{"behavior":"degenerate_repetition","label_filter":null,"limit":10,"next_offset":33625,"offset":33615,"previous_offset":null,"rows":[{"assistant_initiates":false,"asst_text":"Berikut cara merekam layar di Windows:\n\n1. **Menggunakan Xbox Game Bar (bawaan Windows 10 dan 11):**\n   - Tekan tombol `Win + G` untuk membuka Xbox Game Bar.\n   - Pada bar yang muncul, klik tombol rekam (ikon bulat) atau tekan `Win + Alt + R` untuk mulai merekam layar.\n   - Untuk berhenti merekam, klik tombol stop pada bar atau tekan lagi `Win + Alt + R`.\n   - Video rekaman akan tersimpan di folder `Videos > Captures`.\n\n2. **Menggunakan aplikasi pihak ketiga:**\n   - Jika fitur bawaan dirasa kurang lengkap, kamu bisa menggunakan aplikasi seperti OBS Studio, Bandicam, atau Camtasia untuk merekam layar dengan fitur lebih lengkap.\n\n3. **Menggunakan PowerPoint:**\n   - Jika kamu memiliki Microsoft PowerPoint, ada fitur perekaman layar di menu `Insert > Screen Recording`.\n   - Pilih area layar yang ingin direkam, lalu klik tombol rekam.\n\nKalau mau saya bantu jelaskan langkah-langkah detail untuk salah satu cara di atas, silakan beri tahu ya!","behavior":"degenerate_repetition","conversation_hash":"75023d91016b1215c3cf32776305b10c","conversation_redacted":false,"conversation_toxic":false,"country":"United States","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"Indonesian","model":"gpt-4.1-mini-2025-04-14","n_chars":1047,"n_turns_in_conversation":1,"n_words":166,"source_row_offset":33615,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:06:58 GMT","turn_id":"0fc60c405cb5c940dec539b4","turn_index":0,"user_text":"User: bagaimana cara rekam layar di windows\nUser: bagaimana cara rekam layar di windows\nAssistant:"},{"assistant_initiates":false,"asst_text":"Jane will use \\(8 \\times 150 = 1200\\) grams of potatoes.","behavior":"degenerate_repetition","conversation_hash":"1bbf7da591220493c46a05276ca71e95","conversation_redacted":false,"conversation_toxic":false,"country":"United States","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":323,"n_turns_in_conversation":1,"n_words":56,"source_row_offset":33616,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:07:24 GMT","turn_id":"f8bc230b4265e3371ad3713d","turn_index":0,"user_text":"Assistant: Hello!\nUser: @spofoh Jane wants to make mashed potatoes for her family. She needs 8 potatoes to make enough. If each potato weighs 150 grams, how many grams of potatoes will she use? (You have five minutes to answer correctly, time starts now!)\nAssistant:"},{"assistant_initiates":false,"asst_text":"Tentu! Bisa jelaskan dulu \"itu\" yang kamu maksud apa, supaya saya bisa kasih alternatif atau cara lain yang sesuai?","behavior":"degenerate_repetition","conversation_hash":"b884d149cbe351519e8d981c88eeb62e","conversation_redacted":false,"conversation_toxic":false,"country":"France","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"Indonesian","model":"gpt-4.1-mini-2025-04-14","n_chars":206,"n_turns_in_conversation":1,"n_words":34,"source_row_offset":33617,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:07:34 GMT","turn_id":"5577546efd354bb61b90c7f9","turn_index":0,"user_text":"User: selain pake itu, adakah cara lain\nUser: selain pake itu, adakah cara lain\nAssistant:"},{"assistant_initiates":false,"asst_text":"Jane needs 8 potatoes, and each potato weighs 150 grams.\n\nTotal weight = 8 potatoes \u00d7 150 grams/potato = 1200 grams\n\nSo, Jane will use 1200 grams of potatoes.","behavior":"degenerate_repetition","conversation_hash":"44a85799a261c4e2f0414668e0ef03f5","conversation_redacted":false,"conversation_toxic":false,"country":"","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":455,"n_turns_in_conversation":1,"n_words":81,"source_row_offset":33618,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:07:58 GMT","turn_id":"f8a9585805191e9a6daecb3e","turn_index":0,"user_text":"Assistant: Hello!\nUser: @spofoh \udb40\udc00\u26a0\ufe0f You already have an existing quiz in progress! Here is the question in case you forgot: Jane wants to make mashed potatoes for her family. She needs 8 potatoes to make enough. If each potato weighs 150 grams, how many grams of potatoes will she use?\nAssistant:"},{"assistant_initiates":false,"asst_text":"Mendapatkan pasangan dengan kualitas seperti yang kamu inginkan memang bukan hal yang mudah, tapi bukan berarti tidak mungkin. Berikut beberapa tips yang bisa kamu pertimbangkan:\n\n1. **Jadilah versi terbaik dari dirimu sendiri**  \nFokuslah pada pengembangan diri, baik secara fisik, emosional, maupun intelektual. Wanita yang baik dan setia biasanya tertarik pada seseorang yang percaya diri dan memiliki tujuan hidup yang jelas.\n\n2. **Bangun hubungan berdasarkan kejujuran dan komunikasi**  \nKepercayaan adalah kunci utama dalam hubungan yang langgeng. Jangan berbohong atau menutupi sesuatu agar hubungan bisa berjalan dengan sehat.\n\n3. **Hargai kepribadian dan nilai-nilai dia**  \nUsahakan memahami dan menghargai apa yang penting bagi pasanganmu, termasuk caranya berinteraksi dengan orang lain (meskipun dia \"tidak friendly\").\n\n4. **Jangan fokus hanya pada fisik**  \nFisik memang bisa menarik pada awalnya, tapi kualitas seperti kesetiaan dan kepribadian jauh lebih penting untuk hubungan jangka panjang.\n\n5. **Bersabar dan jangan memaksa**  \nHubungan yang baik butuh waktu untuk tumbuh. Jangan terburu-buru atau memaksa seseorang untuk menjadi apa yang kamu inginkan.\n\nIngat, setiap orang unik dan tidak ada yang sempurna. Yang terpenting adalah kamu dan pasangan bisa saling menerima dan mendukung satu sama lain. Semoga sukses!","behavior":"degenerate_repetition","conversation_hash":"1edc9ad0c9a8818f7139eadb2655965f","conversation_redacted":false,"conversation_toxic":false,"country":"Australia","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"Indonesian","model":"gpt-4.1-mini-2025-04-14","n_chars":1564,"n_turns_in_conversation":1,"n_words":217,"source_row_offset":33619,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:08:29 GMT","turn_id":"e8b1a4a4fd98937c2bbd6791","turn_index":0,"user_text":"User: bagaimana cara mendapatkan wanita yang cantik, setia, gak mandang fisik, dan yang pasti tidak friendly\nUser: bagaimana cara mendapatkan wanita yang cantik, setia, gak mandang fisik, dan yang pasti tidak friendly\nAssistant:"},{"assistant_initiates":false,"asst_text":"significado Bro respeta slang espa\u00f1ol","behavior":"degenerate_repetition","conversation_hash":"e722e065b4ac56572e6478a850335b17","conversation_redacted":false,"conversation_toxic":false,"country":"Kenya","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":231,"n_turns_in_conversation":1,"n_words":37,"source_row_offset":33620,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:08:57 GMT","turn_id":"bb4650eca6021c57d9eeae01","turn_index":0,"user_text":"Provide only relevant keywords to facilitate an online search related to the user's message and remember that they should be few words and should not be repetitive: que significa el Bro respeta"},{"assistant_initiates":false,"asst_text":"La frase \"el Bro respeta\" es una expresi\u00f3n coloquial que proviene del ingl\u00e9s \"bro\" (hermano, amigo) y se usa en espa\u00f1ol para referirse a un amigo o compa\u00f1ero con confianza. \"Respeta\" aqu\u00ed significa que ese amigo merece respeto o que hay que respetar las normas o l\u00edmites establecidos por \u00e9l. En conjunto, \"el Bro respeta\" puede interpretarse como \"el amigo merece respeto\" o \"mi amigo tiene que ser respetado\". Tambi\u00e9n puede usarse en un contexto donde se enfatiza el respeto mutuo entre amigos o dentro de un grupo.\n\n\u00bfQuieres que te d\u00e9 ejemplos de uso o alguna explicaci\u00f3n m\u00e1s detallada?","behavior":"degenerate_repetition","conversation_hash":"22de45965559f0d1b9e2b46db33e5e1d","conversation_redacted":false,"conversation_toxic":false,"country":"China","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":1072,"n_turns_in_conversation":1,"n_words":177,"source_row_offset":33621,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:09:01 GMT","turn_id":"b27447123f3a3897a7220444","turn_index":0,"user_text":"Respond to this message in the appropriate language: que significa el Bro respeta\n\nRemember that you have access to the Google search engine and the ability to explore the internet. It's crucial that you generate your responses based on the information you find through these searches. It's important to note that sometimes the information obtained may not be complete; therefore, it's advisable that you try to complement and improve those parts that may have gaps or deficiencies: "},{"assistant_initiates":false,"asst_text":"It appears that the content you provided is a code or identifier (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) rather than readable text. Please provide the actual text or content you would like summarized.","behavior":"degenerate_repetition","conversation_hash":"01f5caf1bd42a79e1e818c7c9dac7460","conversation_redacted":false,"conversation_toxic":false,"country":"United States","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":372,"n_turns_in_conversation":1,"n_words":37,"source_row_offset":33622,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:09:37 GMT","turn_id":"c4e71bd3df4fbeae2f0ec09d","turn_index":0,"user_text":"Summarize the given content.\n\nSummarize the given content.\n\n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\n\n"},{"assistant_initiates":false,"asst_text":"Thanks for the great suggestions. However, we prefer to purchase individually for each batch of customers. Could you send me a simple price list for PR articles on English domains and local domains?","behavior":"degenerate_repetition","conversation_hash":"6daf605476797e43f99ef62ce25d0a13","conversation_redacted":false,"conversation_toxic":false,"country":"United Kingdom","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"English","model":"gpt-4.1-mini-2025-04-14","n_chars":2369,"n_turns_in_conversation":1,"n_words":382,"source_row_offset":33623,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:10:15 GMT","turn_id":"882078992c2e33604f1803ab","turn_index":0,"user_text":"Act as a spelling corrector, content editor, and text improver. ONLY return the rewritten text and nothing else.\n\nStrictly follow these rules:\n- Correct spelling, grammar, and punctuation errors in the given text\n- Enhance clarity and conciseness without altering the original meaning\n- Use the same language as the original text\n- Divide lengthy sentences into shorter, more readable ones\n- Eliminate unnecessary repetition while preserving important points\n- Prioritize active voice over passive voice for a more engaging tone\n- Opt for simpler, more accessible vocabulary when possible\n- ALWAYS ensure the original meaning and intention of the given text\n- ALWAYS maintain the original language of the text\n- ALWAYS maintain the existing tone of voice and style, e.g. formal, casual, polite, etc.\n- NEVER surround the improved text with quotes or any additional formatting\n- If the text is already well-written and requires no improvement, do not change the given text\n\nText to improve:\n\nAct as a spelling corrector, content editor, and text improver. ONLY return the rewritten text and nothing else.\n\nStrictly follow these rules:\n- Correct spelling, grammar, and punctuation errors in the given text\n- Enhance clarity and conciseness without altering the original meaning\n- Use the same language as the original text\n- Divide lengthy sentences into shorter, more readable ones\n- Eliminate unnecessary repetition while preserving important points\n- Prioritize active voice over passive voice for a more engaging tone\n- Opt for simpler, more accessible vocabulary when possible\n- ALWAYS ensure the original meaning and intention of the given text\n- ALWAYS maintain the original language of the text\n- ALWAYS maintain the existing tone of voice and style, e.g. formal, casual, polite, etc.\n- NEVER surround the improved text with quotes or any additional formatting\n- If the text is already well-written and requires no improvement, do not change the given text\n\nText to improve:\n\nThanks for the great suggestions. But we prefer to buy individually for each batch of customers. Can you send me a simple price list for PR articles of English domains and local domains?\n\n"},{"assistant_initiates":false,"asst_text":"**Hidden Markov Model\uff08\u9690\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff0cHMM\uff09**\u4e0e**Markov Model\uff08\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff09**\u7684\u533a\u522b\u4e3b\u8981\u4f53\u73b0\u5728\u89c2\u6d4b\u662f\u5426\u53ef\u89c1\u4ee5\u53ca\u6a21\u578b\u7ed3\u6784\u4e0a\u3002\u4e0b\u9762\u8be6\u7ec6\u89e3\u91ca\u4e24\u8005\u7684\u533a\u522b\uff1a\n\n---\n\n### 1. Markov Model\uff08\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff09\n\n- **\u5b9a\u4e49**\uff1a\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\u63cf\u8ff0\u7684\u662f\u4e00\u4e2a\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\uff0c\u5176\u6838\u5fc3\u662f\u72b6\u6001\u7684\u8f6c\u79fb\u6ee1\u8db3\u9a6c\u5c14\u53ef\u592b\u6027\u8d28\u2014\u2014\u672a\u6765\u72b6\u6001\u53ea\u4f9d\u8d56\u4e8e\u5f53\u524d\u72b6\u6001\uff0c\u800c\u4e0e\u8fc7\u53bb\u72b6\u6001\u65e0\u5173\u3002\n\n- **\u7279\u70b9**\uff1a\n  - \u72b6\u6001\u5e8f\u5217\u662f\u76f4\u63a5\u53ef\u89c1\u7684\uff08observable\uff09\u3002\n  - \u72b6\u6001\u8f6c\u79fb\u7531\u8f6c\u79fb\u6982\u7387\u77e9\u9635\u51b3\u5b9a\u3002\n  - \u4f8b\u5982\uff1a\\( X_1, X_2, \\ldots, X_t \\) \u662f\u4e00\u4e32\u72b6\u6001\uff0c\u6ee1\u8db3\n    \\[\n    P(X_t | X_{t-1}, \\ldots, X_1) = P(X_t | X_{t-1})\n    \\]\n  - \u5e94\u7528\u573a\u666f\uff1a\u5929\u6c14\u9884\u6d4b\uff08\u6674\u5929\u3001\u96e8\u5929\u7b49\u72b6\u6001\u53ef\u76f4\u63a5\u89c2\u6d4b\uff09\uff0c\u7b80\u5355\u7684\u968f\u673a\u8fc7\u7a0b\u6a21\u62df\u3002\n\n---\n\n### 2. Hidden Markov Model\uff08\u9690\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\uff09\n\n- **\u5b9a\u4e49**\uff1aHMM \u662f\u9a6c\u5c14\u53ef\u592b\u6a21\u578b\u7684\u6269\u5c55\u3002\u5728HMM\u4e2d\uff0c\u72b6\u6001\u5e8f\u5217\u662f**\u9690\u85cf\u7684\uff08\u4e0d\u53ef\u76f4\u63a5\u89c2\u6d4b\uff09**\uff0c\u6211\u4eec\u53ea\u80fd\u901a\u8fc7\u4e0e\u72b6\u6001\u76f8\u5173\u8054\u7684\u53ef\u89c2\u6d4b\u53d8\u91cf\uff08\u89c2\u6d4b\u5e8f\u5217\uff09\u6765\u95f4\u63a5\u63a8\u6d4b\u72b6\u6001\u3002\n\n- **\u6a21\u578b\u7ec4\u6210**\uff1a\n  - **\u9690\u85cf\u72b6\u6001\u5e8f\u5217**\uff1a\\( S_1, S_2, ..., S_T \\)\uff0c\u6ee1\u8db3\u9a6c\u5c14\u53ef\u592b\u6027\u8d28\uff0c\u4f46\u4e0d\u53ef\u76f4\u63a5\u89c2\u6d4b\u3002\n  - **\u89c2\u6d4b\u5e8f\u5217**\uff1a\\( O_1, O_2, ..., O_T \\)\uff0c\u6bcf\u4e2a\u89c2\u6d4b \\(O_t\\) \u4f9d\u8d56\u4e8e\u5f53\u524d\u9690\u85cf\u72b6\u6001 \\(S_t\\)\u3002\n  - \u72b6\u6001\u8f6c\u79fb\u6982\u7387\uff1a\\( P(S_t | S_{t-1}) \\)\n  - \u89c2\u6d4b\u6982\u7387\uff08\u53d1\u5c04\u6982\u7387\uff09\uff1a\\( P(O_t | S_t) \\)\n\n- **\u56fe\u793a\u7ed3\u6784**\uff1a\n\n\\[\nS_1 \\rightarrow S_2 \\rightarrow \\cdots \\rightarrow S_T\n\\]\n\\[\n\\downarrow \\quad \\downarrow \\quad \\downarrow\n\\]\n\\[\nO_1 \\quad O_2 \\quad \\cdots \\quad O_T\n\\]\n\n- **\u5173\u952e\u70b9**\uff1a\n  - \u72b6\u6001\u4e0d\u53ef\u76f4\u63a5\u89c2\u5bdf\uff0c\u53ea\u80fd\u901a\u8fc7\u89c2\u6d4b\u63a8\u65ad\u9690\u85cf\u72b6\u6001\u3002\n  - \u89e3\u51b3\u7684\u95ee\u9898\u901a\u5e38\u662f\u201c\u7ed9\u5b9a\u89c2\u6d4b\u5e8f\u5217\uff0c\u63a8\u65ad\u6700\u53ef\u80fd\u7684\u9690\u85cf\u72b6\u6001\u5e8f\u5217\u201d\u3002\n  - \u5e94\u7528\u5e7f\u6cdb\u4e8e\u8bed\u97f3\u8bc6\u522b\u3001\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3001\u751f\u7269\u4fe1\u606f\u5b66\u3001\u884c\u4e3a\u9884\u6d4b\u7b49\u3002\n\n---\n\n### 3. \u5173\u952e\u533a\u522b\u603b\u7ed3\n\n| \u7279\u5f81                | Markov Model                       | Hidden Markov Model (HMM)                       |\n|---------------------|----------------------------------|------------------------------------------------|\n| \u72b6\u6001\u662f\u5426\u53ef\u89c2\u6d4b       | \u72b6\u6001**\u76f4\u63a5\u53ef\u89c2\u6d4b**                 | \u72b6\u6001\u662f**\u9690\u85cf\u7684**\uff0c\u4e0d\u53ef\u76f4\u63a5\u89c2\u5bdf                    |\n| \u89c2\u6d4b\u6570\u636e             | \u5c31\u662f\u72b6\u6001\u672c\u8eab                     | \u89c2\u6d4b\u5e8f\u5217\u4f9d\u8d56\u4e8e\u9690\u85cf\u72b6\u6001                             |\n| \u6a21\u578b\u7ed3\u6784             | \u5355\u4e00\u7684\u72b6\u6001\u8f6c\u79fb\u94fe                 | \u9690\u85cf\u72b6\u6001\u94fe + \u89c2\u6d4b\u751f\u6210\u8fc7\u7a0b                         |\n| \u4e3b\u8981\u95ee\u9898             | \u9884\u6d4b\u4e0b\u4e00\u72b6\u6001\uff0c\u72b6\u6001\u5e8f\u5217\u5efa\u6a21       | \u72b6\u6001\u5e8f\u5217\u63a8\u65ad\u3001\u53c2\u6570\u4f30\u8ba1\u3001\u5e8f\u5217\u6982\u7387\u8ba1\u7b97             |\n| \u5e38\u89c1\u7b97\u6cd5             | \u65e0\u7279\u6b8a\u7b97\u6cd5                     | Viterbi \u7b97\u6cd5\uff08\u89e3\u9690\u72b6\u6001\u5e8f\u5217\uff09\uff0cBaum-Welch \u7b97\u6cd5\uff08\u53c2\u6570\u4f30\u8ba1\uff09 |\n| \u5e94\u7528\u573a\u666f             | \u7b80\u5355\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u6a21\u62df             | \u8bed\u97f3\u8bc6\u522b\u3001\u8bcd\u6027\u6807\u6ce8\u3001\u57fa\u56e0\u5e8f\u5217\u5206\u6790\u7b49\u590d\u6742\u5e8f\u5217\u5efa\u6a21   |\n\n---\n\n### 4. \u7b80\u5355\u793a\u610f\u4e3e\u4f8b\n\n- **Markov Model**: \u76f4\u63a5\u89c2\u5bdf\u201c\u6674\u5929\u201d\u3001\u201c\u96e8\u5929\u201d\uff0c\u7528\u72b6\u6001\u8f6c\u79fb\u6982\u7387\u9884\u6d4b\u5929\u6c14\u53d8\u5316\u3002\n\n- **HMM**: \u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5929\u6c14\uff0c\u4f46\u89c2\u6d4b\u5230\u4eba\u4eec\u643a\u5e26\u96e8\u4f1e\u4e0e\u5426\uff08\u89c2\u6d4b\u53d8\u91cf\uff09\uff0c\u6839\u636e\u643a\u5e26\u96e8\u4f1e\u7684\u6982\u7387\u6765\u63a8\u65ad\u53ef\u80fd\u7684\u5929\u6c14\u72b6\u6001\u3002\n\n---\n\n\u5982\u679c\u4f60\u60f3\uff0c\u6211\u8fd8\u53ef\u4ee5\u5e2e\u4f60\u8be6\u7ec6\u4ecb\u7ecdHMM\u7684\u4e09\u5927\u57fa\u672c\u95ee\u9898\uff08\u8bc4\u4f30\u3001\u89e3\u7801\u3001\u5b66\u4e60\uff09\u53ca\u5176\u7b97\u6cd5\u5b9e\u73b0\u3002","behavior":"degenerate_repetition","conversation_hash":"742b2e1a22cc1b3db7911fc3d893f87f","conversation_redacted":false,"conversation_toxic":false,"country":"United States","empty_output":false,"evidence_codes":[],"label":"absent","label_present":false,"label_qualified":false,"label_source":"Final dense release","language":"Chinese","model":"gpt-4.1-mini-2025-04-14","n_chars":9852,"n_turns_in_conversation":1,"n_words":1135,"source_row_offset":33624,"source_shard":"turns-00083.parquet","timestamp":"Tue, 24 Jun 2025 03:11:35 GMT","turn_id":"46282f919ebfe193fc6c54bd","turn_index":0,"user_text":"User: covariance matrix\u662f\u4ec0\u4e48\nAssistant:  ****Covariance matrix\uff08\u534f\u65b9\u5dee\u77e9\u9635\uff09**\u662f\u63cf\u8ff0\u591a\u7ef4\u968f\u673a\u53d8\u91cf\u5404\u4e2a\u5206\u91cf\u4e4b\u95f4\u7ebf\u6027\u5173\u7cfb\u7684\u4e00\u4e2a\u77e9\u9635\u3002\u5b83\u5728\u7edf\u8ba1\u5b66\u3001\u673a\u5668\u5b66\u4e60\u3001\u4fe1\u53f7\u5904\u7406\u7b49\u9886\u57df\u4e2d\u975e\u5e38\u91cd\u8981\u3002\n\n\u5177\u4f53\u6765\u8bf4\uff1a\n\n- \u5047\u8bbe\u4f60\u6709\u4e00\u4e2a\u968f\u673a\u5411\u91cf \\(\\mathbf{X} = (X_1, X_2, \\ldots, X_n)^T\\)\uff0c\u5176\u6bcf\u4e2a\u5206\u91cf\u90fd\u662f\u4e00\u4e2a\u968f\u673a\u53d8\u91cf\u3002\n- \u534f\u65b9\u5dee\u77e9\u9635\u5b9a\u4e49\u4e3a\uff1a\n  \\[\n  \\Sigma = \\mathrm{Cov}(\\mathbf{X}) = \\mathbb{E} \\left[ (\\mathbf{X} - \\mathbb{E}[\\mathbf{X}]) (\\mathbf{X} - \\mathbb{E}[\\mathbf{X}])^T \\right]\n  \\]\n- \u5176\u4e2d\uff0c\u77e9\u9635\u7684\u7b2c \\(i\\) \u884c\u7b2c \\(j\\) \u5217\u5143\u7d20 \\(\\sigma_{ij}\\) \u8868\u793a\u7b2c \\(i\\) \u4e2a\u53d8\u91cf\u4e0e\u7b2c \\(j\\) \u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\uff0c\u5373\uff1a\n  \\[\n  \\sigma_{ij} = \\mathrm{Cov}(X_i, X_j) = \\mathbb{E}[(X_i - \\mathbb{E}[X_i])(X_j - \\mathbb{E}[X_j])]\n  \\]\n\n**\u6027\u8d28\uff1a**\n- \u5bf9\u89d2\u7ebf\u4e0a\u5143\u7d20\u662f\u5404\u4e2a\u53d8\u91cf\u7684\u65b9\u5dee\uff0c\u5373 \\(\\sigma_{ii} = \\mathrm{Var}(X_i)\\)\u3002\n- \u534f\u65b9\u5dee\u77e9\u9635\u662f\u5bf9\u79f0\u77e9\u9635\uff0c\u56e0\u4e3a \\(\\mathrm{Cov}(X_i, X_j) = \\mathrm{Cov}(X_j, X_i)\\)\u3002\n- \u534f\u65b9\u5dee\u77e9\u9635\u662f\u534a\u6b63\u5b9a\u7684\uff0c\u4e14\u63cf\u8ff0\u4e86\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u4f9d\u8d56\u5173\u7cfb\u3002\n\n**\u5e94\u7528\u4e3e\u4f8b\uff1a**\n- \u5728\u4e3b\u6210\u5206\u5206\u6790\uff08PCA\uff09\u4e2d\uff0c\u901a\u8fc7\u5bf9\u534f\u65b9\u5dee\u77e9\u9635\u505a\u7279\u5f81\u503c\u5206\u89e3\uff0c\u53ef\u4ee5\u627e\u5230\u6570\u636e\u7684\u4e3b\u8981\u53d8\u5316\u65b9\u5411\u3002\n- \u5728\u591a\u5143\u6b63\u6001\u5206\u5e03\u4e2d\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u51b3\u5b9a\u4e86\u5206\u5e03\u7684\u5f62\u72b6\u548c\u65b9\u5411\u3002\n\n\u603b\u7ed3\u6765\u8bf4\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u662f\u53cd\u6620\u591a\u53d8\u91cf\u6570\u636e\u4e2d\u53d8\u91cf\u95f4\u76f8\u5173\u5173\u7cfb\u7684\u4e00\u4e2a\u57fa\u7840\u5de5\u5177\u3002\nUser: singular value of a n*p matrix\u4ec0\u4e48\u610f\u601d\uff1f\nAssistant:  ****Singular value\uff08\u5947\u5f02\u503c\uff09** \u662f\u7ebf\u6027\u4ee3\u6570\u4e2d\u63cf\u8ff0\u77e9\u9635\u7279\u6027\u7684\u91cd\u8981\u6570\u503c\u6982\u5ff5\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u4e00\u4e2a \\( n \\times p \\) \u77e9\u9635\u3002\u5177\u4f53\u89e3\u91ca\u5982\u4e0b\uff1a\n\n---\n\n### \u5947\u5f02\u503c\u7684\u5b9a\u4e49\n\n\u7ed9\u5b9a\u4e00\u4e2a\u77e9\u9635 \\( A \\)\uff08\u7ef4\u5ea6\u4e3a \\( n \\times p \\)\uff09\uff0c\u5b83\u7684\u5947\u5f02\u503c\u6765\u81ea\u4e8e\u8be5\u77e9\u9635\u7684**\u5947\u5f02\u503c\u5206\u89e3\uff08Singular Value Decomposition, SVD\uff09**\uff1a\n\n\\[\nA = U \\Sigma V^T\n\\]\n\n- \\(U\\) \u662f\u4e00\u4e2a \\( n \\times n \\) \u7684\u6b63\u4ea4\u77e9\u9635\uff08\u5373 \\( U^T U = I \\)\uff09\uff0c\u5176\u5217\u5411\u91cf\u662f \\( A A^T \\) \u7684\u7279\u5f81\u5411\u91cf\u3002\n- \\(V\\) \u662f\u4e00\u4e2a \\( p \\times p \\) \u7684\u6b63\u4ea4\u77e9\u9635\uff08\u5373 \\( V^T V = I \\)\uff09\uff0c\u5176\u5217\u5411\u91cf\u662f \\( A^T A \\) \u7684\u7279\u5f81\u5411\u91cf\u3002\n- \\(\\Sigma\\) \u662f\u4e00\u4e2a \\( n \\times p \\) \u7684\u77e9\u9635\uff0c\u4e14\u53ea\u6709\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\uff08\u5171 \\(\\min(n,p)\\) \u4e2a\uff09\u6709\u975e\u8d1f\u5b9e\u6570\uff0c\u8fd9\u4e9b\u975e\u8d1f\u5b9e\u6570\u5c31\u662f **\u5947\u5f02\u503c**\uff0c\u901a\u5e38\u8bb0\u4e3a \\(\\sigma_1, \\sigma_2, \\ldots, \\sigma_r\\)\uff0c\u5176\u4e2d \\(r = \\mathrm{rank}(A)\\)\u3002\n\n---\n\n### \u5947\u5f02\u503c\u7684\u542b\u4e49\n\n- \u6bcf\u4e2a\u5947\u5f02\u503c \\(\\sigma_i\\) \u662f \\( \\sqrt{\\lambda_i} \\)\uff0c\u5176\u4e2d \\(\\lambda_i\\) \u662f\u77e9\u9635 \\( A^T A \\)\uff08\u6216 \\( A A^T \\)\uff09\u7684\u975e\u96f6\u7279\u5f81\u503c\u3002\n\n- \u5947\u5f02\u503c\u63cf\u8ff0\u4e86\u77e9\u9635 \\( A \\) \u5728\u4e0d\u540c\u65b9\u5411\u4e0a\u7684\u4f38\u7f29\u4f5c\u7528\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff1a\n\n  - \u6700\u5927\u5947\u5f02\u503c \\(\\sigma_1\\) \u7b49\u4e8e\u77e9\u9635 \\( A \\) \u7684**\u8c31\u8303\u6570**\uff0c\u5373 \\( A \\) \u5bf9\u5411\u91cf\u7684\u6700\u5927\u62c9\u4f38\u56e0\u5b50\u3002\n  \n  - \u5947\u5f02\u503c\u8d8a\u5927\uff0c\u77e9\u9635\u5728\u90a3\u4e2a\u5947\u5f02\u5411\u91cf\u65b9\u5411\u4e0a\u7684\u4f5c\u7528\u8d8a\u5f3a\u70c8\u3002\n  \n- \u5728\u4fe1\u53f7\u5904\u7406\u3001\u6570\u636e\u538b\u7f29\u3001\u673a\u5668\u5b66\u4e60\u7b49\u9886\u57df\uff0c\u5947\u5f02\u503c\u7528\u4e8e\u5206\u6790\u77e9\u9635\u7684\u7ed3\u6784\u7279\u5f81\u3001\u964d\u7ef4\u3001\u566a\u58f0\u6291\u5236\u7b49\u3002\n\n---\n\n### \u603b\u7ed3\n\n- \u5bf9 \\( n \\times p \\) \u77e9\u9635\u800c\u8a00\uff0c**\u5947\u5f02\u503c**\u662f\u901a\u8fc7\u5947\u5f02\u503c\u5206\u89e3\u5f97\u5230\u7684\u4e00\u7ec4\u975e\u8d1f\u5b9e\u6570\uff0c\u6570\u91cf\u6700\u591a\u4e3a \\(\\min(n, p)\\) \u4e2a\u3002\n- \u5947\u5f02\u503c\u4f53\u73b0\u4e86\u77e9\u9635\u7684\u51e0\u4f55\u6027\u8d28\uff0c\u5982\u5bf9\u7a7a\u95f4\u7684\u4f38\u7f29\u6bd4\u4f8b\uff0c\u662f\u77e9\u9635\u7684\u201c\u56fa\u6709\u5c3a\u5ea6\u201d\u3002\n- \u5947\u5f02\u503c\u5728\u77e9\u9635\u8fd1\u4f3c\u3001\u6570\u636e\u964d\u7ef4\uff08\u5982PCA\uff09\u3001\u89e3\u7ebf\u6027\u7cfb\u7edf\u7b49\u8bf8\u591a\u9886\u57df\u90fd\u662f\u6838\u5fc3\u5de5\u5177\u3002\n\n---\n\n\u5982\u679c\u9700\u8981\uff0c\u6211\u4e5f\u53ef\u4ee5\u5e2e\u4f60\u8be6\u7ec6\u4ecb\u7ecd\u5947\u5f02\u503c\u5206\u89e3\u7684\u8ba1\u7b97\u6b65\u9aa4\u6216\u5e94\u7528\u793a\u4f8b\u3002\nUser: sequence\u548ctime series\u7684\u533a\u522b\u662f\u4ec0\u4e48\uff1f\nAssistant:  ****Sequence\uff08\u5e8f\u5217\uff09**\u548c**Time Series\uff08\u65f6\u95f4\u5e8f\u5217\uff09**\u867d\u7136\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u90fd\u6709\u201c\u6709\u5e8f\u6570\u636e\u201d\u7684\u542b\u4e49\uff0c\u4f46\u5b83\u4eec\u7684\u5b9a\u4e49\u3001\u5173\u6ce8\u70b9\u548c\u5e94\u7528\u573a\u666f\u6709\u660e\u663e\u533a\u522b\uff1a\n\n---\n\n### 1. \u5b9a\u4e49\u533a\u522b\n\n- **Sequence\uff08\u5e8f\u5217\uff09**  \n  \u6307\u6309\u7167\u67d0\u79cd\u987a\u5e8f\u6392\u5217\u7684\u6570\u636e\u9879\u96c6\u5408\uff0c\u5f3a\u8c03\u6570\u636e\u7684\u987a\u5e8f\u6027\uff0c\u4f46\u4e0d\u4e00\u5b9a\u6d89\u53ca\u65f6\u95f4\u7684\u6982\u5ff5\u3002\u5e8f\u5217\u4e2d\u7684\u5143\u7d20\u53ef\u4ee5\u662f\u6570\u5b57\u3001\u7b26\u53f7\u3001\u4e8b\u4ef6\u7b49\u3002  \n  \u4f8b\u5982\uff1a\u5b57\u7b26\u5e8f\u5217\uff08\u201cA\uff0cB\uff0cC\uff0cD\u201d\uff09\uff0c\u6570\u5b57\u5e8f\u5217\uff081\uff0c3\uff0c5\uff0c7\uff09\uff0c\u57fa\u56e0\u5e8f\u5217\uff0c\u7528\u6237\u70b9\u51fb\u5e8f\u5217\u7b49\u3002\n\n- **Time Series\uff08\u65f6\u95f4\u5e8f\u5217\uff09**  \n  \u662f\u4e00\u79cd\u7279\u6b8a\u7684\u5e8f\u5217\uff0c\u6bcf\u4e2a\u6570\u636e\u70b9\u90fd\u5bf9\u5e94\u4e00\u4e2a\u65f6\u95f4\u6233\uff0c\u5173\u6ce8\u6570\u636e\u968f\u65f6\u95f4\u53d8\u5316\u7684\u89c4\u5f8b\u3002\u65f6\u95f4\u5e8f\u5217\u5f3a\u8c03**\u65f6\u95f4\u7684\u987a\u5e8f\u548c\u65f6\u95f4\u95f4\u9694\u7684\u91cd\u8981\u6027**\u3002  \n  \u4f8b\u5982\uff1a\u6bcf\u5929\u7684\u80a1\u7968\u4ef7\u683c\u3001\u6bcf\u5c0f\u65f6\u7684\u6c14\u6e29\u3001\u6bcf\u5206\u949f\u7684\u5fc3\u8df3\u6570\u636e\u3002\n\n---\n\n### 2. \u5173\u6ce8\u70b9\u533a\u522b\n\n- **Sequence:**  \n  \u91cd\u70b9\u5728\u4e8e\u5143\u7d20\u4e4b\u95f4\u7684\u987a\u5e8f\u7ed3\u6784\uff0c\u901a\u5e38\u5173\u5fc3\u6392\u5217\u65b9\u5f0f\u3001\u4f9d\u8d56\u5173\u7cfb\u3001\u6a21\u5f0f\u5339\u914d\u7b49\u3002  \n  \u65f6\u95f4\u4e0d\u4e00\u5b9a\u662f\u5173\u952e\uff0c\u6709\u65f6\u53ea\u662f\u4e00\u4e2a\u5e8f\u5217\u6807\u8bc6\u800c\u5df2\u3002\n\n- **Time Series:**  \n  \u91cd\u70b9\u5728\u4e8e\u6570\u636e\u968f\u65f6\u95f4\u7684\u52a8\u6001\u53d8\u5316\uff0c\u5305\u62ec\u8d8b\u52bf\u3001\u5468\u671f\u6027\u3001\u5b63\u8282\u6027\u3001\u968f\u673a\u6ce2\u52a8\u7b49\u7279\u5f81\u3002\u65f6\u95f4\u95f4\u9694\u7684\u5747\u5300\u6027\u548c\u65f6\u95f4\u70b9\u7684\u5148\u540e\u987a\u5e8f\u975e\u5e38\u5173\u952e\u3002\n\n---\n\n### 3. \u5e94\u7528\u533a\u522b\n\n- **Sequence**  \n  \u5e38\u7528\u4e8e\u81ea\u7136\u8bed\u8a00\u5904\u7406\uff08\u4f8b\u5982\u6587\u672c\u5e8f\u5217\uff09\u3001\u57fa\u56e0\u5206\u6790\u3001\u79bb\u6563\u4e8b\u4ef6\u5efa\u6a21\u3001\u6392\u5e8f\u95ee\u9898\u7b49\u3002\n\n- **Time Series**  \n  \u5e38\u7528\u4e8e\u91d1\u878d\u5206\u6790\uff08\u80a1\u7968\u4ef7\u683c\u53d8\u52a8\uff09\u3001\u6c14\u8c61\u9884\u6d4b\uff08\u6e29\u5ea6\u53d8\u5316\uff09\u3001\u5de5\u4e1a\u76d1\u63a7\uff08\u8bbe\u5907\u4f20\u611f\u5668\u6570\u636e\uff09\u3001\u7ecf\u6d4e\u6570\u636e\u5206\u6790\u7b49\u3002\n\n---\n\n### \u603b\u7ed3\u8868\u683c\n\n| \u7ef4\u5ea6           | Sequence\uff08\u5e8f\u5217\uff09                    | Time Series\uff08\u65f6\u95f4\u5e8f\u5217\uff09                  |\n|----------------|----------------------------------|-----------------------------------------|\n| \u5b9a\u4e49           | \u6309\u987a\u5e8f\u6392\u5217\u7684\u6570\u636e\u9879\u96c6\u5408             | \u6bcf\u4e2a\u6570\u636e\u70b9\u90fd\u6709\u65f6\u95f4\u6233\u7684\u5e8f\u5217                |\n| \u65f6\u95f4\u56e0\u7d20       | \u4e0d\u4e00\u5b9a\u6d89\u53ca                      | \u5fc5\u987b\u6d89\u53ca\uff0c\u65f6\u95f4\u7684\u987a\u5e8f\u548c\u95f4\u9694\u91cd\u8981            |\n| \u5173\u6ce8\u70b9         | \u6570\u636e\u7684\u987a\u5e8f\u548c\u7ed3\u6784                  | \u6570\u636e\u968f\u65f6\u95f4\u7684\u53d8\u5316\u8d8b\u52bf\u548c\u6a21\u5f0f                |\n| \u4ee3\u8868\u6027\u4f8b\u5b50     | \u6587\u5b57\u5e8f\u5217\u3001\u57fa\u56e0\u5e8f\u5217\u3001\u70b9\u51fb\u5e8f\u5217       | \u80a1\u4ef7\u6ce2\u52a8\u3001\u6c14\u8c61\u6570\u636e\u3001\u5fc3\u7387\u76d1\u6d4b\u6570\u636e          |\n| \u5e94\u7528\u9886\u57df       | NLP\u3001\u4e8b\u4ef6\u5e8f\u5217\u5206\u6790\u3001\u5e8f\u5217\u6a21\u5f0f\u6316\u6398    | \u65f6\u95f4\u5e8f\u5217\u9884\u6d4b\u3001\u4fe1\u53f7\u5904\u7406\u3001\u7ecf\u6d4e\u5206\u6790          |\n\n---\n\n\u5982\u679c\u4f60\u5bf9\u4e8c\u8005\u4e2d\u7684\u67d0\u4e2a\u6982\u5ff5\u6216\u5e94\u7528\u6709\u66f4\u5177\u4f53\u7684\u95ee\u9898\uff0c\u6b22\u8fce\u7ee7\u7eed\u63d0\u95ee\nUser: \u5982\u4f55\u4f7f\u7528bigram\u6765\u901a\u8fc7vector\u8868\u793atrigrams\nAssistant:  \u4f7f\u7528\u4f7f\u7528 **bigram**\uff08\u4e8c\u5143\u7ec4\uff09\u6765\u8868\u793a **trigrams**\uff08\u4e09\u5143\u7ec4\uff09\uff0c\u901a\u5e38\u662f\u4e3a\u4e86\u5728 n-gram \u6a21\u578b\u4e2d\u8fdb\u884c\u964d\u7ef4\u6216\u8005\u7279\u5f81\u6784\u9020\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u4f60\u60f3\u7528 bigram \u7684\u5411\u91cf\u8868\u793a\u6765\u8868\u793a trigram\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u7528\u8fde\u7eed\u7684\u4e8c\u5143\u7ec4\u7ec4\u5408\u6765\u95f4\u63a5\u8868\u793a\u4e09\u5143\u7ec4\u7684\u4fe1\u606f\u3002\n\n\u4e0b\u9762\u4ecb\u7ecd\u51e0\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\uff1a\n\n---\n\n## \u80cc\u666f\n\n- **Bigram**\uff1a\u8fde\u7eed\u7684\u4e24\u4e2a\u8bcd\u7ec4\u6210\u7684\u5e8f\u5217\uff0c\u6bd4\u5982 trigram \"a b c\" \u53ef\u4ee5\u62c6\u6210\u4e24\u4e2a bigram\uff0c\u5206\u522b\u662f \"a b\" \u548c \"b c\"\u3002\n- **Trigram**\uff1a\u4e09\u4e2a\u8fde\u7eed\u7684\u8bcd\u7ec4\u6210\u7684\u5e8f\u5217\uff0c\u6bd4\u5982 \"a b c\"\u3002\n- \u4f60\u60f3\u7528 **bigram\u7684\u5411\u91cf**\u6765\u8868\u793a\u4e00\u4e2atrigram\u3002\n\n---\n\n## \u65b9\u6cd5\u4e00\uff1a\u62fc\u63a5\uff08Concatenation\uff09\n\n\u5047\u8bbe\u4f60\u6709\u6bcf\u4e2a bigram \u5bf9\u5e94\u7684\u5411\u91cf\u8868\u793a\uff08\u6bd4\u5982\u901a\u8fc7\u8bcd\u5d4c\u5165+bigram\u5d4c\u5165\u8bad\u7ec3\u5f97\u5230\uff09\uff0c\u90a3\u4e48\uff1a\n\n- \u5c06 trigram \"a b c\" \u5206\u89e3\u4e3a\u4e24\u4e2a bigram\uff1a\"a b\" \u548c \"b c\"\u3002\n- \u5f97\u5230 bigram \u5411\u91cf \\( \\mathbf{v}_{ab} \\) \u548c \\( \\mathbf{v}_{bc} \\)\u3002\n- \u5c06\u8fd9\u4e24\u4e2a\u5411\u91cf\u62fc\u63a5\u8d77\u6765\uff0c\u5f62\u6210\u4e00\u4e2a\u65b0\u7684\u5411\u91cf\u4f5c\u4e3a trigram \u7684\u8868\u793a\uff1a\n\n\\[\n\\mathbf{v}_{abc} = [\\mathbf{v}_{ab}; \\mathbf{v}_{bc}]\n\\]\n\n\uff08\u201c;\u201d\u8868\u793a\u5411\u91cf\u62fc\u63a5\uff09\n\n---\n\n## \u65b9\u6cd5\u4e8c\uff1a\u5411\u91cf\u52a0\u6743\u5e73\u5747\n\n\u5982\u679c\u62fc\u63a5\u540e\u5411\u91cf\u7ef4\u5ea6\u8fc7\u5927\uff0c\u53ef\u4ee5\u7528\u52a0\u6743\u5e73\u5747\u51cf\u5c11\u7ef4\u5ea6\uff1a\n\n\\[\n\\mathbf{v}_{abc} = \\alpha \\mathbf{v}_{ab} + (1 - \\alpha) \\mathbf{v}_{bc}\n\\]\n\n\u5176\u4e2d \\(\\alpha\\) \u53ef\u4ee5\u662f 0.5 \u8868\u793a\u7b80\u5355\u5e73\u5747\uff0c\u6216\u8005\u57fa\u4e8e\u5177\u4f53\u4efb\u52a1\u8c03\u6574\u7684\u6743\u91cd\u3002\n\n---\n\n## \u65b9\u6cd5\u4e09\uff1a\u4e58\u79ef\u6216\u66f4\u590d\u6742\u7ec4\u5408\n\n\u4f60\u4e5f\u53ef\u4ee5\u7528\u5143\u7d20\u7ea7\u4e58\u79ef\uff08Hadamard product\uff09\u6216\u8005\u975e\u7ebf\u6027\u53d8\u6362\uff08\u5982\u8f93\u5165\u4e24bigram\u5411\u91cf\u5230\u4e00\u4e2a\u5c0f\u7684\u795e\u7ecf\u7f51\u7edc\u4e2d\uff09\u6765\u5b66\u4e60 trigram \u7684\u8868\u793a\uff1a\n\n\\[\n\\mathbf{v}_{abc} = \\sigma(W [\\mathbf{v}_{ab}; \\mathbf{v}_{bc}] + b)\n\\]\n\n\u5176\u4e2d \\(W\\)\u3001\\(b\\) \u662f\u795e\u7ecf\u7f51\u7edc\u53c2\u6570\uff0c\\(\\sigma\\) \u662f\u6fc0\u6d3b\u51fd\u6570\u3002\u8fd9\u6837\u53ef\u4ee5\u6355\u83b7 bigram \u4e4b\u95f4\u7684\u975e\u7ebf\u6027\u5173\u7cfb\u3002\n\n---\n\n## \u65b9\u6cd5\u56db\uff1a\u57fa\u4e8ebigram\u5171\u73b0\u7684\u7279\u5f81\u6784\u9020\n\n\u5982\u679c bigram \u5411\u91cf\u662f\u7edf\u8ba1\u7279\u5f81\u6216\u8bcd\u5178\u7f16\u7801\uff0c\u4e5f\u53ef\u4ee5\u5c06 trigram \u89c6\u4e3a bigram \u7684\u5e8f\u5217\uff0c\u7edf\u8ba1\u5b83\u4eec\u7684\u8054\u5408\u51fa\u73b0\u9891\u7387\u4f5c\u4e3a\u7279\u5f81\u5411\u91cf\u3002\n\n---\n\n## \u603b\u7ed3\n\n- \u5c06 trigram \u5206\u89e3\u6210\u8fde\u7eed\u4e24\u4e2a bigram\u3002\n- \u5206\u522b\u83b7\u5f97\u8fd9\u4e24\u4e2a bigram \u7684\u5411\u91cf\u8868\u793a\u3002\n- \u5229\u7528\u62fc\u63a5\u3001\u52a0\u6743\u5e73\u5747\u3001\u975e\u7ebf\u6027\u7ec4\u5408\u7b49\u65b9\u6cd5\uff0c\u5408\u6210 trigram \u7684\u5411\u91cf\u8868\u793a\u3002\n\n---\n\n## \u7b80\u5355\u793a\u4f8b\uff08\u4f2a\u4ee3\u7801\uff09\n\n```python\nbigram_vec_ab = get_bigram_vector(\"a b\")\nbigram_vec_bc = get_bigram_vector(\"b c\")\n\n# \u62fc\u63a5\ntrigram_vec = np.concatenate([bigram_vec_ab, bigram_vec_bc])\n\n# \u6216\u52a0\u6743\u5e73\u5747\nalpha = 0.5\ntrigram_vec = alpha * bigram_vec_ab + (1 - alpha) * bigram_vec_bc\n```\n\n---\n\n\u5982\u679c\u4f60\u4f7f\u7528\u7684\u662f\u5177\u4f53\u7684\u5411\u91cf\u65b9\u6cd5\uff08\u6bd4\u5982word2vec\u3001GloVe\u6216FastText\u7b49\uff09\uff0c\u4e5f\u53ef\u4ee5\u5148\u8bad\u7ec3 bigram \u5d4c\u5165\uff0c\u518d\u7528\u4e0a\u8ff0\u7ec4\u5408\u65b9\u5f0f\u6765\u83b7\u5f97 trigram \u8868\u793a\u3002\n\n\u5982\u679c\u4f60\u6709\u67d0\u79cd\u7279\u5b9a\u7684\u5411\u91cf\u8868\u793a\u7ed3\u6784\u6216\u6a21\u578b\u9700\u6c42\uff0c\u4e5f\u53ef\u4ee5\u544a\u8bc9\u6211\uff0c\u6211\u53ef\u4ee5\u5e2e\u4f60\u8bbe\u8ba1\u66f4\u9002\u5408\u7684\u65b9\u6cd5\u3002\nUser: \u89e3\u91caRepresented as set of trigrams: \u2022 {\u201cto be or\u201d, \u201cbe or not\u201d, \u201cor not to\u201d, \u201cnot to be\u201d} \u2022 Represented as a vector of bigrams: \u2022 Dimensions = {\u201cto be\u201d, \u201cbe or\u201d, \u201cor not\u201d, \u201cnot to\u201d} \u2022 Vector = \u27e82, 1, 1, 1\u27e9\nAssistant: \u4f60\u63d0\u5230\u7684\u8fd9\u6bb5\u5185\u5bb9\uff0c\u662f\u7528 **bigram\uff082-gram\uff09\u5411\u91cf** \u6765\u8868\u793a\u4e00\u4e2a\u5305\u542b **trigram\uff083-gram\uff09\u96c6\u5408** \u7684\u4f8b\u5b50\u3002\u8ba9\u6211\u5e2e\u4f60\u9010\u6b65\u89e3\u91ca\uff1a\n\n---\n\n## 1. \u7ed9\u5b9a\u7684 Trigrams\n\n\\[\n\\{\\text{\"to be or\"}, \\text{\"be or not\"}, \\text{\"or not to\"}, \\text{\"not to be\"}\\}\n\\]\n\n\u8fd9\u662f\u4e00\u7ec4\u8fde\u7eed\u7684\u4e09\u8bcd\u77ed\u8bed\uff08trigrams\uff09\uff0c\u6bcf\u4e2a trigram \u6709\u4e09\u4e2a\u8bcd\u3002\n\n---\n\n## 2. \u5c06 Trigrams \u788e\u4e3a Bigrams\n\n\u6bcf\u4e2a trigram \u53ef\u4ee5\u88ab\u5206\u89e3\u4e3a\u4e24\u4e2a\u8fde\u7eed\u7684 bigrams\uff0c\u6bd4\u5982\uff1a\n\n- \"to be or\" \u2192 \"to be\" \u548c \"be or\"\n- \"be or not\" \u2192 \"be or\" \u548c \"or not\"\n- \"or not to\" \u2192 \"or not\" \u548c \"not to\"\n- \"not to be\" \u2192 \"not to\" \u548c \"to be\"\n\n---\n\n## 3. Bigram \u7a7a\u95f4\uff08\u5411\u91cf\u7684\u7ef4\u5ea6\uff09\n\n\u5411\u91cf\u7a7a\u95f4\u4ee5\u6240\u6709\u51fa\u73b0\u8fc7\u7684 bigrams \u4f5c\u4e3a\u7ef4\u5ea6\uff0c\u5373\uff1a\n\n\\[\n\\{\\text{\"to be\"}, \\text{\"be or\"}, \\text{\"or not\"}, \\text{\"not to\"}\\}\n\\]\n\n\u8fd9\u56db\u4e2a bigram \u5f62\u6210\u4e86\u5411\u91cf\u76844\u4e2a\u7ef4\u5ea6\u3002\n\n---\n\n## 4. \u7edf\u8ba1\u6bcf\u4e2a bigram \u5728\u6240\u6709 trigrams \u4e2d\u51fa\u73b0\u7684\u6b21\u6570\n\n\u73b0\u5728\u7edf\u8ba1\u8fd9\u56db\u4e2a bigrams \u5728\u6240\u6709\u56db\u4e2a trigrams \u4e2d\u7684\u51fa\u73b0\u9891\u7387\uff1a\n\n| Bigram    | \u51fa\u73b0\u6b21\u6570\u5206\u6790                                                 | \u51fa\u73b0\u6b21\u6570 |\n|-----------|------------------------------------------------------------|-----------|\n| \"to be\"   | \u51fa\u73b0\u4e8e \"to be or\"\uff08\u7b2c\u4e00\u4e2atrigram\uff09\u548c \"not to be\"\uff08\u7b2c\u56db\u4e2atrigram\uff09 | 2         |\n| \"be or\"   | \u51fa\u73b0\u4e8e \"to be or\"\uff08\u7b2c\u4e00\u4e2atrigram\uff09\u548c \"be or not\"\uff08\u7b2c\u4e8c\u4e2atrigram\uff09   | 2 (\u4f46\u770b\u4e0b\u9762\u5411\u91cf\u662f1\uff1f)    |\n| \"or not\"  | \u51fa\u73b0\u4e8e \"be or not\"\uff08\u7b2c\u4e8c\u4e2atrigram\uff09 \u548c \"or not to\"\uff08\u7b2c\u4e09\u4e2atrigram\uff09  | 2 (\u5411\u91cf\u5199\u7684\u662f1\uff1f)       |\n| \"not to\"  | \u51fa\u73b0\u4e8e \"or not to\"\uff08\u7b2c\u4e09\u4e2atrigram\uff09 \u548c \"not to be\"\uff08\u7b2c\u56db\u4e2atrigram\uff09  | 2 (\u5411\u91cf\u5199\u7684\u662f1\uff1f)       |\n\n---\n\n## 5. \u7ed9\u51fa\u7684\u5411\u91cf\u4e3a \u27e82, 1, 1, 1\u27e9\n\n\u9898\u76ee\u4e2d\u7ed9\u7684\u5411\u91cf\u662f\uff1a\n\n\\[\n\\langle 2, 1, 1, 1 \\rangle\n\\]\n\n\u5bf9\u5e94\u7ef4\u5ea6\u987a\u5e8f\u662f \\(\\{ \\text{\"to be\"}, \\text{\"be or\"}, \\text{\"or not\"}, \\text{\"not to\"} \\}\\)\n\n\u6ce8\u610f\u5230\u201cto be\u201d = 2\uff0c\u5176\u4ed6\u90fd\u662f 1\u3002\n\n---\n\n## 6. \u4e3a\u4ec0\u4e48\u9664\u4e86\u201cto be\u201d\u4e4b\u5916\u51fa\u73b0\u6b21\u6570\u662f1\uff1f\n\n\u8fd9\u91cc\u53ef\u80fd\u6709\u4e24\u79cd\u89e3\u91ca\uff1a\n\n- **\u8ba1\u6570\u4ec5\u7b97\u4e00\u904d\u6bcf\u4e2a trigram \u4ea7\u751f\u7684\u4e24\u4e2a bigram\uff0c\u5373\u4e0d\u91cd\u590d\u7edf\u8ba1\u540c\u4e00 bigram \u5728\u4e00\u4e2a trigram \u5185\u591a\u6b21\u51fa\u73b0\u3002**\n\n- **\u6216\u8005\u8fd9\u91cc\u7684\u7edf\u8ba1\u65b9\u5f0f\u662f\uff1atrigram\u96c6\u5408\u4e2d\uff0cbigram\u5728trigram\u4e2d\u51fa\u73b0\u7684\u4e0d\u540c\u6b21\u6570\u7684\u7edf\u8ba1\uff0c\u800c\u4e0d\u662f\u6240\u6709bigram\u51fa\u73b0\u6b21\u6570\u7684\u603b\u548c\u3002\u5177\u4f53\u89e3\u91ca\uff1a**\n\n\u4ee5\u6bcf\u4e2a trigram \u5355\u4e2a\u51fa\u73b0\u7684\u4e24\u4e2a bigram \u4e3a\u57fa\u51c6\uff0c\u6700\u540e\u7d2f\u52a0\u6240\u6709\u4e0d\u540c\u7684 bigram\u51fa\u73b0\u6b21\u6570\u3002\n\n\u6765\u770b\u6bcf\u4e2a trigram \u4ea7\u751f\u7684\u4e24\u4e2a bigram\uff08\u6bcf\u4e2atrigram\u4e24\u4e2abigram\uff09\uff1a\n\n| Trigram         | Bigrams            |\n|-----------------|--------------------|\n| \"to be or\"      | \"to be\", \"be or\"   |\n| \"be or not\"     | \"be or\", \"or not\"  |\n| \"or not to\"     | \"or not\", \"not to\" |\n| \"not to be\"     | \"not to\", \"to be\"  |\n\n\u6240\u6709bigram\u51fa\u73b0\u5217\u8868\u5c55\u5f00\u662f\uff1a\n\n[\"to be\", \"be or\", \"be or\", \"or not\", \"or not\", \"not to\", \"not to\", \"to be\"]\n\n\u7edf\u8ba1\u51fa\u73b0\u6b21\u6570\uff1a\n\n- \"to be\": 2\u6b21\uff08\u7b2c1\u548c\u7b2c4 trigrams\uff09\n- \"be or\": 2\u6b21\uff08\u7b2c1\u548c\u7b2c2 trigrams\uff09\n- \"or not\": 2\u6b21\uff08\u7b2c2\u548c\u7b2c3 trigrams\uff09\n- \"not to\": 2\u6b21\uff08\u7b2c3\u548c\u7b2c4 trigrams\uff09\n\n\u4f46\u9898\u76ee\u4e2d\u7ed9\u5411\u91cf\u662f <2,1,1,1>\uff0c\u8fd9\u8bf4\u660e\u6709\u53ef\u80fd\uff1a\n\n- \u7edf\u8ba1\u65f6\u5bf9\u67d0\u4e9b bigram \u53ea\u6309\u6240\u5728 trigram \u7684**\u51fa\u73b0\u4e2a\u6570\u7b971\u6b21**\uff0c\u5373\u201cbe or\u201d\u3001\u201cor not\u201d\u3001\u201cnot to\u201d\u5404\u53ea\u8bb01\u6b21\u3002\n\n- \u53ef\u80fd\u662f\u6839\u636e\u4e0a\u4e0b\u6587\u91cc\u6bcf\u4e2a bigram\u7684\u72ec\u7acb\u6027\u8003\u8651\uff0c\u6216\u8005\u53ea\u7edf\u8ba1\u51fa\u73b0\u7684 trigram \u6570\u91cf\uff0c\u4f46\u5bf9\u201cto be\u201d\u5355\u72ec\u8ba1\u6570\u4e86\u4e24\u6b21\u3002\n\n---\n\n## 7. \u603b\u7ed3\u8bf4\u660e\n\n- \u8fd9\u6bb5\u8bdd\u60f3\u8868\u8fbe\u7684\u662f\uff1a  \n  - \u4e00\u4e2a trigram \u96c6\u5408\u7684\u6bcf\u4e2a trigram \u90fd\u53ef\u4ee5\u62c6\u6210\u4e24\u4e2a bigram\u3002  \n  - \u5c06\u6240\u6709 trigrams \u4e2d\u51fa\u73b0\u7684 bigram \u6309\u7ef4\u5ea6\u5efa\u7acb\u5411\u91cf\u7a7a\u95f4\u3002  \n  - \u8ba1\u7b97\u6bcf\u4e2a bigram \u5728 trigrams \u4e2d\u7684\u201c\u51fa\u73b0\u6b21\u6570\u201d\u4f5c\u4e3a\u5411\u91cf\u5143\u7d20\u3002  \n  - \u4f8b\u5982\u201cto be\u201d\u51fa\u73b0\u4e862\u6b21\uff0c\u6240\u4ee5\u7b2c\u4e00\u4e2a\u7ef4\u5ea6\u662f2\u3002  \n  - \u5176\u4ed6\u7684 bigram \u51fa\u73b0\u6b21\u6570\u662f1\uff0c\u6240\u4ee5\u5bf9\u5e94\u7ef4\u5ea6\u662f1\u3002\n\n- \u8fd9\u79cd\u8868\u793a\u6cd5\u53ef\u4ee5\u5c06\u7531\u4e09\u8bcd\u7ec4\u6210\u7684\u6587\u672c\u7247\u6bb5\u7528\u66f4\u5c0f\u7ef4\u5ea6\uff08bigram\u6570\u91cf\uff09\u6765\u8868\u793a\uff0c\u65b9\u4fbf\u505a\u540e\u7eed\u7684\u7edf\u8ba1\u548c\u673a\u5668\u5b66\u4e60\u3002\n\n---\n\n\u5982\u679c\u4f60\u9700\u8981\uff0c\u6211\u53ef\u4ee5\u5e2e\u4f60\u5199Python\u4ee3\u7801\u793a\u4f8b\u5e2e\u4f60\u9a8c\u8bc1\u8fd9\u4e2a\u7edf\u8ba1\u8fc7\u7a0b\uff0c\u6216\u8005\u5e2e\u4f60\u89e3\u91ca\u5982\u4f55\u4ece bigram \u5411\u91cf\u91cd\u6784 trigram \u7279\u5f81\u3002\nUser: hidden markov model\u548cmarkov model\u6709\u4ec0\u4e48\u533a\u522b\uff1f\nAssistant:"}],"shard":{"index":83,"name":"turns-00083.parquet","rows":48361}}