"style":4449},"top:-2.2479em;",[621,4451],{"className":4452,"style":1217},[737],[621,4454,4456],{"className":4455},[687],[621,4457,4459,4463],{"className":4458},[687,4437],[621,4460,4462],{"className":4461},[687,4441],"線性",[621,4464,4446],{"className":4465},[687],[621,4467,1002],{"className":4468},[1001],[621,4470,4472],{"className":4471},[726],[621,4473,4476],{"className":4474,"style":4475},[730],"height:1.1121em;",[621,4477],{},[621,4479,4482],{"className":4480},[4481],"col-align-l",[621,4483,4485,4655],{"className":4484},[722,974],[621,4486,4488,4652],{"className":4487},[726],[621,4489,4491,4530],{"className":4490,"style":4424},[730],[621,4492,4493,4496],{"style":4427},[621,4494],{"className":4495,"style":1217},[737],[621,4497,4499,4502,4505,4508,4512,4515,4518,4521,4524,4527],{"className":4498},[687],[621,4500],{"className":4501},[687],[621,4503],{"className":4504,"style":693},[692],[621,4506,4326],{"className":4507},[697],[621,4509],{"className":4510,"style":4511},[692],"margin-right:1em;",[621,4513],{"className":4514,"style":693},[692],[621,4516,4181],{"className":4517,"style":4205},[687,688],[621,4519,1040],{"className":4520},[1121],[621,4522,4212],{"className":4523},[687,688],[621,4525,664],{"className":4526},[687,688],[621,4528,1054],{"className":4529},[1148],[621,4531,4532,4535],{"style":4449},[621,4533],{"className":4534,"style":1217},[737],[621,4536,4538,4541,4544,4547,4550,4553,4556,4559,4562],{"className":4537},[687],[621,4539],{"className":4540},[687],[621,4542],{"className":4543,"style":693},[692],[621,4545,4326],{"className":4546},[697],[621,4548],{"className":4549,"style":4511},[692],[621,4551],{"className":4552,"style":693},[692],[621,4554,4181],{"className":4555,"style":4205},[687,688],[621,4557],{"className":4558,"style":1174},[692],[621,4560],{"className":4561,"style":1132},[692],[621,4563,4565,4571,4574,4605,4608,4611,4614,4617,4646],{"className":4564},[1181],[621,4566,4568],{"className":4567,"style":1186},[1121,1185],[621,4569,1040],{"className":4570},[1190,993],[621,4572,658],{"className":4573},[687,688],[621,4575,4577,4580],{"className":4576},[687],[621,4578,664],{"className":4579},[687,688],[621,4581,4583],{"className":4582},[718],[621,4584,4586],{"className":4585},[722],[621,4587,4589],{"className":4588},[726],[621,4590,4593],{"className":4591,"style":4592},[730],"height:0.8641em;",[621,4594,4596,4599],{"style":4595},"top:-3.113em;margin-right:0.05em;",[621,4597],{"className":4598,"style":738},[737],[621,4600,4602],{"className":4601},[742,743,744,745],[621,4603,4379],{"className":4604},[687,745],[621,4606],{"className":4607,"style":911},[692],[621,4609,4237],{"className":4610},[755],[621,4612],{"className":4613,"style":911},[692],[621,4615,785],{"className":4616},[687,688],[621,4618,4620,4623],{"className":4619},[687],[621,4621,664],{"className":4622},[687,688],[621,4624,4626],{"className":4625},[718],[621,4627,4629],{"className":4628},[722],[621,4630,4632],{"className":4631},[726],[621,4633,4635],{"className":4634,"style":4592},[730],[621,4636,4637,4640],{"style":4595},[621,4638],{"className":4639,"style":738},[737],[621,4641,4643],{"className":4642},[742,743,744,745],[621,4644,4379],{"className":4645},[687,745],[621,4647,4649],{"className":4648,"style":1186},[1148,1185],[621,4650,1054],{"className":4651},[1190,993],[621,4653,1002],{"className":4654},[1001],[621,4656,4658],{"className":4657},[726],[621,4659,4661],{"className":4660,"style":4475},[730],[621,4662],{},[108,4664,4665],{},"這就是 linear attention 那一整家族在做的事。",[112,4667,4668],{"id":4668},"代價在分母",[108,4670,4671,4672],{},"這裡有個很容易被忽略的地方：",[122,4673,4674],{},"誤差最大的地方不是分子，是分母。",[108,4676,4677,4678,4910,4911,5100],{},"分子是「加權和」，近似得差一點，輸出只是稍微偏掉；分母是「歸一化常數」，它一錯，整個輸出會跟著縮放。序列越長，",[621,4679,4681,4727],{"className":4680},[624],[621,4682,4684],{"className":4683},[628],[630,4685,4686],{"xmlns":632},[634,4687,4688,4724],{},[637,4689,4690,4692,4694,4700,4706,4712,4714,4716,4722],{},[640,4691,3402],{},[644,4693,1040],{"stretchy":1039},[889,4695,4696,4698],{},[640,4697,1471],{},[640,4699,1387],{},[648,4701,4702,4704],{},[644,4703,1054],{"stretchy":1039},[640,4705,1084],{"mathvariant":1032},[889,4707,4708,4710],{},[644,4709,1437],{},[640,4711,1442],{},[640,4713,3402],{},[644,4715,1040],{"stretchy":1039},[889,4717,4718,4720],{},[640,4719,1480],{},[640,4721,1442],{},[644,4723,1054],{"stretchy":1039},[666,4725,4726],{"encoding":668},"\\phi(q_i)^{\\top}\\sum_j \\phi(k_j)",[621,4728,4730],{"className":4729,"ariaHidden":674},[673],[621,4731,4733,4737,4740,4743,4783,4815,4818,4858,4861,4864,4867,4907],{"className":4732},[678],[621,4734],{"className":4735,"style":4736},[682],"height:1.2849em;vertical-align:-0.4358em;",[621,4738,3402],{"className":4739},[687,688],[621,4741,1040],{"className":4742},[1121],[621,4744,4746,4749],{"className":4745},[687],[621,4747,1471],{"className":4748,"style":997},[687,688],[621,4750,4752],{"className":4751},[718],[621,4753,4755,4775],{"className":4754},[722,974],[621,4756,4758,4772],{"className":4757},[726],[621,4759,4761],{"className":4760,"style":1578},[730],[621,4762,4763,4766],{"style":2305},[621,4764],{"className":4765,"style":738},[737],[621,4767,4769],{"className":4768},[742,743,744,745],[621,4770,1387],{"className":4771},[687,688,745],[621,4773,1002],{"className":4774},[1001],[621,4776,4778],{"className":4777},[726],[621,4779,4781],{"className":4780,"style":1600},[730],[621,4782],{},[621,4784,4786,4789],{"className":4785},[1148],[621,4787,1054],{"className":4788},[1148],[621,4790,4792],{"className":4791},[718],[621,4793,4795],{"className":4794},[722],[621,4796,4798],{"className":4797},[726],[621,4799,4801],{"className":4800,"style":707},[730],[621,4802,4803,4806],{"style":733},[621,4804],{"className":4805,"style":738},[737],[621,4807,4809],{"className":4808},[742,743,744,745],[621,4810,4812],{"className":4811},[687,745],[621,4813,1084],{"className":4814},[687,745],[621,4816],{"className":4817,"style":1132},[692],[621,4819,4821,4824],{"className":4820},[1113],[621,4822,1437],{"className":4823,"style":1656},[1113,1654,1655],[621,4825,4827],{"className":4826},[718],[621,4828,4830,4850],{"className":4829},[722,974],[621,4831,4833,4847],{"className":4832},[726],[621,4834,4836],{"className":4835,"style":2987},[730],[621,4837,4838,4841],{"style":1672},[621,4839],{"className":4840,"style":738},[737],[621,4842,4844],{"className":4843},[742,743,744,745],[621,4845,1442],{"className":4846,"style":1685},[687,688,745],[621,4848,1002],{"className":4849},[1001],[621,4851,4853],{"className":4852},[726],[621,4854,4856],{"className":4855,"style":1716},[730],[621,4857],{},[621,4859],{"className":4860,"style":1132},[692],[621,4862,3402],{"className":4863},[687,688],[621,4865,1040],{"className":4866},[1121],[621,4868,4870,4873],{"className":4869},[687],[621,4871,1480],{"className":4872,"style":1906},[687,688],[621,4874,4876],{"className":4875},[718],[621,4877,4879,4899],{"className":4878},[722,974],[621,4880,4882,4896],{"className":4881},[726],[621,4883,4885],{"className":4884,"style":1578},[730],[621,4886,4887,4890],{"style":2542},[621,4888],{"className":4889,"style":738},[737],[621,4891,4893],{"className":4892},[742,743,744,745],[621,4894,1442],{"className":4895,"style":1685},[687,688,745],[621,4897,1002],{"className":4898},[1001],[621,4900,4902],{"className":4901},[726],[621,4903,4905],{"className":4904,"style":2324},[730],[621,4906],{},[621,4908,1054],{"className":4909},[1148]," 和真正的 ",[621,4912,4914,4952],{"className":4913},[624],[621,4915,4917],{"className":4916},[628],[630,4918,4919],{"xmlns":632},[634,4920,4921,4949],{},[637,4922,4923,4929,4931,4933,4939,4941,4947],{},[889,4924,4925,4927],{},[644,4926,1437],{},[640,4928,1442],{},[640,4930,2581],{},[644,4932,1040],{"stretchy":1039},[889,4934,4935,4937],{},[640,4936,1471],{},[640,4938,1387],{},[644,4940,1045],{"separator":674},[889,4942,4943,4945],{},[640,4944,1480],{},[640,4946,1442],{},[644,4948,1054],{"stretchy":1039},[666,4950,4951],{"encoding":668},"\\sum_j \\kappa(q_i,k_j)",[621,4953,4955],{"className":4954,"ariaHidden":674},[673],[621,4956,4958,4962,5002,5005,5008,5011,5051,5054,5057,5097],{"className":4957},[678],[621,4959],{"className":4960,"style":4961},[682],"height:1.1858em;vertical-align:-0.4358em;",[621,4963,4965,4968],{"className":4964},[1113],[621,4966,1437],{"className":4967,"style":1656},[1113,1654,1655],[621,4969,4971],{"className":4970},[718],[621,4972,4974,4994],{"className":4973},[722,974],[621,4975,4977,4991],{"className":4976},[726],[621,4978,4980],{"className":4979,"style":2987},[730],[621,4981,4982,4985],{"style":1672},[621,4983],{"className":4984,"style":738},[737],[621,4986,4988],{"className":4987},[742,743,744,745],[621,4989,1442],{"className":4990,"style":1685},[687,688,745],[621,4992,1002],{"className":4993},[1001],[621,4995,4997],{"className":4996},[726],[621,4998,5000],{"className":4999,"style":1716},[730],[621,5001],{},[621,5003],{"className":5004,"style":1132},[692],[621,5006,2581],{"className":5007},[687,688],[621,5009,1040],{"className":5010},[1121],[621,5012,5014,5017],{"className":5013},[687],[621,5015,1471],{"className":5016,"style":997},[687,688],[621,5018,5020],{"className":5019},[718],[621,5021,5023,5043],{"className":5022},[722,974],[621,5024,5026,5040],{"className":5025},[726],[621,5027,5029],{"className":5028,"style":1578},[730],[621,5030,5031,5034],{"style":2305},[621,5032],{"className":5033,"style":738},[737],[621,5035,5037],{"className":5036},[742,743,744,745],[621,5038,1387],{"className":5039},[687,688,745],[621,5041,1002],{"className":5042},[1001],[621,5044,5046],{"className":5045},[726],[621,5047,5049],{"className":5048,"style":1600},[730],[621,5050],{},[621,5052,1045],{"className":5053},[1128],[621,5055],{"className":5056,"style":1132},[692],[621,5058,5060,5063],{"className":5059},[687],[621,5061,1480],{"className":5062,"style":1906},[687,688],[621,5064,5066],{"className":5065},[718],[621,5067,5069,5089],{"className":5068},[722,974],[621,5070,5072,5086],{"className":5071},[726],[621,5073,5075],{"className":5074,"style":1578},[730],[621,5076,5077,5080],{"style":2542},[621,5078],{"className":5079,"style":738},[737],[621,5081,5083],{"className":5082},[742,743,744,745],[621,5084,1442],{"className":5085,"style":1685},[687,688,745],[621,5087,1002],{"className":5088},[1001],[621,5090,5092],{"className":5091},[726],[621,5093,5095],{"className":5094,"style":2324},[730],[621,5096],{},[621,5098,1054],{"className":5099},[1148]," 差得越多，輸出就越不可信。",[108,5102,5103],{},"所以我們在評估這類方法時，看的第一個數字不是整體 perplexity，而是分母的相對誤差。",[112,5105,5106],{"id":5106},"實務上的三個檢查點",[5108,5109,5110,5123],"table",{},[5111,5112,5113],"thead",{},[5114,5115,5116,5120],"tr",{},[5117,5118,5119],"th",{},"檢查",[5117,5121,5122],{},"為什麼",[5124,5125,5126,5135,5214],"tbody",{},[5114,5127,5128,5132],{},[5129,5130,5131],"td",{},"分母的相對誤差",[5129,5133,5134],{},"比分子更致命，因為它會整體縮放輸出",[5114,5136,5137,5211],{},[5129,5138,5139,5140],{},"特徵維度 ",[621,5141,5143,5161],{"className":5142},[624],[621,5144,5146],{"className":5145},[628],[630,5147,5148],{"xmlns":632},[634,5149,5150,5158],{},[637,5151,5152],{},[889,5153,5154,5156],{},[640,5155,664],{},[640,5157,3402],{},[666,5159,5160],{"encoding":668},"d_\\phi",[621,5162,5164],{"className":5163,"ariaHidden":674},[673],[621,5165,5167,5170],{"className":5166},[678],[621,5168],{"className":5169,"style":2521},[682],[621,5171,5173,5176],{"className":5172},[687],[621,5174,664],{"className":5175},[687,688],[621,5177,5179],{"className":5178},[718],[621,5180,5182,5203],{"className":5181},[722,974],[621,5183,5185,5200],{"className":5184},[726],[621,5186,5189],{"className":5187,"style":5188},[730],"height:0.3361em;",[621,5190,5191,5194],{"style":1581},[621,5192],{"className":5193,"style":738},[737],[621,5195,5197],{"className":5196},[742,743,744,745],[621,5198,3402],{"className":5199},[687,688,745],[621,5201,1002],{"className":5202},[1001],[621,5204,5206],{"className":5205},[726],[621,5207,5209],{"className":5208,"style":2324},[730],[621,5210],{},[5129,5212,5213],{},"太少則近似粗糙，太多則省不下計算",[5114,5215,5216,5219],{},[5129,5217,5218],{},"序列長度分佈",[5129,5220,5221],{},"短序列幾乎沒有收益，長序列才值得換",[5223,5224,5228],"pre",{"className":5225,"code":5226,"language":5227,"meta":345,"style":345},"language-python shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","# 概念示意：先把 K、V 的累加量算好\nkv = einsum(\"m d, m e -> d e\", phi(K), V)   # O(m d^2)\nz  = phi(K).sum(dim=0)                       # O(m d)\nout = einsum(\"n d, d e -> n e\", phi(Q), kv) \u002F einsum(\"n d, d -> n\", phi(Q), z)\n","python",[130,5229,5230,5237,5242,5247],{"__ignoreMap":345},[621,5231,5234],{"class":5232,"line":5233},"line",1,[621,5235,5236],{},"# 概念示意：先把 K、V 的累加量算好\n",[621,5238,5239],{"class":5232,"line":346},[621,5240,5241],{},"kv = einsum(\"m d, m e -> d e\", phi(K), V)   # O(m d^2)\n",[621,5243,5244],{"class":5232,"line":353},[621,5245,5246],{},"z  = phi(K).sum(dim=0)                       # O(m d)\n",[621,5248,5250],{"class":5232,"line":5249},4,[621,5251,5252],{},"out = einsum(\"n d, d e -> n e\", phi(Q), kv) \u002F einsum(\"n d, d -> n\", phi(Q), z)\n",[112,5254,5255],{"id":5255},"給下一個要調這個模型的人",[108,5257,5258],{},"如果你正在為長序列煩惱，我會建議先把 attention 當成核平滑器看一遍，再決定要不要換模型。",[108,5260,5261,5262,5265],{},"因為換成 linear attention 不是「更快的 attention」，而是",[122,5263,5264],{},"用特徵映射換掉精確的歸一化","——你付出的是準確度，不是免費的午餐。",[108,5267,5268],{},"知道自己在付什麼，比知道自己在用什麼重要。",[5270,5271,5272],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":345,"searchDepth":346,"depth":346,"links":5274},[5275,5276,5277,5278,5279,5280],{"id":607,"depth":346,"text":607},{"id":616,"depth":346,"text":616},{"id":3332,"depth":346,"text":3332},{"id":4668,"depth":346,"text":4668},{"id":5106,"depth":346,"text":5106},{"id":5255,"depth":346,"text":5255},"\u002Fimages\u002Fblog\u002Fattention-kernel.svg","Attention 與核函數對應關係的示意圖","2026-10-20","第一次看到「attention 是核方法」這個說法時，我以為那只是類比。自己推過一次才發現不是——而這件事直接決定了我們該在哪裡砍計算量。",{},"\u002Fblog\u002Fzh-tw\u002Fattention-as-kernel",{"title":602,"description":5284},"attention-as-kernel","blog\u002Fzh-TW\u002Fattention-as-kernel",[5291,5292,5293],"transformer","數學","推論","2026-10-22","ipCLaHTj0DVQiZoXlJ6DPzX7hl68udhNuMH4wa4gke8",1792775653123]