๐Ÿ“‘Paper Review

[paper review] RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space

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Sep 11, 2022
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paper-review-RotatE
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DeepLearning
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๐Ÿ“‘Paper Review
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Sep 6, 2024 03:58 PM
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RotatE๋Š” TransE, ComplEx ๋“ฑ์˜ ๋‹จ์ ์„ ๊ฐœ์„ ํ•œ ์ง€์‹๊ทธ๋ž˜ํ”„ ์ž„๋ฒ ๋”ฉ ๋ฐฉ๋ฒ•์ด๋‹ค. ์ด์ „ ๋…ผ๋ฌธ๋“ค์„ ํฌํ•จํ•œ ์ˆ˜์‹์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.
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ComplEx์™€ ๋น„์Šทํ•˜๊ฒŒ RotatE์—์„œ head, relation, tail์€ complex domain์—์„œ ์ •์˜๋˜์ง€๋งŒ ComplEx๊ฐ€ score function์˜ ์‹ค์ˆ˜๋ถ€๋ถ„๋งŒ ์ทจํ•œ ๊ฒƒ๊ณผ ๋‹ฌ๋ฆฌ ์ œ๊ณฑ์— ์Œ์ˆ˜๋ฅผ ์ทจํ•ด์„œ score function์„ ์ •์˜ํ•˜์˜€๋‹ค. ์ด๋Š” ์ผ๋ฐ˜ complex number์™€ ๊ทธ์˜ complex conjugate์™€์˜ ๋‚ด์ ์„ ์ทจํ•œ ๊ฒƒ๊ณผ ๊ฐ™๋‹ค.
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RotatE์˜ ๊ฐœ๋…์€, relation์„ complex plane์—์„œ์˜ rotation์œผ๋กœ ๋ณด์•„ head์— rotation์„ ์ทจํ•œ ๊ฐ’์„ tail๊ณผ ๋น„์Šทํ•˜๊ฒŒ ๋งŒ๋“ค์–ด์ฃผ๋Š” ๊ฐœ๋…์ด๋‹ค. ์ด์ „ TransE๋Š” ์‹ค์ˆ˜ ๋„๋ฉ”์ธ์—์„œ ์—ฐ์‚ฐ์ด ์‹œํ–‰๋˜์—ˆ์ง€๋งŒ, ์ด๋ ‡๊ฒŒ relation์„ rotation์œผ๋กœ ์ทจ๊ธ‰ํ•˜๋Š” ๊ฒƒ์€ TransE์— ๋น„ํ•ด ํฐ ์ด์ ์ด ์กด์žฌํ•œ๋‹ค.
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๋ฐ”๋กœ ์ง€์‹ ๊ทธ๋ž˜ํ”„์˜ 4๊ฐ€์ง€ ํŒจํ„ด์ธ symmetry, anti-symmetry, inversion, composition์„ ๋ชจ๋‘ ๋ชจ๋ธ๋งํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒƒ์ด๋‹ค.
์˜ค๋ž˜์ „ ๋ฐœํ‘œ๋œ ๋…ผ๋ฌธ์ด์ง€๋งŒ symmetry ์ œ์™ธ ๊ฐ•๋ ฅํ•œ ๋ชจ๋ธ๋ง ์„ฑ๋Šฅ์„ ๊ฐ€์กŒ๊ณ  ๋ชจ๋ธ์ด ์ง๊ด€์ ์ธ TransE๋ฅผ ์˜ˆ์‹œ๋กœ ์‚ดํŽด๋ณด์ž. TransE๊ฐ€ symmetricํ•œ ํŒจํ„ด์„ ์ž„๋ฒ ๋”ฉํ•˜์ง€ ๋ชปํ•˜๋Š” ๊นŒ๋‹ญ์€, score function์„ ๊ณ„์‚ฐํ•˜๋Š” ์—ฐ์‚ฐ์ด real domain์—์„œ ์ทจํ•ด์ง€๊ธฐ ๋•Œ๋ฌธ์ธ๋ฐ, score function์˜ ๊ตฌ์กฐ ๋•Œ๋ฌธ์— ํ•™์Šต์ด ์ง„ํ–‰๋ ์ˆ˜๋ก relation์˜ ํฌ๊ธฐ๊ฐ€ 0, ๊ทธ๋ฆฌ๊ณ  head์™€ tail์ด ๊ฐ™์•„์ง€๋Š” ํ˜„์ƒ์ด ๋ฐœ์ƒํ•˜๊ฒŒ ๋œ๋‹ค. symmetric relation์˜ ์˜ˆ์‹œ๋ฅผ ํ•˜๋‚˜ ๋“ค์–ด๋ณด์ž๋ฉด ์นœ๊ตฌ ๊ด€๊ณ„๊ฐ€ ์žˆ๋Š”๋ฐ, ๋‚˜์™€ ์ •๊ตฌ์„ญ์ด ์นœ๊ตฌ๋ผ๊ณ  ํ•˜๋ฉด TransE์˜ ๋ชจ๋ธ๋ง์„ ๊ฑฐ์น˜๋ฉด head ์™€ tail์˜ ์ž„๋ฒ ๋”ฉ์ด ๊ฐ™์•„์ง์œผ๋กœ์จ ํ•˜๋‚˜์˜ ์ž„๋ฒ ๋”ฉ์ด โ€˜๋‚˜'์™€ โ€˜์ •๊ตฌ์„ญโ€™์„ ๋ชจ๋‘ ๊ฐ€๋ฆฌํ‚ค๊ฒŒ ๋˜๋Š” ๋ฌธ์ œ๊ฐ€ ๋ฐœ์ƒํ•œ๋‹ค. ์ด๋Š” ์ง€์‹๊ทธ๋ž˜ํ”„ ์ž„๋ฒ ๋”ฉ ๊ฒฐ๊ณผ์˜ separation power๊ฐ€ ๋–จ์–ด์ง€๋Š” ๋ฌธ์ œ๋ฅผ ์œ ๋ฐœํ•œ๋‹ค.
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๊ทธ๋Ÿฌ๋‚˜ RotatE์—์„œ๋Š” complex plane์—์„œ ๋Œ€์นญ๋˜๋Š” ๋‘ ์ ์œผ๋กœ ๋‚˜์™€ ์ •๊ตฌ์„ญ์„ ์žก์„ ์ˆ˜ ์žˆ๊ธฐ ๋•Œ๋ฌธ์— symmetricํ•œ ๊ด€๊ณ„๋ฅผ ๋ชจ๋ธ๋งํ•  ์ˆ˜ ์žˆ๋‹ค.
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์ถ”๊ฐ€์ ์œผ๋กœ ์ด ๋…ผ๋ฌธ์—์„œ๋Š” self-adversarial negative sampling์ด๋ผ๋Š” ๋„ค๊ฑฐํ‹ฐ๋ธŒ ์ƒ˜ํ”Œ๋ง ๋ฐฉ๋ฒ•์„ ์ œ์•ˆํ•˜์˜€๋‹ค. ๊ธฐ์กด์˜ ๋„ค๊ฑฐํ‹ฐ๋ธŒ ์ƒ˜ํ”Œ๋ง ๋ฐฉ๋ฒ•์—์„œ๋Š” ๋‹จ์ˆœํžˆ uniformํ•˜๊ฒŒ ๋„ค๊ฑฐํ‹ฐ๋ธŒ ์ƒ˜ํ”Œ๋œ ๊ฒƒ์„ negative pair๋กœ ๋ณด๊ธฐ ๋•Œ๋ฌธ์—, ์–ด๋– ํ•œ ์˜๋ฏธ์žˆ๋Š” ์ •๋ณด๋ฅผ score function์— ์ฃผ๊ธฐ ์–ด๋ ค์› ๋‹ค๊ณ  ํ•œ๋‹ค.
์ด๋Ÿฐ ๊ธฐ์กด์˜ score function์— ๋Œ€ํ•ด ์ €์ž๋Š” ๊ฐ€์ค‘์น˜ ๋ถ€๋ถ„(1/k) ๋Œ€์‹  positive pair์— ๋Œ€ํ•œ negative pair๋“ค์˜ ํ™•๋ฅ ๋ถ„ํฌ๋ฅผ ์ œ์•ˆํ•จ์œผ๋กœ์จ ์œ„์˜ ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ณ ์ž ํ•˜์˜€๋‹ค.
๊ทธ๋ž˜์„œ ์ข‹์€ ์„ฑ๋Šฅ์„ ์–ป์—ˆ๋‹ค๊ณ  ํ•œ๋‹ค~