線型部分空間に基づく学習済み単語埋込空間上の集合演算

PH2-8

石橋 陽一 (NAIST), 横井祥 (東北大/理研), 須藤 克仁 (NAIST/JSTさきがけ), 中村 哲 (NAIST)

背景：単語の「集合」「集合演算」を埋込空間上で定式化したい
l 単語ベクトル集合に対して計算する事は多い。

p 例：「単語ベクトル集合の平均」にやが定義できるか不明

orange 2 Color \ Fruit

Color = {red , blue, . . .}, Fruit = {apple, peach, . . .}<latexit sha1_base64="ZYMjoc5DeW1udsXGjYitGZgh4Jk=">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</latexit>|A \ B| |A \ B|+
集合類似度 Johnson(A, B) =
A
=
{A,
boy,
walks,
.
.
.
},
B
=
{The,
kid
,
runs,
.
.
.
}
|A|
|B|
<latexit sha1_base64="jy2QrO2VYRQprl17Zkg0jTPnQ1Y=">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</latexit>

検証方法
部分空間の中のベクトルの最近傍単語を見て男性ならOK<latexit sha1_base64="qf4f9aenIEYmmXLWXdO9lXnpXAk=">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</latexit>

帰属関係

男性の部分空間は「男性的」という意味を表現できている？

✔ 集合の拡張や文類似度を、埋込空間に定義した集合演算で計算可能に問題の定式化：定式化したい単語集合と集合演算行いたい
計算

確かめたい事l 既存法は「近似的」or「一部の演算のみ実現」

p 例：文を「単語ベクトル集合の平均」として処理✔ 埋込空間で集合演算を定式化

埋込空間上の集合演算の定性的実証<latexit sha1_base64="Z7KYTKqDLXEyifWR2lNbXQop9lQ=">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</latexit>▪集合 Male = {king, man, son, . . .} ▪帰属関係

部分空間の近傍単語上位3件

単語集合（部分空間を張る単語集合には含まれていない単語）

Male
Color ∩ Fruit

概念集合検索タスク ※2<latexit sha1_base64="LEwx7eI/s3rD+lCCtkPhES9yTlw=">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</latexit>

king<latexit sha1_base64="ilCqw/CT9h8GAeywrIwW7NXgAPg=">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</latexit>

必要な
基本演算

▪元

元

boy 2 Male

確かめたい事<latexit sha1_base64="nKsPz8FRhLwEzrpClI+5n/KpDFI=">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</latexit>▪補集合

Male ▪共通部分 Color \ Fruit<latexit sha1_base64="Ee34FHbXOhACH6l81UtTeh3YR4o=">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</latexit>▪和集合

手法：埋込空間における単語集合と集合演算
着想

Male [ Female<latexit sha1_base64="70T6OcHf9QFn8hSD4Ll1hsOI0fY=">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</latexit>

w

king

king

提案する帰属度の計算が具体的なタスクで効果を発揮するか？

検証方法

単語ベクトル集合をそれらが張る部分空間とし、集合演算を部分空間の演算（量子論理）で定式化

集合（例 Male）に入る未知単語（例 boy）検索タスクで確認

単語ベクトル

補集合

直交補空間

手法

Recall@10

Recall@100

Recall@1kMed.

v kingA

SMale

DeepSets

5.5
6.0
5.3

24.2
28.1
29.7

54.3
54.7
58.9

696
641
478

<latexit sha1_base64="rzNiLCFv2CEfuM+YtF0/hcGu3n8=">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</latexit>:= (SMale )?
= {u | 9v 2 SMale , u · v = 0}

最近傍<latexit sha1_base64="wkRTaJEkbXIBuVPanP4VwcWFciY=">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</latexit>

集合 A
Male

king
man

帰属関係

線形部分空間king
Male

SMale = S {king ,man ,... }<latexit sha1_base64="0DBYUBH7/OIsX/IeTG5yYTbE38U=">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</latexit>man<latexit sha1_base64="N4xmmkuI7780DJjn5CZlt90OTKk=">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</latexit>:= span{v king , v man , . . .}(Male, boy) =共通部分（交空間）

A\B

SColor\Fruit(

1 (boy 2 Male)0 (boy 2/ Male)SMale[Female

A[Bµ(SMale , v boy ) = cos ✓SMale ,v boy
部分空間との「なす角」に応じて0から1の連続値を返す|A \ B| |A \ B|+
単語集合間の類似度 ※1 Johnson(A, B) =
|B|
|A|

和空間

和集合

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式変形|A \ B|
=
|A|

P

P

a 2A (B, a)a2A µ(SB , v a )
)
|A|
|A|
ソフト化

1 X
1 X
+
||v
||
µ(S
,
v
)
=
||v
||
µ(S
,
v
)
b
2
A
b
a
2
B
a
SubspaceJohnson(A,B)
単語ベクトル集合間の類似度 ※1
|B|
|A|
b 2B
a 2A
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帰属度( µ )教師なし文類似度タスク（STS） ※1
確かめたい事
提案する集合類似度が具体的なタスクで効果を発揮するか？

検証方法
２つの文の類似度と人手評価との相関を確認（文＝単語集合）
埋込空間:= SMale + SFemale<latexit 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SColor \ SFruit= {v | v 2 SColor , v 2 SFruit }<latexit 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ソフトな帰属度

boy
Male

共通部分

ハードな帰属度

boy

Male

w 2A
boy

brother-in-law, nephews, step-father
orange, peach, mango

手法
Avg-cos

GloVe

DynaMax
SubspaceJohnson
Avg-cos

BERT(1層と12層の平均)

DynaMax
SubspaceJohnson

STS12-16 Avg. ( r / ρ )52.8 / 63.8 / 65.3 / 65.1
- / 63.5
63.7 / 63.6
65.7 / 65.4

<latexit sha1_base64="9WTWbTodty5dj5/1olKwHUtyTeg=">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</latexit>※1 論文からの更新点。論文記載の提案法を改良し、新たな提案法の実験結果を記載した。
※2 論文からの更新点。論文4.2節の実験をベースラインと比較しやすい形で行うように概念集合検索タスク（Zaheer, M., et al.: Deep Sets, in NIPS (2017)）に変更した。