発表番号 110

学習済み埋め込み空間における集合演算1

石橋 陽一,

2,3

横井 祥,

1,4

須藤 克仁,中村 哲

1

1 奈良先端科学技術大学院大学 (NAIST), ２ 東北大学, ３理研AIP, 4 JSTさきがけ

概要
単語埋め込みは自然言語処理の基盤的な道具であり品質評価は重要な課題である。本研究では学習済み埋込空間上での集合の表現と集合演算を実現し評価へ応用する。我々は量子力学で提案されたHilbert空間上の集合演算である
量子論理に着目し、埋込空間で集合と集合演算を表現する。実験では埋込空間上で量子論理による集合演算が可能であること、量子論理に基づく評価が後段タスクのスコアと高い正の相関を持つことを示した。

2

概要•単語埋め込み空間で単語集合の表現や操作がしたい•量子力学で提案された論理体系である「量子論理」
を使った方法を提案•単語埋め込みの評価に応用
red

Color
blue

lemon
orange

Fruit
apple

背景：単語埋め込み空間における単語集合表現

4

言語の数理表現
単語埋め込み：単語をベクトルで表現

vman<latexit sha1_base64="RDeiiWBkOUxiQP3gqBMpndiexTY=">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</latexit>

vking

vwoman<latexit sha1_base64="3yYKYTKAn71m0GjafXLmwgCBkP0=">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</latexit><latexit sha1_base64="8vSo71Mq3qgQv/xc7sBnKBuqcVs=">AAA0pnic3RtbbFxHdRJKcNJSJxRBAVW9kMTNtok5dk1BFUWJk1ZIxY94vbHBG2+96/V6s5u77u56N8l6E6VUiNoVhUahUpBARKCq4oMPfogEqsQzqEKFjwQFiR8kBDSIn1RCQpGWM2fu3Jm5j30kNwRh63rvPffMec15zJxZp1eK+UoV4Nqmze+5571b3te3ddu9973//v7tOz5wpFJaLWeyiUypWCrPphcq2WLeziaq+WoxO7tSzi4cTxezM+nCQf5+ppYtV/Ile7p6ciV79PhCzs4v5TMLVQSVdnzEYklmsyyrswwrseP4u4DPi6yB8AVWZjmCnGBNgvD7KltGzBV8quK4E/i3jPCGg33axU+yIsvjUx4xKvhssd146TS3dcE7j5BeeAv89rw5DuedQ6wSSyO8SCNKCM/h3SLSXsLPabaTDSF1/neeZKgS96ak+LU/n7HXH4z/C5/2oDQmTox4SFo1/Mw49LguacQ6Qff8roh4Uj+L7dK0FfrxcU2Eu5xdiiYPP/1dLmYDP5ssZdhSp+6nn6I32/BZ8ah04BHviUfF5XFnLfX/Z6WxiCxEPL76hakPE6eEwaOCn9UQTTrQ/OavpvsMWvVboxOfXf+2QSeOscWzRHtqGYrpQF2//repLadOnT9HM8av2/3dRhZcXn8Q7ImN6CiixbY5819HTQqUtXKoh4TWEGo++XHEDDbYAQ0mLWhCx7TnyHRwvCAaakJHUSOaGqROtUNCgywhYM+zVbRGVhvtjz9Oq4y+xisIv5JoG4Ebhsdtx3lZaD3LxS5RpJepCvEKp2x7gEZw/1zBu1EDtqrBIrG/4etRUPRekUg5dyHVH/9Q5DJGIlv62eKV1kfviP0sjDmepbKBHibfcQ97kj1FHuL3V+XnSccXpRcFYcso8eIO0q8pk9Xqk346cQZegWNwqLWVcDrLspcwgnnvdfkl3TgM1zxqXvL6b9iy84xGMe/d6q+87hmkfryN5+nv20uhZ9RubKZn6nC7efwQbCOLiUoVZKWKYRed9mnnreTdI99WH1yC38MNx//DJTC1rTh1tunYohYwb7W23mpIc3rgfB1+Bzfhx/BXlKXPla6TVF67COww25hv21jHKw+v9a4s4T490FM2E3470GMsdjeqQvs9/yif1vOQnD9/ceJnjm5i9ygtwlefJ/FTrAHaZXSBqa8Ywu2k6K/QOkLIqka686Dp2CmudUrdSWHGc7ssoeTl66IFmsWsxuMg7Uv4O3318ww+r9IePUhenVI7eRXtpkHdL7HkpsvLcVdcW0oO/vWbOTde2opKswOdcGtrUqV++dJZOFb6YOM16iwMUS+hm6oVNHrYGe2FPx4CH3G59S69l9anXFrRzJmX/hMh9G/PhyuOTYu0eyo58S7yZDMMp/VQa0fh44cPeqqVN/vK3FcI2LXxbLyGl+W89fp7Gn8bbEqba8WjHkK9fst0rfgsz+mQ43vwmbde+Ym7m7uVGtxtBTYyLlbet7HC/MatK7WQPDrmi9AAGrMj031TW+AwzMASxtReBmBP7oJC5pOwoSqZwymNlHJEv0HeyXfSFXf2zd8h+jtAkiw7dT9D8TLMeFezGeB7ebbkwM0Rj2sjutNW1S6vXHALcpXonkd9HflVtIyXdXqzujUkZ6/FfwpX4LI7a7y7WyFegnYVKbQbpeGBPXfhzBu+2VF09NWXtE+RekVVJ1/yrm9Gk0G+3aPdDxLmElUc3p9bY6pXt+r66yJZxzsza0z0p71jBGTNg50kfP5ZRnlzqEcVc1gSvVGHrDkQk57Qr+HzAJOamRsCLM7jGa7BD+EyXNfiyuyZCH+aZHF2CAoi66b6nVpksQTYyXtSzzt9w0mWos6hzAyTLLi7mVB1IoAyr1NWIcPputJZOFZKKCyxrOU5yctiZvfWK7+N9LFanH0Ho195kqgchEG+MOZIuNdHL+ZwXKN56ayhd7zF9vlgnFYKdQ6R9dij4+chAedC5LUMn2+Qp5vSyf6g4t3QuFpaTVBj5umNadskU53oSSjJWYcMLEGcSwv21BgU1hlBNqAEX4Ln4Fl4CTbh+HmkNtnqc0eJaLbHGSy2tkLp7DtL98MsfLn1MIzCMtK39TMapJeHryCX5dbDmp2+iJFUwCvvWE9aIeXYgVtSZcsplGHRtdUivVV6Trr68VxwhPJeleA1x3I1ii35xpVCVnmwZ/49f771EOomfXYBXj32KBTGB+AkLE0k0S4prnurj2PCq4hZgBe4/kz0DLkcc6j3EHneAsomd4JHcZ91Auzau+Pfc6MN52D8L+P3wmYhB6TQ2jPsAJSaf0yly/849Rbk0JYbsDz+z7kLvNLBBu4Vt5D1lxFuQ87YMSbceJrz5JuUI5EXOqztVI+6vitoJPDaj5eNtWbQWTfyLJXDJ35fw0hL4P20g5eg2BJ3HBqUQ8a0uFK+ySF61M4zefKmY8ToTG4fnQIE4bbPAA1P7FttZAuON8sX54qCEfUTG0xf6ZsyqUyvJJP1JObPIA6t4Q60zNXZmG89rHiZO0edY5zqajlkx1lx3zZp3jnFumvRfVLiDtk3RWMUz5qnIpgZv0b4fgwJFVjiXoNQbCU8ceG+pZWveJtQ0BfKFMHjPB/jyuU6Zupf8M6Ip1cVvtcZC9uVhlGGS/AjuNjR1mH27V4SNffmLjzm8eOEJyp70zXhjpXnVOHjJUaQve5Gp8MrexgtJbeXSrAFdTqPhUSm8F0rsOto6i6ljeQsBI5i5b4KdqSnenovi9tU19SC5en7YLZNNyIIJi3e24x4/S1KyubZQ2SWo925nUqn+msvwjGs+i9HRrvz2SjHOhAYfcFno2Fz2Ou5aGTWm/vOhQdaOyK0WHe1r3vcRxzsRA9jlMXFyupzARkijBvHtGmHqyj0VtV74aYqSZ12I0puAQuSx62P8GusiG+637dQdBV1y3kTnvODTs7kqirond7jjbnUe+uRdqLbTqZYR426r2JBfMzK0b0Fbr+zG8TLXHd0J02k+eEbb89Nrl+tbuF71ki/n6C+a+NfIY06qwF/Dk6zJbeboHbuQW/NPuEBn/XCcUeZt7OsJH2saxlFvyyMY5jsq6Gy9yI59SmmXxY7c/7NTChBA87hzrckdMA6eQ5ehMOQxz34JvgTrqjfhJtYPwvjV7KX8O1EgPbie51pykXd6N5JR72TGKQbX9cB0dnT9RzHAmduL1nGv/f07l7FSuzu7a45ZhQ77O6qj14lnnJmhHeHg6WsO3Lu6wLzETcXiQoWtEI3T9r/V+TVL71rzGehfRUNr1d8dj7LrNukZ+Z59Q0F/5nC7cmqVjDR0PbKHbsD9g23hZeP7IjIWe9sReUvprdofYoca4626UnEcTUwwabY09oeV52x8KzBu9aH6ERE7J9WcZzgH+T7MusdIvw9kcdBzLBSyYhUd8fFe9e410rBetf9mLu5SpI6xMj+dyB3pLbvhEGgH8t/M+Tc7GTOz2Rp++ssSQUwQ9PNjxWreF+kY8UKm0PHADRGlR1l4h87+AYg47Y+kjiKb7TFYWYB/3Ll5xwobzcfp8NJPjpjmHk3XIE34AZchh/A3+FmKK0G0eCynGT86+U0NruS6qd/9eg0SprfHdVW5ioGxGdI1jw1zTmEa5ER42unXrsRf3Jqd2MALsJ1lP+7cA1+jhrYtXcz3z+cnfoWTcCQ19z+myPDg0NPDI4cHtm5f9SZij72MfYJajp/mu1nn8eim2CZ4deHfzt8dfgPI3tGxkcSIzMCdfMmZ8wDzPgZee4/DlRqmQ==</latexit>

vqueen<latexit sha1_base64="ajMZkPZi7FqSj3/UIX0oaYblOAU=">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</latexit>

5

単語埋め込みの評価

・良い単語埋め込みとは？…似た単語が近くに埋め込まれている・先行研究：単語の意味評価
評価対象

単語の評価例

計算方法

似ている?

類似度 cos ✓<latexit sha1_base64="v4DNwG0pxXQg+8V8O0Hd7IjgDuk=">AAAm7niczVpvbFvVFb/tIEsLIy2wDQ1BvbUxGNLopCsMIUBNiqZJEDdN8ppsdmNsx3FcO+8Z23HaGheVoWm0aBtUAanThlZt2tA+7MO+DGkS0v4i8WH7UqRO2pdJE4xO8KFIk1Alc+6597173z/7efHEYjl5vvfc3/mdc++559zr5KqVUr0BcGXb9s/ccOPQZ4d37Lzp5s/dMrJr963H6tZ6LV8w8lbFqi3msvVCpWQWjEapUSksVmuF7FquUljIlQ/z/oVmoVYvWeZ841S1cHwtWzRLK6V8toFN1u5bH2dpZrIC22B5ZrE1fGXx8zJrYXuW1ViRWk6yNrXw5wZbRckqfmrguJP4u4btLSl9xpFPswor4acSStTxc4yN4lvH3BlBdwlb+tEt5Lvr5jJcdxGlLJbD9gqNsLC9iE/LiL2Cf+fZXjaB6Pz3EnFokPa2jfi9fzxrnrtj7j/46V5k45ZJkA4bq4l/8xKP25JDqZP0zJ8qKGfbF2P7NGuFfXxcG9sdzQ6iW4cff58j2cK/bZZx+VJH9+NnqEfXUO+hYa4vDfUADdMD8hHp+O6Ts18kTYbHigKOC7akB+Yrf5ofRqxRem/1xTFiqYuZkbkvDAxvoNxyT1Qud740cG6EjTPN465An7x+t/u41x9mj9Ic+ldVmSK5SPHeJpk8W8fYC5YWu4tfdpxeitfXUe9aF256f3d+T6OGAr6CtAbJb9AuGI2l7aEYmD94b3bo9OnNC5LtdIj/6i6P6dhnZK+tO6LeM/HNDfgrXIffwLtwrTNs8+js6JOJkA5j4+7tgw+PVYdL+PqK97XC0oQX73OtRRtVpwzkH+WzegnSS5uXjvxO2ibyme0Rvpudwr+8tXuUCUmhS0iH+0nhV/FzTXJVI5150GzsFUk6UjQW7gjqFpeKr4X9WZrFgqbjMGUU3icws5JxDdF51RDEV0fqxldht13ofsa2Np0vl606vrQ1WJRja1TX8JrJOzdebIXS7oET7m2NVeaPL5yFE9btrVep1pmg6mY0QswEjT4gR3vbvxrSftDR1j97L9YDDtZg5syL/2AI/tbWcF36tEKViyXjXeyT7TCZzl2d3eUvHz3syQ/e3dfe+8qy6nP3nmHP4Dsme73rPYevFpvV5pq4zC3yvReKc4vnfrzw9vd/61RN/012ipybuDa4Ar+Ct+Cq1Oa2RvlzBivVx6Es5i4zIld0jBlgpm/IPC3rxhmsTw2N90xIdWuo1RaAzFd7rJznuA67GI61GYrKeVWbC1tXjLlrdy9/E/FxzZ19f3ZI5T25/kgCtQs0znDMh5eQGp/BVxQLveNjbL+vjWNl0OYQrifuS26CARdC+NoeEGe0Fq1LNzsxp7rulqY1pq1YNWaJety+TWsnkRmw7FmHPKzAHGcL5uw0lM8xajkPFnwLnoIn4AXYhuOXEG2mM+yMMlMXn30dzCSD5c4OsM6+v3ILLMK3O3tgClYR39TPnohXgu+gltXOHs1P38SYLeO7JL1neyEj/cA9qWJwFjksO75apl5l54xjHz/XHqM9s0HtTem5JvbUnB6Hhb1XgLnw8dJm5y60zV6zWXj5xH1QTsbhFKwcSaNfMtz2zjCXhJdRsgzPcfsRfVLySKHdE7TysshtTMbscazWToLZ/Cj5UyfacA6S/0zeBNsFD8igtxfYJFjtv2VytX+ffhuK6MvzsJr8IHURFvicYMU5RN5fxXYTiq6603DiKaWt0HVa3xOeWBCtih9naK9dgWHg+xC+Tdx3xmX24XtYET/x5yZGmoHP81LOoNgST7w1aA+Z1uJKrU3eokftErNvFHSJBN017KfTaZBs9x2g5Yn9WBduwfEW88W5QnBF/ZHzrnrBzUnlAcXMrkkT/h1EYh3ogeXOHdO+rKp0uetPXeMc3UjVQurWutPbpnnniBuOR/fbjHvsvhkao3Q2PRnBveM3Sd4vYbcKKfGstVBsGZ64cHopL4teQ7U+V6MITvL9GC7DVdyp/8DPV54zZnjFNB1W24Yhwxvwa7jU09dh/o3ORM29u5ZPeNax4YnK/mw1nLHipqnbeFsiyF+fxnnJyz0MS/H2ogR7UMe5PyQyxdpVNUC47QO95YLjmLnfAdOpUgeCqp2IuU91S2OwOn8zLHY50wS12R7vb0a8622QyGoeBjofdHYwM7nMSPN5OIFZ/8WBYaflLVsNKyb7xDIp151oVVE1GTo/k85I3bdTrrZ1rW1gnkm9dvG2zu4BeiNaXosue4+UNvoYozwuqqbHAqI/TBuXNLGnoSH0l7H70aayxAadNBRv0RbEx8l98GfMdm9SFcM/K1yFHpM94fv5WABbu2IK6tNvgRIOen+3KL1wu3FK9LQoeoYK0uPOCtE9sPW7nyBd7poiGpuB7g8v/SU1c+6dxhA/jw70WyWRrScDq58pmen994E5tuLcFKhTeVCvqmRsPWMRZac8d0860/sjc1xnbRnR/XBfD+XeD3O6g5h/UZy6+bfJYEELLuCp1hI2YA68AM/DUSjh+Xob/B2r5TfhOubGcvJy4Q3sPRJgvfguOkd7URTbe9mYx9xo0R1CsG28ZgPCuTfyHCcCZ26MPOM/V3pPpqLK+vROzlxyEKfnaNlHzxKPyhmxUDaY5YbkuT+C5D3OXiQyWFD17f4u7v+Fr/5OEyNep2ZpFrpn0fB8xWfnEdK2FTz3Pq++w+R2bRVb56oqmMFge3kn/gf+3RnMNrNrL4wD/cT8DxPyYS+TPzPWrp+zNG1KvHxYo6/ZG/hcQcV1fKUwxAGNabDjTPyDEC/K8s5RM42j+MGmin15VsbfPG2nZCu/3uOYdRqddxUIo3AZXodr8Bb8Ev4F10OxWoTBuZxi/J9MaGyhmhmhfxnqNcp2oDOqK+cGbrQPEdcSXVLyFm5FXoxvnn712tzDs6OtOFyCq8j/J3AFfo8WmM2P8j87Wpj9IduJEzDhdbf/4diB8YkHxw8ePbj30JScimF2J/sKXfJ9jR1i38CN0GD5fR+Ofn707tE98Wr8lfiP4q8J0e3b5JjbmOsn/otPAGTWAu0=</latexit>

vman<latexit sha1_base64="690H7FPFvmE+oT4WM4Z2DK6nedo=">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</latexit>

man
先行
研究

vwoman単語<latexit sha1_base64="p0DwowTezVOJl79K6V2Qqddm/RY=">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</latexit>

woman

✓
<latexit sha1_base64="L0TX4aMl7OM1xC8eli/Ex051Gwc=">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</latexit>6

研究内容：埋め込み品質評価
従来の埋め込み品質評価に欠けている視点• 埋込空間にエンコードされた「単語集合」は我々の直感に合う特性を持つのか?
例１：Maleの中にboyがある

Male

man
king
boy
son

例２：ColorとFruitの共通部分にorangeがある

red

Color
blue

lemon
orange

Fruit
apple

7

単語埋め込みの評価
本研究: 埋込空間における集合の意味評価

評価対象

例

集合

man
king

計算方法
Male
提案法

本研究
集合
の関係

Color
orangeFruit

提案法

提案手法：量子論理に基づく集合表現

9

埋め込み空間における集合演算
行いたい計算（評価のターゲット）<latexit sha1_base64="gukf2gbe3WGbhvfFABSvXzuQZlw=">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</latexit>

e.g., boy 2 Male ,<latexit sha1_base64="XpX3MCFM6eRkYL1EaSXrko7FO1g=">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</latexit>

orange 2 Color \ Fruit , etc

必要な表現
必要な表現

例

単集合

{king}<latexit sha1_base64="Fd04ENS7Koe6v/k7Apc3fVpS8HA=">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</latexit>

Male := {king, man, ...}
<latexit sha1_base64="bmv2wRz26KZH7b8cIkXyWArtqwc=">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</latexit>集合

boy 2 Male<latexit sha1_base64="8ccWN1nu2+8GiMVhkSvoeKwaMJw=">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</latexit>

帰属関係<latexit sha1_base64="nKsPz8FRhLwEzrpClI+5n/KpDFI=">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</latexit>

補集合

Male
Color \ FruitMale [ Female<latexit sha1_base64="Ee34FHbXOhACH6l81UtTeh3YR4o=">AAAQinicrVdNbBtVEH4pJU1LcZwWCSSEakiDCKLRJKr4KapUmgohgVPHzjYRSWPszcZx7ey63q3z47pVQEI0kQCpCpWKREUkhCoOCHHh78SfkLhw6aFXLkB7DBKXSmbe7Nvdt16v7Uj1yvbbeTPfN/Nm3rzdbKmYNy2A2127Htj9YPeenr37Htr/cKQ32nfgjGlcKKuaohpFozyVzZhaMa9ripW3itpUqaxlFrNFbTJbGOXzkxWtbOYNfcJaKWlnFzM5PT+fVzMWioy+PQfYDNOZxpaYygy2iFcG7+dYFeUZVmY5kiyzGkn42GILqFnCOwvtlvG3jPKq0L7k6s+wIsvjXR41TLyPsQH8ypj7OuDOo2Qn3LZ+a26uw7lzqGWwLMqLZGGgPIejOcSex/8J1s+GEZ3/zpIPFrHXHMT3/7ysrz+W+g/vnkFv/DqDxOFgVfBfFXg8lixqLdOYj4qo58QXY4elaO34uF0N5S4zIfrxg9iHXd4q/tdY2reOMnIQO00zMoPZhsHcEYPZhCF+n9aHON57I/koMSnIwTnjlGeN7hrtnTlufYwdJ7tgJAWqnBzVV410VHYBc91c267moO4QXdwL269XkXexhW/yfGv/ziODhlcz1mb6S7TrOvJyFmZmN7dO/yg8tHeQEwHP0Ar+c2nrdbY1bSZbOzwTHn4J78tYMYaw8PPIXrdbSxmpMy/8a9gqM56/Bs5nqFI0iWOU6pjP2ZgZ4XEZ0XmfauavjNTKXw+75kMPeuywyf5y3ZK7lg6DQTu7TJ2Ud+nG3DRieyi1Njjhqy15lf7lyhqcMx6pXqPuOkz9tPXO3UmmmuPf33U1Rb/grBbVnB2BiRa1MJ36E/W+wpPjox/+nexeXd28Ktl4/Sfm9oCC6Nf+2UvsIn5jYraxZrJ4VVlS7HrX39TUR79O9EAuNbX+yeTvH/zA7wR7PKRHNnolZ8CUemCLzsLZ4DZ8Cb/BXcHmj8ZbzwRLsVNQsDOX7hVZizEF9Jnd6fOi4yfwZFEkvxMh55Li1lsz5BGOXFA5rutdDG0dD+0zb0HKhcMVazh1G/3XER8rbu1Oshv+gHvwDfwF26K6SQPZbTTu4XMBvEHBeBGvTiJstI+xIwEZx0pjzCG+nnt2bBMUuBrir7MC8vNVlaozQbXC0WYR3dZLUNU5TwIJMJzcgQrzkOKcoCfjUFhnJNkAA96Et+B1uAJdhHScJeo9rpU+ff3yTdDHGMzV94Kxdmc+AlPwTv0QnIQFxNdlvxAvD+8iy0L9UDDa0xu+XuPPhlf/Tk6882wwFGukDZZ/z8QDvcrj8p9dMmOKnp/LIWee6c7WkF8hxCW3io44HrepujTZeJyVhp3gr/QK6Qc1HKmtZY8lCe1gee8qMir1I3tW8aRv8/P0FTbG6xBuwV2s0J9xpEu9M96yk8fD+ncYMnwLX8NW27UOW9/OPfFy738OkPIwfeP6wXpfx3nPhJyizXR10qUrHe2HIaBPLDgYFoN+Jj4JI/o5PdYbVNqL9Ehq4biIpCZe07jFAIO22Fnx8mZhyKp7PM+glYnjEs6peBRkKPBpIeUbmmOaZK36lnMAE3UTtrFdfwH/wL1QrCphcF9W6GWDbLVSupde59pZOYvnWrX02cKXmxfJV94YSyThUai2fWX12nbqWHKg+jRsYZHdgk/xwPkJI9Ar/6qfjWvJjykBw43LHRycGRkafn7o6PjR/hMnRSp62OPsKWppL7AT7DUsRYWpkY3IV5HvIt9H90dHoi9FX7ZVd3UJm4PM94me+h96wzWX</latexit>

共通部分<latexit sha1_base64="70T6OcHf9QFn8hSD4Ll1hsOI0fY=">AAAQKnicrVddiBtVFL5b67qtmuxaQUGk0e2Kq3Y5uxSVQqF2RQTNNptsuks33ZjMzmbTZGfSzDT7k6ZlFcRuQYWyFiooXRApCj74ouCTfwi+iNCHxbciqO3jCr4U4rln7szcmckkKTRDkjvnnvN959xz7rkz+Uq5aJgA2z277tt9f+8DfXv2PvjQw5Fo/8AjJwz9bFVR04pe1qsz+ZyhlouamjaLZlmdqVTV3FK+rE7nS+N8frqmVo2irk2ZqxX11FKuoBUXikrORJE+0HuTZZjGVLbMFKazJbxyeD/P6ijPsSorkGSFNUjCxyZbRM0K3plot4K/VZTXhfZ5Rz/DyqyId0XUMPA+xobwK2Pu7YK7iJK74bb023NzHc5dQC2d5VFeJgsd5QUczSP2Av5PsUE2iuj8d458MIm9YSO+f/OCtvF46j+8exa98eoME4eNVcN/ReDxWPKotUJjPiqjnh1fjB2QorXi43YNlDvMhOjFD2IfcHjr+N9gWc86yshB7CzNyAxGBwbjrhiMFgzxe7Q+xPHem8nHiCmNHJwzTnlW6c5vb89x68PsCNkFIylR5RSovhqko7CzmOvW2lY1B3VH6OJeWH69hrxLbXyT59v7dwYZVLxasbbSX6Zd15WXc5CZ29w6/r3w0NpBdgQ8Q6v4z6Xt19nStJgs7fBMuPgVvK9ixejCwssje91pLWWk7rzwrmG7zLj+6jifo0pRJY5xqmM+Z2HmhMdVROd9qpW/MlI7f13shgc96LHNJvvLdSvOWtoMOu3sKnVS3qX9ufFjuyiNDjjhqy15lf3p4jqc1h+tX6HuOir66b3MkyH2M5ebVBNWXAbaNMJ0mk82B0pPTY5/+Heyd21t87Jk4/aHmLNHS6KfemfPs3P4jYlZf07zeNVZUuxKx9/UzEc/T/VBITWz8cn0rx98x+8Eezykh/m9ktfIkHpUm53P2WAbvoJf4LZg80bjrmeCpdirULIyl42KrMVYGrTM7uwZ0ZET2PnTkt+JkHMj7dRDK+QxjlxSOK7jXQxtbQ+tM2lRyoXNFfOdin7/NcTHilu/leyF3+AOfAN/wQ5V35ClgewWGvfwhQDesGA8h1c3EfrtY+xgQMaxshhziK+nn5vYhDRcDvHXXgH5+adO1ZmgWuFoc4hu6SWo6uyTOgG6nTtQYAFSnBO0ZBxKG4wkl0CHk/AWvAEXoYeQjrBEs8+x0mavXrgO2gSD+eYe0NdvLURgBt5p7odjsIj4muwX4hXhXWRZbO4PRnv8ktQL/Nlw69/OiXveDIdijXXA8u6ZeKCbuFzes0VmTNHzbTXkTDKc2Qbypwlx2amig7bHHaouSzYuZ823E7yVXiP9oIYttbSssSShHSzv3bSMSv3Imk270rf5efcKm+B1CDfgNlbojzjSpN4Zb3uCxcPOrTBk+Ba+hq2Oax22vt174ubee05LeZj99Oq+5kDXec8J2250NdKlK9s/CCNAn1hwMCoGg0x8Enr/5/TYrVNpL9Ejo4njMpIaeM3iFgMM2mSnxMuViSErzgGaQSsDxxWcU/AoyFHgs0LKNzTHNMha8SznECbqOuxgu/4C/oE7oVh1wuC+rNLLANmqlWyUXrc6WdmL51i19dnEl4+XyVfeGCsk4VEoln1t7cpO6nByqP4MbGGR3YBreOD8gBFotX+VzybV5MeUgFH/cgcHJ8ZGRl8cOTR5aPDoMZGKPvYEe5pa2kvsKHsdSzHNlMjzkcnIychs9Mvo79Ht6B+W6q4eYbOPeT7RP/8HsGck8Q==</latexit>

和集合埋め込み空間における集合演算10

単語埋め込み空間でどのように単語集合を表現し単語集
合間の演算をおこなう？
• 単語埋め込み空間（ユークリッド空間）での集合表現➡ 量子論理 [Birkhoff and von Neumann, 1936]

量子論理• 量子力学特有の現象を扱うために提案された無限多値論理• ヒルベルト空間上の集合演算• ユークリッド空間はヒルベルト空間➡ 単語埋め込み空間に適用可能

11

埋め込み空間における集合演算
必要な表現を 量子論理で表現する

表現

例

単集合

{king}<latexit sha1_base64="Fd04ENS7Koe6v/k7Apc3fVpS8HA=">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</latexit>

Male := {king, man, ...}
<latexit sha1_base64="bmv2wRz26KZH7b8cIkXyWArtqwc=">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</latexit>集合

boy 2 Male<latexit sha1_base64="8ccWN1nu2+8GiMVhkSvoeKwaMJw=">AAADz3icjVFNa9RQFD2Z+FHHj466EdwMDiOuhjdSVApCURA3Yqd12oJpS/J8raHJS0jSkXFQ3OpeXLiyICKu/QO6cenGRX+CuKzoRtDzMungdNrqC0nue/ecc89914sDP82E2LRK9oGDhw6PHSkfPXb8xHjl5Km5NFpPpGrLKIiSBc9NVeBr1c78LFALcaLc0AvUvLd23eTnOypJ/UjfybqxWgzdVe2v+NLNeBRV3qOOKm7BRQCFMncOQu4y3EfCqDfIPSJuElf5dXi6E7UGHxqrRDk50oHEOuI90Gand8E28se4qC4JZ+n5xu0PhSejXh7R8RChW2gYRHUf97kqqyhmUvL0rt3+nf8/3eFeh1E3iAi3kcuVmmiIfFVHg2YR1FCs6ajyhoL3aMXIh5TQlJYUc2kwxV00IVg2wyJLuSyZ0awctOuQlTKOmZMckMvxKLL6p5p7o5nmbMkqAd8kb6guvoi3Ykt8Eu/EV/FrT61ermG8dPn3+lwVL48/OzP785+s7asasPb1nGEFV3KvZiBxfmK6kH1+5+GLrdnJmXrvvNgQ3+j/ldgUH9mB7nyXr1tq5iXKHEBz53WPBnMXG81LjYnWRG3qWjGKMZzFOVzgfV/GFG5iGm1I67P1w/pdgt2yH9iP7Sd9aMkqOKcxtOynfwClStA1</latexit>

帰属関係<latexit sha1_base64="nKsPz8FRhLwEzrpClI+5n/KpDFI=">AAARRHicrVdNbBtFFJ6UkqYFaocigYRQDWkQQTR6CaGgSpVKAwgJnDp23EQkjbE3G8e1s+t6N86P61YBCdFUAqQqVCoSiEgIVRw4cAGJEz8VEhcuPfTKBWi5BcSlwrx5O7s7u+u1HVGvbM++ee/7vpn3ZmY3Vy4VDBPgZteue3bf272nZ+++++5/YH8k2vvgKUNfqihqWtFLemUqlzXUUkFT02bBLKlT5YqaXcyV1MlccZT3T1bVilHQtQlztayeXszmtcJ8QcmaaNJ79+hshmlMZctMYTpbxCuL93OshvYsq7A8WVZYnSy8bbIF9CzjnYlxK/hbQXtNeJ93/GdYiRXwroAeBt7HWD9+Zcx9HXAX0LITbsu/NTf34dx59NJZDu0litDRnsfWHGLP4/8E62NDiM5/Z0mDSex1G/G9Xy9oG4+k/sG7p1CN12eAOGysKv4rAo+PJYdeK9TmrRL62eOLsUPSaK3x8bg62h1mQvTiB7EPObw1/K+zjGceZeQgdoZ6ZAajDYOxIwajCUP8Ls0Pcbz7evJhYkojB+eMU55VuvPH2308+ig7RnHBkRSpcvJUX3XyUdgS5rq5t1XNQd9BurgKS9cryLvYQpvc31rfWWRQ8WrG2sx/mVZdRypnYWZ2c+vkd0KhtYLsEfAMreI/t7aeZ8vTYrK8wzPh4pfxvoIVo4sIL4+sut1cykidqfDOYavMuHp17M9SpagSxyjVMe+zMLNCcQXR+T7VTK+M1Eqvi133oAcV22yyXu5bdubSZtBpZVdoJ+W7tD83fmwXpd4GJ3y2JVWZHy+uwxn9odoV2l2HaD/t72BdNoseFtF++7Mh9hGxe+9cux/pOUf33cmYH/9ICP7/q2BDzCi3m7RaLA4DY+phPo3HGr3Fx8dHP/g92b22tnlZinEzFHN2r6I4aby959k5/MZEr7/ac3jVWFLKNGlJTX14faIH8qmpjY8nf37/W34n2OMhu7tflTxHhrR7t9gTORvchC/hJ7gt2LyjceczwVLsJShauctERD3HWBq0md2Zs+KsSuCZmJZ0J0JO1LRbbU2Qea3HigrHddTFMNZWaJ3WC1IubK6Y73nBr19DfKy59VvJbvgF7sDX8Btsi/ojD2S30LjCZwJ4A4LxHF6djNAfH2OHAzaOlcExh2g98/TYJqThcoheewbkJ8MaVWeCaoWjzSK65ZegqrOfYRKg27kDBeYhxTlBS8ahuMHIcgl0eAPehNfgInQR0jGWaPQ4Udr01QvXQBtjMNfYC/r6rfn9MAVvNw7CCVhAfE3WhXgFeAdZFhoHg6M9ecmzS3qz4da/nRP3JB4IxRpug+VdM/HAbuJyeU9dmTFFT/6VkNPacHrryJ8mxGWnig7bittUXYZiXM6qbyV4K71K/kEP22p5WW3JQitYXrtpGZX2I6s37Vrf4k8CL7IxXodwA25jhf6ALU3aO+MtT4p42IkehgzfwFew1Xauw+a3cyVu7r1PMFIepj+5eqDR23HesyHnXDNfjXzpykT7YBDoEws2hkSjj4lPQo9+Ti8kOpX2Ij1Mm9guIamB1zQuMcBBm+y0eO00cciKc4DOYJSB7TL2KXgUZGng08LKFzTHNCha8UxnPybqGmzjdv0F/AF3QrFqhMG1rNJrEsWq5UyEXkTbRdmT50S11Gzia9kLpJVvjGWy8FEoVnx17cp26miyv/YkbGGR3YBP8cD5HkegVf9SPhtXkx9RAob80x1snBoeHDoyODI+0nf8hEhFD3uUPUFb2vPsOHsVSzHNlMjLkWLEjCxFr0f/jG5H/7Zcd3WJmAPM84n++x94Wl9x</latexit>

補集合

Male
Color \ FruitMale [ Female<latexit sha1_base64="Ee34FHbXOhACH6l81UtTeh3YR4o=">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</latexit>

共通部分<latexit sha1_base64="70T6OcHf9QFn8hSD4Ll1hsOI0fY=">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</latexit>

和集合

12

量子論理による集合演算の表現
集合
線型部分空間集合

線型部分空間<latexit sha1_base64="XPwlykeCBV64zFXT9kPagGPwhTA=">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</latexit>

Male = {king, man, ...}
<latexit sha1_base64="/fwlMaf3Fz0loGsorRu02Szi2Ec=">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</latexit>

S Male := span{vking , vman , ...}

vking
<latexit sha1_base64="8vSo71Mq3qgQv/xc7sBnKBuqcVs=">AAA0pnic3RtbbFxHdRJKcNJSJxRBAVW9kMTNtok5dk1BFUWJk1ZIxY94vbHBG2+96/V6s5u77u56N8l6E6VUiNoVhUahUpBARKCq4oMPfogEqsQzqEKFjwQFiR8kBDSIn1RCQpGWM2fu3Jm5j30kNwRh63rvPffMec15zJxZp1eK+UoV4Nqmze+5571b3te3ddu9973//v7tOz5wpFJaLWeyiUypWCrPphcq2WLeziaq+WoxO7tSzi4cTxezM+nCQf5+ppYtV/Ile7p6ciV79PhCzs4v5TMLVQSVdnzEYklmsyyrswwrseP4u4DPi6yB8AVWZjmCnGBNgvD7KltGzBV8quK4E/i3jPCGg33axU+yIsvjUx4xKvhssd146TS3dcE7j5BeeAv89rw5DuedQ6wSSyO8SCNKCM/h3SLSXsLPabaTDSF1/neeZKgS96ak+LU/n7HXH4z/C5/2oDQmTox4SFo1/Mw49LguacQ6Qff8roh4Uj+L7dK0FfrxcU2Eu5xdiiYPP/1dLmYDP5ssZdhSp+6nn6I32/BZ8ah04BHviUfF5XFnLfX/Z6WxiCxEPL76hakPE6eEwaOCn9UQTTrQ/OavpvsMWvVboxOfXf+2QSeOscWzRHtqGYrpQF2//repLadOnT9HM8av2/3dRhZcXn8Q7ImN6CiixbY5819HTQqUtXKoh4TWEGo++XHEDDbYAQ0mLWhCx7TnyHRwvCAaakJHUSOaGqROtUNCgywhYM+zVbRGVhvtjz9Oq4y+xisIv5JoG4Ebhsdtx3lZaD3LxS5RpJepCvEKp2x7gEZw/1zBu1EDtqrBIrG/4etRUPRekUg5dyHVH/9Q5DJGIlv62eKV1kfviP0sjDmepbKBHibfcQ97kj1FHuL3V+XnSccXpRcFYcso8eIO0q8pk9Xqk346cQZegWNwqLWVcDrLspcwgnnvdfkl3TgM1zxqXvL6b9iy84xGMe/d6q+87hmkfryN5+nv20uhZ9RubKZn6nC7efwQbCOLiUoVZKWKYRed9mnnreTdI99WH1yC38MNx//DJTC1rTh1tunYohYwb7W23mpIc3rgfB1+Bzfhx/BXlKXPla6TVF67COww25hv21jHKw+v9a4s4T490FM2E3470GMsdjeqQvs9/yif1vOQnD9/ceJnjm5i9ygtwlefJ/FTrAHaZXSBqa8Ywu2k6K/QOkLIqka686Dp2CmudUrdSWHGc7ssoeTl66IFmsWsxuMg7Uv4O3318ww+r9IePUhenVI7eRXtpkHdL7HkpsvLcVdcW0oO/vWbOTde2opKswOdcGtrUqV++dJZOFb6YOM16iwMUS+hm6oVNHrYGe2FPx4CH3G59S69l9anXFrRzJmX/hMh9G/PhyuOTYu0eyo58S7yZDMMp/VQa0fh44cPeqqVN/vK3FcI2LXxbLyGl+W89fp7Gn8bbEqba8WjHkK9fst0rfgsz+mQ43vwmbde+Ym7m7uVGtxtBTYyLlbet7HC/MatK7WQPDrmi9AAGrMj031TW+AwzMASxtReBmBP7oJC5pOwoSqZwymNlHJEv0HeyXfSFXf2zd8h+jtAkiw7dT9D8TLMeFezGeB7ebbkwM0Rj2sjutNW1S6vXHALcpXonkd9HflVtIyXdXqzujUkZ6/FfwpX4LI7a7y7WyFegnYVKbQbpeGBPXfhzBu+2VF09NWXtE+RekVVJ1/yrm9Gk0G+3aPdDxLmElUc3p9bY6pXt+r66yJZxzsza0z0p71jBGTNg50kfP5ZRnlzqEcVc1gSvVGHrDkQk57Qr+HzAJOamRsCLM7jGa7BD+EyXNfiyuyZCH+aZHF2CAoi66b6nVpksQTYyXtSzzt9w0mWos6hzAyTLLi7mVB1IoAyr1NWIcPputJZOFZKKCyxrOU5yctiZvfWK7+N9LFanH0Ho195kqgchEG+MOZIuNdHL+ZwXKN56ayhd7zF9vlgnFYKdQ6R9dij4+chAedC5LUMn2+Qp5vSyf6g4t3QuFpaTVBj5umNadskU53oSSjJWYcMLEGcSwv21BgU1hlBNqAEX4Ln4Fl4CTbh+HmkNtnqc0eJaLbHGSy2tkLp7DtL98MsfLn1MIzCMtK39TMapJeHryCX5dbDmp2+iJFUwCvvWE9aIeXYgVtSZcsplGHRtdUivVV6Trr68VxwhPJeleA1x3I1ii35xpVCVnmwZ/49f771EOomfXYBXj32KBTGB+AkLE0k0S4prnurj2PCq4hZgBe4/kz0DLkcc6j3EHneAsomd4JHcZ91Auzau+Pfc6MN52D8L+P3wmYhB6TQ2jPsAJSaf0yly/849Rbk0JYbsDz+z7kLvNLBBu4Vt5D1lxFuQ87YMSbceJrz5JuUI5EXOqztVI+6vitoJPDaj5eNtWbQWTfyLJXDJ35fw0hL4P20g5eg2BJ3HBqUQ8a0uFK+ySF61M4zefKmY8ToTG4fnQIE4bbPAA1P7FttZAuON8sX54qCEfUTG0xf6ZsyqUyvJJP1JObPIA6t4Q60zNXZmG89rHiZO0edY5zqajlkx1lx3zZp3jnFumvRfVLiDtk3RWMUz5qnIpgZv0b4fgwJFVjiXoNQbCU8ceG+pZWveJtQ0BfKFMHjPB/jyuU6Zupf8M6Ip1cVvtcZC9uVhlGGS/AjuNjR1mH27V4SNffmLjzm8eOEJyp70zXhjpXnVOHjJUaQve5Gp8MrexgtJbeXSrAFdTqPhUSm8F0rsOto6i6ljeQsBI5i5b4KdqSnenovi9tU19SC5en7YLZNNyIIJi3e24x4/S1KyubZQ2SWo925nUqn+msvwjGs+i9HRrvz2SjHOhAYfcFno2Fz2Ou5aGTWm/vOhQdaOyK0WHe1r3vcRxzsRA9jlMXFyupzARkijBvHtGmHqyj0VtV74aYqSZ12I0puAQuSx62P8GusiG+637dQdBV1y3kTnvODTs7kqirond7jjbnUe+uRdqLbTqZYR426r2JBfMzK0b0Fbr+zG8TLXHd0J02k+eEbb89Nrl+tbuF71ki/n6C+a+NfIY06qwF/Dk6zJbeboHbuQW/NPuEBn/XCcUeZt7OsJH2saxlFvyyMY5jsq6Gy9yI59SmmXxY7c/7NTChBA87hzrckdMA6eQ5ehMOQxz34JvgTrqjfhJtYPwvjV7KX8O1EgPbie51pykXd6N5JR72TGKQbX9cB0dnT9RzHAmduL1nGv/f07l7FSuzu7a45ZhQ77O6qj14lnnJmhHeHg6WsO3Lu6wLzETcXiQoWtEI3T9r/V+TVL71rzGehfRUNr1d8dj7LrNukZ+Z59Q0F/5nC7cmqVjDR0PbKHbsD9g23hZeP7IjIWe9sReUvprdofYoca4626UnEcTUwwabY09oeV52x8KzBu9aH6ERE7J9WcZzgH+T7MusdIvw9kcdBzLBSyYhUd8fFe9e410rBetf9mLu5SpI6xMj+dyB3pLbvhEGgH8t/M+Tc7GTOz2Rp++ssSQUwQ9PNjxWreF+kY8UKm0PHADRGlR1l4h87+AYg47Y+kjiKb7TFYWYB/3Ll5xwobzcfp8NJPjpjmHk3XIE34AZchh/A3+FmKK0G0eCynGT86+U0NruS6qd/9eg0SprfHdVW5ioGxGdI1jw1zTmEa5ER42unXrsRf3Jqd2MALsJ1lP+7cA1+jhrYtXcz3z+cnfoWTcCQ19z+myPDg0NPDI4cHtm5f9SZij72MfYJajp/mu1nn8eim2CZ4deHfzt8dfgPI3tGxkcSIzMCdfMmZ8wDzPgZee4/DlRqmQ==</latexit>

S Male<latexit sha1_base64="KV0dgqI/G0bb4sVxpFf3g55wud8=">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</latexit>

vman<latexit sha1_base64="RDeiiWBkOUxiQP3gqBMpndiexTY=">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</latexit>

13

量子論理による集合演算の表現
共通部分
２つの部分空間の共通部分

共通部分

共通部分
<latexit sha1_base64="/xCrZH9+qZjDvz7ZULCUxq1rlEs=">AAA4LHic3RtrbFtX+bSMkmZjaRmCaWiaoW1Wb0n4kpUETRS1aZmQRh6N4yYQJyZ2HMexc53Zjt3WcauOCbFk2mBVmVQkEBUITUjwgz9UAk3iWbQfA4lOKmh/QLxWxJ9OQkKVzHfOued1H/Z1e6ciYtm+/u53vtf5Hud85ya1XsiVKwDXd+x8zz3v3fW+rt3d9973/vt79uz9wMlycaOUzsTTxUKxNJtaLGcKOSsTr+QqhczseimzuJYqZGZS+WP0/kw1UyrnitZ05fR6Zn5tMWvllnPpxQqCinsf+jNJEItkSI2kSZGs4WsRfy+ROsIXSYlkGeQUaTAIva6QFcRcx18VHHcKP0sIr9vYZyV+ghRIDn/lEKOMvyPkAL51mt0BeOcQ0glvjt+aN8WhvLOIVSQphBfYiCLCs3i1hLSX8Xua7CODSJ1+LjAZKox7Q1B88U/nrK0HY//GXwdRGhMnyngIWlX8Ttv0qC4pxDrFrulVAfGEfhGyX9OW60fHNRAuOUuKJg83/f0Ss47fDZI0bKlTd9NPsjvd+FvxKLfhEeuIR1nyeHct9f9npbGQLMR4fOVzUx9mnOIGjzJ+V3w0aUPz67+a7jJo1W6PTmx265sGnZgPnRjGHM0ewrYBtP7q36d2nTlz8YKDPqfTWto0yxntqB5g7zt9dbMZWtl6EKyJ7fAo4ox02/5VQ03yLCtmUQ8BrSLU/OXG4R5SJ0c1mJoJAaV4dfRYarOMhjmm4YSmF/MYql2frVtYlLmdeI0SelUdkNC0YPGjLByeDmLGzNkwZ5LypR6+bszxqKYjH+POXzWMlRLGEq3A9J1AChzXD49yoF4VQc4RiV1kmbLEqjhdISg/OWpIN2rANjRYqP4E1+GHcBVuyGoS1mw4/YdDamw15ISa0cdhz6DOGXyF7n8yi+kR3Wf7Q3j6xzw80YRFyJPkMPMMpw+VbakatieaNuqTWUtYkkIG2Cuh8dJzle5Z3bYkx1hFpd7qjAt69ymEb7BVJqd4mN0R0tARZ8kmviMaRPi7m35fCzydU8IRiaHM+NylZE/sQ6HRC1W21NOFa82HQpeN1yHha155yu2HXllPeV1CesmG7SVu7DXptSYu901TpkizS/jcxDl4CVbheHO3w9P8ZOnziJlWseCvedi8WlWQsG3ZfkbDmPeg+iuvewqpr7XwPP1+ayn0GhDEZnp18bebww/BMta1fO3mZaWyYRed9ln7ruDdId9mF1yB38FN2//9JQi7ShjSnO29WIPfwi34MfwNZemS0rWTymkXju1nG/NuC+s45aHrRimLv0/3dpTNuN/2dhiLwUaVWdfFPcql9QIkFi5enviZrRvv4QiL0D3aafzmFbNVRueYZn31s5Oiv85Wo1xWNVLOg6Zju7jWKQWTwoznVllCyUvXE4tsFjMaD7XW0FcyamXhJa9OqZW8/uskp8TmionLS3HXpS0FB/cuwLlWNGkrKo02dPytrUmV/OXz52G1+MH6K4T29wZZRy9I1fIaPWSPdsKf8IEfktw6l95J6xOSVjhz5qQ/7EP/zny4bNu0wPafRTveeZ5s+OE0H27uzX/0xDFHtXJmX5H78jL/63fFmj3v6e8pfNXJlGMdznnUfKjXbpsu7j9pTocs3YfOvP7ST+zO2u3V4KAV2Mi4WHnfwArzG1lXqj55dMwVoR40Zg9Nd03tghMwA8sYU30EwJrcD/n0x2FbVTKbUwopZRn9OvNO2osoy9k3X4Pss5dJsmLX/TSLlyFCzxYaHr6XI8s23BzxhDYimLaqdjnlgtuQq8iuadTXkF9Zy3gZ+4REt4bg7LT4T+EaXJWzRs9YyowXp11BCq1GaXhgzV0696prdhQdffUl7FNgHdWKnS/p2Utak0HcPahdDzDMZVZxaJd8k6iO+Yb01yVmHefMbBJ+SuQcwyGbDuwEw6ffJZQ3i3pUMIcl0Bt1yKYNMelx/eouDzCpmbnBw+JGX8mvy8P9aZLEyHHI86yb7LFrUYTEwUrck3zG7t5PkiTr34vMMEm8zxjiqk54UKZ1KpJPU7pa12tFSsgtsaLlOcErQswzFKf8FtLHanH+bYx+5Um8cjAM5gtjtoR9LnpRm+Mmm5f2GjrHR0i/C0ZpJVFnH1lXHxu/CHG44CNvxPD5OvN0UzrVzemXHqu4RojeHxJjFtgd07YJos6DJqEoZh3SsAwxKi1YU2OQ3yIMsg1F+AJ8EZ6G52EHjl9AapPNLjmKR7M1TmCpuRuK599evh9m4UvNR2AUVpC+RbSTUqSXgy8jl5XmI5qdPo+RlMd3zraesELStgO1pMqWUyjDkrTVErur9JyU+tFccJLlvQqDV23LVVlsiTtSClHlwZr5z8LF5sOom/DZRXh59THIj/fCaVieSKBdklT3ZhfFhJcRMw/PUv0J7zxTOeZQ70HmeYsom9gJzuM+6xRY1XfGvyOjDedg/C/j98JOLgck0doz5CgUG39Ipkr/PPM6ZNGW27Ay/q+5S7TSwTbuFXcx668g3IKssWOMy3iac+SbpC2REzqk7VTnpe9yGnF8H8G3hbVmwF430iyVxV/0uoqRFsfraRsvzmKLX1GoVw4Z0+JK+SaF6FG7QMT5t44RZSfj/eyszAu3dQaoO2I/0kI273iLuOJcUTCifmKb6Ct9UyaV6ZVkop5E3RnEpjXUhpa5OhtzrYcVL3PnqHOMsbpa8tlxluXdBpt3SrEmLdovJG6TfZNsjOJZdVQEM+NXGb4bQ0A5Fr/WICy24o64kHfZypffjSvosyUWweM0H+PK5QZm6l/QzoijV+W/1xnz25X6UYYr8CO43NbWfvYNLomae3MXHnX4cdwRlZ3pGpdjxUmf/3iB4WWvu9HpcMruR0vJ7aTibUGdzuM+kcl9N+LZdTR1F9KGchYC81i53wRL7gNDoar1sqhNdU0jsDJ9H8y26EZ4wdznzEFmxOlvYVI2zx5CsxzbnVvJVLKn+hysYtV/ITTa7U/YKdZRz+jzPmH3m8O7dro+961LDzT3hmixYLUvOO6jNna8gzHK4nxl9WmPDOHHjWJabIerKHRW1TvhpipJjUQMuTnMSx5ZH+HXWBFfk08lKbqKesS+45/zvU7OxKrK657e441K6p31SNvRbSVTtK1GwauYFx+zcgS3wJ13dr14meuOYNKEmh++9sbc5NablV10zxrq8wnq6TP3CmnUXg24c3CKLMtugtq5e901+4RHXdbzxx0lzs6ykvTxwDLyfpkfRz/ZN3xl70Ry1qeYfoHvzOnz0VCEOlzAnW+R64B18gI8Bycgh3vwHfAWrqhfg1tYP/Pj1zJX8O6Eh/b86eoUy0VBdG+no95J9NKNruuA0TkYeI6jnjPXZzw757975Suxu7e7pphh7LCDVR+9Shy2Z4R2h72lrNly9gfAfFTmIl7BvFbo5kn7/4q8+lvvGtNZaF1F/esVnZ1Pkcgd0jPzvHpCwX2mcGeyqhVMOLSdckffBfv628LJR3RExKy3t6LyF9NbtD5FljRGW/QkYrgamCBT5DPaHledsdCsQbvWx9mJCN8/beA4zt/L90XWO87wD4YeB1HDSuaTsHLHRXvXuNdKwlbgfszdXCUJHaLyWdaQc0dyzz4YAPYXcV8M2hf7iP03WdzzPZJgBTDNppseK1bwusCOFctkDh0D0BgVMk/4v1fRDUBatj4SOIputPlhZh4/qfJzNpS2m9fY4SQdnTbMfACuwatwE67C9+EfcMuXVp3RoLKcJvSfMNjYzHqyh/3DVbtRwvxyVEuZKxgQn2Sy5ljTnEKoFmk+vnrmlZuxJ6cO1HvhMtxA+b8N1+HnqIFVfSf93ROZqW+wCRh0mtt9cXJoYHB44NCJQ/uOjNpT0UU+Qj7Gms4j5Aj5LBbdOEkP9w/HhhPD8yM/GPn9yB9H3uKoO3fYYx4gxt/IX/8LMivxkQ==</latexit>

Color \ Fruit<latexit sha1_base64="4WDwJiNqY2wwRvjD1j6bDoyE5CM=">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</latexit>

S Color \ S Fruit= {v | v 2 S Color , v 2 S Fruit }<latexit sha1_base64="0yxTnNJjtmbMEAb4NMu7UA+sThQ=">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</latexit>

S Color<latexit sha1_base64="EjyLRZD7+9YoRj/OnDRnvvRareg=">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</latexit><latexit sha1_base64="i3l0P1HlTp1AkLZ92O2poKIunok=">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</latexit>

S Fruit

14

量子論理による集合演算の表現
ソフトな帰属関係
部分空間とベクトルのなす角度（正準角度）のcos

帰属関係

ソフトな帰属関係

boy 2 Malecos ✓<latexit sha1_base64="VWueNAoUXfpaxDn9RAxaP4SOHAw=">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</latexit><latexit sha1_base64="WX8iTkCHk1HZ/jUwTGvx5rQJtM8=">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</latexit>

vboy<latexit sha1_base64="P9BlQtkfLEJ0qEGhKdW2gbfb4Rc=">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</latexit>✓<latexit sha1_base64="x8AjJ2vH9cRBDJ7MrY7esFNePFk=">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</latexit>

Male

S Male<latexit sha1_base64="KV0dgqI/G0bb4sVxpFf3g55wud8=">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</latexit><latexit sha1_base64="9L3iB7ATsiP7AKORuVJzr8JZMVg=">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</latexit>⇢✓ := min arccos✓|u · vboy |kukkvboy k◆

u 2 S Male

量子論理による集合演算の表現（その他） 15
表現対象

量子論理的表現単集合

1次元部分空間{king}{kvking | k 2 R}

<latexit sha1_base64="Fd04ENS7Koe6v/k7Apc3fVpS8HA=">AAAQyHicrVdNbBtVEH4pJU0LOA5FAgmhGtIggmg0jsKPKlUqDUIIcOrY2cYiaYy92TiunV3Xu3V+XLdKkRBNJUCqQqUiUREJoYoDh16KxIk/gbhw6aFXLkB74BAkQKpk5s3+vd312i7gle2382a+b97MvHm7+Uq5qBsAN3t23LPz3t5dfbv33Hf/A5H+6MCDx3TtVFVWJFkra9VMPqcr5aKqSEbRKCuZSlXJLeXLynS+NM7np2tKVS9q6pSxWlGOL+UKanGhKOcMFGkDu+JslqlMYctMZhpbwiuH9/OsjvIcq7ICSVZYgyR8bLBF1KzgnYF2K/hbRXnd0j7j6M+yMiviXRE1dLyPsSH8iph7uuAuouRuuE399txch3MXUEtjeZSXyUJDeQFH84i9gP9TbJDFEZ3/zpEPBrE3bMR3fz6rbjyS/hPvnkJvvDrDxGFj1fBftvD4WvKotUJjPiqjnr2+GNsvrNZcH7droNxhJkQvfhB7v8Nbx/8Gy3riKCIHsbM0IzLoHRj0u2LQWzAk/qf4EMc7r6ceJiYJOThngvKs0J3f3p7j1gfZIbILrqRElVOg+mqQjsxOYa5ba5vVHNQdoYt7Yfr1MvIutfFNnG/v30lkUPBqxdpKf5l2XVdezsHs3ObW0a8sD80dZK+AZ2gV/7m0fZxNTZPJ1A7PhItfwfsqVoxmWXh5RK87xVJE6s4LbwzbZcb1V8P5HFWKInCMUx3zORMzZ3lcRXTep1r5KyK189fFbnjQgx7bbKK/XLfixNJm0GhnV6mT8i7tz40f20VpdMAJj7bgVfbb8+twQnuofom6a9zqp512ZSvbMbINevxvo+bHfzYE/79VkW6ti8sNqliTQ0ebRphO87HmQOnxyfH3f031rq1tXhRs3DjFnA5Ssrq9d/YMO43fmDXrr7g8XnWWEuJNvqQzH3w31QeFdGbjo+kf3/uS31nsiZAO6/dKjJEudNA2fYmzwU34HL6H2xabdzVuPJMszV6Ckpm7bL9VUzEmgTq7M3vSOi+SeC5Jgt/JkFNNcqq1FfIoRy7JHNfxLoa2tofmibko5MLmivnObL//KuJjza3fSvXCT3AHrsMvsG3VH2kgu4nGPXwmgDdsMZ7Gq5sV+u1j7EBAxrGyuOYQX088PbEJElwM8deOgPh0VqfqTFKtcLQ5RDf1klR19nNEEjQ7dyDDAqQ5J6ipBJQ2GEkugAZvwJvwGpyHHkI6xJLNPsdKnbl89iqoEwzmm7tBW7+1EIEMvNXcB0dgEfFV0S/EK8LbyLLY3Bdc7dELQqfyZ8Otfzsn7mk4HIo12gHLu2cSgW7icnlPPpExTU/f1ZATU3dmG8gvEeKyU0UHbI87VF2WbFzOmm8neCu9RvpBDVtqapljQUI7WNy7kohK/ciclVzpOX4av8gmeB3CDbiNFfoNjlShdybanhSJsFM1DBm+gGuw1THWYfHt3hM3996nCCEPM1cu720OdJ33XMg510pXJV26stFBGAH6xIKDuDUYZNYnqUU/pZcCjUp7iR5oDRyXkVTHawa3GOCiDXbcevUzcMmyc4DOopWO4wrOyXgU5GjhM5aUb2iOqZO17AnnECbqKmxju/4MfoM7oVh1wuC+rNKrCtkqlWw/vQx2srKD51i19dnAV6MXyFfeGCsk4auQTfva2qXt9MHUUP1J2MIiuwEf44HzNa5Arf0hfzKppD6kBMT94Q4Ojo2OxJ8bGZscGzx8xEpFH3uUPUEt7Xl2mL2CpSgxOfJD5PfIX5G/o69GK9Hl6KqpuqPHstnLPJ/ouX8AhvpEng==</latexit><latexit sha1_base64="I6WBwxChD7HqW0+gxuC8SJ/PNL8=">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</latexit>

S?
Male<latexit sha1_base64="lLGU/+nRRJEwWDByj/W1RmaxkEw=">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</latexit>

補集合

直交補空間
S Male<latexit sha1_base64="KV0dgqI/G0bb4sVxpFf3g55wud8=">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</latexit><latexit sha1_base64="nKsPz8FRhLwEzrpClI+5n/KpDFI=">AAARRHicrVdNbBtFFJ6UkqYFaocigYRQDWkQQTR6CaGgSpVKAwgJnDp23EQkjbE3G8e1s+t6N86P61YBCdFUAqQqVCoSiEgIVRw4cAGJEz8VEhcuPfTKBWi5BcSlwrx5O7s7u+u1HVGvbM++ee/7vpn3ZmY3Vy4VDBPgZteue3bf272nZ+++++5/YH8k2vvgKUNfqihqWtFLemUqlzXUUkFT02bBLKlT5YqaXcyV1MlccZT3T1bVilHQtQlztayeXszmtcJ8QcmaaNJ79+hshmlMZctMYTpbxCuL93OshvYsq7A8WVZYnSy8bbIF9CzjnYlxK/hbQXtNeJ93/GdYiRXwroAeBt7HWD9+Zcx9HXAX0LITbsu/NTf34dx59NJZDu0litDRnsfWHGLP4/8E62NDiM5/Z0mDSex1G/G9Xy9oG4+k/sG7p1CN12eAOGysKv4rAo+PJYdeK9TmrRL62eOLsUPSaK3x8bg62h1mQvTiB7EPObw1/K+zjGceZeQgdoZ6ZAajDYOxIwajCUP8Ls0Pcbz7evJhYkojB+eMU55VuvPH2308+ig7RnHBkRSpcvJUX3XyUdgS5rq5t1XNQd9BurgKS9cryLvYQpvc31rfWWRQ8WrG2sx/mVZdRypnYWZ2c+vkd0KhtYLsEfAMreI/t7aeZ8vTYrK8wzPh4pfxvoIVo4sIL4+sut1cykidqfDOYavMuHp17M9SpagSxyjVMe+zMLNCcQXR+T7VTK+M1Eqvi133oAcV22yyXu5bdubSZtBpZVdoJ+W7tD83fmwXpd4GJ3y2JVWZHy+uwxn9odoV2l2HaD/t72BdNoseFtF++7Mh9hGxe+9cux/pOUf33cmYH/9ICP7/q2BDzCi3m7RaLA4DY+phPo3HGr3Fx8dHP/g92b22tnlZinEzFHN2r6I4aby959k5/MZEr7/ac3jVWFLKNGlJTX14faIH8qmpjY8nf37/W34n2OMhu7tflTxHhrR7t9gTORvchC/hJ7gt2LyjceczwVLsJShauctERD3HWBq0md2Zs+KsSuCZmJZ0J0JO1LRbbU2Qea3HigrHddTFMNZWaJ3WC1IubK6Y73nBr19DfKy59VvJbvgF7sDX8Btsi/ojD2S30LjCZwJ4A4LxHF6djNAfH2OHAzaOlcExh2g98/TYJqThcoheewbkJ8MaVWeCaoWjzSK65ZegqrOfYRKg27kDBeYhxTlBS8ahuMHIcgl0eAPehNfgInQR0jGWaPQ4Udr01QvXQBtjMNfYC/r6rfn9MAVvNw7CCVhAfE3WhXgFeAdZFhoHg6M9ecmzS3qz4da/nRP3JB4IxRpug+VdM/HAbuJyeU9dmTFFT/6VkNPacHrryJ8mxGWnig7bittUXYZiXM6qbyV4K71K/kEP22p5WW3JQitYXrtpGZX2I6s37Vrf4k8CL7IxXodwA25jhf6ALU3aO+MtT4p42IkehgzfwFew1Xauw+a3cyVu7r1PMFIepj+5eqDR23HesyHnXDNfjXzpykT7YBDoEws2hkSjj4lPQo9+Ti8kOpX2Ij1Mm9guIamB1zQuMcBBm+y0eO00cciKc4DOYJSB7TL2KXgUZGng08LKFzTHNCha8UxnPybqGmzjdv0F/AF3QrFqhMG1rNJrEsWq5UyEXkTbRdmT50S11Gzia9kLpJVvjGWy8FEoVnx17cp26miyv/YkbGGR3YBP8cD5HkegVf9SPhtXkx9RAob80x1snBoeHDoyODI+0nf8hEhFD3uUPUFb2vPsOHsVSzHNlMjLkWLEjCxFr0f/jG5H/7Zcd3WJmAPM84n++x94Wl9x</latexit>

Male

S?
Male = {u | u · v = 0 (v 2 S Male )}<latexit sha1_base64="7Yg3ZVk95AApjBr+nV4HR9Q3uHw=">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</latexit><latexit sha1_base64="EnWMMvwEIz1BvPcoqY1+LYXbN6s=">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</latexit>

和空間

和集合

Male [ Female<latexit sha1_base64="hFHKVa3IPjCISOK3pVe3lebk6No=">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</latexit><latexit sha1_base64="jB7YiEFleSMgvjEm7SzwTYxd0kE=">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</latexit>（ハードな）

帰属関係

boy 2 Male<latexit sha1_base64="WX8iTkCHk1HZ/jUwTGvx5rQJtM8=">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</latexit>

S Male + S Female

S Male + S Female= {u + v | u 2 S Male , v 2 S Female }<latexit sha1_base64="tEQWPrL+RYdIT5Oaw/Xzp49rAZg=">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</latexit>

部分空間の元vboy 2 S Male<latexit sha1_base64="xx+RIVuUWqnuIMzzXxO2VZ05Nuc=">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</latexit>

S Male<latexit sha1_base64="KV0dgqI/G0bb4sVxpFf3g55wud8=">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</latexit>

実験定性的評価：量子論理が埋込空間で集合を表現できている？
仮説：orange ベクトルは Color \ Fruit 部分空間の近傍

17<latexit sha1_base64="rMLPoZgZnTsewzoTH+f4wqjKVUw=">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</latexit>

e.g. Color \ Fruit からサンプリング<latexit sha1_base64="GxvJcb72/fCyyBHZo7bvc/9egrg=">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</latexit>に埋め込まれている

orange?
検証方法： Color \ Fruit 部分空間からランダムにベク
トルをサンプリングし最近傍の単語を確認<latexit sha1_base64="rMLPoZgZnTsewzoTH+f4wqjKVUw=">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</latexit>

結果： Color \ Fruit 部分空間に orange が含まれる<latexit sha1_base64="rMLPoZgZnTsewzoTH+f4wqjKVUw=">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</latexit>（他の集合も同様の結果）<latexit sha1_base64="CwcdcfZD2ptHB9wyfx2D2mXCUDg=">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</latexit>

部分空間

最近傍単語*

Color \ FruitMale [ Femaleorangegranddaughter<latexit sha1_base64="kMO9WB7jv9kaG5fchQNSsFuRbBc=">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</latexit><latexit sha1_base64="qFUN4k7wls2yz6OBiR/z0DEheig=">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</latexit>

Male [ Female \ Male [ Female(= Male [ Female)<latexit sha1_base64="s3q8VCmT2EEoxb/1+Dpc0t3w8Bk=">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</latexit>

grandmothergrandmotheraunts

grandfather

bride

girl

brothers* 複数サンプリングしたベクトルとのcos類似度が0.5以上の単語の上位4件

定量的評価：量子論理が埋込空間で集合を表現できている？
仮説

18<latexit sha1_base64="/l4uXLgz/ouJn8/ZI5PXR36AaYM=">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</latexit>✓(Male,boy) < ✓(Male,apple)

vapple<latexit sha1_base64="CSsmfE4VPoGPtvPz0rxyuuCUnRQ=">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</latexit><latexit sha1_base64="a91+tJHJT3W0NDhoQYSZQY2xCIk=">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</latexit>→ cos(S Male , vboy ) > cos(S Male , vapple )→ cos(S Male , vboy )vboy<latexit sha1_base64="P9BlQtkfLEJ0qEGhKdW2gbfb4Rc=">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</latexit><latexit sha1_base64="lAQJYszb+gJhaEL+F+/45jnD1b0=">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</latexit>cos(S Male , vapple ) > 0<latexit sha1_base64="NWNq8OCqhPOtsUSzvL5KwjiDwQs=">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</latexit>✓(S ,v ) … 部分空間とベクトルの正準角度
cos(S , v) … 部分空間とベクトルの正準角度のcos<latexit sha1_base64="oR2aB7x1WrbMT8Va+o1TOX/5vSU=">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</latexit>

データ (S, w, w0 ) の例（部分空間を張る単語集合Sにwとw は含まない）<latexit sha1_base64="oMaZH1Cv7nUdM5EFVgy7Bajg7R0=">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</latexit><<latexit sha1_base64="QBRcRKanqRAqlBzQw7j1AKR+CIg=">AAAiknicxVpdbFtFFp4WNqRll7RQAVqEuJuS0JQ0OimFRZVATbparUTjpkluE7CJsR3Hce3cG2zHaWtc1C5aLS3aH6pQqUggKhCqeOCBFyohIVH+JB7gpUhF4gUJ8VPES5GQUCVz5szce+f+2dfEErFs3ztz5jvfnJnzM9dJLxXz5QrA5XXrr7v+D103dG/YeOMf/3RTz6bNNx8sm8ulTFbPmEWzNJNOlbPFvJHVK/lKMTuzVMqmFtPF7HS6sJf3T1ezpXLeNKYqR5ayjy+mckZ+Pp9JVbDJ3LzpVpZgBsuyFZZhJlvEVwrv51gN21OsxHLUcpjVqYVfV9gCSi7hXQXHHcbPErbXpPQxWz7BiiyPd3mUKOO9xvrwrWJujKA7jy3t6BbyzXVzGa47h1ImS2N7kUaY2J7DqznEnsfvKbaVDSM6/5wlDhXSXrcQ//PV08bJ2yd/xrttyMYtM0A6LKwqfmckHp9LGqUO0zW/KqKcNT+N3a3MVsyPj6tju62ZEN34fuy7bb01/K6zpMuOKrIfO0k9qoZyCw2TbWkoB2gY65B9SMe/903cRpp0zyyyOC54Ji0wX/hwqhux+ui91hfH0OJnkz2Tt3YMr6Pc0o8ULzX+3HFuhI0rzX0uS3deu1t93Oq72UO0hv5dVSAvzpGv10kmw5bR74KlRWTxyw7Ry+H1d9S72ISb2t+c35OoIYuvIK1B8isUAaOxtCykgfG/bye6jh5dPS3ZjoXYr+yymIp9TPZauiPqPda/ugKfwTV4G76Bq41ui0djQ5tMhHQYG3dvG3y4r9pcwvdXf1s7LEF4/W3utWijypR9/KN8s56FxOzquf3vybmJXGZZhEezI/jNW5t7mZAUuoR0uJ0c/CW8L0muzkh7HZQ5tvIkFSkaC7cHNfNLh6+J/SlaxayiYy9lFN4nMFOScQnRecUQxFdFasbXwa670P2MLW0qXy67ZNvS0mBSji1RTcPrJe/aeLEdlHoLnHBrK6ySHzx7HA6ZW2pnqM4ZpsqmL4LPBI3eKUd72+8Lad9la2ufvRfrfhurM2vmxX8gBH9te7gsbVqkysWU/i7iZD1MpnFnY3PhLwf2evKDN/pasa8gqz537zH2FL412evd72l81diEstbEZXKGx17ITc6cfGn6k/++Y1dNvyU7Rc5NXBtchjfhY7gitbln49hzHCvVv0FBrF2yR+5ojelgJK5PPinrxnGsT3WF93hIdas7uy0Ame92rZDhuDY7DcdaDEXlvKCshaVL89TuXv4G4uOeO/79RJeT9+T+IwnULtA4w0Ef3oDU+BS+oszQO15jO3xtHCuJcw7hemh7bBV0OB3C17KAOJ/VaF+62Yk1VXXXFK2asmOdMbPU47ZtQjmJjINprTpkYB4mOVswJsagcJJRyykw4TF4Ah6BZ2Edjp9FtPFGtz3KiJ99+jwYMQZzjQ1gHv9+/iaYgX827oJRWEB8Qz13Il4e/oVaFhp3KXZ6FH22gO+8tJ5lhaS0A7ek44MTyGHOttUc9TrzHLfnx8+0BylmVqi9Ki1XxZ6S3WOzsGIFGNO/zK427sS5WXs2Bc8f2g6FWD8cgfn9CbRLks+90c0l4XmULMAJPn9EH5E84jjvYdp5KeQ2KH32cazWDoNR/Sn2qu1tuAaxr2M3wnrBA5Jo7Wk2Amb9i2S69MPRTyCHtjwFC7Ef42dhmq8JVpxdZP0FbDcg56o7dduf4soOXab9PezxBdHq8OMMrb0rMHR878G3gXFnSGYfHsNyeMevq+hpOl5PSTmdfEtc8dagGDKm+JWzN3mL6rWzzHqaoEoM0HOGHXQ6DZJtHgFqHt/XmnAL9jfN5+cOgsvr959y1QtuTk4ecJhZNemAP4JIrJ0tsNy5Y8yXVR1d7vpT1ThJT6NKIXVr2e6t07pzxBXbojssxi2ib5LGODqrnozgjvhVkvdLWK1CSlwrLeRbuscv7F7Ky6JXd1pPlMiDYzwewyW4gpH6fX6+8pwxwyumsbDaNgwZLsBbcK6lrcPsG52Js/buWn7As491j1e2N1fdHiueNDUbb0kE2ev3OjP5+YehOey9OGsbG7QGKs69Ib4tdr9TRYRbrqPPyajaNZLpZE/1GTiEeeq5jmEn5HOhEuZ4q8YekfMUrc4eGAk9JY3YI9XdN+pqW1baOmaZ+Mtnb2ls7qA1okXi6LL3SGm9jTGOxUWefzhgt4Vp45IG9lQUhPZyTDvanLi2QrWxw1u0BfGxozV8hPH5Xcq7/N7BddD5s7ttTWLPYABXK8MH9alPLQak1nZP/a1wm3FydK49mgbpcceg6BZY+7OKIF3uHBiNTUejw/8/jY+f/LzSxc9PHf0VROSGkcBsPSrziv/5VZrN2ydb5xQZ1OtkXUvPYETZUc+zEpXpvZE5LrO69Od2uC+Hcm+HOZ2Zp54Tp0T+yyeejWt4ol8AU8wBM+BpeAYO4Cn3BKyDL7G6exeuYWYsxC5lL2Dv/oDZi99N0xSJosy91RwzmBlNOvMGz41XCEA42yKv8UDgyg2SZfznIO9JSlTov99Jj0uu/bS3Mblp6/AQ0J8WfrGVyb9xc9PrLEGLwcPmIv0cVsHrIpq8jK84Tg1wIhU8dIsf8XkqytgFXQJH8VJxCfsyrICfPFzFZSs/hnPMMo3OuAJjHx4xzsNV+BjegO/gWihWjTA4lyOM/xhMY7NLyR76Wb/VKGvr2KOacq7gBnuQuObpYcIy/RODgVI0vnr0zNXJ3RN9tX44h8ejS/AKXIaLOAOj+lPmtQPZiRdpAcAyt//CWoCDO4eGHxjadWDX1j2jcim62R2slw7jf2V72D9wA+gso53WLmjvaRd7t/Tu7h3p3StE16+TY25hrr/efb8COudIqw==</latexit>(Male, boy, apple)✓(Male,boy)<latexit sha1_base64="95ts7narIR0YPyQZhHLYKWxNRKY=">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</latexit>✓(Male,apple)<latexit sha1_base64="dp8EvYEvZOUAqOTCMkv1hzr5Dpk=">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</latexit>(Color \ Fruit, orange, man)<latexit sha1_base64="zdSIbODAqlzaF2V4+CBc6D9xTOQ=">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

平均集合帰属度

SCORE =

1
|D|

X

<latexit sha1_base64="pQ1PRn8j5Gxx1f72XqRPzCCV4pw=">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</latexit>( cos(S , vw )cos(S , vw0 ) )(S,w,w )2D

結果：集合の要素である単語のベクトルは要素でない単語のベクトルよりも集合の部分空間に近い
集合タイプ

集合

共通部分

和集合

平均集合帰属度

0.146

0.292

0.084

19

評価への応用：単語埋め込み評価と後段タスクとの相関
集合の評価

Color \ Fruit の中に orange が入っている
Color \ Fruit の中に man が入っていない<latexit sha1_base64="rMLPoZgZnTsewzoTH+f4wqjKVUw=">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</latexit><latexit sha1_base64="rMLPoZgZnTsewzoTH+f4wqjKVUw=">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</latexit>

ColororangeFruitman<latexit sha1_base64="pe0ZgWdYtllvZ8EgZN/Fh8lvOqc=">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</latexit>（例） orange 2 Color \ Fruit の評価<latexit sha1_base64="VqyTNg4i56YaQLNjC7sN3yK4fSM=">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</latexit>

1.集合 Color \ Fruit を量子論理で部分空間として表現<latexit sha1_base64="ccSijcHMuzdJPMar93axhaGHK/8=">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</latexit>

S = S color \ S Fruit<latexit sha1_base64="/xCrZH9+qZjDvz7ZULCUxq1rlEs=">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</latexit>

S Color \ S Fruit<latexit sha1_base64="qu2ygV+GHoigFhIXSkB7wfrbYnw=">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</latexit>

2. orange との正準角度、man との正準角度を計算<latexit sha1_base64="YBKrI9COY7hGAQjNBeaYZdBm/9w=">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</latexit>

vman

cos(S , vorange )cos(S , vman )3. スコアを計算 score(Color \ Fruit, orange, man)<latexit sha1_base64="uevSx6UHfYwnM0VdoK7Wqa76G5U=">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</latexit><latexit sha1_base64="el4VSR1sd98oPgqZPgGFaZE2WoU=">AABDQHic5RxtbFtX9XaMknZjbRmCCTTN0DaN1zScdGWgiaHaLQhp5KNx3ATixsSO47h2n9PYddo6adUxIZpODFZ1k4oEouJDEz/4wR8qgSaNr6L9GCB1UpH4g4QYKwKhTkKaKplz73333Y9337OdvtABsZw8n3fu+brnnnPPedfJLVRKtTrAjQ33vOved298T8+mzffd/94Htmzd9r7DteqJxXwhna9WqouTuZlaoVJyCul6qV4pTC4sFmaO5SqFiVz5AL0/0Sgs1kpVZ7x+aqFw5NhM0SnNlfIzdQRVt8WOkQxxSIEskTypkmP4msHPs6SJ8BmySIoMcpKsMAi9rpN5xFzAT3UcdxJ/LyK86WKf8fAzpEJK+KmEGDX8HCM78a3S3NwB7xJCuuHN8cN5UxzKu4hYVZJDeIWNqCK8iFezSHsO/46T7WQQqdPf00yGOuO+Iih+7U9nndWHUv/CT30ojY4TZzwErQb+zbv0qC45xDrJrulVBfGEfjGyQ9GW60fHrSDc4+xR1Hn46e/wMJv4d4VkNVuq1P30s+zOZvwsedTa8Eh1xaPm8VhfS/3vWWkoIgsxHl/9/NgHGae0xqOGf+sBmrSh+cKvxns0Wktro5OaXP2WRicVQCeFa45GD2HbDrT++htjG0+fvnTRoM/phEubZzGjHdWd7H2nr81shuZXHwJn5EJ0FHFGNrv+tYSalFlULKIeAtpAqP7Jj8M9pEkSCkzOhIBSvCZ6LLVZQcEcUnAi04t5DNWu39UtKsrcTjxHCb0aBiQyLdj6kRaOTgcxY/ps6DNJ+VIPX9DmOOnDPcCiTRVXWNCYz+K9EywLryg2XGJjZt1R1KdsvsRx6eo7FYBp6lBl8XWR5X66r5C0Epp8SQ12QoHZaKtYqmYFNvPh/M0oJKmug9fDDfgRXIObXs6Lgrbfxzlkie3YTKgeITjsONqugC8dk87Egma9hjLbkdrGi8hqdOp3ZzO6lZWyeGTK8KQnyJMsT5h+UXOlojvXps+W/V4EFhankAH2yii81Lir+ruUJXjFpiyr9Ul2R8hDR5why/iOKRC5Kk36/SF4KqeMZi2VgoT644iZ78PX2rS3O6ozaUzt+K7shE9HFU6tNcsoqHpRKsBG9QVqKyWJK9rSGfZnVsm/rNERuuXw1SRjPrupXrZbsbMZpYK03q1p3GhjCbt2/T4K5qyr0mS8mdDXfjD9SKPC1OXsltQHItxPcfml9ELuGDjlvPPC+d9Pf9/Vls4jzSIzXkTIuFUpvaqwnWjdnSVas+ZZfVzT7vYp1wMMcw4xZ5jtlzvwXWHtZbe6NsdwyLKBnWH49O8iyltEPerMp/s1yLIL0elx/Zq+WdWpZZR5Vi1FV3hfyBrv990TMscjo6jmrOioqnLGyKfYDK2PlNyL+izr1vSKOEI+7fpNuzE6v7Vw2rMmTlxCUPTT7ZDCXDKCkfIzXpxW18gg8/tlcpB5NN8LnMBx3N5pxnXJ/b2LcRMefJDh92kS00omrcm6FKCbDXMXw42viyZyx5pyuYZrZZu/VEea2TB3eT5h9wx9lxAPXE02XOnZ0eaFb19+MDJq7exv4nRXUYkKt8lGzLAdREGDi/2isGxK2bXwT/mudoRh86fL0H6+TdnMHXGeUaS0/jMWUneFnWtpXwfBekbmp7mnKtdbH4qMnvqWexfbzPjrmYxl9y13tBlfDe3HFjYycXmNo8sUa/WIeR85C8/BUTjY2mTsbYNk6bfUXmE1VbDmUfOSsX/9bdl+RqOY9071l16n1gc2CfT6IUwKtefQic3Ubkaw3Qw/BEfr9fLcbrNSzajwJO0z7l3Bu0u+rR64Cr+DW67/B0sQdbdBk+ZM76Ul+C3chp/AX1CWHk+6dlKZdhEZw24b/W6IdUx5aC/VkyXYp3u7imbcb3u7XIudjaqxJ5H+UT6tpyEzfenKyCuubvy5plmP6tWozQq2yjvITpL+Aut1clktVa+iY7t1rVLqTAp9PYdFCSmvmrklD7mfUHcTcg9hk1ffAwTLG7xXMSXWd1lcXlntqBz8PWaz5xhcDYbT6aRXHcv+8vw5OFp9f/NFVi0Meru3dmvGNnqvO9qEPxYA3+dx6156k9bHA/ada50zk/7jAfTvzIdrrk0rbK9bddc7j5MrQTith1vbyh85dMDIVmb0FbEvmq6k5LEUQH1pzXRjqUka06FIn3pMvPrcT92nzWvLwZ1mYC3iYuZ9DTPMb7y8EtTBHPKtUAuNyX3jPWMb4RBMwByuqX4C4IzugHL+Y3BBZjKXUw4pFRn9JvNOWvfUvNnXX4Psdy+TZN7N+3m2XvYSet5mxeJ7JTLnwvURjykjOtNW5i5TLliDXFW3L7CInlNiWouIV3BPDanWEJxNi/8MrsM1b9ZkX1X2HMJGKXjgTF0++5Jvdv7fe7u6B3TW21XWtfIUU64r/aki96dRrLMPQplH3ewWNxfFSBqczL3Z4+6JllGSZWdaRGQYJfZnRWmZJyyUaZ6KlfOUrvKMdd6TkFtiXolzgldMud+wyO8gfcwW597E1S89iWcOhmHtGUp6cZfjMpuX9hqa40X3QoVRWlnUOUDWo48OX4I0XAyQN6b5fJN5ui6dfEq2x/NYyTVG1OdOYsw0u6PbNkPkGalRqIpZhzzMQYpKC87YEJRXCYNcgCp8Eb4ET8F52IDjp5HaaKvHG8VXszNMYLa1Carn3px7ACbhy61HIAnzSN8hyulBpFeCryCX+dYjip2+gCupjO+Saz1hhaxrB2pJGS3HUIZZz1az7K7Uc9TTj8aCwyzu1Rm84VquwdaWuONJIbI8OBNvT19qPYy6CZ+dgeePPgrl4V44BXMjGbRLlure6qGY8DxiluFpqj9ST7hyTKHeg8zzZlA2UQkewTrrJDiNt4a/6602nIPhPw/fB/dwOSCL1p4gCaiu/CGbW/zb6VehiLa8APPDf5+6TDMdXMBacSOz/jzCHShqFWPaW09TRrzJuhKZ0L1KpXrE811OI43v/fh2MNcMuPtGGqWK+IleN1jXf4CMu3hptrb4FYXaYsiQsq6kb1KIumqniTgTqmLE2TPpPax7b8MNjwBNY+3HQmSzr7eYb51LCtqqH7lA1J2+LlP4kx1fBHFp7W1DS9+dDfn2w5KXXjmqHFNe/7h9d1k87REW3SMkbhN9s2yM5NkwMoIe8RsM348hoByLXysQtrbSxrrw7rKdL7+bltCnF9kKHqbxGHcuNzFS/4J2RoxeVXCtMxRUlQZRhqvwY7jS1tZB9u1ckvDnDbbosRZd097YtZ91u1udDlP2IFphJ9lsFvSfMPGvTO67MWvXUdddSBvJsxA4gpn7dXC8OjASqkovi9pU1TQG8+P3w2RIN8IGW9vZQtPfoqS8Ts9QWXXuZHPZLY1n4Chm/Wcjox3UvefnSUWFkbCuPtu500TgHHZ7djQy69En0K1tEVqss9zXOa54cp3uYoy0eFo5XdIZN4rpsApXUuguq3fDTWaSJRLT5OYwmzxefoRfY0Z82Tupbz9Jwu+EnenxSyt2VbZ7/hM4fQFxIrhH2o5umEzxthp1nsVsfPTM0bkF7ryza+NlO0nQTppI48M3XpsaXX29vpHWrJGeYZTfyPDvkJLubsAfg3NkjvhPjNru6n3ChM96wbhJYnaWpaS7O5aR98uCOAbJbp55lbJ3IznrU4w/yytz+p1BqEITLmLlW+U6YJ68CM/AIShhDb4B/og76pfhNubP8vD1wlW8O2LR3jzX3E73djqqnUSbbnRfJ087dzbHcevM9XvfJwmvrPlO7O5V1xQzigq7s+yjZgnzJJJfyu7PGMoMZtuh60/a3ynyqu93/klb+zOFO5PVPI0btdzxdbBvsC1MPqIjIma9vRWlv+jeovQpimQlGdKT+O88G2z/5pVXcdHeNdZaWVjtuB9zN3dJQoe4952oiGNHdut2GAD2E/NfDLoX24n7M1rd+gOSYQkwz6abPlas43WFPVaskSl0DEBj1MkRwv/lAC0A8l7rI4OjaKHNH2aW8TdVfsqF0nbzMfZwko7Wj93uhOvwEtyCa/BD+CvcDqTVZDSoLKcI/WIyG1tYyG5h/4Sg3Shhfm9UqMx1XBCfZLKWWNOcQqgWeT6+cfrFW6knxnY2e+EK3ET5vwM34OeogdN4K/+9Q4Wxb7IJGDTN7b84vHdg8PGBfYf2bd+fdKeih3yYfJQ1nT9B9pPPYdJNk3wikSgmFhLHk68k30j+I/lPjnrPBnfMg0T7Sb79b7zM37k=</latexit>

vorange<latexit sha1_base64="38pKR/HiF4/UjDlxa95vI98zj5o=">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</latexit>

S Color<latexit sha1_base64="EjyLRZD7+9YoRj/OnDRnvvRareg=">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</latexit><latexit sha1_base64="NsNT3D0f1Ds9A62harVjDOVsd+4=">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</latexit>= cos(S , vorange )cos(S , vman )<latexit sha1_base64="i3l0P1HlTp1AkLZ92O2poKIunok=">AAA4lHic3RtdbFtX+bSMkmZjbRnaJqZpF9pm9ZaGL10J0bSiNu0mpJGfxnETiBMTO47j2rnObMdu66RVx4RYMjFYFSYVCUQFQhMPPPBCBWgSbFC0h8FDJxWJFyQErIiXTkJClcx3fu75uT/2dXOnImLZvv7ud76/8/2c852b9HIxX6kC3Ni2/SP3fHTHx7p2dt9738fv37V7zydOVUor5Uw2kSkVS+Wp9FwlW8zb2UQ1Xy1mp5bL2bmldDE7mS4cp/cna9lyJV+yJ6pnl7MzS3M5O7+Qz8xVEVTa88hDJElskiV1kiElsoSvOfw9TxoInyNlkmOQM2SNQeh1lSwi5jL+quK4M/hZRnhDYJ+X+ElSJHn8lUeMCv62yH586zS7Q/DOI6QT3hy/NW+KQ3nnEKtE0ggvshElhOfwah5pL+D3BNlL+pE6/ZxlMlQZ9zWH4jf/csFefzj+b/x1AKUxcWKMh0Orht8ZQY/qkkasM+yaXhURz9HPIvs0bbl+dNwawiVnSdHk4aW/T2I28HuNpAxb6tS99FPsTjf+VjwqbXjEO+JRkTw+XEv9/1lpOCILMR7f+NL4Q4xTwuBRwe9qgCZtaH7ntxNdBq36ndGJT61/z6ATD6ATx5ij2cOxbQitv/X38R3nzm1ectHndFpLm2E5ox3V/ey91Vc3m6HF9YfBHt2IjiLOSLfwrzpqUmBZMYd6ONAaQs1fXhzuIQ1yTIOpmXCgFK+BHkttltUwhzWcyPRiHkO16xW6RUWZ24nXKEevmgsSmRYsfpSFo9PBmTFzNsyZpHyphy8bczzkwT3Osk0JIyxozHN4b4VVYWUfTsOb++qM0jyr3vSdREocNwiPcqIeaaHUlsQusSxbZisAurpQPnbMkHLIgK1osEh9EW7AT+Ea3JSVKKqZdPseh9TZSsoNNSOXw15AnbP4itx3ZQbUs0Gv8Ivo9I/7eLEJs8jT5AjzDLcPVYRUa8ITTRv1yoznWJJC+tgrqfHS85zuWUqW4AiJ+0THEXbHkYeOOE9W8W1pEMfjvfR7W+DpnJKGtXQK3QFyReod05dTu+IPRkYvUtnSzxevNz8VuWy83jl+6ZfTvD7rlyGVhyalP60If/JiL0kPN3G5H5syWc0uxztHL8CrcBpONHe6fDJIll6f+GoVN8GaR82rVbWJ2pbtZzSKeQ+rv/K655D6UgvP0++3lkKvF2FspleiYLu5/BBsY/3M14h+VqoYdtFpnxd3Hd4d8m12wVX4I9wS/h8sQdQVxZDmfM9mHf4At+Hn8DeUpUtK104qt104dpBtzLstrOOWh65PpSzBPt3TUTbjftvTYSyGG1Vh3R3vKI/Ws5Cc3bwy+muhG+8VORahe8Gz+M1ra6uMzjHNShxkJ0V/ma1cuaxqpJwHTcd2ca1TCieFGc+tsoSSl64b5tgsZjUeak2hr3nUqsJPXp1SK3mDV1Ruib1rGIvhLktbOhy8Owb3utKkraistaETbG1NqtTbL1+E06VPNl4ntI/YzzqHYaqW3+hDYrQb/lQA/LDk1rn0blqfk7SimTM3/YEA+lvz4YqwaZHtWUsi3nmeXAvCaT7a3FP49Mnjrmrlzr5O7ivI/K/fdVb3BV9/T+OrQca1uVY86gHU63dMF/eqNKdDju5ZJ9959Zeig3dnNThsBTYyLlbed7HC/F7WlVpAHh32RKgPjanDE13jO+AkTMICxlQvAbDH9kEh81nYUJVMcEojpRyj32DeSfsXFTn75qufffYwSRZF3c+weDlE6BnGmo/v5cmCgJsjntJGhNNW1S63XHAHcpXYNY36OvKraBkvK05idGs4nN0W/xVch2ty1uhZToXx4rSrSKHVKA0P7OnLF97wzI6io6++HPsUWee2KvIlPePJaDI4dw9o130Mc4FVHNqNXyWqM78i/XWeWcc9M6uEn0a5x3DIqgs7yfDpdxnlzaEeVcxhSfRGHbIqICY9rl/D4wEmNTM3+Fjc6EEFdYS4P43h7v8EFHjWTe0StcgiCbCT96ReEKcEYyTFzgmczDBG/M8yEqpO+FCmdcoqZChdrUO2KCXklljU8pzDyyLmWY1bfhvpY7W4+D5Gv/IkXjkYBvOFYSFhr4deTHBcZfPSXkP3eIsc9MAorRTqHCDr6SdGNiEBlwLktQyfbzBPN6VTfZ+D0mMVV4vonSRnzCy7Y9o2SdS50xiUnFmHDCxAnEoL9vgwFNYJg2xACb4CX4Xn4WXYhuNnkdpYs0uO4tFsjxCYb+6E0sX3F+6HKfha8zEYgkWkbxPtRBbp5eHryGWx+Zhmpy9jJBXwnRfWc6yQEnagllTZchxlmJe2mmd3lZ5jUj+aC06xvFdl8JqwXI3FlnNHSuFUebAn/zO72XwUdXN8dg5eO/0EFEZ64CwsjCbRLimqe7OLYsJriFmAF6n+hHepqRzTqHc/87w5lM3ZCc7gPusM2LUPRn4oow3nYOSvI/fCdi4HpNDak+QYlNb+lEqX/3nuHcihLTdgceRf05dppYMN3CvuYNZfRLgNOWPHmJDxNO3KNykhkRt6SNupzkjf5TQS+D6KbxtrTZ9YN9IslcNf9LqGkZbA6wmBl2Cxxa8o1C+HDGtxpXyTQvSonSXOObuOEWMn8AfZmZwfbusM0HDFvtVCNv94szxxrigYUT+6QfSVvimTyvRKMqeexLwZRNA61IaWuTob9qyHFS9z56hzjLO6Wg7YcVbk3TU275RiXVr0oCNxm+ybYmMUz5qrIpgZv8bwvRgOlGPxaw3CYivhigt5l618+d2Egr5YZhE8QvMxrlxuYqZ+i3ZGXL2q4L3OcNCuNIgyXIWfwZW2tg6yb3hJ1Nybu/CYy48TrqjsTNeEHLu188O70elwyx5ES8ntpuJvQZ3OkwGRyX3X8u06mro70kZyFgIzWLnfA1vuAyOhqvWyqE11TS1YnLgPplp0I/xg3vPsMDPi9rcoKZtnD5FZju3O7VQ6tav2EpzGqv9KZLTbn8ZTrGO+0ed/Gh80h3ftJH76+5cfaO6J0GLhal943McFdqKDMcrifGX1BZ8MEcSNYtpsh6sodFbVO+GmKkmdWIbcHOYnj6yP8DusiG/Kp58UXUXdEneCc77fyZmzqvK7p/d4Y5J6Zz3SdnRbyRRrq1H4KubHx6wc4S2w9c6uHy9z3RFOmkjzw7ffnR5bf6+6g+5ZI30+QT3l5l0hDYnVgDcHp8mC7CaonbvfXbNPeMxjvWDcIeLuLCtJnwwtI++XBXEMkn0lUPZOJGd9iolX+M6cPocNJWjAJdz5lrgOWCcvwUtwEvK4B98Gf8YV9ZtwG+tnYeR69ireHfXRnj/FnWa5KIzu7XTUO4l+utF1HTA6B0LPccx35nrlM3qtd9Z8JXb3dtcUM4oddrjqo1eJI2JGaHfYX8q6kPNgCMzHZS7iFcxvhW6etP+vyKu/9a4xnYXWVTS4XtHZeYZYW6Rn5nn1hIL3TGFrsqoVTDS03XLHPgT7BtvCzcfpiDiz3t6Kyl9Mb9H6FDmyNtSiJxHH1cAoGSfPantcdcZCswbtWp9gJyJ8/7SC4zh/P993st4Jhn8g8jiIGVYyn5qVOy7au8a9VgrWQ/dj7uYqydEhJp97jTh3pHbvhT5gf5b3ol9c7CXib6y0+8ckyQpghk03PVas4nWRHStWyDQ6BqAxqmSG8H/johuAjGx9JHEU3Wjzw8wCflLlpwWUtpuX2OEkHZ0xzLwfrsMbcAuuwU/gH3A7kFaD0aCynCX0nz3Y2Oxyahf7x652oxzzy1EtZa5iQAwyWfOsaU4hVIsMH1879/qt+NPj+xs9cAVuovw/gBvwG9TArn2Q+dHJ7Ph32QT0u83tvTh1qK9/oO/wycN7jw6Jqegij5DPsKbz58lR8kUsugmSGdgc+MXAWwNvDz44+Mzg8cFnOer2bWLMA8T4Gxz5L0qoAn8=</latexit>

評価方法
全集合のスコアのマクロ平均を計算

S Fruit評価への応用：単語埋め込み評価と後段タスクとの相関

仮説:
集合帰属度と後段タスクのスコアに正の相関がある
後段タスク: SentEval
２つの文の意味的類似性の判断: MRPC, SICK-E
感情分析: MR, CR, MPQA SST-5
テキスト分類: SUBJ, TREC

評価対象: 次元の異なる８つの単語埋め込み（GloVe）
埋め込み空間の次元: {25, 50, 100, 200}
埋め込み空間の前処理（中心化）あり/なし

20

21

評価への応用：単語埋め込み評価と後段タスクとの相関•ベースライン (Analogy)：単語ペアの関係を２つのベクトルのなす角度で評価•８つの学習済み単語埋め込みの散布図（横：埋め込み評価スコア, 縦：後段タスクのスコア）•結果：後段タスクと提案法の評価スコアには正の相関がある
Analogy（従来法）

提案法

評価タイプ

単語の関係

集合の関係

50.00

50.00

40.00

40.00

30.00
20.00

後段タスクのスコア

後段タスク（SST-5*）
と埋め込み
評価スコア
のρ

後段タスクのスコア

手法ρ=0.90

10.00
0.00

0.20

0.30

0.40

Analogyのスコア*他の後段タスクでも同様の結果

0.50

ρ = 0.80

30.00

ρ=0.78

20.00
10.00
0.00

0.03

0.05

0.08

0.10

提案法のスコア

0.13

0.15

0.18

結論

22

既存の単語埋め込み評価は単語の意味評価
単語埋め込み空間における集合の表現（量子論理）を評価に応用
単語埋め込み空間で単語集合・単語集合間の関係（量子論理）のモデリングを実現
量子論理を用いた単語埋め込み評価と後段タスクのスコアに正の相関